Insights on Enzymes and Polymers from Molecular Dynamics Simulations: Applications to Dihydrofolate Reductase Complexes and Starburst Dendrimers Citation Naylor, Adel Marie (1989) Insights on Enzymes and Polymers from Molecular Dynamics Simulations: Applications to Dihydrofolate Reductase Complexes and Starburst Dendrimers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/0789-jw44. https://resolver.caltech.edu/CaltechTHESIS:11132009-134341582 Abstract Examples are given for the role of simulation and theory in designing artificial biomimetic and biocatalytic systems. Simulations on the β-alanine starburst dendrimer polymers indicate that, for the higher generation systems: (1) ~50% of the surface area is internal, and (ii) ~50% of the spheroidal volume is solvent- filled. These studies suggest a design for encapsulating and delivering dopamine to the kidney for cardiovascular therapies. Investigations of the penta-erythritol based polyether starburst dendrimers show that: (i) the later generations lack any internal surface area or volume and (ii) the dense-packed limit for these polymers to be the third generation, consistent with experiment. For Dihydrofolate Reductase (DHFR), the modeling and simulations: (i) explain the high degree of kinetic similarity between two dissimilar forms of DHFR; (ii) indicate why site specific mutation (Phe-31→Tyr-31, Leu-54→Ile-54, or Leu-54→Gly-54) causes a significant change in the catalytic rate; and (iii) suggest modifications to engineer E. coli Chicken hybrid proteins capable of reducing folate. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Chemistry Degree Grantor: California Institute of Technology Division: Chemistry and Chemical Engineering Major Option: Chemistry Thesis Availability: Public (worldwide access) Research Advisor(s): Goddard, William A., III Thesis Committee: Baldeschwieler, John D. (chair) Goddard, William A., III Grubbs, Robert H. Richards, John H. Defense Date: 1 February 1989 Additional Information: Article title in 1989 commencement program -- Insights on Enzymes and Polymers from Molecular Dynamics Simulations: Application to Dihydrofolate Reductase Complexes and Starburst Dendrimers -- differs slight from title in thesis file (PDF). Funders: Funding Agency Grant Number Department of Energy (DOE) UNSPECIFIED Triton Bioscience UNSPECIFIED ARCS Foundation UNSPECIFIED Record Number: CaltechTHESIS:11132009-134341582 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11132009-134341582 DOI: 10.7907/0789-jw44 Related URLs: URL URL Type Description https://doi.org/10.1021/bk-1989-0392.ch006 DOI Article adapted for Section I. https://doi.org/10.1126/science.3125607 UNSPECIFIED Article adapted for Appendix III. Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5377 Collection: CaltechTHESIS Deposited By: Tony Diaz Deposited On: 17 Nov 2009 21:46 Last Modified: 15 Sep 2021 01:16 Thesis Files PDF - Final Version See Usage Policy. 14MB Repository Staff Only: item control page

Insights on Enzymes and Polymers from Molecular Dynamics Simulations: Applications to Dihydrofolate Reductase Complexes and Starburst Dendrimers Thesis by Adel Marie Naylor In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California ln.stitute of Technology Paaadena, California 1989 (Submitted February 1, 1989) - 11- @1989 Adel Marie Naylor All Rights Reserved - lll- This thesis is dedicated to my family: Tom, Titi, Maura, and Joel Naylor and Adeline Parente and to my "adopting" families: the Baugha, Kantorczyka, and Nollara - IV- To laugh often and love much; to win the reapect of intelligent peraona and the affection of children; to earn the approbation of honeat critica and to endure the betrayal of falae frienda; to appreciate beauty; to find the beat in othera; to give of one 'a aelf; to leave the world a bit better, whether by a healthy child, a garden patch, or a redeemed aocial condition; to have played and laughed with enthuaiaam and aung with ezultation; to know that even one life haa breathed eaaier becauae you have lived thia i.1 to have aucceeded. Ralph Waldo Emeraon - v- For unto whomaoever much ia given, of him ahall be much required; and to whom men have committed much, of him they will aak the more. Luke 12:,18 - Vl- Acknowledgments The passage in Luke 12:48 holds a great deal of significance for me. I know that much has been given to me ... a loving family, cherished friends, intellectual abilities, and a deep faith, to list but a few. To that end, one of the most special ( and challenging) gifts I have received is the opportunity to do graduate study at Caltech. A number of individuals contributed significant time, energy, and love to make my California experience a productive and memorable one. Bill Goddard is an enthusiastic and inspiring research advisor whose love for science is contagious ( and tireless!). The privilege of working with a scientist as talented and as insightful as Bill is an experience offered to only a few. I was fortunate that the opportunity was presented to me. I also want to thank Yvonne Goddard for her sacrifices to accommodate the time that Bill spends away from his family to be with his research group. Additionally, I must thank my "pseudo" second advisor, Steve Benkovic. His continued interest in our DHFR simulations, and encouragement when times were tough, will always be remembered with gratitude. It has indeed been a privilege, and a pleasure, for me to collaborate with Steve and his Penn State associates Carol Fierke, Chris Falzone, and Joe Adams. Don Tomalia's enthusiasm for the Starburst Dendrimers sparked the simulation studies. A number of agencies supplied financial support for my endeavors at Caltech. The Department of Energy, Energy Conversion and Utilization Technologies generously funded my graduate research. Triton Bioscience also supplied funds for part of this work. An ARCS Foundation Fellowship assisted in the acquisition of texts and in defraying some living expenses. A Dreyfus Travel Fellowship enabled - Vll- me to visit a number of industrial research labs. Various past and present members of the ever-growing Goddard Research Group have made the hours at Caltech challenging, interesting, and, of course, educational. The "old timers," i.e., Barry Olafson and Marv Goodgame, provided many amusing examples of group folklore through both actions and tales. Emily Carter presented the ultimate challenge; I grew to be a bit stronger in character because of her. Mark Brusich always spoke kind words, performed generous deeds, and offered tremendous amounts of support and encouragement. Kim Schugart helped me to keep an appropriate perspective on graduate school. Barbara Garrison provided friendship, guidance, and was an excellent role model. Janice Peters offered the example of a true Christian. Alan Mathiowetz kept me chuckling with his somewhat infrequent WAG's World cartoon strip and helped to blow off some Pasadena dust with our DDs. Terry Coley always managed to sustain a levelheaded, calm state, no matter what the situation or crisis; lucky for me he had the office next door. Jon Hurley provided great computer help and some amusing anecdotes on life. Ann Miller always offered a cheery good morning and delicious matzo ball soup. Kevin Plaxco brought a biological perspective, and many smiles, to 148 Noyes. Gilles Ohanessian shared his amusing wit and worldly perspective on life and science. Carol Scrivner was a great help in translating WAGscript and providing a quiet, secluded office. And finally, Adria McMillan and Siddharth Dasgupta were always available to supply constant doses of support, encouragement, and love. Life in the Goddard Group would have been significantly less pleasant for me without Adria's hugs and Dr. D.'s comaraderie. There are also a few special non-group Techers that made the time in Noyes more enjoyable. David Kaisaki is an exceptional friend. He has an uncanny - Vlll- sense of knowing when to encourage, when to tease, and when to supply Godiva chocolate! Bob (JB) Driscoll kept me smiling with amusing stories and great company. Mary Selman was very encouraging during the job hunt and thesis writing times. Paul Hipes was a great quantum TA and a fine example of how one graduate student should help another. My involvement in St. Philip's parish kept me sane through some of the more difficult periods of my California passage. Anne Burgard is a valued friend and has helped me to begin to "let go and let God." Heidi Heil and Karen Royer allowed me the privilege of accompanying them on the beginning of their RCIA journeys. Many other RCIAers, especially Judy Nollar, Shirley Kealey, Sharon Kealey, Marty Smith, Kevin and Jana Huerter, Bruce and Kola Popp, Tom and Janet Selenski, broadened my understanding and experience of Christianity. Gary Bauler, a.k.a. Msgr. B., provided exceptional spiritual nourishment and warm friendship. I am very grateful for the many kind gestures, words of encouragement, and loving prayers sent my way from all of my special friends at St. Philip's. A number of families welcomed me into their lives while I was on the West Coast. Gene and Dora De Blasio were my California grandparents. They gave the Thanksgiving holiday a unique Pennsylvania flair and made Palm Springs get-away weekends special treats. Leo, Beth, and Bill Cowan provided that sense of security associated with "going to Grandma's." I would have felt quite displaced were they not just an hour's drive away! Mary Cowan was more like a big sister than a cousin and John Sadler helped me keep the family dynamics in perspective. Don, Judy, Donald, Annemarie, Jenny, and Joe Nollar made Pasadena home and introduced me to the delights of California nature. Kevin and Jana Huerter allowed me to delight in the joy of their children Alex, Justin, - lX- and Ryan and to form an ever-so-special bond with Justin Quinlan! Some other new friends entered my life while I was at Caltech. Shirley Whitmore was a fun roommate; she gave me lessons in the art of "blending" frosting and I, in return, taught her how to remove labels from wine bottles. Wally Reiher always answered my questions about BIOGRAF in an honest and direct manner; he offered alot of encouraging words, too. Sharon Kealey is a special gift from the Lord. She generously opened her home, and her heart, to me. Sharon showed me what it takes to be a maid-of-honor and a responsible godparent. She made the last few years of graduate school so much more pleasant. Laurie Carlson made life more cheerful; she was a great walking companion, needlework buddy, and confidante. Laraine Balk was a great job-hunt consultant and I will never forget our freeway experience! My friends from pregraduate school days remain the extra special people that I have grown to love and depend upon. Diane Balk Palguta continues to show me what constitutes true friendship. My life would be so greatly deminished without her presence ( thank you Phyllis!). Eileen Ogelesby Hemminger keeps me smiling with her thoughtfulness and her absurdities. Larry, Mary, Matt, Laura, Nick and Julie Baugh are rare and cherished jewels. Words cannot adequately convey just how special each one is to me. Judy, David, Todd, and Amy Kantorczyk are my first adopting family. Their love and encouragement made the transition into adulthood a bit easier. Thank goodness, though, that I'll finish school before Amy starts college! My Dow friends continued to support my scientific endeavors throughout graduate school. Jack Martin and Stan Strycker encouraged my pursuits. Linda Myers nurtured my dreams and helped me deal with the realities of graduate school. John Daniel and Bert Schuster were great friends. Emily Matthews - xrema.ined my "sister-in-Baugh." Bob Broersma was always willing to chat about cardiovascular pharmacology, especially if it involved dopamine! Then there was Bob Vance. Without Bob's gentle harassing I would not have even made application to Caltech, much less accepted the challenge. And, again, without Bob's patient ear and hearty laugh, I probably would not have met the challenge. And, finally, the greatest supply of support came from my family. My parents, Tom and Titi, my sister Maura, my brother Joel, and my Nanny Adeline, all banded together to shower me with tremendous amounts of love and encouragement. I shudder to think of how different my life would be if it were not for the education they struggled to provide and the values they instilled through their examples. I love each one of you! - Xl- Abstract: Examples are given for the role of simulation and theory in designing artificial biomimetic and biocatalytic systems. Simulations on the ,8-alanine starburst dendrimer polymers indicate that, for the higher generation systems: (i) ~50% of the surface area is internal, and (ii) ~50% of the spheroidal volume is solventfilled. These studies suggest a design for encapsulating and delivering dopamine to the kidney for cardiovascular therapies. Investigations of the penta-erythritol based polyether starburst dendrimers show that: (i) the later generations lack any internal surface area or volume and (ii) the dense-packed limit for these polymers to be the third generation, consistent with experiment. For Dihydrofolate Reductase (DHFR), the modeling and simulations: (i) explain the high degree of kinetic similarity between two dissimilar forms of DHFR; (ii) indicate why site specific mutation (Phe-31--+Tyr-31, Leu-54--+Ile-54, or Leu-54--+Gly-54) causes a significant change in the catalytic rate; and (iii) suggest modifications to engineer E. coli-Chicken hybrid proteins capable of reducing folate. - Xll- Table of Contents Acknowledgments ..................................................... v1 Abstract .............................................................. xi Overview of the Thesis .............................................. 1 Section I. Application of Simulation and Theory to Biocatalysis and Biomimetics ..................................................... 5 Section II. Dendritic Macromolecules: Molecular Simulation of Starburst Dendrimers .................. 44 1. Introduction .......................................................... 47 1.1 Synthetic Strategies .............................................. 50 2. Calculational Details .................................................. 59 2.1 Molecular Simulation Details ..................................... 59 2.2 Determination of Properties ...................................... 62 3. Results and Discussion ................................................ 68 3.1 End-to-end Distances ............................................. 75 3.2 Radius of Gyration ............................................... 83 3.3 Moments of Inertia ............................................... 87 3.4 Surface Calculations .............................................. 87 3.5 Volume Calculations ............................................. 102 3.6 Surface vs. Volume Analysis ..................................... 116 4. Utilization of ,B-Alanine Internal Void Spaces ......................... 122 5. Conclusions .......................................................... 130 Notes and References ................................................ 131 - Xlll- Section III. Dihydrofolate Reductase: Molecular Simulation of Wild-type and Mutant Enzyme Complexes ........................................................ 133 1. Introduction ......................................................... 136 2. Pertinent Experimental DHFR Studies ............................... 144 2.1 Crystal Structures ............................................... 144 2.2 Isotope Studies .................................................. 149 2.3 Kinetic Profile ................................................... 152 2.4 The Active Site Asp-27 .......................................... 155 3. Homology Studies .................................................... 158 3.1 E. coli and L. caJei Bacterial Forms ............................. 158 3.2 Chicken DHFR .................................................. 169 4. Simulation Strategies ................................................. 174 4.1 Models for Starting Complexes .................................. 174 4.2 Force Field ...................................................... 184 4.3 Simulation Protocols ............................................ 185 5. Methotrexate Simulations ............................................ 190 5.1 Full Structural Studies ........................................... 190 5.2 Orientation of Pteridine Ring in Bound MTX .................... 194 5.3 Site Region Studies .............................................. 207 6. Dihydrofolate Simulations ............................................ 220 7. Single-Site Mutations ................................................ 233 7.1 Phe-31--+Tyr-31 ................................................. 233 7.2 Leu-54--+Ile-54 ................................................... 239 7.3 Leu-54--+Gly-54 ................................................. 248 8. Segment Mutations .................................................. 261 - XIV- 9. Summary ............................................................ 270 10. Conclusions .......................................................... 272 Notes and References ................................................ 273 Appendix I. Force Fields ........................................ 275 Appendix II. Starburst Dendrimers V: Molecular Shape Control ........................................ 279 Appendix III. Insights into Enzyme Function from Studies on Mutants of Dihydrofolate Reductase ........................ 291 Appendix IV. Insights into Enzyme Catalysis from Studies on Mutants of Dihydrofolate Reductase ........................ 299 Appendix V. Solvent Potential ................................... 320 -1- Overview of the Thesis The overall goal of our research is to develop theoretical tools useful in designing artificial biocatalytic systems. In the long term, one would envision the development of biocatalysts that could convert methane into more valuable (or more transportable) fuels or could convert syngas (CO + H 2 ) into various fuels and feedstocks. In the short term, we are focusing on systems capable of selective oxygenations or reductions. We hope to develop principles that would allow us to design and develop artificial systems having the selectivity of the cytochrome P-450 enzymes that play a key role in the oxidation of long chain alkanes and the epoxidation of alkenes. Although selective, the various cytochrome P-450 enzymes involve complex assemblies ( cofactors, co-enzymes) that would be difficult to reproduce and control in an artificial system. Thus, we would hope to incorporate catalytic control procedures as effective as those in P-450, yet delete the excess baggage special to biological systems (e.g., cofactor, bulk protein necessary to elicit stability and to create substrate binding pockets, etc.) Consequently, we have focused our research on two aspects of this complex problem: (i) the design of artificial systems that possess precision, controlable sites capable of selectively encapsulating and delivering smaller molecules, and (ii) understanding the detailed structural and chemical aspects of enzyme active sites involved in and affecting the important catalytic processes, i.e., substrate binding, rate of catalysis, product release. We begin by presenting a chapter written for the ACS Monograph Series on Impact of Surface and Interfacial Structure on Enzyme Activity. It gives a concise overview of our work and serves as an excellent introduction to the studies presented, in much greater detail, in sections two and three of this thesis. -2The second section of the thesis presents the details of our simulation studies on two classes of starburst dendrimer polymers. This work represents the theoretical component of a collaborative project, including experimental chemists at Dow Chemical under the direction of Donald Tomalia. The first class of starburst dendrimers, typified by the macromolecules based on an ammonia core and ,B-alanine monomers, possesses open and extended forms for the early generations (one through three) but adopt more spheroidal structures for generations 5 and above. The higher generation ,B-alanine dendrimers contain internal hollows, connected by channels, that run the length of the entire polymer assembly. Our studies on these higher generation polymers indicate that: (a) ~50% of the surface area is internal, and (b) ~50% of the spheroidal volume is solvent-filled. Such systems provide the opportunity to selectively design unique polymers with internal binding sites. The sequestering of dopamine in a catechol modified starburst dendrimer is included to illustrate the potential utility of these dendritic materials as therapeutic delivery systems. The second class of starburst dendrimers, typified by the penta-erythritol polyether series, is found to have spherical forms at very early generations. For this type, the later generations lack any internal surface area or volume. Calculations of the amount of surface area available to terminal generation hydroxyl groups indicate the dense-packed limit for these polyether dendrimers to be the third generation, consistent with experiment. The third section of the thesis focuses on the results of our investigations on complexes of Dihydrofolate Reductase (DHFR). These represent the fruit of a collaborative experimental/theoretical program designed to probe the details of DHFR's catalytic requirements and properties. The experimental component of the project is directed by Professor Stephen J. Benkovic (The Pennsylvania -3- State University). The theoretical portion of the research project is being done under the supervision of Professor William A. Goddard III at Caltech's Molecular Simulation Facility. The work presented here focuses on three aspects of this collaborative effort. First, we discuss the analysis of the sequence, structure, and chemical homology of three distinct forms of DHFR ( E. coli and L. ca&ei bacterial sequences and the Chicken form). Experimental kinetic studies indicate a remarkable similarity in the free-energy profile for the reduction of dihydrofolate by E. coli and L. ca&ei DHFR, despite a mere 27% sequence homology ( vide infra). We use computer graphics and macromolecular docking, combined with homology assignments, to explain this congruence in the catalytic reactivity of the bacterial systems. The analysis is then extended to include the Chicken form of the protein, which has a distinctly different reaction profile and is more similar in function to mammalian DHFR. This interspecies comparison provides the opportunity to begin piecing together an understanding of what contributes to the subtle differences in reductive chemistry exhibited by these enzymes. The second component of the DHFR investigations involves molecular simulation studies of wild-type E. coli DHFR binary (with methotrexate inhibitor) and ternary (with dihydrofolate substrate and NADPH cofactor) complexes. These calculations offer insights on the catalytic reduction of dihydrofolate to tetrahydrofolate as well as control studies for computer mutagenesis experiments. A brief discussion of the simulation methods employed in these theoretical investigations of DHFR complexes is also included. And finally, the third segment focuses on the selected modification of the E. coli DHFR using both single-site mutation and protein loop substitutions. The site-directed mutagenesis studies probe the role(s) of specific amino acid -4- residues in the functioning of E. coli DHFR. Segment mutants were constructed to engineer a bacterial DHFR protein with properties more similar to those of the mammalian enzyme (which has the ability to reduce folate to dihydrofolate). These hybrid proteins are based on the bacterial DHFR (from E. coli) where a loop, with amino acid sequence identical to the corresponding region of the Chicken DHFR, has been inserted into the protein matrix. Thus, we will show in the ensuing sections that the application of molecular simulation tools provides new insights and deeper understanding of experimental studies. As experience with such simulations accumulates, and as predictions are made on more complex systems amenable to experiment, it will become increasingly feasible to use the theoretical methods on unknown systems. -5- Section I Application of Simulation and Theory to Biocatalysis and Biomimetics -6- The text of this section is a chapter coauthored with William A. Goddard III. It has been submitted to the ACS Monograph Series on Impact of Surface and lnterfacial Structure on Enzyme Activity. -7- Application of Simulation and Theory to Biocatalysis and Biomimetics Adel M. Naylor and William A. Goddard III Contribution No. 7818 from the Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Technology, Pasadena, California 91125 Examples a.re given for the role of simulation and theory in biocatalysis and biomimetics. Simulations on the novel Sta.rburst Dendrimer polymers are used to suggest a design for encapsulating and delivering dopamine to the kidney for cardiovascular therapies. For Dihydrofolate Reductase (DHFR), the simulations (i) indicate why a particular mutation (Phe-31 to Tyr-31) causes a significant change in the catalytic rate, (ii) explain the high degree of kinetic similarity between two dissimilar forms of DHFR, and (iii) suggest that the stable form of the enzyme/substrate complex is not the reactive one. A goal of our research efforts is to develop the theoretical tools useful in designing artificial biocatalytic systems for the production offuels and chemical feedstocks. In the long term, one would envision the development of biocatalysts that could convert methane into more valuable (or more transportable) fuels or to convert syngas ( CO + H2) into various fuels and feedstocks. In the short term, we are focusing on systems capable of selective oxygenations or reductions. We would hope to develop artificial systems with the selectivity of cytochrome P450 enzymes that play a role in selective oxidation of long chain alkanes and selective epoxidation of alkenes (1 ). Although selective, the various cytochrome P-450 enzymes involve complex assemblies ( cofactors, co-enzymes) that would be difficult to reproduce and control in an artificial system (see Figure 1). Thus, we would hope to incorporate catalytic control procedures as effective as those in P-450, yet delete the excess baggage special to biological systems (e.g., cofactor, bulk protein necessary to ellicit stability and to create substrate binding pockets, etc.) To that end we have focused our research on two aspects of this complex problem: (i) the design of artificial systems that possess precision sites capable of selectively encapsulating and delivering smaller molecules, and (ii) understanding the detailed structural and chemical aspects of enzyme active -8- Figure 1. Schematic representation of cytochrome P-450 indicating the excess baggage carried by many biological catalysts. -9- 02 ~ Figure 1. -10- sites involved in and affecting the important catalytic processes, i.e., substrate binding, product release, rate of catalysis. Starburst Dendrimers : Molecular Encapsulation A recent synthetic development has led to a new class of polymers called "starburst dendrimers" (2) that provide the opportunity for design of precise encapsulation strategies. These novel materials (i) start with an initiator unit (termed the "core") that possesses multiple sites for monomer condensation and (ii) use monomer subunits terminating in functional groups that allow for regularized growth and multiple branching at the next generation. With the appropriate use of protecting groups and synthetic strategies, each generation of monomer condensation can be completed before embarking on a new one. Because of the unique chemical requirements for dendrimer formation, these polymers grow in a systematic manner, producing materials with a well-defined number of monomer subunits and a quantized number of terminal groups (Figure 2). With precise topology and chemical properties suitable for the encapsulation of specific target molecules that could be delivered to particular organs (by recognition of surface molecules), one could, in principle, change the monomer from generation to generation, developing onion-like molecules where every layer of the onion has a different chemical composition, thickness, or number of branching sites. Thus, one can imagine designing and synthesizing complex polymer structures where (i) internal layers are suitable for encapsulation of the desired molecule, (ii) outer layers are suitable for recognizing binding sites on the organ to which the target molecule is to be delivered, and (iii) intermediate layers protect the target molecule in the blood stream but release them (a) upon binding of the outer layer to recognition sites, (b) upon radiation with external light or charged particles or ( c) upon change in acidity or solvent associated with the target organ. /3 - Alanine Dendrimers. To illustrate this application, consider the ,B-alanine dendrimers where the core unit is ammonia (with three condensation sites) and the monomer unit is an amino amide (with two branch sites) as depicted below. 0 H I N H / 'H Core II ✓H -CH 2 -CH 2-C-~ -CH 2 - CH 2-N, H H Monomer Experimentally it has been possible to develop complete dendrimers up through the tenth generation. However, no experimental structural data are available (these materials are fractal and do not crystallize). We have been carrying out molecular dynamics simulations on these ,B-alanine dendrimers up through generation 9 (3) using the molecular simulation facilities of POLYGRAF (from Biodesign, Inc., Pasadena, CA 91101). These investigations indicate a dramatic change in the overall structural properties for the .8-alanine systems as these polymers grow past generation 4. The early generation dendrimers -11- Figure 2. Cascade growth pattern for the ,8-alanine type dendrimers from the core ammonia unit up to generation 4. -12- ~ z 0 f f f ~ ffi z LIJ C, £' z r f*f f~f f C"') z 0 N :i: z ~ z a: f LIJ LIJ z C, ....= f bC ~ t f-<-<, f N z 0 i== <( a: LIJ z LIJ C, f r f \ z 0 z-f i== <( a: L.IJ I rr zL.IJ :r LIJ \-="z,-:::c /'-' :c \) ~ z£' f~ . N C, a: 0 0 -13- (generations 1 through 3) possess very open and well-extended structures. These structures are hemispherical disks (with the core nitrogen responsible for the curvature) but there is no real inside to the polymer. This topology for the early generation systems is strikingly different from earlier proposals (4), but these hemispheric structures provide a simple interpretation of observed nuclear magnetic resonance relaxation times (Naylor, A. M.; Goddard III, W. A.; Keifer, G. E.; Tomalia, D. A. J. Am. Chem. Soc., in press 1988). We find a distinct change in structural properties for those polymers above generation 5. The overall structure of the polymers is more sphere-like, with ample internal hollows connected by channels that run the length of the polymer assembly. These interior cavities should be suitable for sequestering guest molecules. Thus, in Figure 3, which limns a generation 6 dendrimer, we find an overall spherical structure containing a channel running through the interior of the polymer from one side to the other! To better illustrate the space available in the interior, we show in Figure 4 the solvent-accessible surface for the polymer (generation 6). [The solvent-accessible surface is constructed using the approach developed by Michael Connolly (University of California, San Diego) and is based on the definitions for molecular surfaces proffered by Frederic Richards (5). The molecular surfaces are composed of dots located in terms of a probe sphere {radius= 1.4 A for water) rolling along the van der Waals spheres of the outer (accessible) atoms of the polymer.] Here we have used graphical slabbing to remove from view the front and rear portions of the image. The channels and cavities in this structure are representative of those found in the higher generation P-alanine dendrimers. Dopamine - Sequestered Dendrimers. As an illustration of the dimensions of these channels and of how dendrimers might be used to sequester small molecules, we have used the molecular simulation capabilities of POLYGRAF to predict the optimum conformations for several dopamine 1 molecules H2N - CH2 - CH2 - Q O H DOPAMINE OH 1 inside this starburst polymeric matrix. Dopamine was chosen because it is a good candidate for effective sequesterization in a t,-alanine type dendrimer. Its size and shape are suitable for the cavities and channels found to exist in the higher generation P-alanine systems. From a chemical standpoint, dopamine possesses both the hydrogen bond donor and acceptor sites needed for favorable binding interactions to the polymer's carbonyl, amide, and amino substituents. We estimate that a generation 6 polymer should be capable of holding 15-20 molecules of dopamine. Figure 5 illustrates a dopamine/dendrimer complex with examples of the conformations adopted by the sequestered molecules and the polymeric material. -14- Figure 3. A representative structure for a generation 6 ,6-alanine dendrimer where generations 1 to 4 are colored red, generation 5 is shown in light blue, and generation 6 is yellow. Figure 4. A view of a generation 6 dendrimer with its solvent-accessible surface displayed and clipped to reveal the nature of the internal cavities and channels found in the higher generation ,6-alanine dendrimers. -15- Figure 3. Figure 4. -16- Figure 5. A view of various dopamine molecules (magenta) bound in the inner regions of a ,8-alanine dendrimer (generations 1 through 5 in light blue; generation 6 in yellow). Figure 7. A catechol-modified, dopamine-loaded ,8-alanine dendrimer where the dopamines are displayed in magenta, generations 1 through 5 in light blue, generation 6 in yellow, and the catechol cap in red. -17- Figure 5. Figure 7. -18- Pharmacologically, the ability (i) to seleetively detver dop~ne to peripheral kidney receptors without eliciting complications due to the presence of dopamine receptors in the central nervous system (CNS) and (ii) to maintain a supply of nonmetabolized dopamine would be advantageous in cardiovascular hypertension therapy (6). The additional issues presented by this type of application include the dimensions of the dendrimer encapsulated dopamine and the target ting of the unit to the appropriate dopamine receptor sites. The dimensions of the higher generation ,B-ala.nine dendrimers ( see Figure 6 with the minimum diameter plotted as a function of generation) are such that these dopamine/dendrimer complexes would not readily cross the CNS bloodbrain barrier. In order to ensure the delivery to kidney dopamine receptors, we suggest modifying the terminal amine sites of the polymer with catechol fragments, as shown in 2 ···CH2-CH,-!-CH2-CH2-QOH ~ ~OH DENDRIMER CATECHOL 2 This leads to surface features resembling dopamine and may lead to selective binding at dopamine receptor sites (Figure 7). The polymer encapsulation matrix should protect the catecholamine from rapid metabolic inactivation. These studies provide structural models that should be useful for analyzing the dopamine/dendrimer systems. The next step is to test the effectiveness of these modified materials for encapsulation of dopamine (and related materials) and to determine how effectively they are delivered to the kidney centers. As such experiments proceed, continuing simulation will be useful in providing a quantitative framework for understanding various results. We expect that the judicious selection of a core unit, internal monomer subunits, and terminal monomer fragments will allow the design of dendrimers to complex with specific guest molecules and to deliver them to specific sites. It will, of course, be essential to develop synthetic schemes that allow for chemical control and fidelity. Dihydrofolate Reductase : Roles of Precise Structure in Catalysis In designing new catalysts, it is essential to understand how the character of the active site (including cofactor) controls catalytic activity since one will want to modify this active site or cofactor. As a prototype for such studies, we have carried out a series of molecular simulations on the Dihydrofolate Reductase (DHFR) system. -19- Figure 6. A plot of the ,B-alanine dendrimers "short" diameter ( see text) as a function of generation. These diameters were calculated from our molecular simulations and based on the average of the smallest principal moment of inertia. 75 - - - - - - - - - - - - - - - - - - , 60 2 z 45 0 C, ~ 30 I I I I N 0 I I / 15 o....----- , , , , , , , 1 2 3 4 5 6 7 GENERATION Figure 6. , I -21- Introduction a.nd Ra.tiona.le. DHFR is a.n idea.I system to study for a. number of rea.sons. The ca.ta.lytic properties of DHFR a.re such that under normal physiologic conditions and with the NADPH cofactor bound, 7,8-dihydrofola.te (DHF) is reduced to 5,6,7,8-tetra.hydrofolate (THF) (7). Thus DHFR plays an important role in cell metabolism by maintaining a supply of THF. THF is used by the cell as both a cofactor and in substrate quantities in the synthesis of deoxythymidine. By inhibiting the production of THF, deoxythymidine synthesis is curtailed, nucleic acid replication comes to a. ha.It, and cell proliferation ceases. It is this biochemical cascade which supplies the pha.rma.cologica.l and chemotherapeutic applications of inhibitors to DHFR. The abundant experimental data. on DHFR provide both inspiration and detailed checks upon theoretical studies. The crystal structures of DHFR from two bacteria.I sources have been resolved, reported, and coordinates made available through the Brookhaven Data Base (8-10). The kinetic profiles of the enzyme under va.rious conditions and, hence, mechanistic details have been determined (11,12). The recombinant DNA protocols for the successful study of site-directed mutants of DHFR have been reported (13-17). DHF 3 is composed of (from left to right, below) a pterin ring, a bridging methylene unit, p-aminobenzoa.te, and a glutamate fragment. H I H2N ~ ~ N N~-- I ,,' H; O CO2 I CH 2- N - 0 - , C-N-C-CH2-CH2-C02 ,' I ,' I \\ I I I II - ,N ,,....N H /J 0 ', H / , __ ,' H THF H H 4 It is the N5-C6 double bond (circled, above) of 7,8-DHF that is reduced to 5,6,7,8-THF (4) by DHFR. Methotrexate (MTX), an important chemotherapy and anti-bacteria.I agent, is chemically quite simila.r to DHF (differences a.re circled). -22- MTX 5 MTX 5 contains the same benzglutamate fragment as DHF (but with a methylated amine) and a pteridine ring with an amino substitution at position 4. Indeed, we find smilar binding sites for MTX and DHF on DHFR. The crystal structure of the E.coli DHFR/MTX binary complex (9) reveals that the inhibitor binds in the active site in a kinked fashion (Figure 8). Asp-27 forms a salt-bridge to the bound pteridine ring while Phe-31 allows for the bend in the bound inhibitor. The remainder of the active site cavity surrounding the pterin ring is composed of amino acid residues that create a very hydrophobic environment. Before embarking on designing improvements into the catalytic sequence, it is useful to know the detailed kinetics of the system. A profile of the steady-state kinetics of the E. coli form of DHFR was recently reported by Fierke, Johnson, and Benkovic (12). This study used stopped flow fluorescence and absorbance spectroscopies to measure the rates of ligand association and dissociation and the binding constants of key intermediates in the catalytic sequence, as diagrammed in Figure 9. This study revealed that the catalytic step, i.e., the N5-C6 double bond reduction, proceeds at a steady-state rate of 950 sec- 1 , whereas the rate of THF product release was only 12.5 sec- 1 , making it the rate-limiting step. Hence, any design modifications to increase the turnover of this system should focus first upon increasing the product off-rate. A Synthetic Mutant : Phe - 31 -+ Tyr - 31. We now turn to using molecular simulation methods to examine some a.rea.s of the biocatalytic properties of DHFR that a.re not easily investigated experimentally. The general methods used for our studies incorporate computer graphics, molecular force fields, energy minimization, and molecular dynamics. BIOG RAF (from Biodesign, Inc., Pasadena, CA 91101) was the molecular simulation package used for these investigations. The AMBER force field was used for the calculations (18). As an illustration of the use of simulations, we consider the eft'ect on rate of a site mutation of DHFR. Benkovic et al. used recombinant-DNA techniques to synthesize the protein where Phe-31 was transformed into Tyr-31 {14). Preliminary experimental studies indicated a change in the pK. of Asp-27 in this mutant form of the enzyme. Molecular simulations were run on both the wildtype enzyme and the Tyr-31 mutant to assess the structural cha.nges produced by such a. modification. -23- Figure 8. The active site of E. coli DHFR with MTX and NADPH bound. Figure 10. A comparison of MTX bound to wild-type DHFR (red MTX and Phe-31; blue active site residues) and Tyr-31 mutant protein (yellow MTX, Tyr31, and active site residues). -24- Figure 8. Figure 10. -25- Figure 9. Steady-state kinetic cycle for the reduction of 7,8-DHF to 5,6,7,8-THF via DHFR. -26- SUBSTRATE BINDING FORWARD. 40 µM-1 s-1 ,---, BACKWARD• 40 ,., ....... : ~ ) , , , - LOSE NADPH 1.75 5· 1 ~ u ~ UADPH --~ DHF: ',, . ~ ~ F ....•.. PRODUCT RELEASE FORWARD= 12.5 s· 1 BACKWARD. 2 µM ' ,., UADPH THF I CATALYTIC REACTION FORWARD= 950 s· 1 BACKWARD= 40 s· 1 a ✓ LOSE THF ¥ 245·1 ~ NADP• RELEASE OXIDIZED COFACTOR FORWARD= 200 s-1 BACKWARD= 5 µM ·1 5-1 Figure 9. BIND REDUCED T'H,F COFACTOR FORWARD= 8 µM 1 5· 1 BACKWARD= 85 s 1 ' - LOSE1THF 145· -27- The starting structure for our wild-type protein complex was based upon the crystallographic data, where the L. ca.sei NADPH coordinates were used to model the cofactor into the E. coli system. To create the Tyr-31 mutant, the replace facility of BIOGRAF was used. For both series of simulations, a 10 A solvent shell ( containing experimental plus supplemental waters) surrounded the protein complexes. Counter ions were positioned near charged amino acid side chains to achieve electroneutral systems. The structures were then equilibrated via a sequence of molecular dynamics and energy minimization calculations. Our calculations show that the pteridine ring is relatively undisturbed by the introduction of the Tyr hydroxyl group, yet the benz-glutamate portion of the bound substrate (or inhibitor) is markedly displaced (see Figure 10). We find that the mutant -OH group produces a 'bump' on the surface of the hydrophobic pocket near the benzyl group that disrupts the binding of the benz-glutamate fragment. This suggests that the product off-rate from the DHFR/NADPH/THF complex should be affected markedly by this substitution. Kinetic studies have verified that the product off-rate for the Tyr-31 form of E. coli DHFR is 50 times faster than that of wild-type protein (14)! Natural Mutants: E.coli and L. ca.sei. Consider now the question of how different one can make the active site without affecting the chemistry. The overall amino acid sequence homology between the E. coli and L. ca.sei forms of DHFR is only 27%. However, as shown in Figure 11, a Gibbs free energy comparison of the steady-state data for the E. coli and the L. ca.sci proteins shows that the reaction kinetics for these two forms of the enzyme are remarkably similar {19). In fact (using the ternary DHFR/NADPH/DHF complex as the energy reference), the energy differences between the two are, at every step, within 1 kcal/moll Using the x-ray crystal structures and reorienting them so that the MTX of both complexes a.re superimposed {by docking one structure with respect to the other), we see that the conformation of MTX bound to the E. coli DHFR is very similar to that of MTX in the L. ca.sei ternary crystal complex. The orientations of both the pteridine and the benzyl rings are identical for the two complexes and the backbone atoms of the glutamate substituent also align quite nicely. The discrepancy in these two forms of bound MTX occurs at the C-6 ca.rboxylate group of the glutamate fragment, a position far removed from the catalytic site. A glance at the two different enzymes reveals that this difference in conformation is due to the positions of positively cha.rged amino acid side chains on opposite sides of the opening for the active site (Arg-52 for the E. coli form and His-28 for the L. ca.sei complex). The results of docking the L. ca.sei structure to the E. coli show that the overall folds for these two proteins are quite similar. Regions of secondary structural elements, i.e., a-helices and ,8-sheets, a.re conserved, while insertions and deletions in the amino acid sequences occur in loop regions located a.bout the exterior regions of the enzyme. The structural domains of the DHF and NADPH binding sites are maintained. In the comparison of the DHF substrate binding pockets, one finds that nature, in some instances, substitutes like for like by using -28- Figure 11. A Gibbs free energy plot of the kinetic profiles for E. coli (solid) and L. ca~ei ( dotted) DHFR (19). 15 I ....... .. 101 I \ (\ --- -r-- I 5 • I I I I R K... t···· ~ I I 0 E ro u .::x:. ..__.. 0 CJ <l I -Sr ~NADPH V ENADPH +DHF ENADPH DHF u . -1 OJ-15 I V ErHF +NADP+ +NADPH E NADP+ THF REACTION COORDINATE Figure 11. \ I \ • ENADPH NADPH +THF ETHF I N \0 I -30- (1) different aromatic side chains [as Trp-30 (E. coli= Ee)-+ Tyr-29 (L.caJei Le), Tyr-100 (Ee) -+ Phe-103 (Le), and Phe-153 (Ee) -+ Tyr-155 (Le) indicate] or (2) different aliphatic side chains [as Ile-5 (Ee) ---+ Leu-4 (Le), Leu-36 (Ee) --+ Val-35 (Le), and Leu-112 (Ee) --+ Val-115 (Le) demonstrate]. But there also are examples where aliphatic is substituted for uomatic (and vice versa) as with Ile-50 (Ee) -+ Phe-49 (Le) and Tyr-111 (Ee) - t Leu-114 (Le). Simila.r substitution patterns are found in the NADPH cofactor binding site, where, in addition to those types described above, charged residues are maintained [i.e., His-45 (Ee)-+ Arg-44 (Le) and Lys-76 (Ee)-+ His-77 (Le)]. Using these superimposed structures with the MTX (from both crystal structures) a.nd the NADPH (from the L. ea&ei complex) as guides, the active site regions are identified for both enzymes. Here we define the active site to be those amino acids containing a.ny atom within 7 A of either of the bound substrates. Analyses of the residues in the active site region determine that the amino acid sequence homology in this portion of the protein is 35% (see Table = I). The two docked active site regions (with MTX bound) are shown in Figure 12. Examination of the docked active sites reveals that there are three general types of amino acid residues involved in the construction of the active site surface: (1) amino acid residues conserved between the two bacterial forms of DHFR, e.g., Phe-31 (Ee) and Phe-30 (Le); (2) amino acid residues that differ between the two sequences and contribute chemically different side chains to the construction of the active site, e.g., Ile-50 (Ee) and Phe-49 (Le); and (3) amino acid residues that differ between the two sequences but contribute only chemically homologous main chain atoms to the construction of the active site, e.g., Ala-6 (Ee) and Trp-5 (Le). Thus, by modifying the definition of homology to also include those residues in the active site supplying only backbone atoms, one obtains a generalized 'chemical homology' of the active site. Indeed, the 'chemical homology' between the E. coli and the L. c,uei substrate binding pockets becomes 60% (19)! A comparison of the solvent accessible surfaces [as described a.hove; (5)] for these segments of the protein further substantiates these remarkable structural similarities. The surface areas mapped out for these regions agree within 93%. The solvent accessible sufaces for the MTX pteridine and the NADPH nicotinamide rings are essentially interchangeable for the two different sequences, as illustrated in Figure 13. Hence, we see that nature creates essentially identical reactive surfe.ces for these bacterial DHFR systems from different amino acid building blocks (19) (Benkovic, S. J.; Adams, J. A.; Fierke, C. A.; Naylor, A. M. Ptcridines, in press 1988). The components necessary for DHFR's ability to catalytically reduce the N5-C6 double bond of 7,8-DHF to 5,6,7,8-THF are conserved. The carboxylate group that supplies a proton to the pterin ring is present in both the E. coli and -31- Table I. Comparison° of DHFR Active Site Residues from E. coli 1.nd L. caui. Residueb 4 E.coli L. caui 5 6 7 8 9 10 13 L A A L A V F w A Q N R 14 15 16 17 V G n G M K e L d g 29 30 31 32 18 19 20 21 22 23 24 25 a m p w n L p A D L a w F k p w h L p D D L h y F r 42 43 44 45 46 47 48 49 50 m G R h E G R r T T w V y E s s f 61 62 63 64 65 L s s h Q Q h 26 33 34 35 36 r n a q T T V 51 52 53 54 55 56 57 g p L p G R L p E R 27 28 p k R R 66 67 68 74 75 76 77 78 79 93 94 95 p G t w V K s V D V I G e D y V V H D V A I A G 96 97 98 99 100 101 102 103 111 113 114 115 G G r V y E q F y T H G A q f T a F 1 T R 122 123 124 125 153 D T T H f f K m y D p V L 112 V • Bold upper case indicates homologous, lower case indicates nonhomologous, 1.nd nonbold upper case indicates backbone chemical homology, a.s described in the text. • Numbered for the E. coli form. -32- Figure 12. A comparison of the docked E. coli (red MTX and enzyme) and L. ca.,ei (yellow MTX and NADPH; blue enzyme) active sites. The conserved Phe's are shown to the right of the pteridine rings. The substituted side chains [Ile-50 (Ee) and Phe-49 (Le)] appear in the 12 o'clock position above the benzyl ring. The chemically homologous main chain contributors [Ala-6 (Ee) and Trp-5 (Le)] are shown in the 7 o'clock position. Figure 13. Dotted surface comparison showing the congruence of the E. coli (red) and L. ca.,ei (blue) active sites. -33- Figure 12. Figure 13. -34- the L. caaei sites as an Asp side chain. The hydrophobic pocket that surrounds the reactive pteridine moeity and prevents the aqueous environment from disturbing the catalytic process is formed by varied amino acids but maps out the same surface area and hydrophobic character. The hydride donating NADPH nicotinamide ring is positioned adjacent to the reactive center even though the NADPH binding sites are composed of different amino acid sequences. Conformation of Bound Inhibitor. Another area under investigation focuses on the conformation(s) of the substrate and an inhibitor (MTX) bound to DHFR. The form of the DHFR/MTX complex is known from the crystallographic studies of Kraut et al. (8-10). However, the orientation of the bound pterin ring in the reactive DHFR/DHF is known to differ dramatically from the MTX crystal structure (20). Basically, these differences arise because there are two possible orientations of the pterin ring in the active site; one is flipped by 180° with respect to the other. Isotope labelling experiments on THF show that the reactive DHF must be bound in the conformation flipped from that observed by x-ray for MTX. In order to understand these differences, we ran simulation studies on altered forms of bound MTX and DHF to investigate the structural and energetic properties of these systems. The starting structures for our binary DHFR/MTX calculations were based upon the crystallographic data. For the experimental form of bound MTX we used the coordinates a.s they were reported. For the pteridine-ftipped form of bound MTX, termed MTX-flipped, we rotated a.bout the C6-C9 and C9-N10 bonds of MTX to produce a starting conformation with the pteridine ring positioned in the active site but with its face flipped 180° (Figure 14). To be consistent with experiment, the bound MTX inhibitor was protonated at Nl (21). For both systems we used the experimentally determined solvent plus additional water to create a 10 A solvent shell around the enzyme-inhibitor complex. Electroneutral systems were achieved by positioning the appropriately charged counter ions near to cationic and anionic side chains. The entire solvated protein and inhibitor systems were then equilibrated with a sequence of molecular dynamics and energy minimization calculations (using BIOGRAF and the AMBER force field). These simulations indicate that the active site of DHFR can accommodate both forms of the bound MTX. After equilibration of both the experimental and the flipped forms, the ca.rboxyla.te group of Asp-27 is found to be involved in a salt bridge with the pteridine ring of the inhibitor. The hydrophobic pocket surrounding the pterin ring ha.s adjusted adequately to either conformation of the bound MTX. The energetic profiles indicate that the experimentally observed form of MTX bound to DHFR is ~3 kcal/mol lower in energy than the flipped form of the bound inhibitor. Conformation of Bound Substrate. Now the question of the conformation of bound DHF substrate was addressed. Simulations were run on DHFR/DHF /NADPH ternary complexes to investigate both the structural and energetic requirements associated with the reactive and nonreactive forms of DHF (see Figure 14). As above, the crystallographic information available for -35- Figure 14. The orientations of the MTX and DHF pteridine rings in the active site of D HFR. -36- (a) MTX - unflipped (crystal) :N,o,,:_H~x:\ -s::N 'N' .J L ---- '- -P" H2N ::,...N ~ ./ N_;' H ..... CfiAo-pO:_HYX:',' N',_..H ._ ____ IN J --~ \,' /c-lA5P 21 ~ 9 O (c) DHF - unflipped (non-reactive) NH2 ··· O o~ ~ -P" N·····H - O II N~NH2 - · I cSH (b) MTX -flipped (d) DHF - flipped (reactive) Figure 14. "c-iAsp27I ol' -37- the E. coli binary and L. ca.,ei ternary complexes (with MTX) was used to generate starting structures for the molecular simulations. The coordinates for the E. coli bound NADPH were modeled based upon those from the L. ca,ei ternary complex. The DHF units were positioned based upon the coordinates of the MTX. For these simulations, the carboxylate group of Asp-27 was protonated while the pterin ring of the substrate was not protonated at the Nl position. Again, solvent and counterions were included and all atoms of the structures were relaxed and equilibrated during the calculations. The simulations indicate that there are two favorable conformations of bound DHF in the active site of DHFR, each analogous to the favorable conformations of MTX. The amino acid side chains that create the hydrophobic portion of the active site reposition themselves to allow for either form of the pteridine ring. In the reactive orientation (termed DHF-fiipped), the Asp-27 COOH prongs the C4 oxygen and the N3 sites. In the nonreactive conformation (termed DHF-unfiipped), the carboxylate group straddles the Nl and the NS positions. The energetic results of the simulations find the unftipped nonreCJctive form (analogous to the x-ray form in MTX) of the pteridine ring lower in energy than the reactive form by ~4 kcal/mol! This result seems to contradict experiment since no radio-labeled product resulting from DHF reduction accommodates this orientation of bound substrate. Closer examination of the active site regions reveals that the reducible C-N bond of the pterin ring differs substantially with respect to the positions of the NADPH nicotinamide rings. In the low energy nonreactive state, the NADPH C'4 site is 4.1 A from the carbon of the pteridine N5-C6 double bond, while in the higher energy reactive form, this interatomic distance is reduced to only 3.2 A! The shorter distance for hydride transfer during catalysis favors the reactive conformation even though the energetics slightly favor the nonreactive form of bound DHF. This information clearly suggests a kinetic mechanism for the control of DHF reduction to THF via DHFR. Figure 15 depicts the relationship between the NADPH nicotinamide ring and the reactive DHF substrate. Wu and Houk have used ab initio calculations to propose a mechanism for hydride transfer to the methyl iminium cation (22). Their results indicate that H- transfer proceeds via a syn transition state structure with a C-H-C angle of 150-160° and a C-C interatomic distance of 2.6 A (see Figure 16). What we find for the reactive form of bound DHF and NADPH in an equilibrated ground state is a pseudo-syn orientation of the reacting ring systems, a C-H-C angle of 155°, and an equilibrium distance of 3.2 A between the two carbon centers (19). In contra.st to the nonreactive conformer of DHF, simulations suggest that the equilibrium distance between the two reacting carbons is 4.1 A. The key difference in character is the orientation of the pterin and nicotinamide rings. In the productive conformation, the two-ring systems adopt positions that allow for H- transfer from the nicotinamide center to C6, while this relationship is not accommodated by the nonreactive bound conformation o! DHF. In order to address the reaction rates o! these species, we could monitor the C-C distance as a function of time. Taking the probability distribution of C-C -38- Figure 15. The catalytic pocket of DHFR showing the relationship between the NADPH nicotinamide ring (left) and the reactive DHF pteridine ring (right). -39- Figure 15. -40- Figure 16. Proposed model for hydride transfer from NADPH to DHF (19). () is the angle between the C4' of NADP+, the H- being transferred, and C6 of DHF. -41- /" NH DHF H N - NH - C ... C I -- ~je ,,,,,, ,,,,,, ,,,,,, ,,,,,, / R ,,,,,, ,,,,,, ,,,,,, ~-=---=-- , N5+- l ••••••••• NADPH Figure 16. •• -42- with the reaction rate as a function of C-C distance, one should be able to predict relative reaction rates. However, qualitatively the large differences in equilibrium position certainly suggest a significant difference in rate. A test of this prediction would be to use NMR NOE experiments to examine conformation. We predict that over 90% of the bound complexes are the nonreactive forms. Summary We have examined several systems chosen to illustrate the current role of theory a.nd simulation in biomimetics and biocatalysis. It should be clear that the theory is not done in a vacuum (so to speak) but rather that the theory becomes interesting only for systems amenable to experimental analysis. However, the examples illustrate how the theory can provide new insights and deeper understanding of the experiments. As experience with such simulations accumulates and as predictions are made on more and more complex systems amenable to experiment, it will become increasingly feasible to use the theory on unknown systems. As the predictions on such unknown systems are tested with experiment and as the reliability of the predictions increases, these techniques will become true design tools for development of new biological systems. Acknowledgments This work was funded by a grant from the Department of Energy, Energy Conversion and Utilization Technologies. The DOE-ECUT program funded this work with the hope that development of simulation techniques would eventually have an impact on development of new, industrially useful processes for biotechnology and biocatalysis. We especially wish to acknowledge the foresight of Drs. Jim Eberhardt, Minoo Dastoor, and Jovan Moacanin in encouraging these efforts. The equipment used was also funded by the ONR/DARPA ( Contract No. N00014-86-K-0735) and by a grant from the Division of Materials Research, Materials Research Groups, of the National Science Foundation (Grant No. DMR84-21119). We thank Professor Stephen J. Benkovic of the Pennsylvania State University and Dr. Donald A. Tomalia of The Dow Chemical Company for numerous helpful discussions and for materials in advance of publication. Literature Cited 1. Cytochrome P - 450 : Structure, Mechanism, and Biochemistry; Ortiz de Montecellano, P. R., Ed.; Plenum Press: New York, 1986. 2. Tomalia, D. A.; Baker, H.; Dewald, J.; Hall, M.; Kallas, G.; Martin, S.; Roeck, J.; Ryder, J.; Smith, P. Macromolecules 1986, 19, 2466-2468. 3. Naylor, A. M.; Goddard III, W. A. Polymer Preprints 1988, 29, 215-216. 4. Tomalia, D. A.; Hall, M.; Hedstrand, D. M. J. Am. Chem. Soc. 1987, 109, 1601-1603. 5. Richards, F. Ann. Rev. Biophys. Bioeng. 1977, .§, 151-176. 6. Kebabian, J. W.; Agui, T.; van Oene, J.C.; Shigematsu, K.; Saavedra, J. M. Trends in Pharmacological Sciences 1986, 96-99. 7. Greatly, J. E. Adv. Pharma.col. Chemother. 1980, 17, 37-102. -43- 8. Matthews, D. A.; Alden, R. A.; Bolin, J. T.; Filman, D. J.; Freer, S. T.; Hamlin, R.; Hol, W. T. J.; Kisliuk, R. L.; Pastore, E. J.; Plante, L. T.; Xuong, N; Kraut, J. J.Biol.Chem. 1978, 253, 6946-6954. 9. Bolin, J. T.; Filman, D. J.; Matthews, D. A.; Hamlin, R. C.; Kraut, J. J. Biol. Chem. 1982, 257, 13650-13662. 10. Filman, D. J.; Bolin, J. T.; Matthews, D. A.; Kraut, J. J. Biol. Chem. 1982, 257, 13663-13672. 11. Stone, S. R.; Morrison, J. F. Biochemistry 1984, 23, 2753-2758. 12. Fierke, C. A.; Johnson, K. A.; Benkovic, S. J. Biochemistry 1987, 26, 40854092. 13. Villafranca, J.E.; Howell, E. E.; Voet, D. H.; Strobel, M. S.; Ogden, R. C.; Abelson, J. N.; Kraut, J. Science 1983, 222, 782-788. 14. Chen, J.-T.; Mayer, R. J.; Fierke, C. A.; Benkovic, S. J. J. Cellular Biochem. 1985, 29, 73-82. 15. Howell, E. E.; Villafranca, J. E.; Warren, M. S.; Oatley, S. J.; Kraut, J. Science 1986, 231, 1123-1128. 16. Taira, K.; Chen, J.-T.; Fierke, C. A.; Benkovic, S. J. Bull. Chem. Soc. Jpn. 1987, 60, 3025-3030. 17. Mayer, R. J.; Chen, J.-T.; Taira, K.; Fierke, C. A.; Benkovic, S. J. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 7718-7720. 18. Weiner, S. J.; Kollman, P.A.; Case, D. A.; Singh, U. C.; Ghio, C.; Alagona, G.; Profeta, Jr., S.; Weiner, P. J. Am. Chem. Soc. 1984, 106, 765-784. 19. Benkovic, S. J .; Fierke, C. A.; Naylor, A. M. Science 1988, 239, 1105-1110. 20. Charlton, P.A.; Young, D. W.; Birdsall, B.; Feeney, J.; Roberts, G. C. K. J. Chem. Soc., Chem. Commun. 1979, 922-924. 21. Cocco, L.; Temple, Jr., C.; Montgomery, J. A.; London, R. E.; Blakley, R. L. Biochem. Biophys. Res. Commun. 1981, 100, 413-419. 22. Wu, Y.-D.; Houk, K.N. J. Am. Chem. Soc. 1987, 109, 2226-2227. -44- Section II Dendritic Macromolecules: Molecular Simulation of Starburst Dendrimers -45- The text of this section is part of an article coauthored with William A. Goddard III and Donald A. Tomalia. It is to be submitted to Angewandte Chemie. -46- Abstract The structure and properties of two classes of star burst polymers were studied using molecular dynamics simulations. One class, typified by the starburst dendrimers based on an ammonia core and ,8-alanine monomers, possesses open and extended forms for the early generations (one through three) but adopt more spheroidal structures containing internal hollows connected by channels that run the length of the assembly for generations 5 and above. The studies on these higher generation polymers indicate that: (a) ~50% of the surface area is internal, and (b) ~50% of the spheroidal volume is solvent-filled. Such systems provide the opportunity to selectively design unique polymers with internal binding sites. The sequestering of dopamine in a catechol-modified starburst dendrimer was modeled to illustrate the potential utility of these dendritic materials as therapeutic delivery systems. A second class, typified by penta-erythritol polyether dendrimers, is found to have spherical forms at very early generations. For this type, the later generations lack any internal surface area or volume. Calculations of the amount of surface area available to terminal generation hydroxyl groups indicate the dense-packed limit for these polyether dendrimers to be the third generation, consistent with experiment. -47- 1. Introduction A novel class of polymers called "starburst dendrimers" has recently been discovered by Tomalia et aJ. 1 - 7 These unique polymeric materials (a) start with an initiator unit, termed the "core," which possesses multiple sites for condensation, and (b) use monomer subunits that terminate in functional groups, each of which allows for multiple branching sites. Using various synthetic strategies, it is possible to ensure that these polymers grow in a very systematic manner, producing materials with a well-defined number of monomer subunits and a quantized number of terminal groups, as shown schematically in Figure 1. Thus, the initial condensation of monomers to fully saturate the core unit produces a generation 1 dendrimer. The subsequent condensation of monomers to saturate the terminal functional groups of the generation 1 moiety yields the generation 2 dendrimer. This process is repeated to create higher generation polymeric dendrimers. The strategies employed to synthesize this type of polymer involve the selective use of protecting groups 5 or multistep condensations1 •4 so that each generation can be completed before starting a new one. Thus nearly ideal, synthetically perfect materials can be made for characterization and can be used to proceed to subsequent generations. Unfortunately, even though each molecule has the same topological structure, there are an enormous number of possible conformations (these systems are fractal in nature) so that, despite their uniformity, there is no long-range order for x-ray crystal structure analysis. Thus, to date, there are no detailed experimental structural characterizations to guide the design of these new materials. This work ( using molecular simulations) presents the first such structural characterization of starburst dendrimers. Based on this work, we are able to discuss some properties and possible functional applications. -48- Figure 1. Schematic two-dimensional representation of a starburst dendrimer growth cascade. -49- '-=t z 0 f f ~ ffi z w (!) M z 0 i"' f f f ~ a: w z w (!) . ~ QI ~ ::, ·- bO ~ f N r-\~ f~ f rI \ I f z z-f l '@-z / z f z 0 ~ a: w zw (!) .,.. z 0 ~ a: w zw (!) w a: 0 (.) -50- 1.1 Synthetic Strateg~es A variety of core units and monomer fragments have been used to synthesize a wide range of different starburst dendrimers containing various interior environments and surface functional groups. Generally speaking, these materials are produced via propagation techniques that include "time-sequenced, step-growth" components involving either: (a) differentiated, polyfunctional reagents used in molar excess quantities, or (b) elaborate protecting/deprotecting group chemistry. To assure starburst branching ideality, the condensations must be essentially quantitative, and the reaction conditions must be such that intramolecular looping or intermolecular bridging is minimized. The molecular simulation studies presented in this work have focused on two types of starburst dendrimers: (a) the polyamidoamines and (b) the pentaerythritol polyethers. The synthetic methods to produce these materials and the experimental characterizations are summarized below. 1.1.1 Polyamidoamine Starburst Dendrimers The polyamidoamine dendrimers (PAMAM), also referred to as the /3alanine systems, begin with an ammonia core unit (1) and contain the amidoamine monomer building block (2) shown below. CORE MONOMER 1 2 The ammonia initiator core contains three condensation sites, thus producing a tridirectional dendrimer. Each monomer building block terminates with an -51- amino group containing two sites for branching and continued growth. Hence, the number of monomers added doubles from one generation to the next. After addition, these polymers have terminal, surface amino groups. Table 1 contains a listing of the number of monomers, per generation, for the PAMAM series. The synthetic scheme employed in the production of these dendrimers falls into the excess reagent category. It is outlined in Figure 2. The first step in the synthesis involves exhaustive Michael addition of methylacrylate to a suitable amine group, either the core unit or the terminal amino groups from the preceding generation. The resulting esters are then exhaustively amidated with excess ethylenediamine to produce the next full generation polyamidoamine. Interruption of this synthetic cascade after the methylacrylate condensation yields ester-terminated oligomers, referred to as the half-generation materials. Early work with the polyamidoamine starbursts indicated that it would be quite difficult to synthesize these highly branched polymers, without bridging, above generation 5. 6 Recent studies have shown, however, that generations one through ten can be produced highly monodispersed with high branching idealities (~ 95 mole %) as determined by C 13 nuclear magnetic resonance spectroscopy. 8 Size exclusion chromatography (SEC), low-angle laser light scattering, and intrinsic viscosity measurements have been used to determine molecular weights, polydispersities, and hydrodynamic diameters of the polymers. 7 The results for generations 1 through 11 are listed in Table 2. -52- Table 1. Pertinent information for the ,B-alanine dendrimers investigated with molecular simulation. Monomers Condensation Total Generation New Total Sites Atoms" 1 3 3 6 34 2 6 9 12 3 4 12 24 21 45 24 48 5 6 48 93 96 94 214 454 934 96 192 1894 7 8 192 384 189 381 765 384 768 3814 7654 9 10 768 1536 1533 3069 1536 3072 15334 30694 11 3072 6141 6144 61414 " This is the number of atoms actually included in the simulation; i.e., it ignores hydrogen atoms bonded to carbon since these are treated implicitly. -53- Figure 2. Synthetic scheme for the polyaminoamide starburst dendrimers. -54- 0 // 0 (1) CH2 CH COMe 0 // NHC \\ r - - i NH YNY CNH NH 3 (CORE) 0 Y.- 11 2 r--, CNH NH 2 (GENERATION 1) 111 NH2 ~ H2N'..r' NH2 y ~ NrN'(N'"'- REPEAT NH2 (1) & (2) /N"'H2N I NH2 REPEAT (1) & (2) (GENERATION 2) NH2 H2N TERM:NAL NH2 ~ L-----J"' ~ / \ NH2 N . - - - N ,.r' ( HN N 2 GROUPS ' N ,..r' - - - - - . . H2N / N "'""-\ /NH2 N ~ 1' /N, INITIATOR CORE 2' DENDRIM::R REPEATING UNIT NH2 3' ,..,..,N__.N"""""NH2~ H2N \ ~ GENERATIONS NH2 NH2 (GENERATION 3) Figure 2. -55- Table 2. Experimentally determined dimensions for the dendrimers. Molecular Weight Diameter (A) Generation Exp. 0 Theory Viscosity SEC PAMAM-1 - 360 11 11 PAMAM-2 - 1,044 17 16 PAMAM-3 - 2,070 22 24 PAMAM-4 5,200 5,154 31 31 PAMAM-5 10,700 10,633 40 40 PAMAM-6 21,600 21,591 53 56 PAMAM-7 44,000 43,503 67 66 PAMAM-8 88,000 87,341 76 75 PAMAM-9 174,000 175,006 90 90 PE-1 9.8 PE-2 18.6 PE-3 25.9 PE-4b a Molecular weight for generations 1 through 3 too low to be determined. b Not experimentally available. Table 3. Pertinent information for the polyether dendrimers investigated with molecular simulation. Monomers a Condensation Total Generation New Total Sites Atoms 0 1 4 5 12 53 2 12 17 36 173 3 36 53 108 533 4 108 161 324 1613 This is the number of atoms actually included in the simulation; i.e., it ignores hydrogen atoms bonded to carbon since they are treated implicitly. -56- 1.1.2 Polyether Starburst Dendrimers The polyether dendrimers are composed of penta-erythritol fragments, both core (3) and monomer units ( 4), as depicted below. CORE MONOMER 3 4 The penta-erythritol core contains four hydroxyl condensation sites leading to a tetra-directional dendrimer. The monomer units are attached via hydrolytically stable ether linkages and terminate with three hydroxyl groups. Thus, the molecular weights of these polymers, as well as the number of surface hydroxyl groups, triple from generation to generation, as listed in Table 3. The scheme employed in the synthesis of these macromolecules involves protect/deprotect strategies, as outlined in Figure 3. The branch junctures are preformed as part of a bicyclic orthoester reagent. Dendrimer construction involves using an alkoxide functionalized bicyclic orthoester to displace bromide groups from either : (a) penta-erythritol tetrabromide to produce the first generation, or (b) the appropriately brominated dendritic materials to yield higher generation materials. Experimentally, these polyether oligomers have been synthesized and characterized up through generation 3. A complete fourth generation has been unattainable under present synthetic conditions. The available analytical data are presented in Table 2. -57- Figure 3. Strategy used for the synthesis of the penta-erythritol polyether starburst dendrimers. -58- Figure 3. -59- 2. Calculational Details 2.1 Molecular Simulation Details The dendrimers used as starting structures for the molecular dynamics simulations were "synthesized" using the polymer and dendrimer build facilities of POLYGRAF. 9 The molecular mechanics simulations were carried out with POLYGRAF using the AMBER force field developed for simulating proteins and nucleic acids. 10 The valence part of this force field describes the energy and forces in terms of a superposition of 2-body bond stretches, 3-body angle bends, and 4-body torsion and inversion terms. In addition, nonbond interactions are described with fixed charge electrostatic terms, with Lennard-Jones 12-6 potentials to account for van der Waals interactions, and a Lennard-Jones 12-10 potential to modulate the electrostatic terms involved in hydrogen bonding. A detailed description of the force field potential functions is presented in Appendix I. For the electrostatic component of these simulations, partial charges for the monomer fragments were determined based upon values in AMBER10 for analogous amino acid subunits. The partial charges used for each of the core and monomer subunits and the force field atom types are listed in Tables 4 and 5. Initial molecular dynamics simulations were run for the ,8-alanine dendrimers generations 1 through 5 with explicit solvent present ( within 10 A of the polymer). For larger dendrimers we used a mean-field approximation to solvation. The common approximation with dielectric constant e = R led to structures that were much more compact than when water molecules were included explicitly in the simulation. To obtain good agreement between mean-field and explicit solvent simulations required e :::::::: SR. Hence, final simulations were run using a mean-field approximation for an aqueous environment that incorporated a distance-dependent dielectric constant with e = BR. -60- Table 4. Force field atom types and point charge information for ,B-alanine dendrimers. Atoma Typeb IBAC EBAd Cl C_32 0.280 0.280 C2 C_32 0.039 0.039 C3 C--2 0.526 0.526 01 0--2 -0.500 -0.500 Nl N--2Hl -0.520 -0.520 HNl H_N 0.248 0.248 C4 C_32 0.200 0.054 cs C_32 0.227 0.100 N2 N_3 -0.500 -0.867 HN2 H_N2 - 0.320 a See structure 2 for definitions. b BI0GRAF Reference Manual. c IBA = Inner ,B-Alanine. d EBA= End ,B-Alanine. -61- Table 5. Force field atom types and point charge information for polyether dendrimers. Atom0 Type& CPEC IPEd EPEe Cl C_3 0.400 0.256 0.256 C2 0.286 0.256 0.211 -0.386 -0.336 -0.550 H C_32 Q_3 H __ Q - - 0.31 C3 C_32 0.286 -0.016 -0.169 0 a See structures 3 and 4 for definitions. !> BIOGRAF Reference Manual. c CPE = Core PolyEther. d IPE = Inner PolyEther. e EPE = End PolyEther. -62The molecular dynamics calculations were run at a simulation temperature of 300°K and time step of 1 fs with structural and energetic information recorded at 50 fs sampling intervals. For structure and data analysis, the first picosecond was used strictly for equilibration of the system, and the remaining simulation time was used for data collection and analysis. 2.2 Determination of Properties Various structural properties of these macromolecular assemblies were calculated from the molecular simulation trajectories. The average end-to-end distance, average radius of gyration, and average principal moments of inertia were determined from the final 4 ps of the simulations. Various molecular surfaces were generated for a structure for each dendrimer generation. 2.2.1 End-to-end Distances The simplest measure of the "size" of the macromolecule is the maximal end-to-end distance, which is defined as the average of the mazimal terminal heteroatom-to-terminal heteroatom distance determined. at the end of each of the 800 sampling intervals. This may be considered as the diameter, as discussed further in Section 3. For the ,8-alanine series, this diameter is the maximum terminal nitrogen-to-terminal nitrogen distance, while in the polyether class, the distances are maximal terminal oxygen-to-terminal oxygen positions. 2.2.2 Radius of Gyration Another measure of the size of a macromolecule is given by its radius of gyration, which can be thought of as the average displacement of each atom from the center of mass (cm) of the system as defined in (1). -63- Here, MTot is the total mass and number of atoms. The Rg value was calculated at the end of each sampling interval of the molecular simulation, and the values from the final 4 ps were averaged. For a sphere of uniformly distributed atoms, the sphere diameter (Dg) is related to Rg by Dg = 2-Js/3, Rg 2.2.3 Moments of Inertia The moments of inertia provide a simple measure of molecular shape. The moment of inertia tensor is defined in (2). (2) Diagonalizing {Iij} leads to the principal axes and principal moments Ix, Iy, and I.. If Ix = Iy = I. the molecule is spherical. If I. :::::: 0 and Ix = Iy, the molecule is linear. If Ix = Iy and I. =/=- O, the molecule is a symmetric top that is prolate if I. < Ix,y or oblate if I. > Ix,y. The values for the total moment of inertia and the components along the principal axes were calculated from the simulated polymer structures at each sampling interval and averaged over the final 4 ps. 2.2.4 Surface Calculations Richards 11 introduced two useful rigorous quantitative definitions for the qualitative concept of a molecular surface: (1) the vdw molecular aurface and (2) the solvent acceuible Jurface. Consider that each atom is surrounded by a sphere corresponding to its van der Waals radius. The vdw molecular surface is the lotus of exposed sphere segments. The solvent accessible surface is produced by rolling a sphere with a radius of the solvent (1.4 A for water) around the vdw surface. The solvent accessible surface is the locus of sphere midpoints, and hence an internal exposed surface will be found only for cavities sufficiently large to hold the solvent. -64- In order to obtain quantitative measure for the internal cavities as a function of polymer growth, we calculated the molecular surfaces for the dendrimers for a sequence of probe radii from Oto 11 A. 2.2.4.1 Molecular Surfaces The vdw molecular surface is made up of two portions: (a) the contact surface, which is that part of the van der Waals surface readily accessible to the probe sphere and (b) the re-entrant surface, defined as the inward facing portion of the probe sphere when it is in contact with more than one atom. The molecular surface maps out the contact point., between the probe sphere and the atomic van der Waals spheres as illustrated in Figure 4. Thus, surfaces generated with larger and larger probe spheres become more smooth and approach a limiting surface as the probe radius approaches infinity. An algorithm for generating vdw molecular surfaces was used in the display and analysis of the starburst dendrimers. The method uses the approach developed by Michael Connolly 12 and is available in POLYGRAF. All molecular surfaces were calculated with a density of 8.0 dots per A2 • For generations 5 and above (in the ,B-alanine set), the number of probes necessary for the surfacing exceeded the dimensions of the program. To circumvent this problem the surfaces were calculated in segments, determined by generation and excluding those atoms of different generations, patched together, and then corrected for the slight discrepancy in the area associated with each patch. -65- Figure 4. Schematic representation of molecular surface definitions. A section through part of the van der Waals envelope of a dendrimer monomer is shown with the atomic centers numbered. The vdw molecular surface is illustrated by the heavy line surrounding the atomic spheres. The accessible surface is mapped out by the center of probe spheres 1 (solid line) and 2 ( dashed line). -66- Figure 4. -672.2.4.2 Accessible Surfaces The acce.,.,ible .5urface of a molecule differs from its molecular surface counterpart in that the surface is defined in terms of the center of the probe sphere as it is rolled along the van der Waals' surface of the molecule. Thus, the accessible surface produced continues to increase in size as the radius of the probe sphere increases. This surface type is also illustrated in Figure 4. The GEPOL87 Program, 13 available from the Quantum Chemistry Program Exchange but not yet interfaced with a graphics facility, was the method used to calculate the solvent accessible surfaces. This algorithm is a modification of the Connolly methodology, which incorporates a means of estimating the volume contained within the surface, as described in 2.2.5. The NDIV parameter was set to 3 for all calculations. 14 The dimensions of this program are such that the higher generation polyamidoamine polymers could be treated as one entire entity. 2.2.5 Molecular Volumes GEPOL87, 13 in the process of creating the solvent accessible molecular surfaces, uses a polyhedral procedure to determine appropriately sized polyhedrons surrounding each atom. The volume enclosed by such polyhedral surfaces is then calculated and tallied to produce an estimate of the total volume contained within the surface. Thus, we have also generated the volume information for those systems surfaced with GEPOL87. -68- 3. Results and Discussion The molecular dynamics simulations show that the character of the structures adopted by the ,8-alanine dendrimers changes as the number of generations increases. The early generation dendrimers (generations 1 through 3) are very open and well extended, resembling starfish with arms shooting out in various directions. These are just large molecules and have a hemispherical disk structure, with a curvature arising from the nitrogen core and with no real inside to the polymer. Wire-frame structures of generations 1 through 4 are shown in Figure 5. This open, extended topology for the early generation systems is strikingly different from earlier proposals, 3 but these hemispheric structures provide a simple interpretation of observed nuclear magnetic resonance relaxation times 15 (preprint in Appendix II). The molecular simulations indicate a dramatic change in the overall structural properties for the ,8-alanine systems as they grow past generation 4. What is starfishlike for the early generation PAMAM's becomes a tangled mass by generation 5. At higher generations the structures are more spherelike, as illustrated in Figure 6, and the later generations do tend to be on the outside of the polymer. A better definition of the structure is given in Figures 7 and 8 where the vdw molecular surface is displayed, thus defining the outside of the molecule. The early generations are somewhat amorphous in shape, but the later ones are clearly shperical. These views from the outside give little clue as to the internal character of these systems. The internal structure is shown more clearly in Figures 9 and 10, where graphical slabbing is used to cut out a section from the middle of the polymer. The early generation dendrimers have little internal character but already by generation 4 there are substantial nooks and crannies, which by generation 6 have evolved into a labyrinth of channels and cavities. -69- Figure 5. Wire-frame presentations of the starfishlike early generation ,8-alanine starburst dendrimers (one through four) . The core nitrogen is depicted in red, the terminal generation is shown in light blue, and the inner generations are yellow. Figure 6. Wire-frame presentations of the later generation ,8-alanine starburst dendrimers (five through seven) . The core nitrogen is depicted in red, the terminal generation is shown in light blue, and the inner generations are yellow. Generation 4 is also displayed to facilitate size comparisons with the earlier generation polymers, as presented in Figure 5. -70- Figure 5. Figure 6. -71- Figure 7. V dw molecular surface displays for the early generation ,8-alanine starburst dendrimers (one through four) illustrating the varied shapes adopted by these open, starfishlike molecules. Figure 8. V dw molecular surface displays for the later generation ,8-alanine starburst dendrimers (five through seven) illustrating the spheroidal nature of these macromolecules. Generation 4 is also included to illustrate its position as transition generation and to facilitate shape comparisons with the earlier generation polymers, as presented in Figure7. -72- Figure 7. Figure 8. -73- Figure 9. Slabbed views of the vdw molecular surface displays for the early generation ,8-alanine star burst dendrimers (one through four) illustrating the lack of an interior region to these polymers. Figure 10. Slabbed views of the vdw molecular surface displays for the later generation ,8-alanine starburst dendrimers (five through seven) illustrating the extensive internal channels and cavities associated with these materials. -74- Figure 9. Figure 10. -75These later systems clearly have well-defined internal structures. In contrast to P AMAM, the penta-erythritol polyether dendrimers show dramatically more compact, spherical structures by the third generation. Generation 1 might be loosely considered open and extended, but at generation 2, and cer- tainly above, these polymers are very densely packed spheroidal moieties lacking in any appreciable interior void spaces. This is shown in Figure 11 (wireframe), Figure 12 (full vdw surface), and Figure 13 (interior slabs). The addition of the vdw molecular surface, as depicted in Figure 13, clearly shows the densely packed characteristics of the interior of these materials. In order to quantify these structural characteristics, a series of computational analyses were performed, as summarized below. 3.1 End-to-end Distances The average diameter for both sets of polymers increases linearly with generation. Table 6 contains the calculated maximal end-to-end distances for generations 1 through 7 of the ,B-alanine dendrimers. We find that these diameters range from ~13A (for generation 1) through ~80A (for generation 7) with an increase of ~lOA per generation. Previously, Tomalia et al. used CPK models as a means of estimating limits to the sizes of the ,B-alanine systems. 3 These diameters were obtained by: (1) fully extending a CPK model to measure an upper limit to the molecular diameter and (2) compressing the CPK unit to arrive at a lower diameter limit. These CPK-derived dimensions do indeed bracket the simulated maximal end-to-end distances, as shown in Figure 14. A comparison of the calculated diameters with those determined via viscosity and size-exclusion chromatography (SEC) studies (given in Table 2) indicates that the maximal end-to-end distances are ~lOA -76- Figure 11. Wire-frame presentations of the penta-erythritol, polyether star- burst dendrimers (generations one through four). The core penta-erythritol unit is depicted in red, the terminal generation is shown in yellow, and the inner generations are drawn in light blue. -77- Figure 11. -78- Figure 12. V dw molecular surface displays for the penta-erythritol, polyether starburst dendrimers (generations one through four) illustrating the dense, spheroidal nature of these macromolecules. Figure 13. Slabbed views of the vdw molecular surface displays for the penta- erythritol polyether starburst dendrimers (generations one through four) illustrating the congestion and lack of extensive, internal, void spaces associated with these materials. -79- Figure 12. Figure 13. -80- Table 6. Simulated maximal end-to-end distance and radius of gyration for the dendrimers. End-to-end Radius of Gyration (A) Generation Distance (A) Rg PAMAM-1 12.63 5.77 Dtl, 14.9 PAMAM-2 24.33 9.81 25.3 PAMAM-3 34.55 13.47 34.8 PAMAM-4 47.03 15.82 40.9 PAMAM-5 56.53 18.90 48.8 PAMAM-6 68.47 21.52 55.6 PAMAM-7 79.85 26.91 69.5 PE-1 12.69 5.13 13.3 PE-2 21.40 7.76 20.0 PE-3 29.93 10.51 27.1 PE-4 40.06 14.43 37.3 " DRc defined in Section 2.2.2. -81- Figure 14. Diameters for the PAMAM starburst dendrimers. The CPK-based values ( dotted lines) bracket both the experimental (solid line) and simulated ( dashed lines) dimensions. Figure 15. Diameters for the polyether starburst dendrimers. The CPK-based values (dotted lines) fall short of the experimental numbers (solid line), while the simulated dimensions (dashed line) are a bit high. -82- PAMAM Dendrimers 100 --- 80 o<{ 'Q) +-' 60 Q) E cu 0 40 20 2 3 4 5 6 7 8 9 10 Generation Figure 14. 60.------....-------r--------,------.------.------, Polyether Dendrimers 50 .- 40 -- o<{ '- SEC (experimental) $Q) 30 E co 0 20 10 0'------~---~---__.___ _ __..__ _ _~ - - - ~ 0 1 2 3 Generation Figure 15. 4 5 -83- larger than the experimental diameters. This difference is most likely due to the simulated values, taking into account only the maximal end-group displacement. Averaging many across-polymer distances may lead to a more representative diameter for these systems. The polyether dendrimers also exhibit a linear increase in average maximal end-to-end distance as reported in Table 6. Because of the differences in length and :flexibility of the penta-erythritol units relative to the ,8-alanine fragment, these polymers span a ~13A to ~40A range (generations 1 to 4) with an average increase at each generation of ~9A. The calculated values are in very good agreement with estimates for the diameters from SEC measurements. A plot of these simulated dimensions, plus the CPK-based values reported by Tomalia and co-workers, is presented in Figure 15. In this case, the simulated values exceed those derived from CPK models for the higher generation polyethers. This difference is most probably due to the simulated structures' alleviating some of the congestion by allowing some slight distortions in the bond and angular components of the system. The CPK units, on the other hand, are locked into idealized sp 3 hybridized angles and bond lengths. 3.2 Radius of Gyration The radius o{ gyration of a. macromolecule is also indicative of its size. The calculated radius of gyration, Rg, and its corresponding spherical diameter for the investigated dendrimers are presented in Table 6. Within each of the series studied, the radius of gyration increases with generation. For the higher generation ,8-ala.nine dendrimers as well a.s the later generation polyethers, the diameters derived from the radius of gyration are in excellent agreement with the experimental diameters. The predicted diameters for the low generation dendrimers -84- are a bit high when compared with the experimental data. This difference is due to the nonspherical nature of the early generation dendrimers (as discussed below). The experimental measurements would reflect the minimal "diameter" of the polymer ellipsoid and hence would be smaller than a uniformly spherical diameter. An examination of the radius of gyration of these macromolecules as a function of the total number of dendrimer monomers is shown in Figure 16. These plots indicate that the early generation ,8-alanines exhibit a linear increase in Rg as a function of the monomer number, which is indicative of the open, extended form adopted by these molecules. The higher generations, however, show a more gradual increase in Rg with the number of monomers, deviating from the rapid rise in Rg displayed by the early generation samples. This behavior is consistent with the spheroidal form adopted by the larger polyamine dendrimers. For the polyether series, the change in R 1 as a function of the total number of monomer units is gradually increasing in an exponential fashion, indicative of a spherical shape. By comparing equivalent generations from the two sets, we see that the penta-erythritol-based dendrimers have a radius of gyration that is smaller than the corresponding ,8-alanine macromolecule. For instance, the generation 3 polyether value has Rg ~10.5, while the PAA generation 3 polymer has R 1 ~13.5. Thus, the radius of gyration measure indicates that the polyether macromolecules are more compact than their polyaminoamide counterparts. -85- Figure 16. The calculated radius of gyration versus the total number of monomers for the PAMAM and polyether starburst dendrimers. Figure 17. The aspect ratio (I. /Ix) versus generation for the P AMAM and polyether starburst dendrimers. -86- 30 • 25 C 0 ·.;:; 20 ('lj L.... >- - (!) 15 0 Cl) :::, '"O 10 ('lj cc 50 100 150 200 250 300 350 400 7 8 Total Number of Monomers Figure 16. 4 0 "+=i C'CS X a:_ t5 . . . . 3 (1) N a.Cl) <( 2 1 2 3 4 Generation Figure 17. 5 6 -873.3 Moments of Inertia To quantify the changes in shape of the macromolecules with generation, the total moments of inertia, as well as their components along the principal axes, are reported in Table 7. For the ,B-alanine series, the asymmetry of the structures clearly decreases as the number of monomers in the polymer increases. The early generations are quite asymmetric (Iz/Ix = 4.4 to 2.7), with all three principal moments unequal. The asymmetry drops to 1. 7 for generation 4 and continues to decrease to a plateau at 1.3 for generations 5 and above. A plot indicating this change in asymmetry is presented in Figure 17. These components of the moment of inertia indicate that above generation 4 the P AMAM polymers have the form of an oblate spheroid. The polyether dendrimers, on the other hand, have principal moments that are more evenly distributed at quite an early stage of dendrimer growth (see Figure 17). Even at generation 2 the aspect ratio for this series has dropped to 1.8 and by generation 4 it is 1.4. Hence, at generations 2 and above, these penta-erythritol polymers have a more regularized, spheroidal shape. 3.4 Surface Calculations To quantify the changes in structure associated with dendrimer growth, e.g., the open and accessible surface area of the polymer and the amount of interior void space present, solvent accessible surfaces for the two series of starburst dendrimers have been calculated at different probe radii. By varying the size of the probe, it is possible to determine the dependence of surface area and volume on probe size and then estimate the amount of interior surface area and internal volume available for contact with guest and/ or solvent molecules. -88- Table 7. Moment of inertia data for the dendrimers. a Generation l!!-otal %Ix %ly %Iz PAMAM-1 1.056 11.26 38.58 50.16 lz / Ix 4.5 PAMAM-2 9.914 13.85 28.61 57.54 4.2 PAMAM-3 43.24 18.77 29.92 51.31 2.7 PAMAM-4 129.3 24.59 34.85 41.56 1.7 PAMAM-5 379.2 29.06 34.54 36.40 1.3 PAMAM-6 991.6 29.52 33.54 36.94 1.3 PAMAM-7 3131. 29.88 31.16 38.96 1.3 PE-1 1.459 17.09 35.82 47.09 2.8 PE-2 11.43 23.38 35.03 41.59 1.8 PE-3 65.38 26.71 31.12 42.17 1.6 PE-4 381.5 28.53 32.51 38.96 1.4 Units of 104 amu A2 • -89- 3.4.1 Total Accessible Surfaces The area of the accessible surfaces, calculated at various probe radii for the ,8-alanine and polyether dendrimers, are reported in Tables 8 and 9. General In order to guide the analysis of the solvent accessible surfaces, we consider an ideal spherical case. For such a system, the surface area, SAS, is defined as (3) where R is the radius of the ideal sphere and pis the radius of the probe used to calculate the accessible surface. Rearranging this equation to arrive at the dependence of SAs on p produces: J5;; = 2v',rR + 2v',rp. (4) For this idealized case, the slope of the plot is 3.545, and the p=0 intercept is at ~ = 3.545R. Thus, the intercept of a linear plot of p vs ./Si:s provides a means of determining the radius of the spherical system. Polyether Graphs o f ~ vs. p for the polyether starbursts are shown in Figure 18. We find that for p~ 4.2 A, the dependence of ./Si:s on pis indeed linear. However, the surface area is larger at smaller values of p. This deviation is attributed to internal curvature and surface irregularities. Linear regression analysis 16 was performed on various subsets of the data to determine which set of points was most appropriate for a linear fit. The results indicate that using those values with p ~ 4.2 A yield linear fits with correlation coefficients of 1.000 and standard errors in intercept and slope less than 0.22 and 0.03, respectively. (Adding data -90- Table 8. Accessible surface area (A 2 ) for the polyether dendrimers calculated with GEPOL87. Probe Radius Generation 0.0 1.4 2.8 4.2 1 549.17 765.54 1051.26 1398.53 2 1781.85 1934.31 2235.70 2667.28 3 5148.33 3900.64 3873.04 4370.07 4 14368.73 6845.72 6610.91 7152.19 Probe Radius Generation 5.6 7.0 8.4 9.8 1 1796.87 2256.94 2754.01 3281.44 2 3196.05 3774.21 4387.94 5102.32 3 4992.10 5684.79 6446.97 7211.77 4 7889.57 8725.35 9584.28 10511.3 -91- Table 9. Accessible surface area (A 2 ) for the ,8-alanine dendrimers calculated with GEPOL87. Probe Radius Generation 0.0 1.4 2.8 4.2 1 358.50 656.32 980.99 1334.14 2 1013.68 1726.50 2259.79 2748.47 3 2373.64 3910.87 4977.63 5624.37 4 5011.30 7726.73 9117.60 9766.34 5 10236.64 14699.83 16117.63 15283.05 6 21252.73 28028.39 25933.17 21868.78 7 42952.36 54285.37 44796.43 34105.96 Probe Radius Generation 5.6 7.0 8.4 9.8 1 1731.22 2183.89 2690.10 3239.48 2 3268.57 3843.61 4503.23 5203.55 3 6194.16 6865.55 7641.02 8441.37 4 10349.21 11106.71 11970.14 12889.87 5 15150.64 15577.47 16415.86 17367.34 6 21042.03 21646.39 22432.90 23540.87 7 30214.66 29851.21 30811.59 31779.59 Probe Radius Generation 11.2 12.6 14.0 1 3833.08 4463.65 5148.77 2 5959.41 6752.39 7619.38 3 9349.68 10307.94 11332.52 4 13870.10 14969.33 16134.53 5 18491.75 19746.39 20971.44 6 24895.35 26230.37 27647.16 7 33183.39 34738.20 36346.64 -92- Figure 18. The Jaccessible surface area versus probe radius for the polyether starburst dendrimers. Solid lines represent linear regression fits (p ~ 4.2), while dashed lines connect the calculated values. Figure 19. The Jaccessible surface area versus probe radius for the PAMAM starburst dendrimers. Solid lines represent linear regression fits (p ~ 7.0), while dashed lines connect the calculated values. -93- - 120 \ \ 110 \ ~ 100 Iffi t... <( Q) (.) C'O 't:: :J (/) Q) Polyether Dendrimers \ Gen4 \ \ \ \ 90 '' 80 70 60 b, Gen3 ---- Gen2 Gen 1 50 15 40 (/) (/) OJ 30 t) (.) <( 10 0 0 1 3 2 5 4 7 6 8 9 10 Probe Radius {A) Figure 18. PAMAM Dendrirners OO 1 2 3 4 5 6 7 8 9 10 11 Probe Radius (A) Figure 19. 12 13 14 15 -94points with p less than 4.2 gave fits with much higher error values.) The results from fitting these data to the equation (5) are reported in Table 10. Once again, the polyether structures behave as spheroidal units. The slopes (B1) range from 3.6 to 3.2, all close to the value B1 = 3.545 for a sphere. The sphere radii calculated from the intercepts compare quite well with the diameter calculated from the radius of gyration and the experimental size-exclusion chromatographic measurements (see Tables 2 and 6). The deviation from linearity observed at small pleads to valuable additional information. A probe with large p cannot interact with any interior regions of the polymer, and hence, the surface produced reflects purely the exterior portion of the macromolecule. For smaller probe spheres, however, the probe can access certain interior regions of the molecule and can produce an accessible surface that contains segments of both the exterior and the interior regions of the macromolecule. Indeed, this deviation from linearity at small p enables one to determine what portion of the calculated accessible surface is due to interior hollows. This value is arrived at using: (a) the regression equation to predict the surface area expected of a spheroidal unit at p = 1.4 A; (b) subtracting this amount from the calculated accessible surface area (again with p = 1.4 A); and ( c) taking the ratio of this difference to the expected external accessible surface area. For the polyether polymers, no more than ~20% of the accessible surface area is associated with interior regions of the molecule. PAMAM The Pi:s versus p analysis of the P AMAM series shows that the higher generation dendrimers, i.e., 4 and above, have profiles similar to the polyether -95- Table 10. Regression fits of probe radius versus (accessible surface area)½ for the polyether dendrimers. Generation Ba0 Ba1 Rideal RCB1 Regd GEPOV1 Excess! 1 22.487 3.561 6.34 6.32 754.7 765.5 0.01 (0.165) (0.023) 36.830 3.519 10.39 10.47 1744. 1934. 0.11 (0.186) (0.026) 51.851 3.375 14.63 15.36 3201. 3901. 0.22 (0.161) (0.022) 70.946 3.214 20.01 22.07 5709. 6846. 0.20 (0.214) (0.029) 2 3 4 a The value given in parenthesis represents the standard error. b Calculated using ideal slope of 3.545. c Calculated using fit slope, B 1 • d Calculated from the regression fit with probe = 1.4 A. 13 with probe e Calculated using GEPOL87 f Fraction of surface that is internal. = 1.4 A. -96- macromolecules (see Figure 19 and Table 11). With larger probe spheres the accessible surfaces mapped out do depend linearly upon p. For the ,B-alanines, the best regression fits were achieved with p 2:'. 8.4 A. The correlation coefficients were all 2:: 0.997. For this series, however, the slopes of the fitted lines are ~3.0 instead of the 3.545 value expected of a perfect sphere. The radii of the molecules determined from the intercepts again agree quite well with the Dg obtained from the predicted radius of gyration (see Table 6). The amount of estimated internal surface area increases dramatically above generation 4. For the generation 4 dendrimer, which we have already concluded (on the basis of the aspect ratio analysis) to be at the transition from an open and extended structure to a more spheroidal moiety, only ~2% excess accessible surface area is found (see Table 11). By generation 7, however, we find that the internal surface is 120% of the external surface area. This provides a quantitative measure of the internal hollows so obvious in Figure 10. For generations 5 and 6, the internal surface is 30% and 70%, respectively, of the amount of external surface area. Thus, from generations 5 thru 7 the interior surface area is increasing and there is no indication of the filling-in expected when surface congestion dominates. 3.4.2 Normalized Accessible Surface Area The total accessible surface area data (presented in Tables 8 and 9) may also be used to calculate the change in surface area per added monomer, i.e., the normalized accessible surface area. This analysis of the data is given in Tables 12 and 13. Figures 20 and 21 illustrate this normalized change in surface area plotted as a function of increasing probe size. -97- Table 11. Regression fits of probe radius versus (accessible surface area)½ for the (3-alanine dendrimers. Generation Bo0 Bo1 Rtdcal RCB1 Regd GEPOU Excess! 1 22.13 3.55 6.24 6.23 734.1 656.3 -0.11 (0.118) (0.010) 36.87 3.60 10.40 10.24 1756. 1727. -0.02 (0.096) (0.008) 58.61 3.41 16.53 17.19 4018. 3911. -0.03 (0.382) (0.034) 82.784 3.146 23.35 26.31 7602. 7727.00 0.02 (0.578) (0.051) 102.542 3.009 28.93 34.08 11400 14700 0.29 (0.739) (0.065) 124.636 2.965 35.16 42.04 16590 28030 0.69 (0.569) (0.050) 151.918 2.739 42.86 55.47 24260 54290 1.24 (1.453) (0.128) 2 3 4 5 6 7 0 The value given in parenthesis represents the standard error. b Calculated using ideal slope of 3.545. c Calculated using fit slope, B 1 • d Calculated from the regression fit with probe = 1.4 A. c Calculated using GEPOL87 13 with probe = 1.4 A. f Fraction of surface that is internal. -98- Table 12. Accessible surface area (A 2 ) per added monomer for the polyether dendrimers calculated with GEPOL87. Probe Radius Transition 0.0 1.4 2.8 4.2 Core-+ 1 99.84 119.89 142.28 167.91 1 -+ 2 102.72 97.40 98.70 105.73 2 -+ 3 93.51 54.62 45.48 47.30 3-+ 4 85.37 27.27 25.35 25.76 Probe Radius Transition 5.6 7.0 8.4 9.8 Core-+ 1 194.62 222.57 249.52 266.46 1 -+ 2 116.60 126.44 136.16 151.74 2-+ 3 49.89 53.07 57.20 58.60 3 -+ 4 26.83 28.15 29.05 30.55 -99- Table 13. Accessible surface area (A 2 ) per added monomer for the ,8-alanine dendrimers calculated with GEPOL87. Probe Radius Transition 0.0 1.4 2.8 4.2 Core-+ 1 104.97 173.74 234.87 289.79 1-+ 2 109.19 178.36 213.13 235.72 2-+3 113.33 182.03 226.49 239.66 3-+4 109.90 158.99 172.50 172.58 4-+5 108.86 145.27 145.83 114.93 5-+6 114.75 138.84 102.25 68.60 6-+7 113.02 136.76 98.25 63.74 Probe Radius Transition 5.6 7.0 8.4 9.8 Core-+ 1 342.68 395.72 456.05 508.39 1 -t 2 256.23 276.62 302.19 327.35 2-t3 243.80 251.83 261.48 269.82 3-t4 173.13 176.72 180.38 185.35 4-t5 100.03 93.14 92.62 93.28 5-t6 61.37 63.22 62.68 64.31 6-t7 47.77 42.73 43.64 42.91 Probe Radius Transition 11.2 12.6 14.0 Core-+ 1 562.11 611.82 660.16 1-2 354.39 381.46 411.77 2-t3 282.52 296.30 309.43 3-t4 188.35 194.22 200.08 4-t5 96.28 99.52 100.77 5-t6 66.70 67.54 69.54 6-t7 43.17 44.31 45.31 -100- Figure 20. The normalized surface area versus accessible surface probe radius for the polyether dendrimers. Dashed lines connect the calculated values. Figure 21. The normalized surface area versus accessible surface probe radius for the PAMAM dendrimers. Dashed lines connect the calculated values. -101- 280~~--r--.-----.------,---,---,--,----,---------r----,-----,--r--,-r--,----,---------r----,-----r-----r-r--, -- - N <( 240 rn ~ 200 <( Q) ~ 160 't: ::J (f) 120 ""C Q) N 80 ~' , '~ ----?-----<1Gen3 ' ---"?---'""9----..r:J----"140 --o-- --o----~----er----0-----0 Gen 4 rn ,' E ~ 0 'b-- _ z 2 1 3 4 5 6 7 8 9 10 Probe Radius (A) Figure 20. 800 o<( N -- 700 rQ)n 600 - PAMAM Dendrimers ~ <( Q) (.) 500 rn 't: ::J 400 (f) ""C Q) 300 N rn E 200 0 100 ~ z 0 0 1 2 3 4 5 6 7 8 9 10 11 Probe Radius (A) Figure 21. 12 13 14 15 -102Polyether For the polyether dendrimers, the van der Waals area (probe = 0.0 A) 1s approximately constant for all four cases. As the size of the probe grows, however, only generations 1 and 2 permit the accessible surface area to increase with the probe sphere. Both generations 3 and 4 exhibit enough congestion that the area per monomer cannot rise with the value of the probe. ~SAs per monomer at p = 1.4 provides a means of calculating the area per hydroxyl head group on the surface of the polymer sphere. Each terminal hydroxyl group has access to ~40A 2 at generation 1, ~30A 2 at generation 2, ~20A 2 at generation 3, but < l0A 2 by the fourth generation. This area is significantly less than the area measured for dense-packed hydroxyl groups in a bilayer plane, 17 indicating the sterically forbidden nature of this fourth generation polyether. PAMAM For the ,B-alanine polymers, the early generations (one through four) are open enough to allow for an increase in the normalized surface area as the measuring probe is increased. At the fifth generation and above, however, the spheroidal nature of the polymers requires that monomers from the last added generation be near enough to each other that the change in surface area begins to decrease with increasing probe sphere. At the seventh generation, ~150A 2 are still available to each terminal amino group, well above the dense-packed limit. 3.5 Volume Calculations The calculated volumes contained within the solvent accessible surfaces allow estimates of the volume contained within interior regions of the polymer matrices. For the polyether series, the above discussions suggest that there will be little -103- or no internal volume. On the other hand, such analyses should offer a means of quantifying the amount of open, solvent-filled space available to the higher generation ,B-alanine dendrimers. 3.5.1 Total Accessible Surface Volumes We again return to the sphere as our model for deriving accessible surface relationships. For this system, the volume enclosed by the accessible surface VAs would be: (6) where R is the radius of the ideal sphere and pis the radius of the probe used to calculate the surface. Rearranging Equation 6 to arrive at the dependence of VAS on p yields: (7) For this ideal case, the slope of the plot is 1.612 while the intercept is 1.612 R. As with the analysis of the surface areas of the accessible surfaces, the intercept of a linear plot of p vs ~ provides another means of estimating the radius of the spherical system. Plots of WAs as a function of probe radius for both the polyether and polyamidoamine dendrimers are shown in Figures 22 and 23. As in the surface area analysis, those volumes calculated with large values of p show a linear dependence on probe radius. A deviation from this linearity is observed for the volumes calculated with smaller probe spheres. Now the volume is less than ideal because of internal cavities. Polyether For the polyether macromolecules, the solvent accessible volume data are -104- Figure 22. The ~accessible volume versus probe radius for the polyether starburst dendrimers. Solid lines represent linear regression fits (p 2: 2.8), while dashed lines connect the calculated values. Figure 23. The ~accessible volume versus probe radius for the PAMAM starburst dendrimers. Solid lines represent linear regression fits (p 2: 5.6), while dashed lines connect the calculated values. -105so.--..--..--..--..--..--..---..----,---,---,---,----,---,---,---,----,----,----,---,---,---,---,--, Polyether Dendrimers 45 Gen4 -40 oc::( ..__,, Gen 3 a, 35 E Gen2 >Q) 25 Gen 1 :J 30 0 pCJ) 20 CJ) a, 15 9 ""10 C") 5 00 1 4 3 2 5 6 7 8 9 10 Probe Radius (A) Figure 22. 90 - PAMAM Dendrimers 80 Gen? Gen6 o..__,, <( 70 Gens Q) E 60 Gen4 50 Gen3 :J 0 >Q) Gen2 .0 Gen1 CJ) CJ) Q) (.) (.) <( C") 0 o 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Probe Radius (A) Figure 23. -106- given in Table 14. We find an excellent fit of the data to the equation (8) (regression analysis on those data points with p ~ 2.8 A produces fits with correlation coefficients of 1.000 and standard errors in intercept and slope less than 0.20 and 0.025, respectively). The slopes, B 1 ~1.7, are slightly greater than the value of 1.612 derived for the perfect sphere, while the radii calculated based upon the intercepts are in very good agreement with the SEC values and only 1-2 A shorter than both those values derived from the surface area analysis and the simulation end-to-end distance averages. These regression equations can be used in conjunction with the volume calculated at p=l.4A, to estimate the amount of internal volume found in each generation of these highly branched polymeric materials. Based on the ratio C/D, where C is the difference between the volume predicted from the regression equation and that calculated directly with GEPOL and Dis the predicted value of the volume (all at p = 1.4 A), we conclude that less than 15% of the volume available to the polyether dendrimers is composed of open, solvent-filled void spaces. These values are reported in Table 15. PAMAM For the higher generation polyamidoamine series ( data presented in Tables 16 and 17), we find a good fit to Equation 8 for large p (using p 2 7.0 A leads to correlation coefficients of 1.00 and standard errors less than 0.30 and 0.03 in intercept and slope, respectively). The values for the regression coefficients are given in Table 28. These models indicate that the higher generation (3alanine macromolecules deviate from perfect spheroids much more so than do the polyether molecules. The regression slopes are ~1.97, as opposed to the -107- Table 14. Volume (A 3 ) for the polyether dendrimers' accessible molecular surface calculated with GEPOL87. Probe Radius Generation 0.0 1.4 2.8 4.2 1 454.59 1370.42 2635.61 4345.96 2 1510.21 4132.68 7064.97 10496.14 3 4619.03 10970.85 16329.28 22156.25 4 13972.33 27176.48 36462.87 46104.86 Probe Radius Generation 5.6 7.0 8.4 9.8 1 6585.22 9462.27 12848.35 17076.22 2 14649.72 19540.23 25210.93 32019.72 3 28755.81 36258.23 44812.57 54086.09 4 56725.52 68472.88 80972.71 94761.37 -108- Table 15. Regression fits of probe radius versus (accessible surface volume)½ for the polyether dendrimers. Generation Ba0 Ba1 Rtdeal RCB1 Regd GEPOLe Excess! 1 9.128 1.706 5.66 5.35 1527. 1370. 0.12 (0.099) (0.015) 14.336 1.787 8.89 8.02 4774. 4133. 0.16 (0.140) (0.021) 20.571 1.776 12.76 11.58 12260 10970 0.12 (0.166) (0.025) 28.368 1.772 17.60 16.01 29360 27180 0.08 (0.170) (0.025) 2 3 4 0 The value given in parenthesis represents the standard error. b Calculated using ideal slope of 1.612. c Calculated using fit slope, B 1 • d Calculated from the regression fit with probe = 1.4 A. e Calculated using GEPOL87 13 with probe = 1.4 A. f Fraction of volume that is available to solvent. -109- Table 16. Volume (A 3 ) for the ,8-alanine dendrimers' accessible molecular surface calculated with GEPOL87. Probe Radius Generation 0.0 1.4 2.8 4.2 1 282.63 994.04 2145.37 3766.20 2 824.05 2751.68 5611.57 9145.33 3 1928.65 6364.17 12706.59 20255.46 4 4096.89 13192.30 25225.92 38623.18 5 8412.50 26252.35 48339.59 70924.95 6 17351.33 53026. 72 92106.31 125804.38 7 34972.90 106197.38 177653.69 233070.69 Probe Radius Generation 5.6 7.0 8.4 9.8 1 5906.48 8665.09 12108.64 16293.96 2 13374.97 18303.49 24252.87 31030.76 3 28627.54 37862.92 48107.71 59165.50 4 52811. 78 67872.30 84057.50 101403.63 5 92261.61 113890.90 136317.63 159344.30 6 155793.61 186056.42 216789.08 248711.38 7 277783.28 320233.16 365147.72 406996.88 Probe Radius Generation 11.2 12.6 14.0 1 21242.91 26982.12 33686.20 2 38982.20 47832.92 58053.8°1 3 71653.23 85590.51 100811.23 4 119824.20 140141.56 162130.08 5 184872.42 212534.92 240697.69 6 283577.41 318908.97 356308.06 7 453033.31 501130.94 550634.44 -110- Table 17. Regression fits of probe radius versus ( accessible surface volume)¼ for the ,8-alanine dendrimers. Generation Ba0 Ba1 Rtdcal 4 27.313 1.954 (0.298) (0.028) 34.911 1.961 (0.263) (0.024) 43.469 1.971 (0.286) (0.027) 55.172 1.923 (0.302) (0.028) 5 6 7 a Regd GEPOL 11 Excess! 16.94 Ral 13.98 27130 13190 1.06 21.66 17.80 53400 26250 1.03 26.97 22.05 98790 53030 0.86 34.23 28.69 193700 87550 1.21 The value given in parenthesis represents the standard error. b Calculated using ideal slope of 1.612. c Calculated using fit slope, B 1 . d Calculated from the regression fit 13 with probe = 1.4 A. with probe = 1.4 A. c Calculated using GEPOL87 f Fraction of volume that is available to solvent. -111- value of 1.612 expected from the model. The molecular radii determined from the intercept values are in very good agreement with the SEC data and short compared to Dend-end and the DsA from surface area analyses. These linear regression equations may be used in conjunction with the calculated volumes (at p=l.4 A) to predict the amount of volume not occupied by polymeric material. This analysis suggests that ~50% of the volume contained within these higher generation ,8-alanine starburst dendrimers is available for solvent or guest molecules. 3.5.2 Normalized Accessible Surface Volumes The accessible surface volume data (presented in Tables 18 and 19 ) also allow for the calculation of the change in volume per added monomer. Figures 24 and 25 illustrate this change in normalized VAs plotted as a function of increasing probe size. There should be an increase in volume as probe radius grows. This increase would exhibit, under ideal, noncongested circumstances, a dependence upon the radius, and hence p, to the third power. For the polyether dendrimers, the van der Waals volume (probe= 0.0 A) is approximately constant for all four cases. As the probe sphere increases, however, only generations 1 and 2 are of the form to permit the volume to show substantial increase with the probe sphere. Generations 3 and 4 both exhibit enough congestion so that the volume per monomer can rise only slightly with an increase in probe. For the ,8-alanine series, the change in VAs per monomer does not differ by generation at low values of p. It is only at p 2'.'. 5.6 A that a separation is achieved in the probe vs. t:J.. VAs plots. As with the ether polymers, it is the lower generation materials (one through four) that structurally permit a substantial increase in normalized volume at high probe radii. Because of the spheroidal -112- Table 18. Volume (A.3 ) per added monomer for the polyether dendrimers' accessible molecular surface calculated with GEPOL87. Probe Radius Transition 0.0 1.4 2.8 4.2 Core-+ 1 86.39 241.09 422.96 640.58 1 -+ 2 87.97 230.19 369.11 512.52 2 -+ 3 86.36 189.95 257.34 323.89 3 -+ 4 86.60 150.05 186.42 221.75 Probe Radius Transition 5.6 7.0 8.4 9.8 Core-+ 1 898.01 1195.69 1498.19 1843.74 1 -+ 2 672.04 839.83 1030.22 1245.29 2 -+ 3 391.84 464.39 544.49 612.95 3-+ 4 258.98 298.28 334.82 376.62 -113- Table 19. Volume (A 3 ) per added monomer for the ,8-alanine dendrimers' accessible molecular surface calculated with GEPOL87. Probe Radius Transition 0.0 1.4 2.8 4.2 Core-+ 1 85.85 283.13 572.55 942.34 1 -+ 2 90.24 292.94 577.70 896.52 2 -+ 3 92.05 301.04 591.25 925.84 3 -+ 4 90.34 284.51 521.64 765.32 4 -+ 5 89.91 272.08 481.53 672.95 5 -+ 6 93.11 278.90 455.90 571.66 6 -+ 7 91.78 276.93 445.56 558.68 Probe Radius Transition 5.6 7.0 8.4 9.8 Core-+ 1 1384.89 1905.04 2525.36 3204.93 1 -+ 2 1244.75 1606.40 2024.04 2456.13 2 -+ 3 1271.05 1629.95 1987.90 2344.56 3 -+ 4 1022.68 1250.39 1497.91 1759.92 4-+ 5 821.87 958.72 1088.75 1207.10 5 -+ 6 661. 79 751. 72 838.24 930.91 6 -+ 7 635.36 698.84 772.70 824.79 Probe Radius Transition 11.2 12.6 14.0 Core-+ 1 3958.25 4761.27 5632.80 1 -+ 2 2956.55 3475.13 4061.27 2 -+ 3 2722.59 3146.47 3563.12 3-+ 4 2007.12 2272.96 2554.95 4-+ 5 1355.17 1508.20 1636.83 5 -+ 6 1028.18 1108.06 1204.27 6 -+ 7 882.58 949.07 1012.12 -114- Figure 24. The normalized volume versus accessible surface probe radius for the polyether dendrimers. Dashed lines connect the calculated values. Figure 25. The normalized volume versus accessible surface probe radius for the PAMAM dendrimers. Dashed lines connect the calculated values. -115- 2000 1800 - 0~ Q) E ::::, 0 1600 1400 1200 > 1000 "O Q) .N 800 ro E L.. 600 0 z 400 200 0 0 1 2 4 3 5 6 7 8 9 10 Probe Radius (A) Figure 24. 6000 PAMAM Dendrimers 5500 p, 5000 ~4500 Q) E 4000 ::::, 0 3500 > 3000 "O Q) .N 2500 ro 2000 E L.. 0 1500 z 1000 500 00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Probe Radius (A) Figure 25. -116- shape of generations 5 through 7, only modest increases in this volume index are observed. 3.6 Surface vs. Volume Analysis The analysis of the accessible surface volume, expressed as a function of surface area, also sheds insight on the spherical nature of these macromolecules. For an ideal sphere of radius R, the volume of the accessible surface at probe radius p is given by: (6) while the area mapped out by that molecular surface is: (3) Rearranging these two equations for constant value of R + p, i.e., a single probe radius, gives the dependence of volume on surface area, namely: (9) Thus, for a perfect sphere, a plot of Ln(SAs) vs Ln( VAs) would have a slope of 1.5 and an intercept of ~-2.364. Polyether This suggests fitting the accessible surfaces generated for the polyether dendrimers to the equation (10) leading to the results presented in Table 20 and in Figure 26. As the radius of the probe sphere used to calculate the accessible surface is increased, -117- Table 20. Regression fit of Ln (surface area) versus Ln (volume) for the polyether dendrimers. Probe BCI0 BCI1 0.0 -0.519 1.049 (0.080) (0.010) -1.854 1.357 (0.518) (0.066) -2.100 1.429 (0.297) (0.037) -2.102 1.445 (0.215) (0.026) -2.179 1.462 (0.203) (0.025) -2.145 1.462 (0.189) (0.022) -2.152 1.467 (0.095) (0.011) -2.250 1.480 (0.173) (0.020) 1.4 2.8 4.2 5.6 7.0 8.4 9.8 11 The value given in parenthesis represents the standard error. -118- Figure 26. The Ln (volume) versus Ln (surface area), at various probe radius values, for the polyether starburst dendrimers. The solid line represents the fit derived for the case of an ideal sphere. Figure 27. The Ln (volume) versus Ln (surface area.), at various probe radius values, for the PAMAM starburst dendrimers. The solid line represents the fit derived for the case of an ideal sphere. -119- Polyether Dendrimers 12 Probe (A) + 0.0 )( 1.4 • 2.8 11 ■ a> 10 :::J > 5 )( 5.6 D 7.0 C. 8.4 0 9.8 0 E O .._... Solid Sphere Limit ~ 4.2 9 + )( + )( 8 + )( 7 6 7 6 8 9 10 Ln (Surface Area) Figure 26. 16~~--r-~--.----.----,----,-----.--,---,--.,.....--,---.-.- PAMAM Dendrimers 15 Probe (A) 14 0.0 " 1.4 • 2.8 + 13 a> 12 E C: _J 4.2 0 5.6 7.0 0 ::J 11 0 -> ■ Solid Sphere Limit . . 8.4 0 9.8 A 10 )( )( )( 11.2 • 12.6 V 9 • • 14.0 )( 8 7 6 5..___.__~__._-~~-~~--'-----'-~-~--'--~~ 5 6 7 8 9 Ln (Surface Area) Figure 27. 10 11 12 -120- (1) the value of the intercept increases from -0.519 (p = 0.0) to -2.250 (p = 9.8) very systematically, approaching the limiting value of -2.364, and (2) the slope of the line also approaches its limiting value of 1.5, increasing from 1.049 (p = 0.0) to 1.480 (p = 9.8). Thus, with increasing size of probe radius, the behavior of the polyether dendrimers approaches that of a perfect sphere. PAMAM The situation is a bit more complicated for the ,8-alanine series. Linear fits of Ln(SAs) vs. Ln( VAs) at various p for the full aet of polyamidoamine polymers produce slopes and intercepts that do approach the spherical limits, although more slowly than those seen with the polyethers (see Tables 20 and 21). Increasing the value of p to 11.2, 12.6 and 14.0 A verifies this slow convergence towards the ideal values. If, on the other hand, we partition these polyamino dendrimers into two sets, the early generations (1 through 3) and the later generations (4 through 7); prior to the linear regression studies, our analysis is much different. Under these conditions, we find that the higher generation materials do, in fact, behave more like spherical units. The fitted slopes and intercepts (plotted in Figure 27) now more quickly converge ( albeit from the direction opposite that of the polyethers) to the limiting values predicted from the analysis of a sphere. The early generation polymers, however, still exhibit slow convergence of the regression values, indicative of their open, nonspherical nature. -121- Table 21. Regression fit of Ln (surface area) versus Ln (volume) for the ,8-alanine dendrimers. Full Set Gen 1 to 3 Gen 4 to 7 Probe Bo B1 Bo B1 Bo B1 0.0 -0.262 1.006 -0.332 1.016 -0.146 0.994 (0.025) (0.003) (0.057) (0.008) (0.042) (0.004) 0.015 1.060 0.120 1.045 -0.080 1.062 (0.032) (0.004) (0.076) (0.010) (0.046) (0.005) -0.282 1.149 0.112 1.099 -1.160 1.237 (0.163) (0.018) (0.267) (0.034) (0.272) (0.027) -0.911 1.262 -0.267 1.182 -2.780 1.451 (0.286) (0.032) (0.252) (0.032) (0.260) (0.026) -1.282 1.328 -0.588 1.244 -3.513 1.555 (0.331) (0.036) (0.268) (0.033) (0.312) (0.032) -1.427 1.359 -0.838 1.289 -3.439 1.562 (0.308) (0.034) (0.161) (0.019) (0.292) (0.030) -1.509 1.377 -1.073 1.327 -3.169 1.544 (0.253) (0.027) (0.227) (0.027) (0.200) (0.020) -1.572 1.391 -1.158 1.344 -2.820 1.516 (0.207) (0.221) (0.116) (0.014) (0.357) (0.036) -1.632 1.402 -1.345 1.371 -2.853 1.524 (0.190) (0.020) (0.132) (0.015) (0.138) (0.014) -1.650 1.409 -1.400 1.381 -2.449 1.488 (0.135) (0.014) (0.000) (0.000) (0.171) (0.017) -1.765 1.423 -1.483 1.392 -2.484 1.494 (0.138) (0.014) (0.000) (0.000) (0.328) (0.032) 1.4 2.8 4.2 5.6 7.0 8.4 9.8 11.2 12.6 14.0 a The value given in parenthesis represents the standard error. -122- 4. Utilization of ,B-Alanine Internal Void Spaces As an illustration of the dimensions of the channels in the ,B-alanine dendrimers and of how these materials might be used to sequester small molecules, molecular simulation capabilities were used to predict the optimum conformations for several dopamine (5) molecules inside this starburst polymeric matrix. 5 Dopa.mine was chosen because it is a good candidate for effective sequesterization in a ,B-alanine type dendrimer. Its size and shape are suitable for the cavities and channels found in the higher generation ,B-alanine systems. From a chemical standpoint, dopa.mine possesses both the hydrogen-bond donor and acceptor sites needed for favorable binding interactions to the polymer's carbonyl, amide, and amino substituents. Pharmacologica.lly, the ability (i) to selectively deliver dopamine to peripheral kidney receptors without eliciting complications because of the presence of dopamine receptors in the central nervous system (CNS) and (ii) to maintain a. supply of nonmetabolized dopamine might be advantageous in cardiovascular hypertension therapy. 18 The additional issues presented by this type of application include the dimensions of the dendrimer-encapsulated dopamine and the targeting of the unit to the appropriate dopamine receptor sites. Based upon the calculated internal volume of these polymers and the volume of dopa.mine itself, we estimate that a. generation 6 polymer should be capable of holding 20-25 molecules of dopamine. Molecular simulations were carried out -123- with ten dopamine guest molecules sequestered in the channels of a generation 6 ,B-alanine host dendrimer. Initially, the polymer matrix was maintained as a rigid entity, while the small molecules optimized their positions within the interior regions. Subsequent calculations then allowed both polymeric host and dopamine guest moieties to relax and equilibrate. Figure 28 illustrates this dopamine/dendrimer complex with examples of the conformations adopted by the sequestered molecules and the polymeric material. The vdw surfaces for the components of this complex are included in the photo to highlight the nice fit of dopamine within the dendrimer channels. After 1.5 and 3.0 ps of simulation time, the environment of the heteroatom units of the ten encapsulated dopamine molecules, i.e., the terminal amino group and the two aromatic hydroxyl substituents, were examined. Of the twenty total dopamine amino group interactions, twelve were involved in hydrogen bonding to polymeric carbonyl oxygen atoms, three were near the dendrimer amide units, and five occupied sites distant enough from the polymer to be accessible to the solvent. For the forty possible hydroxyl group interactions, twenty-two were capable of donating a hydrogen for interaction with either amino nitrogens (15 times) or carbonyl oxygens (7 times), and fourteen were close enough to participate in hydrogen bonding by acting as acceptor to amide protons. In only four instances were the hydroxyl groups free from polymer interaction to hydrogen bond with solvent. The dimensions of the higher generation ,B-alanine dendrimers ( see Figure 29 with the minimum diameter plotted as a {unction of generation) are such that these dopamine/dendrimer complexes would not readily cross the CNS bloodbrain barrier. The advantage of the dendrimer technology is that we can modify the surface -124- Figure 28. Illustration of dopamine (red) sequestered in the internal channels and pockets of a generation 6 ,B-alanine starburst dendrimer. The inner generations of the polymer (one through five) are shown in light blue, while the outer, sixth, generation is displayed in green. Figure 30. A catechol-modified (yellow terminal groups) ,B-alanine starburst dendrimer (light blue) with bound dopamine molecules (red). -125- Figure 28. Figure 30. -126- Figure 29. The minimal diameter versus generation for the ,8-alanine starburst dendrimers. -127- 60 z 0 ~ 45 ~ 30 <t: 15 1 2 3 4 5 GENERATION Figure 29. 6 -128- layer to ensure delivery to the desired site. Thus, condensing dihydroxyphenyl aceta.ldehyde with the terminal amino group leads effectively to dopaminelike surface catechol fragments, as shown in (6). ···CH2-CH2-!-CH2-CH2 - Q o H ~ ~OH DENDRIMER CATECHOL 6 Figure 30 illustrates this hybrid dendrimer complex. The catechol modification to the dendrimer should allow it to recognize dopamine receptor sites and bind sufficiently well to help increase the concentration near these sites. However, the composite dendrimer should be displaced by dopamine as it diffuses out of the dendrimer. Thus, the dendrimer serves as: (1) a polymer encapsulation matrix to protect the catecholamine from rapid metabolic inactivation, (2) a block to transport across the blood-brain barrier, and (3) a concentration enhancer near the receptor sites. These studies provide structural models that should be useful for analyzing the dopamine/dendrimer systems. The next step is to test the effectiveness of these modified materials for encapsulation of dopamine ( and related materials) and to determine how effectively they are delivered to the kidney centers. As such experiments proceed, continuing simulation will be useful in providing a quantitative framework for understanding various results. The judicious selection of a core unit, internal monomer subunits, and terminal monomer fragments should allow for the design of dendrimers to complex with specific guest molecules and to deliver them to specific sites. It will, of -129- course, be essential to develop synthetic schemes that allow for chemical control and fidelity. -130- 5. Conclusions The molecular simulations indicate a qualitative change in the overall shape and character of the ,B-alanine dendrimers as the polymer grows from generation 1 to generation 7. The shape transition from an open, extended structure to a spheroidal moiety takes place at the fourth generation. Concurrent with this shape change is the introduction of internal cavities and channels in the polymer matrix. These interior regions possess a surface area approximately equivalent to the amount found on the exterior of the polymer spheroid. Similarly, the volume associated with these solvent-filled void spaces is ~50% of that contained within the full spheroid. These internal regions can be used for sequestering small molecules, as illustrated by the example of the dopamine-loaded and catechol-modified delivery dendrimer. Materials of this type could be designed to encapsulate selected target molecules or to contain sites for modification to produce catalytically active buried pockets. The penta-erythritol polyether dendrimers were found to possess structures and properties quite different from those of the polyamidoamine series. The structures adopted by the polyethers are dense and spherelike early in the polymer growth cascade. Only negligible amounts of interior surface area and volume were found for these materials. Estimates of the amount of surface area per hydroxyl head group indicated that this generation 4 dendrimer should not be structurally stable, consistent with experimental observation. .. 131- Notes and References (1.) D. A. Tomalia, H. Baker, J. Dewald, M. Hall, G. Kallos, S. Martin, J. Roeck, P. Smith. Polym. J., Tokyo, 1985, 17, 117. (2.) D. A. Tomalia, H. Baker, J. Dewald, M. Hall, G. Kallos, S. Martin, J. Roeck, J. Ryder, P. Smith. Macromolecule., 1986, 19, 2466. (3.) D.A. Tomalia, M. Hall, D.M. Hedstrand. J. Am. Chem. Soc. 1987, 109, 1601. (4.) D. A. Tomalia, V. Berry, M. Hall, D. M. Hedstrand. Macromolecule.,, 1987, !O, 1164. (5.) H. Hall, A. Padias, R. McConnell, D. A. Tomalia. J. Org. Chem., 1987, 5!, 5305. (6.) P.B. Smith, S. J. Martin, M. J. Hall, D. A. Tomalia. Applied Polymer AnalyJia and Characterization. Edited by J. Mitchell, Jr. Hanser Publishers: New York (1987), p. 357. (7.) D. A. Tomalia, D. M. Hedstrand, L. R. Wilson. Kirk-Othmer Encyclopedia of Polymer Science and Engineering, 1989, in press. (8.) L. Wilson and D. Downing, personal communication. (9.) POLYGRAF is an interactive molecular mechanics/graphics program available from Molecular Simulation, Inc. Pasadena, CA. All simulations were performed on DEC VAX 8650 and Alliant FX8/8 computers, and structures were displayed on Evans & Sutherland PS330 and PS390 series graphics systems. (10.) S. J. Weiner, P.A. Kollman, D. A. Case, U. C. Singh, C. Ghio, G. Alagona, S. Profeta, Jr. P. Weiner. J. Am. Chem. Soc. 1984, 106, 765. (11.) F. M. Richards. Ann. Rev. Biophya. Bioeng. 1977, 6, 151. (12.) M. L. Connolly. J. Appl. Cry.,t. 1983, 16, 548. -132(13.) J. L. Pascual-Ahuir, E. Silla. QCPE Program Number 554. (14.) NDIV specifies the division level for the triangles on the surface of the atomic spheres. Accuracy improves as NDIV is increased, but cpu time also increases with NDIV. Generation 1 ,8-alanine dendrimer was used to investigate NDIV=l,2,3,4,5. The calculated surface areas and volumes were well converged at NDIV =3. With NDIV =4 or 5, any improvement in the calculated values was less than 0.1 % but the cpu utilization had increased by a factor of 3 (NDIV=4) or 10 (NDIV=5). Hence, it was determined that the recommended value of NDIV =3 was most suitable. (15.) A.M. Naylor, W.A. Goddard III, G. E. Keifer, D.A. Tomalia. J. Am. Chem. Soc., 1989, in press. (16.) PLOTIT Interactive Graphics and Statistics available from Scientific Programming Enterprises, Haslett MI. (17.) C. Tan.ford, The Hydrophobic Effect. A Formation of Micellea and Biological Membranea. Wiley Interscience: New York (1980). (18.) J. W. Kebabian, T. Agui, J. C. van Oene, K. Shigematsu, J. M. Saavedra. Trenda in Pharmacological Science., 1986, 96. -133- Section III Dihydrofolate Reductase: Molecular Simulation of Wild-type and Mutant Enzyme Complexes -134- Portions of the text of this section will compose an article coauthored with William A. Goddard III and Stephen J .Benkovic. It is to be submitted to the Journal of the American Chemical Society. -135- Abstract: Molecular modeling and simulation tools were used to investigate various Dihydrofolate Reductase (DHFR) complexes. Three distinct sources of DHFR were analyzed in homology studies. The sequence homology between E. coli and L. ca.,ei proteins is less than 30%. Our investigations indicate that the chemical homology for the catalytic pocket is ~70%, explaining the remarkable similarity in their steady-state kinetic profiles. The inclusion of Chicken DHFR yields only ~60% chemical homology with the bacterial forms, suggesting subtle differences in the character of the active site. This molecular modeling and subsequent simulation were used to engineer E. coli• Chicken hybrid enzymes targeted to reduce folate. The structure and properties of DHFR complexes (E. coli, single-site mutants, and Chicken loop E. coli hybrids) were studied using molecular dynamics simulations. The calculations on the wild-type E. coli enzyme indicate: (a) the energetically favored conformation of bound methotrexate's (MTX) pteridine ring is that found in the crystal studies; (b) the active site region accommodates either the xtl or the anti form of both MTX and dihydrofolate (DHF); and ( c) the Anti-DHF ternary complex is favored for catalysis with a ground-state hydride transfer distance of ~3.6 A. The investigations on single-site mutants revealed structural changes that explain the experimental kinetic data. Phe-31-+Tyr-31 introduces reorientation of substrate binding that is consistent with the observed increase in the product off-rate (the rate-limiting step). Modifications of the alkyl side chain at position 54 (Leu-54-+Ile-54 or Leu-54-+Gly-54) increase the separation between the cofactor (nicotinamide) and substrate (pteridine) reaction centers, thus increasing the rate of hydride transfer sufficiently so that it becomes rate-limiting. -136- 1. Introduction Over the 30 years since the discovery that the cancer therapy agent methotrexate (MTX) acts by inhibiting the transformation of dihydrofolate (DHF) to tetrahydrofolate (THF), thereby inhibiting Dihydrofolate Reductase, there have been numerous experiments providing detailed data on many aspects of various forms of the enzyme and its chemistry. 1 This wealth of data makes it an ideal system for our interests, which are to examine how changes in the active site of an enzyme affect function and reactivity. Dihydrofolate Reductase (DHFR) catalyzes the reduction of 7,8- dihydrofolate (DHF; 1) to 5,6,7,8-tetrahydrofolate (THF; 2), as depicted below. DHFR Pteridyl moiety 1 2 This reduction requires: (1) a hydride (H-) to be transferred to the substrate from a nicotinamide adenine dinucleotide phosphate (N ADPH) cofactor source that is bound in a ternary complex with DHFR and DHF, and (2) a proton (H+) to be supplied from some source (possibly H20). Figure 1 illustrates the DHFR,DHF,NADPH ternary complex. This structure is one of the products of the work described in this document. The product THF is an important coenzyme in a number of one-carbon transfer reactions. Its most important role, though, is in the synthesis of thymidylate (dTMP) from deoxyuridylate (dUMP) by thymidylate synthetase. In this metabolic process, THF not only is the source of a carbon fragment but is also used as a reductant. Hence, it is used in substrate, rather than coenzyme, quan- -137- Figure 1. The active site of wild-type E. coli Dihydrofolate Reductase with dihydrofolate a.nd NADPH (both shown in red) bound. The solvent surface of the active site is mapped out by the series of dots. Figure 3. Wild-type E. coli DHFR with MTX (red) and NADPH (light blue) bound in their respective sites. Asp-27 (dark blue), involved in protonation of the substrate pteridine ring, is shown salt-bridged to the MTX. Phe-31 (green) a.nd Leu-54 (blue) are strictly conserved residues that form part of the substrate binding site. -138- Figure 1. Figure 3. -139- tities. The THF pool must be maintained by the DHFR-catalyzed reaction. This metabolic cycle is depicted in Figure 2. Inhibition of DHFR leads to a deficiency of dTMP and ultimately to a disruption of nucleic acid biosynthesis. It is this mechanism that is the biochemical basis for the antifolate drugs that have found therapeutic applications. 1 The known inhibitors of DHFR may be divided into classical and nonclassical subsets. The classical inhibitors are closely related structurally to the folic acid natural substrates of DHFR. Thus, they are expected to bind to the enzyme in a manner quite similar to normal substrates but cannot be easily reduced, preventing the DHFR from transforming DHF to THF. Methotrexate (MTX; 3), shown below, is one important example of a classical DHFR inhibitor. H I H2N~*N N l , ,N '' : ~ , N O CO2 I A CH2-N~C-N-C-CH2-CH2-CCJi ____F\__ II I '- ', NH2 -,. I , ~ - _. I , -1- I HI ' , CH3 , \ ' H I ~ 3 Many nonclassical inhibitors, chemically distinct from the folic acid derivatives, have been identified. 1 •2 These agents may well bind to the enzyme in a manner quite different from that of the natural substrates. Recent advances in experimental methodologies have made possible the investigation of structure-function relationships in this enzyme system. The crystal structure of DHFR from two bacterial sources (E. coli and L. ca.,ei) has been solved, refined to a 1. 7A resolution, 3 -e and made available tp the scientific community through the Brookhaven Protein Database. The study of DHFR from L. ca.,ei involved the ternary complex of enzyme, MTX (inhibitor), and NADPH (cofactor). The crystal structure of E. coli DHFR was determined as a dimer of -140- Figure 2. Metabolic cycle encompassing the reduction of DHF to THF by DHFR. -141- HCHO ...... s, 1o - methylene THF _\_~_::S::e::,ri:..:,:ne:..H~y!.:d:.:.;ro:.:.x:.!..y.;.;..m..;.et_h.:..yl_tr_an_s_fe_ras_e_---:• THF Thymidylate Synthetase DHF Figure 2. -142- the one-to-one complex of enzyme with MTX. The gene for E. coli DHFR production has been located and sequenced, 7 thus allowing use of site-directed mutagenesis to synthesize mutants for directly assessmg the roles of specific amino acids in catalysis, folding, and stability of the enzyme protein. 8 - 15 The full steady-state kinetic profile of E. coli DHFR has been recently refined and reported. 11 As a result, DHFR provides an excellent system for a collaborative experimental/theoretical program designed to probe the details of DHFR's catalytic requirements and properties. The experimental component of the project is centered at The Pennsylvania State University under the direction of Professor Stephen J. Benkovic. The theoretical portion of the research project is being done within the Molecular Simulation Facility at the California Institute of Technology under the supervision of William A. Godda.rd III. The work presented here focuses on three aspects of this collaborative effort. First, we present the analysis of the sequence, structure, and chemical homology of three forms of DHFR from different species (E. coli and L. ca,ei bacterial sequences and the Chicken form). Experimental kinetic studies indicate a remarkable similarity in the free-energy profile for the reduction of dihydrofolate by E. coli and L. ca1ei DHFR, despite a mere 27% sequence homology ( vide in- fra). Computer graphics and macromolecular docking, combined with homology assignments, offer an explanation for such congruence in the catalytic reactivity of the bacterial systems. The analysis is then extended to include the Chicken form of the protein, which has a distinctly different reaction :=rofile and is more similar in function to mammalian DHFR. This interspecies comparison provides the opportunity to begin piecing together an understanding of what contributes to the subtle differences in reductive chemistry exhibited by these enzymes. -143- The second subject involves molecular simulation studies of wild-type E. coli DHFR-MTX binary and DHFR-DHF-NADPH ternary complexes. These investigations offer insights on the catalytic reduction of dihydrofolate as well as controls for computer mutagenesis experiments. A brief discussion of the simulation methods employed in the theoretical investigations of various DHFR complexes is also included. And finally, the third segment focuses on the selected modification of the E. coli DHFR, using both single-site mutation and protein-loop substitutions. The site-directed muta.genesis studies were undertaken to probe the role( s) of specific amino acid residues in the functioning of E. coli DHFR. Figure 3 illustrates the location within the protein, and proximity to the substrate binding site, of several of these targeted amino acids. Segment mutants were constructed to engineer a bacterial DHFR protein with properties more similar to those of the mammalian enzyme (which has the ability to reduce folate to dihydrofolate). These hybrid proteins are based on the bacterial DHFR (from E. coli) where a loop, with amino acid sequence identical to the corresponding region of the Chicken DHFR, has been inserted into the protein matrix. Before embarking on discussions of the modeling and simulation work, it is important to put the relevant experimental studies into perspective. The next section presents a synopsis of the DHFR experimental information germane to this work. -144- 2. Pertinent Experimental DHFR Studies The abundant experimental data on DHFR provide both inspiration and detailed checks upon theoretical studies. The crystal structures of DHFR from two bacterial sources have been resolved, reported, and coordinates made available through the Brookhaven Data Base. 3 - 6 Isotope studies have identified the stereochemistry of the tetrahydrofolate product, providing information on the orientation of bound, reactive substrate. 16 The kinetic profiles of the enzyme have been determined under various conditions, providing mechanistic details. 11 •13 •17 2.1 Crystal Structures From the crystal studies, it is apparent that the backbone structures of both the E. coli and L. caaei sources of DHFR are quite similar despite an only ~29% direct sequence homology between the two forms. Figure 4 illustrates this overall structural similarity in the folding pattern of these bacterial DHFR proteins. The backbone is composed of ~35% ,8-sheet structure with the remainder consisting of four a-helices and interconnecting loops. The conformation of the bound methotrexate inhibitor is also quite similar in the two crystals. The 2,4-diaminopteridine ring sits in a pocket, which allows for specific hydrogen bond and electrostatic interactions of an Asp residue (27 in E. coli = Ee; 26 in L. ca,ei = Le) with the amino substituent at position 2 and with Nl. A conserved Thr residue (113 Ee, 116 Ee) and an intervening fixed water molecule are also involved in hydrogen-bonds to N2. The pyrazine portion of MTX is not directly hydrogen-bonded to the protein but is involved in solvent H-bonding. A strictly conserved Phe ring (31 Ee, 30 Le) is involved in nonpolar contacts with both the pterin and benzoyl rings of the bound inhibitor. The glutamate side chain of the MTX has different conformations in the two -145- Figure 4. A. Protein backbone structure for E. coli DHFR-MTX binary crystal complex. The MTX inhibitor is located in the center of the figure. Figure 4. B. Protein backbone structure for L. ca.sei DHFR-MTX-N ADPH ternary crystal complex. The MTX inhibitor and NADPH cofactor are located in the middle of the figure. Figure 4. C. Protein backbone structure for Chicken DHFR-NADPH binary crystal complex. The NADPH cofactor is found a.t the left center of the figure. -146- Figure 4. A. Figure 4. B. -147- Figure 4. C. -148- complexes, even though it binds, in both instances, to the conserved Arg-57 through the a carboxylate group. An NADPH binding site distinct from the substrate binding site does not exist in the DHFR system. Instead there are substrate and cofactor domains that contain overlapping portions of the primary sequence, as illustrated by the display in Figure 3. No major reorganization of secondary structure is noted between the L ca.,ei (with NADPH bound) and E. coli (lacking the NADPH cofactor) forms. From the crystal study of the ternary complex, the only contacts found between the adenine ring of NADPH and the enzyme are hydrophobic. The pyrophosphate bridge region of NADPH is stabilized by hydrogen-bonding to enzyme backbone amido groups, bridging solvent molecules, and the side chains of Arg44 (Le) and Thr-45 (Le). The binding of the nicotinamide ribose appears to be fairly specific, making hydrophobic contacts with a number of invariant residues (Ile-3, Gly-14, and Gly-99 Le) and H-bonding through its hydroxyl groups to the carbonyl oxygen of His-18 (Le) and the side chains of Asp-125 and Ser-48. The adenosine ribose interactions with DHFR appear to be weaker and less specific, containing only one hydrogen bond between the protein and the ribose, mediated by a water molecule. The 21-phosphate group is involved in hydrogen bonding and/or salt bridges to Arg-43, Thr-63, His-64, and Gln-65 (all Le). The nicotinamide functional group of the NADPH resides in a pocket created by predominantly invariant amino acid residues. The A side of the ring is in contact with the pteridine binding site, while the B side is surrounded by a group of hydrophobic side chains that exclude solvent molecules. An interesting characteristic of this binding site is that three protein oxygen atoms are positioned in close proximity to C2, C4 and C6 of the nicotinamide ring. The carboxamide group is coplanar with the nicatinamide ring but is rotated 180 degrees from the -149- minimal energy solution conformation. In addition to this published crystallographic information on the bacterial DHFRs, unpublished structural data for this enzyme from the Chicken source were generously made available from Matthews and coworkers in prerelease form. 18 These experimental data for the Chicken protein were obtained for the DHFR · NADPH binary complex. The coordinates for the structure were refined to 1. 7 A resolution. The overall fold of the Chicken form matches quite well with that of the bacterial forms, as illustrated in Figure 4. The major differences between the bacterial and Chicken tertiary structures involve inserted amino acid residues that a.re typically confined to loop regions on the exterior portion of the protein. The differences in sequence between the Chicken and bacterial DHFRs, as well as the variations introduced by the loop insertions, will be elaborated upon further below. 2.2 Isotope Studies Young and coworkers 18 used deuterium isotope studies, in conjunction with absorption and nuclear magnetic resonance spectroscopies, to identify the stereochemistry of 5,6,7,8-tetrahydrofolate produced by Dihydrofolate Reductase. The reduction of DHF using NADPH and DHFR produces THF that gives the biologically active S diasteriomer when converted into folinic acid. This defines the absolute stereochemistry at C6 of the enzymatic DHF as S. Therefore, the re-face of DHF is the side subject to attack by the NADPH cofactor, as diagrammed in Figure 5. It is also known that the 4-pro-R hydrogen of the nicontinamide ring is the one involved in transfer to DHF, thus establishing that the orientation adopted by the two reacting rings during catalysis is different from the orientation of MTX's bound pteridine moiety. -150- Figure 5. A schematic view of the orientation of the nicotinamide (NADPH) and pteridine (DHF) reacting centers involved in hydride transfer. -151- /" NH DHF H --~N NADPH Figure 5. -152- DHFR from certain sources will also reduce folate (4) to DHF. 19 4 With the L. caaei form, this reduction is ~100 times slower than that of DHF. During the enzymatic reduction of folate, it is again the 4-pro•R hydrogen transferred to the pteridine ring. Spectroscopy reveals that the isotope is transferred to the ai face of the C7 in folate. The enzyme catalyzed hydride transfer, for the reduction of both DHF and folate, involves the same face of NADPH and the same face of the folic acid substrate. Thus, there is no major difference in the orientation of reactive DHF or folate substrate binding. 2.3 Kinetic Profile A profile of the steady-state kinetics of the wild-type E. coli form of DHFR was recently reported by Fierke, Johnson, and Benkovic. 11 This study used stopped.flow fluorescence and absorbence spectroscopies in combination with competetive binding assays to measure the rates of ligand association and dissociation as well as the binding constants of key intermediates in the catalytic sequence. A diagram of this steady-state profile of the native form of E. coli DHFR is shown in Figure 6. A number of surprising findings came of this work. The Benkovic studies 11 revealed that the catalytic step, i.e., the N5-C6 double bond reduction, proceeds at a steady-state rate of 950 sec- 1 • The steady-state rate of THF product releaae, however, is only 12.5 sec- 1 , thus making product release the rate-limiting step! -153- Figure 6. Steady-state kinetic scheme for wild-type E. coli DHFR. -154- SUBSTRA'E 81N'.Jl",G FORWAR:J. 40 µM·' s·' ,---, 1 '---8-AC_K_W_A_R_D_•_4_0_s·_ _ __,······· :~~ u -- ~ a ; .. ..... LOSE NADPH 17Ss· 1 ~ PRO:J0C- RE~EASE FORWA?:J = ',2 5 s. 9ACKWARO • 2 cl.V ; u ...._ ........... CA_A_'r::C 9EAC710N .:oRwA::;J = gsc s·· BAC><WA=.J = 40 s·· , U a' H'F RE~E.ASE OXIDIZEJ co;:ACTOR FORWA::1,'J = 200 s· 1 BACKWARD. SµM·' s·' Figure 6. 8:ND R::'.:IUCED COFACTOil FOilWAR:J = 8 µM-· s. SACKWA::;'.) = 85 s·· -155- The rate of THF release from the enzyme depends significantly upon whether the cofactor binding site is occupied. The off-rate for THF from the DHFR • THF • NADP+ ternary complex is 2.4 sec-I, while the loss of NADP+ decreases this rate to 1.4 sec-I. With the addition of NADPH to the enzyme complex, the product off-rate is markedly increased to 12.5 sec-I. Thus, THF release is facilitated by the presence of the reduced NADPH cofactor, indicative of a second role for the NADPH cofactor. Mutant forms of E. coli DHFR have been studied in a series of experiments quite similar to those used to determine the wild-type, steady-state profile. 8 ,ll,ll-IS The results germane to our simulation studies are presented in Table 1. These values indicate that modifications at position 54 (a strictly conserved leucine residue) to Ile or Gly lead to the following changes in the kinetics: (a) the substrate binding affinity decreases by more than one order of magnitude; (b) the hydride transfer rate decreases by more than 30 fold; and ( c) the steady-state rate of product release increases by more than eight fold. For both single-site mutants, the rate-limiting step becomes hydride transfer, rather than product release, thus decoupling the transformation rate from the process of cofactor binding. 2.4 The Active Site Asp-27 From chemical precedent, the mechanism for imine reduction favors preprotonation of the pteridine NS followed by hydride transfer. Examination of the pH dependence of the steady-state turnover showed that the rate -:onstant for the isolated hydride transfer step is dependent on an acidic group with pK. ~ 6.5, a value that is the same for free, binary, or ternary complex forms of the enzyme. The identity of this acidic active site residue was clearly shown to be Asp-27 (E. -156- Table 1. Steady-state kinetic data9 •14 for wild-type and position 54 mutants of E. coli DHFR. Leu-54 Gly-54 Ile-54 Binding (µM) EnHF 0.21 1.9 350 Dissociation ( sec- 1 ) EnHF 22 ~300 300 ETHF 1.4 >300 60 ENADP+ THF 2.5 - 100 ENADPH 12.3 - 90 THF Hydride Transfer (sec- 1 ) 950 29 31 -157- coli) by its replacement with Asn or Ser, resulting in two mutant DHFRs that require preprotonated DHF for catalysis. 10 -158- 3. Homology Studies Steady-state kinetic studies of the different DHFR system from E. coli and L. ca.,ei (only 27% sequence homology) reveal a remarkable similarity in the free- energy profiles for DHF to THF. 13 In order to understand why this congruence in catalytic profile occurs for such different proteins, we undertook investigations of the similarity in sequence, structure, and chemical homology of the E. coli and L. ca.,ei forms of DHFR. Studies using computer graphics with macromolecular docking were combined with both sequence and chemical homology assignments to offer an explanation for the agreement in catalytic reactivity of these bacterial systems. This work is described in detail below and presented as portions of the manuscripts included in Appendices III and IV. This structure-sequence study was also extended to include the Chicken DHFR form which, along with other mammalian DHFR systems, has a reaction profile quite distinct from the bacterial systems. Such an interspecies comparison provides the opportunity to begin piecing together an understanding of the origins of the subtle differences in reductive chemistry exhibited by these enzymes. 3.1 E. coli and L. ca.,ei Bacterial Forms The molecular display and manipulation facilities of BIOGRAF 20 were used to analyze these bacterial DHFR crystal complexes. This analysis involved docking the enzyme complexes, determining the substrate and cofactor binding sites, and comparing the amino acid residues and active site molecular surfaces. 3.1.1 Coordinate Transformation The initial step was to dock the crystallographic form of the entire L. ca.,ei ternary complex onto the coordinate space of the E. coli binary complex so as to match the MTX of the two systems. The results of this docking exercise are -159- illustrated in Figures 7 and 8. Here the E. coli backbone structure is shown in yellow with the bound MTX in red, while the docked L. ca.,ei segment is drawn in light blue. Figure 7 clearly illustrates the structural agreement in overall folding of these two bacterial forms of DHFR. Figure 8 highlights the similarity of MTX binding and the criterion used for docking the L. ca.,ei complex to that of the E. coli. 3.1.2 Identification of the Site Regions In order to focus on the sequence homology of the active site region, we defined the 6ub6trate active 6ite as all residues having any atom within 7 A of any atom of the MTX. This resulting substrate active site has 52 amino acids (out of a total of 159 for the E. coli or 162 for the L. ca.,ei) as listed in Table 2. The NADPH active 6ite was identified in an analogous manner but based solely on the position of the L. ca,ei-bound NADPH. For these two DHFR complexes, a slight discrepancy in the definition of the NADPH active site was encountered. The differences were due to the fact that the L. ca.,ei form was indeed a ternary complex with NADPH bound, while the E. coli structure lacked this small molecule. The L. ca,ei system had the protein segment from Asp-16 through Trp-21 securing the position of the N ADPH moiety, while the binary E. coli protein permitted the analogous Glu-17 through Trp-22 region to be ex- tended and somewhat more removed from the empty cofactor site. Hence, the 7A distance cutoff produced the full inclusion of L. caaei Asp-16 to Trp-21 while missing a few of the residues in the E. coli complex. To insure appropriate analyses, the full E. coli segment from Glu-17 through Trp-22 was added to those amino acids identified to be within 7 A, thus producing an NADPH active site containing 59 amino acid residues. These residues are listed in Table 3. -160- Figure 1. Comparison of the overall protein fold of the E. coli (yellow) and L. caaei (light blue) forms of DHFR. The MTX inhibitor (red from E. coli and blue from L. caaei) and NADPH cofactor (blue from L.caaei) are shown in their cavities. Figure 8. Active site comparison of the E. coli and L. caaei bacterial forms of DHFR. The docking criterion is clearly illustrated by the agreement in structure of the two bound MTX molecules (red from E. coli and blue from L. caaei). The solvent surfaces are also displayed highlighting the high degree of agreement between the two active sites. -161- Figure 8. -162- Table 2. Homology of the substrate binding site0 for DHFR. E. coli Leu-4 L. casei Phe-3 Classa Back Involvement in the Active Site deep in pterin pocket Ile-5 Leu-4 Whole side cha.ins allign near diamino portion of site and Phe-31(30) Ala-6 Trp-5 Back f3C allignment; Trp ring away from pterin site, stacked with Phe-103 Ala-7 Ala-6 Exact methyl group part of pterin pocket Leu-8 Gln-7 Ba.ck interacts with other residues forming pocket Ala-9 Asn-8 Back sides removed from pterin site Asn-18b Gly-17 - { interacts with Ala-19b His-18 - Nicatinamide ribose } Met-20b Leu-19 Whole side cha.in into the pterin/nic/benz site Pro-21b Pro-20 Exact hugs NADPH ribose Trp-22 Trp-21 Exact edge of pterin pocket Asn-23b His-22 Whole under the pterin/benz site Leu-24 Leu-23 Exact pterin pocket Pro-25 Ala-26 Pro-24 Asp-25 Exact Back base of helix on the side of helix away from site Asp-27 Asp-26 Exact Bridge to pteridine Leu-28 Leu-27 Exact MTX kink region Ala-29 His-28 Sides imidazole interacting with 6-CO2- Trp-30 Tyr-29 Whole rings allign; edge of pterin site Phe-31 Phe-30 Exact pteridine hydrophobic pocket Lys-32 Arg-31 Whole straddles both CO2- of MTX -163- Table 2. ( continued) E. coli Arg-33 L. casei Ala-32 Classa Involvement in the Active Site Back on helix side away from site Asn-34 Gln-33 Back on helix side away from site Thr-35 Thr-34 Exact side toward MTX; buffered by Phe-30 /31 Leu-36 Val-35 Whole edge of glutamate site Asp-37 Gly-36 Back Asp side chain a.t surface Val-40 Met-39 Whole interacting with Phe-31/30 Met-42 Val-41 Whole removed from site region Thr-46 Thr-45 Exact nic site near benz/amine portion Trp-47 Glu-48 Ser-49 Ile-50 Gly-51 Tyr-46 Glu-47 Ser-48 Phe-49 Pro-50 Back behind MTX benz site Exact toward NADPH site Exact toward NADPH site Whole behind benz of MTX Whole kink; edge of benz site Arg-52 Lys-51 Arg-52 Exact E. coli with 6-CO2- of MTX; L. casei pointing in different direction Pro-53 Pro-53 Exact kink away from site Leu-54 Leu-54 Exact benz/glutamate site Pro-55 Pro-55 Exact end of glutamate site Gly-56 Glu-56 Back Glu side chain out on surface of enzyme Arg-57 Arg-57 Exact salt bridge to MTX CO2- ( CT) Met-92 Val-95 Whole far back side of pterin site pocket Val-93 Ile-96 Back into bulk of protein Ile-94 Ala-97 Whole hydrophobic pterin pocket Gly-95 Gly-98 Exact {backbone forms side to Gly-96 Gly-99 Exact nic/pterin(N4-N5) site} - -164- Table 2. ( continued) a E. coli Tyr-100 L. casei Phe-103 Cla.ss0 Whole Involvement in the Active Site point toward pterin/nic site Tyr-111 Leu-114 Back { good backbone and side allignment; Leu-112 Val-115 Back composes the /3 sheet below Leu-4 Thr-113 Thr-116 Exact to Leu-8; near/behind 2-4 diamino site} His-114 Arg-117 Ile-115 Leu-118 on the outside of the enzyme away from the active site Whole deep in pterin site near MTX Nl (near Trp22/21) Phe-153 Tyr-155 Back Sides next to Asp-26/27 As discussed in Section 3.1.3, classification scheme defined as: Exact: the two amino acid residues are identical in type. Back: the backbone atoms align, while the side chain atoms are oriented away from the active site. Sides: the side chains align toward the bound substrate. Whole: the backbone atoms and side chain atoms align as best possible with the side chain oriented toward the active site. b Not well aligned because of the absence of NADPH in the E. coli crystal structure. -165- Table 3. Homology of the cofactor binding site11 for DHFR. E. coli Ile-5 L. casei Leu-4 Class11 Whole Involvement in the Active Site away from Nie near Pterin site Ala-6 Trp-5 Back E. coli Ala-6 + Leu-8 side = L. casei Trp-5 side + Gln- 7 side Ala-7 Ala-6 Exact near amide of Nie ring Leu-8 Gln-7 Back E. coli Ala-6 + Leu-8 side= L. casei Trp-5 side + Gln- 7 side Ala-9 Val-10 Val-13 Asn-8 Arg-9 Leu-12 Back Back Back Far removed from site Far removed from site Pterin pocket Ile-14 Ile-13 Exact floor of Nie ring site Gly-15 Gly-14 Exact edge of Nie site Met-16 Lys-15 Back sides both point to outside of enzyme Glu-17" Asp-16 Back side chains out to surface of enzyme Asn-18" Ala-19" Gly-17 His-18 Back Back Nicotinamide ribose site side chains at enzyme surface Met-20" Leu-19 Whole Nicotinamide / pterin site Pro-21" Pro-20 Exact Edge of nicotinamide pocket Trp-22" Trp-21 Exact Nicotinamide/pterin pocket Asn-23 His-22 Whole MTX glutamate site Leu-24 Asp-27 Leu-23 Asp-26 Exact Exact Pterin site toward pterin ring area Phe-31 Phe-30 Exact pterin site -166- Table 3. ( continued) E. coli Met-42 Gly-43 L. casei Val-41 Gly-42 Involvement in the Active Site Whole located behind Nie ribose Exact part of adenosine binding site Arg-44 Arg-43 Exact adenosine phosphate neutralizer His-45 Arg-44 Whole diphosphate site charge neutralizer Thr-46 Thr-45 Exact back of diphos/Nic site Trp-47 Tyr-46 Back sides stack with Phe-49/Ile-50 Glu-48 Glu-47 Exact sides point out to surface of enzyme; 2nd segment of amino acids over from diphos site Ser-49 Ser-48 Exact OH points toward Nie ribose Ile-50 Phe-49 Whole back part of Nicotinmide/benz site Ile-61 Leu-62 Val-61 Leu-62 Whole Exact far removed from Aden ribose site Adenosine binding pocket Ser-63 Thr-63 Whole -OH interacts with Aden phos Ser-64 His-64 Whole His ring stacks with Aden base, Ser -OH in same place Gln-65 Gln-65 Exact displacement by the Adenosine phosphate group Pro-66 Glu-66 Back out to surface away from site Gly-67 Asp-67 Back out to surface away from site Thr-68 Tyr-68 Sides E. coli Thr-68 + Trp-47 sides = L. casei Tyr-68 + Tyr-46 sides Trp-74 Val-75 Sides E. coli Trp- 74 + Thr-68 sides = L. casei Val-75 + Tyr-68 sides Val-75 Val-76 Exact sides into bulk of enzyme Lys-76 His-77 Back sides away from site cavity at surface of enzyme Ser-77 Asp-78 Back Val-78 Val-79 Exact side chains away from site at enzyme surface edge of Adenenosine base site Asp-79 Ala-80 Back CO2- to outside of enzyme; away from site Class0 -167- Table 3. ( continued) a E. coli Val-93 L. casei Class4 Involvement in the Active Site Ile-96 Back into bulk of protein Ile-94 Ala-97 Whole E. coli Ile-94 + Ile-50 sides = L. casei Phe49 + Ala-97 sides; edge of Pterin/Nic site Gly-95 Gly-98 Exact near Nic/Pterin interface Gly-96 Gly-99 Exact base of diphosphate binding area Gly-97 Ala-100 Back CH3 points away from diphosphate site Arg-98 Gln-101 Whole interact with either diphosphate or Adenosine phosphate Val-99 Ile-102 Whole Tyr-100 Glu-101 Phe-103 Thr-104 form part of Adenenosine base and ribose site Whole nicotinamide site Back sides away from site area Gln-102 Ala-105 Whole Phe-103 Phe-106 Exact might be some adjustment when NADPH binds buried into bulk of enzyme Ile-115 Leu-118 Sides Nie end behind Trp22/21 Asp-122 Asp-125 Exact H-bonding to nicotinamide ribose Thr-123 Thr-126 Exact behind Nie ribose and diphos regions His-124 Phe-125 Lys-127 Met-128 Back sides to surface and far removed from site far, far back of Nie site Whole As discussed in Section 3.1.3, classification scheme defined as: Exact: the two amino acid residues are identical in type. Back: the backbone atoms align, while the side chain atoms are oriented away from the active site. Sides: the side chains align toward the bound substrate. Whole: the backbone atoms and side chain atoms align as best possible with the side chain oriented toward the active site. 1, Not well aligned because of the absence of NADPH in the E. coli crystal structure. -168- 9. 1.!I Compartson ot the Slte Regions In comparing the amino acids for different DHFRs, we considered corresponding residues, as those having the same positional and functional role on the basis of type, alignment, and role at the surface of the binding sites. Tables 2 and 3 include this comparison information for the methotrexate/ dihydrofolate and NADPH sites, respectively. For the MTX/DHF site, 20 of the 52 amino acids are identical, leading to a 38% sequence homology. For the NADPH site, 22 of the 59 residues are the same, leading to a sequence homology of 37%. Combining the sequence data for the MTX/DHF and NADPH active sites produces a catalytic pocket composed of 85 amino acid residues, 31 of which are conserved between the E. coli and the L. ca,ei forms (36% sequence homology). To facilitate and refine this active site comparison, a new classification scheme was devised for comparison of residues between E. coli and L. ca.sei. If the corresponding residues are exactly the same for both forms, e.g., Ala-6 Ee and Ala-7 Le, the residue match is considered as "e:i:act," as in the normal definition of homology. If, on the other hand, the two residue types differ, we define three possible classification types: (1) whole: where the ba.ckbone and the side chain a.toms are well aligned between the two forms a.nd where the side chain is oriented toward the active site; (2) ,ide: where the side chains align toward the bound substrate and/or cofactor but without reasonable agreement of the backbone sites; (3) bad~: where the backbone atoms are in very good positional agreement, while the side chain fragments are oriented away from the active site into the bulk of the enzyme or at the surface of the protein; (4) none: neither backbone or side chain is aligned. The chemical homology scale is defined as consisting of all residues that -169- are either ezact (if identical) or of type back (if different). Using the chemical homology scale, an additional 14 residues in the MTX/DHF pocket and 19 amino acids in the NADPH binding site (see Tables 2 and 3) are homologous. Thus, the chemical homology for the E. coli and L. caaei forms is: (a) 65% for the substrate binding region, (b) 69% for the cofactor site, and ( c) 69% for the entire catalytic pocket, even though the sequence homology is less than 30%. This close chemical homology may be visualized with the solvent-accessible molecular surface 21 •22 of the substrate and cofactor pockets. These surfaces were calculated with a 1.4 A. probe sphere, consistent with a water molecule probe, and displayed with BIOG RAF. The areas mapped out by these surfaces agree within 95%. The agreement between the molecular surfaces for the E. coli and the L. caaei forms is illustrated in Figure 8. 3.2 Chicken DHFR Because of the importance of mammalian DHFR in cancer therapy, and because of the dramatic differences in the reaction profile for mammalian and bacterial DHFR, it is quite important to understand the subtle differences between these forms of DHFR. Such knowledge might facilitate designing therapeutic agents that would be species-selective for interaction with DHFR. For this reason, this structure-sequence analysis was extended to include a Chicken DHFR, the only nonbacterial form of DHFR for which there is detailed structural information. The crystal structure ofthe DHFR,NADPH binary complex has been solved to a 1. 7 A. resolution by Matthews and coworkers 18 and the coordinates generously made available to our lab. The overall sequence homology for this protein with the bacterial forms is <30%. As with the two bacterial forms of this en- -170- zyme, however, the fold of the Chicken form of the protein has a close similarity to that of both the E. coli and L. caJei structures (see Figure 4). The macromolecular docking of the Chicken binary complex was carried out to optimize the fit of the NADPH of Chicken with that of L. caJei. The cofactorbinding site of chicken DHFR was defined as described above, using Chicken NADPH. To define the MTX substrate-binding cavities of Chicken DHFR, we used the MTX from the docked L. caJei complex. A comparison of the site sequences for the three forms of DHFR analyzed in this study is given in Table 4. For the substrate binding site, only 15 of the 52 possible residues (29%) are equivalent, while in the NADPH binding site, only 14 out of the 59 postions (24%) are sequence-homologous. Thus, for the entire catalytic site region, there is only 24% sequence homology, i.e., 20 of the possible 85 residues. Using the chemical homology scale, the agreement between the binding pockets of these three forms of DHFR is greatly increased to: ( a) 58% for the substrate site (15 exact plus 15 backbone out of 52 total positions); (b) 56% for the NADPH binding site (14 exact plus 19 backbone out of total of 59 positions); and (c) 54% for the overall catalytic pocket (20 exact plus 26 backbone out of 85 total site residues). The chemical homology of Chicken DHFR with either bacterial DHFR is ~60% for the catalytic site region, which is ~10% less than the agreement found between the E. coli and L. ca1ei bacterial forms. Thus, we should expect that the free-energy profile for the steady-state kinetic pathway of the Chicken DHFR would not be as closely aligned as the two bacterial systems. Experimental testing of this conclusion is under way. The major distinction in reaction profiles for these forms of DHFR is that -171- Table 4. Comparisona of DHFR active site residues from E. coli, L. casei, and Chicken. Residue& 4 5 6 7 8 9 10 13 14 15 E. coli L 1 A A L A V V 1 G L. casei F 1 w A Q N R L 1 G Chick s 1 V A V C Q G 1 G 16 17 18 19 20 21 22 23 24 25 E. coli M E N A m p n L p L. casei K D G H I p h L p Chicle K D G N 1 p w w w p p L r 26 27 28 29 30 31 32 33 34 35 36 E. coli A d I a w F k R N T I L. casei D d I h y F r A Q T V Chick N e y k y F q R M T s 37 40 42 43 44 45 46 47 48 E. coli d g m G r h T w e L. casei g m V G r r T y e m G k k T w f 54 55 56 57 L p G R Chicle 49 50 51 52 1 g R 53 p f p k R p L p E R 1 p n R p L k D R 61 62 63 64 65 66 67 68 74 75 E. coli 1 L s s q p G t w V L. casei V L t h q e D y V V Chicle V L s r e I K e 1 s E. coli L. casei Chicle s s s -172- Table 4. ( continued) 76 77 78 79 92 93 94 95 96 E. coli K s V D m V 1 G G L. casei H D V A V I a G G Chick K s 1 D I V G G 97 98 99 100 101 102 103 111 112 E. coli G r V y E q f y L L. casei A q 1 f T a f L V Chick T a V y K a a F V 113 114 115 122 123 124 125 153 E. coli T H 1 D T H f f L. casei T R 1 D T K m y Chick T R 1 D T F f f "Bold upper case indicates homologous, lower case indicates nonhomologous, and nonbold upper case indicates backbone chemical homology, as described in Section 3.1.3 of the text. "Numbered for the E. coli form. -173- for Chicken DHFR, the rate of folate reduction to DHF is about 100 times the rate for the two bacterial species. 20 This difference in rate may be related to the subtle differences between the bacterial and avian site homologies, as will be expanded upon in Section 8. -174- 4. Simulation Strategies Because of the difficulty in obtaining detailed structural information about DHFR substrate cofactor complexes and the difficulty of obtaining these data for a sequence of mutated systems, we have used molecular mechanics and molecular dynamics simulations to predict structures appropriate for solvated complexes at room temperature. 23 This procedure involves describing the energy of the ~3500 atom system (including solvent) as a superposition of two-body, threebody and four-body interactions ( the force field). Using this force field the forces are calculated for each geometry and Newton's equations are solved to predict the dynamics. For these studies we used the AMBER force field, 24 and the molecular dynamics and energy minimization calculations were carried out with the BIOGRAF 20 molecular simulation program (which has the dynamics integrated with three-dimensional graphics displays). This marriage of calculational abilities with visual ease provides the tool necessary for theoretical investigations of biochemical systems. Specifics of the approaches used to define the starting structures for the simulations are presented below. This discussion is followed by a brief presentation of the force field used in the calculations and a discussion of the strategies developed to preceed from initial enzyme complex to equilibrated form. The results and conclusions from each set of simulations are presented and discussed in detail in Sections 5 through 8. 4.1 Models for Starting Complexes As will be discussed, such molecular simulations are quite useful in predicting changes in structure that are due to mutations or to binding of substrates or -175- other molecules. However, these techniques are not yet adequate for predicting the optimal folding of the complete protein. Consequently it is essential to use an initial starting structure, which defines the overall protein folding. A complete experimental crystal structure would provide an ideal starting structure for the calculations. Unfortunately, only partial experimental structural data are available, as outlined in Section 2. Consequently, a number of manipulations and assignments were necessary to generate the initial structure data sets required for the molecular simulations. For the studies presented here, we constructed DHFR binary and ternary complexes, suitably solvated. In some studies, alternate conformations of bound substrate or inhibitor were required. Mutant protein structures were also needed. Some details of the procedures employed to add the missing pieces to the available experimental data are described in the following sections. 4. 1. 1 Proteins The crystallographic coordinates for E. coli Dihydrofolate Reductase were obtained from Brookhaven Data Files as reported by Matthews et al. 5 •6 For this form of the enzyme, the crystal structure file contained two independent protein molecules in the unit cell, designated as A and B (equivalent to 1 and 2, respectively, as reported in the literature). One methotrexate (MTX) inhibitor molecule is bound to each protein molecule in a one-to-one complex. The crystallographers indicate that chain B is preferred for structural comparisons because it is more complete and less perturbed by intermolecular contacts than is chain A. For these reasons, the simulations were done using chain B as the starting D HFR structure. The completion of the DHFR starting structure involved 2 stages. The -176- Brookhaven files do not contain coordinates for the carboxylate groups of Glu129 and Asp-131. The Replace facilities of BIOGRAF were used in conjunction with the reported atomic postions of residues 129 and 131 to generate initial coordinates for these carboxylate groups. The crystallographic file also included coordinates for alternate conformations (A and B) of His-45, Ser-64 and Asp122. Matthews and coworkers indicate that in all cases the A form is believed to be the major conformer. In each case energy minimization calculations also indicated that the A form is lower in energy than the B form. Consequently, the A conformer was used for these studies. 4.1.2 Substrate and Inhibitor Orientation The starting structures for either the bound substrate or the inhibitor simulations were based upon the crystallographic data for the MTX bound to DHFR. For the experimental form of bound MTX, referred to as MTX-xtl, the coordinates were used as reported. For the pteridine-:flipped form of bound MTX, termed MTX-anti, the C6-C9 and C9-Nl0 bonds of MTX were rotated to produce a starting conformation with the pteridine ring positioned in the active site but with its face :flipped 180° (Figure 9). To be consistent with experiment, both forms of bound MTX inhibitor were protonated at Nl 25 • As with the MTX, two orientations of the bound aubatrate were con:o_dered. The DHF units were positioned based upon: (a) the crystal coordinates of the MTX and hence termed DHF-xtl, and (b) the modeled coordinates of the :flipped pteridine ring form (DHF-anti). The chemical structure of the bound MTX was "mutated" into that of the natural substrate; i.e., the carbonyl oxygen at position 4 of the pteridine ring was converted to an amino substituent and the benzoylamino unit was methylated. To be consistent with experimental observations, -177- Figure 9. The two orientations for the bound pteridine ring studied using molecular simulations. The unflipped form corresponds to the conformation found in the crystal complexes (referred to as xtl in the text) and the flipped form is achieved by rotation about the C6-C9 and C9-N10 bonds (equivalent to the anti form). -178- (b) MTX -flipped (d) DHF • flipped (reactive) Figure 9. -179- the carboxylate group of Asp-27 was protonated, while the pterin ring of the substrate was not protonated at the Nl position. For studies of folate substrate with DHFR, the starting DHF-anti structure was altered to reflect a bound folate molecule. As with the dihydrofolate substrate, the carboxylate group of Asp-27 was protonated and the Nl position was unprotonated. 10 •25 4.1.3 Position of NADPH Cofactor The coordinates for the E. coli bound NADPH were modeled based upon those from the L. caaei ternary complex. The L. caaei system docked with respect to the E. coliform (discussed in 3.1.1) provided starting coordinates for NADPH bound to the E. coli protein. Addition of the NADPH cofactor to the E. coli binary complex necessitated two types of modifications to the full system. First, the solvent shell had to be corrected ( vide infra). The water molecules lining the vacant NADPH site were deleted from the starting ternary form and appropriate counterions were positioned near the anionic sites of the NADPH. The other changes involved the position of the protein loop holding the NADPH into its binding site. In the E. coli binary crystal structure, residues Glu-17 through Trp-22, are in an extended conformation open and away from the vacant cofactor binding site. The analogous amino acids in the L. caaei ternary complex, however, are moved in toward the bound NADPH and assist in positioning the cofactor. Hence, the orientation of this fragment in the E.coli protein was modeled after that of the L. caaei. This modification was accomplished by substituting for the coordinates of the E. coli residues the backbone atoms of the docked L. caaei structure, thus creating a series of glycine amino acids. The side -180- chain positions were then determined by using the Replace facility of BIOGRAF in conjunction with molecular simulation (as discussed below) and the L. ca-,es crystal structure. 4. 1.4 Salvation The Brookhaven data file for E. coli DHFR contains coordinates for the oxygen atoms of 197 water molecules associated with chain B. The coordinates for two ions were also reported, one c1- and one Ca+ 2 • The c1- was located between the side chains of His-45, Thr-46, Val-99 and Gln-102. It was maintained in the coordinate file. The ca+ 2 , on the other hand, was located at the periphery of the protein structure. In our simulations we typically use Na+ and c1- counterions, and since the Ca+ 2 was not sequestered by protein, it was removed from the starting structure file. Additional water was added to the starting file with the Solvate option of BIOGRAF. 20 The diamond lattice type was used for the water addition. A grid spacing of 2.8 A and a close contact cutoff distance of 2.8 A were used. These values allowed for adequate H-bonding between solvent and protein as well as for the appropriate density for water. The MTX and eleven regions of the protein were defined and used for the segmented solvation. Solvent was added to a distance of 5 A. This addition generated coordinates for an additional 458 waters, for a total of 655. In such simulations it is important to consider electroneutral systems to avoid spurious energetics. This was achieved by positioning the appropriately charged counterions near cationic and anionic side chains. Certain water oxygens were selected to be changed into counterions near charged amino acid side chains, i.e., the side chains of Asp, Glu, Arg, and Lys. The positions were determined by -181- the coordinates of the next-nearest water. For the DHFR binary MTX simulation starting file, the results are listed in Table 5. After the above manipulations, the final solvent for the binary complex simulation was composed of 619 waters (197 experimental and 422 modeled into the system), 23 Na+ (all modeled waters converted to ions) and 13 c1- (1 experimental and 12 modeled waters converted to ions). For the ternary complexes, with DHF natural substrate, 21 waters were deleted from the NADPH binding site. The starting structure for solvent within the active site region was examined using solvent accessible surfaces. 21 •22 The solvent accessible molecular surfaces for the bound inhibitor or substrate, the NADPH cofactor, the active site of the protein, and the water molecules within 8 A of the bound small molecules were generated (with a 1.4 A probe radius). Visual examination of these molecular surfaces indicated that no vacancies or steric crowding were present. Thus an appropriate amount of solvent was present in the active site. 4.1.S Site Mutations The Replace portion of BIOGRAF was used to introduce site-specific mutants into the E. coli Dihydrofolate Reductase enzyme. This manipulation substitutes the desired mutant amino acid side chain for that of a preselected wild-type residue. The backbone atoms of the two amino acids, i.e., the new mutant and the native form, are superpositioned, while the side chain for the substituting residue is positioned to mimic the location of the natural amino acid. If the mutation involves loss of a substantial portion of the side chain, e.g., the E. coli Leu-54 to Gly-54 modification, appropriate solvent molecules are added to the site of the substitution. -182- Table 5. Those charged residues with neighboring HOH's changed into counter-ions. Aspartate Residues Number HOH Distancea 11 A-29 5.2236 27 MTX-Nl 3.5537 37 E-13 6.0585 69 B-76 4.9038 70 B-78 5.5722 79 G-22 5.9090 87 E-25 4.6601 116 F-14 5.7514 122 A-76 5.1697 127 F-21 6.2717 131 F-17 4.5473 132 C-40 6.0440 142 F-1 5.1459 144 I-2 4.7541 Arginine Residues 11 Number HOH Distanceb 12 C-52 4.9490 33 H-14 5.5488 44 B-74 4.5535 52 MTX-CD 5.5419 57 MTX-CT 4.1729 71 E-47 4.8016 98 A-81 5.3439 158 C-49 5.5145 159 X-2 4.8605 To aspartate ;-carbon. "To arginine guanadinium carbon. -183- Table 5. ( continued) Glutamate Residues Number HOH Distance0 17 A-63 5.5756 48 J-6 5.9410 80 B-81 5.6403 90 Lys-38 101 A-60 6.1143 118 A-16 5.7055 120 A-45 5.0320 129 C-46 6.6427 134 A-79 4.8605 139 C-15 5.6683 157 C-18 5.4142 Lysine Residues 0 Number HOH Distance" 32 E-9 4.8595 38 Glu-90 58 E-39 4.9874 76 E-56 4.8419 106 G-25 4.9956 109 C-34 5.3602 154 C-7 5.5638 To glutamate 5-carbon. " To lysine terminal nitrogen. -184- 4.1.6 Loop Insertions The investigations 'of hybrid Dihydrofolate Reductase proteins depended upon the construction of "segment mutant" enzymes. This task was facilitated by using the BIOGRAF Protein Builder. The Insert feature permits segments of amino acids to be added to selected regiom !" a protein structure. For the E. coli - Chicken hybrids discussed in Section 8, loop regions of the E. coli protein were extended, based upon the sequence and structure of the Chicken form. In loop-hybrid 1 (LHl), the E. coli segment Ile-Gly-ArgPro-Leu-Pro-Gly-Arg-Lys-Asn (sites 50 - 59) was replaced by the Chicken sequence Leu-Pro-Glu-Lys-Asn-Arg-Pro-Leu-Lys-Asp-Arg-Ile-Asn (positions 61 72). The coordinates of the atoms in this new loop were assigned from those of the docked Chicken structure file. Similarly, E. coli Leu-36 was changed to reflect the Chicken sequence Ser-Thr-Ser-His-Val-Glu-Gly-Lys-Gln (positions 39 through 47 in the wild-type Chicken structure) to yield loop-hybrid 2 (LH2). 4.2 Force Field The molecular mechanics simulations were carried out with BIO GRAF, using the AMBER force field developed for describing proteins and nucleic acids 24 • This force field method involves harmonic potential functions for bond stretches and angle bends and cosine expansion potentials to describe torsions and inversions. The nonbond interactions are described with fixed charge electrostatic terms, with Lennard-Jones 12-6 potentials to account for van der Waals interactions, and a Lennard-Jones 12-10 potential to modulate the electrostatic terms involved in hydrogen bonding. A more detailed description of the force field potential functions is presented in Appendix I. The water potential employed for these simulations is based upon the Jorgen- -185- son TIPS model 26 but uses the Pettitt modification for flexible waters. 27 This potential places charges on each atom (QH = + 0.40, Qo = - 0.80) and uses Lennard-Jones 12-6 potentials on both O and H. See Appendix V for details of this water potential. For the electrostatic energies, the partial charges for the amino acid residues were the values from AMBER. The atomic charges for methotrexate, dihydrofolate, folate, and NADPH were based upon values reported for analogous amino and nucleic acid fragments, and are given in Table 6. 4.3 Simulation Protocols The series of calculations run on the solvated DHFR complexes consisted of two separate· phases. The first phase was designed to bring the full system into equilibration. The second phase involved structural and energetic analyses. Each phase made use of molecular dynamics and energy minimization. A brief discussion of these techniques as well as their implementation in the equilibration and analysis of the DHFR complexes is presented below. 4.3.1 Energy Minimization and Molecular Dynamics In energy minimization, the coordinates of the atoms in the molecular system a.re modified so as to decrease the energy of the entire system to a minimum. Given the set of 3N independent coordinates x = (x1 ,x2 ,x3 , ••• ,x) for the N atoms of the macromolecular system, we evaluate the potential energy function V = V(x) and the force on each atom Fi = -VVi = - :;1 • Conjugate gradient techniques are used to find the energy minimum rapidly. This method changes the 3N dimensional coordinate vector in a direction determined by the force but corrected by information from previous minimizations. Such energy minimization is useful for refining molecular structures, i.e., -186- Table 6. Point charges for DHFR substrates and rnethotrexate inhibitor. Atorna MTX DHF THF Nl -0.5000 -0.7020 -0.7020 HNl 0.4800 - - C2 0.8400 0.8420 0.8420 NA2 -0.6600 -0.7580 -0.7580 HNA2 0.3500 0.3300 0.3300 N3 -0.7000 -0. 7460 -0.7460 HN3 - 0.3400 0.3400 C4 0.8100 0.7140 0.7140 NA4 -0.7900 - - -0.4590 -0.4590 OA4 - HNA4 0.3400 - - C4A -0.1500 -0.0880 -0.0880 NS -0.7500 -0.7390 -0.5000 C6 0.7800 0.7800 0.1000 C7 0.1200 0.1200 0.1000 N8 -0.6500 -0.7500 -0.5000 HN8 0.3900 0.3400 0.3400 CSA 0.6000 0.4900 0.4900 C9 0.0800 0.0800 -0.0490 Nl0 -0.3800 -0.4440 -0.4440 CM 0.1000 - - HNlO - 0.3200 0.3200 Cll -0.1300 -0.1300 -0.1300 C12 0.0650 0.0650 0.0650 Cl3 0.0650 0.0650 0.0650 Cl4 -0.1300 -0.1300 -0.1300 C15 0.0650 0.0650 0.0650 C16 0.0650 0.0650 0.0650 -187- Table 6. ( continued) Atom C 0 MTX DHF THF 0.5300 0.5300 0.5300 0 -0.5000 -0.5000 -0.5000 N HN CA CT -0.5200 -0.5200 -0.5200 0.2500 0.2500 0.2500 0.2400 0.2400 0.2400 0.5600 0.5600 0.5600 01 -0.7800 -0.7800 -0.7800 02 -0.7800 -0.7800 -0.7800 CB CG CD 0.0000 0.0000 0.0000 -0.2000 -0.2000 -0.2000 0.6200 0.6200 0.6200 OEl -0.7100 -0.7100 -0.7100 OE2 -0.7100 -0.7100 -0.7100 0 Labeled as in: o,r.,.....o 0 C I II CH 2 - N 9 10 .,.....o C - N - CH -CH2-CH2-C a ~ r 11'-o H I -188- reducing steric crowding and adjusting bond lengths and angles to values near their optima. In addition, the relative energies of different conformations provide information about relative stabilities. However, for such complex molecules as enzymes, there can be several local minima. The conjugate gradient techniques lead to converged local minima of the potential surface closest to the starting point. Hence, the initial molecular structure greatly influences the final, minimized form. In such complex systems energy minimization calculations generally do not produce conformations that are very different from the starting, unrefined structure. In molecular dynamics, the trajectory of the system at finite temperature (usually 300K in our studies) is calculated by solving Newton's equations for an interval of time. In such calculations, the 3N components of force on each of the N atoms are calculated for the geometry at time t 0 and Newton's equation is VV(x1) (1) solved, using the coordinates and velocities at time to, to predict the coordinates and velocities at time t = t 0 + S, where S ~ 10- 15 sec. Using the new coordinates at time t 0 + S, the 3N components of force are calculated and used to predict the coordinates at time to+ 28, etc. 4.3.2 Initial Relaxations and Equilibration The calculations used to bring the macromolecular systems into equilibrium proceeded in a stepwise manner that introduced additional segments of the complex with each phase of the process. In all cases, the initial structure was minimized to relieve the possibility of highly strained interactions. Once any repulsive van der Waals or high-energy covalent terms were reduced, equilibration was achieved by the use of molecular dynamics at T=300K. -189- The first portion of the structure to be relaxed was the solvent. Initially, the added water and counterions were allowed to equilibrate (made movable), while the structure of the protein, small molecules ( substrate, inhibitor, cofactor) and experimental solvent was maintained in its initial form (kept fixed). The results from this equilibration were then used in the next step where all solvent molecules were movable, while the enzyme complex was held in a fixed postion. Starting with this structure with relaxed solvent and nonrelaxed enzyme complex, we equilibrated the full system with the following series. First, the side chain units and small molecules bound to the catalytic pocket, along with all solvent molecules, were relaxed, using molecular dynamics, while the positions of all protein backbone atoms were held fixed in their original position. After this side chain equilibration, we then completely relaxed all atoms in the structure, using dynamics to form the starting structure for the molecular simulations. 4.3.3 Production Runs We next evaluated the energetics and structures during a series of quencheddynamics calculations, allowing all atoms (including solvent) to move freely and to equilibrate during such quenched-dynamics runs. The structures were periodically minimized to find the local structure corresponding to that point on the dynamics trajectory. For such minimizations, only the structure of the protein, substrate/inhibitor, and cofactor portions of the complex were permitted to adjust, while the solvent components were held in their equilibrated positions. These minimized structures were used for full and component energy analysis as well as for structural comparisons, as discussed in detail in the various sections below. After each such minimization, the dynamics were continued with the structure prior to the minimization. -190- 5. Methotrexate Simulations Molecular simulations on DHFR-MTX complexes were used to bench-mark the computational method and strategies. These calculations focused on three basic issues. First, is the force field adequate to produce the structure of DHFR complexes in good agreement with experiment? Second, do the simulations indicate the appropriate preference for the orientation of MTX binding? And third, is it possible to examine a smaller subset of the macromolecular assembly and retain the accuracy and reliability of the simulation results? The results of computational studies and analyses to address these questions are given below. 5.1 Full Structural Studies The DHFR-MTX binary structure ( constructed as described as in Section 4) was the starting point for calculations to test the validity of this force field and simulation methodology. The protein complex contained the MTX inhibitor bound in its crystallographic conformation. The macromolecule was equilibrated, as discussed above, and quench-dynamics simulations were carried out with energy minimization, at 0.5 ps intervals. Root mean-square (RMS) comparison of the protein and MTX inhibitor structures during dynamics simulations and after structural refinement were compared with those of the crystallographic complex. The results of this analysis are given in the first column of Tables 7 and 8. Using heavy atoms only for the protein and inhibitor complex, the agreement between calculated structures and the crystal are within 0.90 A. When only the protein backbone heavy atoms are considered, as illustrated in Figure 10, the RMS difference between theory and experiment is slightly improved to within 0. 75 A, indicating better agreement for the backbone of the structure than for the side chains. This is expected in light -191- Table 7. RMS deviations (heavy atoms only) of theoretical and experimental structures for full MTX/DHFR binary complexes. Dynamics XTL 0.5 1.0 1.5 0.5Dyn 0.86 0.00 1.0Dyn 0.87 0.41 0.00 1.5Dyn 0.88 0.47 0.39 0.00 2.0Dyn 0.90 0.52 0.44 0.40 0.5Min 0.83 0.21 1.0Min 0.85 1.5Min 0.87 2.0Min 0.89 Minimized 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.20 0.20 0.20 0.28 0.00 0.35 0.27 0.00 0.42 0.34 0.27 0.00 Table 8. RMS deviations (backbone atoms only) of theoretical and experimental structures for full MTX/DHFR binary complexes. Dynamics XTL 0.5 0.5Dyn 0.66 0.00 1.0Dyn 0.69 0.30 0.00 1.5Dyn 0.69 0.35 0.27 0.00 2.0Dyn 0.72 0.39 0.33 0.29 0.5Min 0.66 0.14 1.0Min 0.67 1.5Min 0.69 2.0Min 0.72 1.0 1.5 Minimized 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.13 0.14 0.14 0.23 0.00 0.29 0.22 0.00 0.34 0.28 0.22 0.00 -192- Figure 10. The experimental (yellow protein backbone and red MTX) and theoretical (light blue) structures for the DHFR-MTX binary complex. Figure 11. Active site comparison of the experimental (yellow protein and red MTX) and theoretical (light blue) structures for the DHFR-MTX binary complex. -193- Figure 10. Figure 11. -194- of the greater rotational flexibilty associated with protein side chains relative to that of the backbone atoms. Figure 11 shows a comparison of the theoretical and experimental ( crystal structure) active site regions including the amino acid side chains and MTX inhibitor. RMS comparisons may also be used to provide a general indication of the changes in structure as the simulation proceeds. This is accomplished by determining the RMS difference between: ( a) subsequent time segments of the molecular dynamics run, (b) appropriate pairs of dynamics and quenched structures, and ( c) refined structures from neighboring intervals of the dynamics relaxation. The results from these studies are also given in Tables 7 and 8. The RMS dynamics comparisons for these DHFR,MTX binary simulations indicate that the structures vary by ~0.40 A from one 0.5 ps interval to the next (only ~0.29 A for the backbone positions). This difference drops to ~0.27 A., once the structures have been refined (~0.22 A for the main-chain atoms). The differences between the dynamics forms and the corresponding minimized structures are quite small ( ~0.20 A for the full protein and only ~0.14 A for the residue backbones), indicating only subtle changes in structure during the energy minimization refinement process. These results indicate reasonable agreement between theory and experiment (the enzyme structure has been refined to 1. 7A.) and supports the utilization of the AMBER force field in simulations of Dihydrofolate Reductase complexes. 5.2 Orientation of Pteridine Ring in Bound MTX As described in Section 2, there are two reasonable orientations for the pteridine ring of bound methotrexate. To study the relative structural and energetics for these two orientations, simulations were run with MTX in its flipped pterin -195- ring form, MTX-anti, to compare with the above MTX-xtl studies. The starting flipped-MTX protein complex was modeled as described in Section 4.1.2. Equilibration and production simulations, were identical to those run on the crystallographic form of bound MTX with DHFR. The results of various energetic analyses of these two MTX DHFR complexes are reported in Tables 9 to 13. First, we present an analysis of the methotrexate inhibitor. Disregarding any contribution that is due to the enzyme or solvent, the simulations indicate that the energy of the crystallographic form of the bound MTX inhibitor is only slightly favored (by ~0.5 kcal) over that of the flipped form (see Table 9). The contribution to the energy from the torsional terms, Eq,, is ~50% lower in the crystal form than in the flipped form, while the ang~e and nonbond terms, E9, EvdW, and Ee1 are more favorable for the flipped MTX. In all, the two conformations are equivalent, within the limits of the force field. With the inclusion of the DHFR protein, the MTX conformational energy gap broadens. Evaluating the energy with the MTX as movable and the protein as fixed (thus including only nonbonded interactions between the enzyme and inhibitor) indicates that the crystallographic MTX is more stable than its flipped counterpart by ~10 kcal (Table 10). As in the case of the isolated inhibitors, the lower torsional energy of the xtl form dominates this preference, but in the presence oi the protein, the nonbond energy terms favor the flipped form by only ~2 kcal. Thus, the enzyme stabilizes the xtl form of MTX by ~10 kcal more than it stabilizes the flipped form of this inhibitor. In order to estimate the effect that the inhibitor has on the energy of the protein, we evaluate the energy of the complex with both the inhibitor and the protein macromolecule as movable. Under these circumstances, the energy of the -196- Table 9. Energetics for full MTX binary simulations: MTX movable, protein ignored. MTX-xtl. Time ETot Eb E11 E4> Ew EvdW Ee1 NBs 0.5 33.43 9.11 17.49 10.80 2.01 10.37 -16.36 613 1.0 45.20 10.16 21.10 16.05 3.16 12.34 -17.60 616 1.5 39.71 9.66 18.80 13.11 3.02 11.29 -16.17 617 2.0 42.96 10.20 19.50 14.33 2.88 11.17 -15.12 617 AVG 40.33 9.78 19.22 13.57 2.78 11.29 -16.31 616 MTX-a.nti. 0.5 39.80 11.41 14.84 25.89 3.77 4.77 -20.88 622 1.0 40.64 12.08 13.70 28.92 3.67 4.08 -21.82 619 1.5 41.32 11.23 14.77 26.78 3.89 4.42 -19.78 614 2.0 41.53 12.00 15.32 26.38 3.65 4.60 -20.42 613 AVG 40.82 11.68 14.66 26.99 3.75 4.47 -20.73 617 -197- Table 10. Energetics for full MTX binary simulations: MTX movable, protein fixed. MTX-xtl. Time ETot Eb Et1 E,t, E"' EvdW Ee1 NBs 0.5 -159.98 9.11 17.49 10.80 2.01 -30.28 -169.12 9669 1.0 -154.95 10.16 21.10 16.05 3.16 -28.52 -176.90 9654 1.5 -156.54 9.66 18.80 13.11 3.02 -27.46 -173.67 9583 2.0 -155.50 10.20 19.50 14.33 2.88 -27.28 -175.13 9599 AVG -156.74 9.78 19.22 13.57 2.78 -28.39 -173. 71 9626 MTX-anti. 0.5 -154.18 11.41 14.84 25.89 3.77 -33.90 -176.19 9529 1.0 -139.62 12.08 13.70 28.92 3.67 -34.13 -163.86 9601 1.5 -142.85 11.23 14.77 26.78 3.89 -34.28 -165.25 9680 2.0 -151.42 12.00 15.32 26.38 3.65 -35.29 -173.49 9719 AVG -147.02 11.68 14.66 26.99 3.75 -34.40 -169.70 9632 -198- crystallographic form is favored by ~145 kcal, with dominant differences arising from the torsional, inversion, and electrostatic components (see Table 11). This energy difference appears rather large; however, this difference is less than 1 kcal per amino acid residue of the enzyme. Another way of examining the effect of the MTX on the protein matrix is to consider only the site region of the protein, i.e., those residues in the enzyme with any atom within 8 A of the bound MTX, and its interaction with the inhibitor. The energetic results of evaluating such a system are presented in Table 12. For the treatment with both the inhibitor and site portion of the protein movable, the MTX-xtl complex is once again energetically favored over the anti form by ~100 kcal. As above, the torsional and inversion terms contribute significantly to this difference, and the nonbond interations continue to favor the crystallographic form. To extract from such energy differences the amount that is due solely to the energy of the site region of the protein, it is necessary to evaluate the interaction energy of inhibitor with the site, i.e., the energy of the movable MTX in the presence of the fixed site. Such an analysis indicates that the crystallographic conformation is ~10 kcal better stabilized by the enzyme site than is the flipped form. Thus, the energy of the XTL-site region is ~90 kcal more stable than the energy of the flipped-site region. The role of solvent in the energetic differences of these complexes was also examined in Table 13. This table contains the energetic information for the cases with full DHFR-MTX binary complex (as movable atoms) immersed in its aqueous surroundings (fixed atoms). The inclusion of the fixed solvent contributes to the nonbond energy through van der Waals and electrostatic terms. The overall energy difference between the two forms of the inhibitor-bound complex is -199- Table 11. Energetics for full MTX binary simulations: MTX and protein movable. MTX-xtl. Time ETot Eb E, E.,, E.., EvdW Ee1 NBs 0.5 -1808. 70 189.56 485.49 468.38 70.20 -768.88 -2253.45 165899 1.0 -1813.22 190.50 492.13 467.09 70.61 -768.56 -2265.00 166400 1.5 -1811.18 195.86 497.38 465.38 74.68 -757.69 -2287.10 166740 2.0 -1830.38 194.93 486.62 469.62 74.89 -747.56 -2308.37 167256 AVG -1815.87 192.71 490.36 467.62 72.60 -760.67 -2278.48 166574 MTX-anti. 0.5 -1713.30 191.22 463.19 507.36 130.73 -773.20 -2232.60 165224 1.0 -1660.72 190.35 490.49 502.82 133.12 -756.72 -2220.77 166469 1.5 -1652.94 195.84 489.04 503.32 134.36 -744.16 -2231.34 167196 2.0 -1656.55 206.16 477.36 501.68 136.64 -746.34 -2232.05 167492 AVG -1670.88 195.89 480.02 503.80 133.71 -755.11 -2229.19 166595 -200- Table 12. Energetics for full MTX binary simulations: MTX and site region movable, remainder of protein ignored. MTX-xtl. Time ETot Eb Es Etf> E"" EvdW Ee1 NBs 0.5 -600.15 97.24 206.53 212.97 31.71 -302.40 -846.21 65257 1.0 -597.37 100.08 209.89 209.77 30.85 -301.52 -846.43 65217 1.5 -597.22 104.12 212.52 196.37 31.48 -297.88 -843.84 65187 2.0 -599.19 100.78 210.88 206.72 33.95 -292.72 -858.79 65378 AVG -598.48 100.56 209.96 206.46 32.00 -298.63 -848.82 65260 MTX-anti. 0.5 -521.21 98.12 199.99 251.65 62.57 -287.49 -846.06 64610 1.0 -495.19 97.39 208.98 252.22 61.20 -285.23 -829.75 65119 1.5 -491.03 97.80 200.53 259.54 67.00 -279.66 -836.25 65136 2.0 -487.82 105.05 202.05 254.45 64.25 -273.30 -841.00 65349 AVG -498.81 99.59 203.06 254.47 63.76 -281.42 -838.27 65054 -201- Table 13. Energetics for full MTX binary simulations: enzyme complex movable, solvent fixed. MTX-xtl. Time ETot Eb E11 Erl> Ew EvdW Ee1 NBs 0.5 -22907.58 189.56 485.49 468.38 70.20 -993.11 -23128.09 363957 1.0 -23208.60 190.50 492.13 467.09 70.61 -978.29 -23450.64 365128 1.5 -23270.86 195.86 497.69 465.38 74.68 -971.03 -23533.44 366201 2.0 -23378.22 194.93 486.11 469.62 74.89 -963.18 -23640.59 366690 AVG -23191.32 192.71 490.36 467.62 72.60 -976.40 -23438.19 365494 MTX-anti. 0.5 -22990.99 191.22 463.19 507.36 130.73 -947.21 -23336.29 364501 1.0 -23159.19 190.35 490.49 502.82 133.12 -926.34 -23549.63 366734 1.5 -23295.09 195.84 489.04 503.32 134.36 -912.65 -23704.99 367858 2.0 -23403.78 206.16 477.36 501.68 136.64 -909. 73 -23815.90 368148 AVG -23212.26 195.89 480.02 503.80 133.71 -923.98 -23601.70 366810 -202- ~20 kcal, favoring the noncrystallographic, flipped form. This difference may be due to the different surface energies for our final shell of solvent ( which could be eliminated by using periodic boundary conditions). Hence, while the solvent will be included in all simulations, the energetic analysis will focus only on the nonsolvent portion of the complexes. The substrate binding pocket of DHFR is able to accommodate either the xtl or the anti conformation of the pteridine ring, as illustrated in Figures 12 through 14. After simulated relaxation and equilibration, a comparison of the binding of the MTX-xtl and MTX-anti forms, shown in Figure 14, indicates that: ( a) the pteridine rings, initially coplanar, have adopted orientations that result in a relative twist of~ 45°; (b) the phenyl rings, which occupied identical positions at the start of the simulations, have rotated and now exhibit a twist of ~ 30°; and (c) the glutamate fragments maintained their structural agreement. The amino acid residues in the active site adjust their positions to accommodate the two forms of inhibitor complexation. The conformation of the Phe-31 side chain in the MTX-anti structure is rotated ~ 40°, relative to its location in the MTX-xtl system, requiring the Cc51 center of Ile-94 to be displaced by ~1.5A. The structural reorganization associated with the other active site side chains is typically lA, or less. The carboxylate group of Asp-27 is capable of salt-bridging to the MTX-xtl pteridine ring at the Nl and NA2 positions, with oxygen-tonitrogen separations of ~3.0A, as illustrated in Figure 12. This electrostatically favorable interaction is disrupted in the MTX-anti binding conformation (see Figure 13). The energetic examination of the DHFR inhibitor species in the manner described above illustrates another interesting possibility. The energetic data for the movable MTX in a fixed protein "solvent" are remarkably similar for the two -203- Figure 12. The equilibrated DHFR active site region with MTX (red) bound in the xtl form. Phe-31 is visible to the right of the inhibitor's phenyl ring, Leu-54 appears above the pteridine ring, and Asp-27 is shown salt-bridged to the pteridine ring at the far right of the photo. Figure 13. The equilibrated DHFR active site region with MTX (green) bound in the anti form. Phe-31 is visible behind the inhibitor's phenyl ring, Leu-54 appears above the pteridine ring, and the salt-bridge involving Asp-27 is no longer present. -204- Figure 12. Figure 13. -205- Figure 14. The MTX xtl and anti equilibrated active sites depicting the different conformations adopted by the pteridine and benzyl groups. - 206- Figure 14. -207- situations considered, i.e., the full protein structure and just the site residues (see Tables 11 and 12). This agreement in the two energy profiles offers support for the concept of simulating these biochemical complexes with the active site movable and the remainder of the protein fixed. This approach to the calculations is advantageous in that it decreases the computational time by more than a factor of two. A series of computations were designed to further investigate the possibility of using site-region simulations for subsequent studies. The results are presented in the next section. 5.3 Site Region Studies The substrate active site region of the E. coli DHFR was identified, based upon the position of the bound MTX inhibitor in the crystal structure. Work by Labanowski and coworkers 28 indicated that residues farther than 8 A from the bound substrate did not contribute significantly to the nonbond energy terms. Hence, the substrate active site was defined to be those residues containing any atom within 8 A of the bound MTX in either the crystal or the flipped forms. This definition resulted in an active site containing 72 amino acid residues, as listed in Table 14. The solvent molecules within 8 A of the bound MTX and site protein were identified as site-solvent. Site simulations were run for both the crystallographic and the flipped forms of bound MTX. For the molecular simulation energy expressions, bound inhibitor, site protein, and site solvent were defined to be movable, while the remainder of the enzyme and surrounding solvent were held fixed. The structure equilibration steps were identical to those for the full protein complex. The results from these site simulations were then compared with the corresponding runs where the entire enzyme complex was relaxed. The analysis consisted of structural integrity as -208- Table 14. Those DHFR amino acid residues within 8 A of bound MTX. Ser-3, Leu-4, Ile-5, Ala-6, Ala-7, Leu-8, Ala-9, Val-10 Ile-14, Gly-15 Asn-18, Ala-19, Met-20, Pro-21, Trp-22, Asn-23, Leu-24, Pro-25, Ala26, Asp-27, Leu-28, Ala-29, Trp-30, Phe-31, Lys-32, Arg-33, Asn-34, Thr-35, Leu-36, Asp-37 Val-40, Ile-41, Met-42, Gly-43, Arg-44, His-45, Thr-46, Trp-47, Glu-48, Ser-49, Ile-50, Gly-51, Arg-52, Pro-53, Leu-54, Pro-55, Gly-56, Arg-57, Lys-58, Asn-59 Met-92, Val-93, Ile-94, Gly-95, Gly-96, Gly-97, Arg-98 Tyr-100, Glu-101 Leu-110, Tyr-111, Leu-112, Thr-113, His-114, Ile-115, Asp-116 Phe-125 Tyr-151, Cys-152, Phe-153, Lys-154, Ile-155 -209- well as energetic comparisons. The results from the structural analysis of the site simulations and comparisons with those structures form the full enzyme calculations are given in Tables 15 through 24. The RMS studies of the site simulations heavy and main chain atoms (comparing only those in the active site region), given in Tables 15 and 16, are quite similar to the results obtained for both the entire protein complex (given in Tables 7 and 8) and the site region only (see Tables 17 and 18) of the fully relaxed systems. Thus, the active site, as a whole, is not grossly perturbed in structure when performing simulations that use boundary conditions of the nonsite portion of the enzyme. The possibility remained, however, that the amino acids adjacent to the fixed regions of the structure, referred to as site termini, might be distorted. To determine if this was the case, RMS structural comparisons were made of just the termini residues. The results, itemized in Tables 19 through 22, indicate that the positions of the site terminal amino acids were comparable to those of the full site region and the full protein. The forces on the atoms in the termini residues were also examined (see Table 23). When the remainder of the protein was ignored for the force evaluation, the values calculated from the structures produced from the site simulations agreed quite well with those forces acting on the same atoms in the files from the full protein relaxation. Similar agreement between site and full simulations was found when the nontermini amino acids of the protein were held fixed for the force analysis. Direct comparisons of the corresponding active site structures from the site and full simulations are given in Table 24. These RMS values indicate that: (a) there is good overall agreement in the structure of the active site region when just the active site is allowed to relax, and (b) the terminal residues are not distorted -210- Table 15. RMS deviations (heavy atoms only) of theoretical and experimental site structures for site MTX/DHFR simulations. Dynamics XTL 0.5 1.0 1.5 XTL 0.00 0.5Dyn 0.76 0.00 1.0Dyn 0.86 0.49 0.00 1.5Dyn 0.92 0.57 0.45 0.00 2.0Dyn 0.92 0.58 0.51 0.37 0.5Min 0.74 0.23 1.0Min 0.84 1.5Min 0.90 2.0Min 0.92 Minimized 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.19 0.19 0.20 0.40 0.00 0.49 0.34 0.00 0.54 0.40 0.24 0.00 Table 16. RMS deviations (backbone atoms only) of theoretical and experimental site structures for site MTX/DHFR simulations. Minimized Dynamics XTL 0.5 1.0 1.5 XTL 0.00 0.5Dyn 0.58 0.00 1.0Dyn 0.69 0.35 0.00 1.5Dyn 0.75 0.41 0.30 0.00 2.0Dyn 0.76 0.44 0.33 0.25 0.5Min 0.58 0.15 1.0Min 0.68 1.5Min 0.74 2.0Min 0.75 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.14 0.13 0.13 0.31 0.00 0.36 0.25 0.00 0.41 0.29 0.16 0.00 -211- Table 17. RMS deviations (heavy atoms only) of theoretical and experimental site structures for full MTX/DHFR simulations. Dynamics XTL 0.5 1.0 1.5 XTL 0.00 0.5Dyn 0.85 0.00 1.0Dyn 0.88 0.43 0.00 1.5Dyn 0.85 0.46 0.39 0.00 2.0Dyn 0.88 0.49 0.39 0.38 0.5Min 0.83 0.21 1.0Min 0.85 1.5Min 0.85 2.0Min 0.87 Minimized 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.21 0.19 0.19 0.28 0.00 0.35 0.25 0.00 0.38 0.28 0.23 0.00 Table 18. RMS deviations (backbone atoms only) of theoretical and experimental site structures for full MTX/DHFR simulations. Dynamics XTL 0.5 1.0 1.5 XTL 0.00 0.5Dyn 0.65 0.00 1.0Dyn 0.66 0.30 0.00 1.5Dyn 0.64 0.34 0.24 0.00 2.0Dyn 0.67 0.39 0.29 0.27 0.5Min 0.61 0.14 1.0Min 0.64 1.5Min 0.65 2.0Min 0.67 Minimized 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.13 0.13 0.14 0.22 0.00 0.29 0.20 0.00 0.33 0.24 0.22 0.00 -212- Table 19. RMS deviations (termini heavy atoms only) of theoretical and experimental site MTX/DHFR simulations. Dynamics XTL 0.5 1.0 1.5 XTL 0.00 0.5Dyn 0.59 0.00 1.0Dyn 0.71 0.41 0.00 1.5Dyn 0.74 0.44 0.29 0.00 2.0Dyn 0.72 0.43 0.34 0.26 0.5Min 0.59 0.19 1.0Min 0.71 1.5Min 0.73 2.0Min 0.72 Minimized 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.18 0.15 0.16 0.32 0.00 0.36 0.19 0.00 0.39 0.23 0.15 0.00 Table 20. RMS deviations ( termini backbone atoms only) of theoretical and experimental site MTX/DHFR simulations. Dynamics XTL 0.5 1.0 1.5 XTL 0.00 0.5Dyn 0.46 0.00 1.0Dyn 0.57 0.29 0.00 1.5Dyn 0.58 0.31 0.22 0.00 2.0Dyn 0.58 0.32 0.26 0.16 0.5Min 0.48 0.15 1.0Min 0.57 1.5Min 0.58 2.0Min 0.58 Minimized 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.16 0.10 0.11 0.24 0.00 0.27 0.13 0.00 0.29 0.17 0.10 0.00 -213- Table 21. RMS deviations (termini heavy atoms only) of theoretical and experimental full MTX/DHFR simulations. Dynamics XTL 0.5 1.0 1.5 XTL 0.00 0.5Dyn 0.82 0.00 1.0Dyn 0.81 0.42 0.00 1.5Dyn 0.82 0.45 0.36 0.00 2.0Dyn 0.80 0.51 0.42 0.44 0.5Min 0.81 0.22 1.0Min 0.80 1.5Min 0.81 2.0Min 0.81 Minimized 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.19 0.19 0.21 0.26 0.00 0.31 0.24 0.00 0.38 0.31 0.28 0.00 Table 22. RMS deviations ( termini backbone atoms only) of theoretical and experimental full MTX/DHFR simulations. Minimized Dynamics XTL 0.5 1.0 1.5 XTL 0.00 0.5Dyn 0.63 0.00 1.0Dyn 0.62 0.30 0.00 1.5Dyn 0.58 0.32 0.23 0.00 2.0Dyn 0.63 0.38 0.32 0.33 0.5Min 0.62 0.15 1.0Min 0.61 1.5Min 0.59 2.0Min 0.64 2.0 0.5 1.0 1.5 2.0 0.00 0.00 0.12 0.13 0.13 0.22 0.00 0.23 0.18 0.00 0.32 0.29 0.29 0.00 -214- Table 23. Force acting on atoms of termini residues. Termini of Active Site Site Series with Full Series with Remainder of Protein: Remainder of Protein: Simulation Ignored Fixed Ignored Fixed 0.5Dyn 26.96 29.62 27.86 29.96 1.0Dyn 29.26 32.63 26.69 28.67 1.5Dyn 25.91 28.19 22.81 24.82 2.0Dyn 27.95 30.29 27.21 29.31 0.5Min 12.35 10.04 11.60 9.97 1.0Min 12.49 10.28 11.93 9.80 1.5Min 12.40 10.37 11.65 9.47 2.0Min 11.84 10.04 11.84 9.51 Table 24. RMS deviations from direct comparison of theoretical structures for full abd site MTX/DHFR binary complexes. Site Residues Termini Residues Heavy Main Heavy Main 0.5Dyn 0.98 0.73 0.94 0.68 1.0Dyn 1.06 0.78 0.95 0.69 1.5Dyn 1.06 0.84 0.99 0.67 2.0Dyn 1.11 0.89 0.97 0.71 0.5Min 0.94 0.70 0.89 0.65 1.0Min 1.02 0.77 0.96 0.67 1.5Min 1.05 0.84 0.96 0.67 2.0Min 1.10 0.88 0.97 0.71 Simulation -215- by the presence of the fixed boundary. Thus, limiting the scope of the simulation to just the active site region does not appear to introduce unreasonable structural features at the protein boundary regions. The results of the energetic analysis on simulations of the DHFR-MTX site are given in Tables 25 through 27. The energetic profile of the MTX inhibitor (Table 25) was slightly different from that found simulating the full complex. Overall, the energy of the small molecule was of the same order of magnitude in both cases. In the site studies, the crystallographic form of MTX was ~8 kcal higher in energy than the flipped form of the bound inhibitor. Comparing the site MTX to full MTX energies indicates that: (a) the anti forms are essentially equivalent, and (b) the most significant difference between the two xtl complexes arises from the torsional component to the energy. Thus, it appears that the decrease in flexibility of the protein structure in the site simulations most noticeably affects the torsional degrees of freedom associated with the bound inhibitor. The introduction of the active site protein as "solvent" to the MTX indicates that the crystallographic complex is the more stable one (numerical data in Table 26). The site MTX complex in the crystal conformation is ~7.5 kcal lower in energy than the corresponding flipped structure. Thus, the protein stabilizes the experimentally observed form of the inhibitor ~15 kcal better than it stabilizes the anti form. Hence, the site simulations indicate that the experimentally observed form of the protein inhibitor complex is lower in energy than that form with the flipped pterin ring. This conclusion is in agreement with the results found from the full protein MTX calculational studies and supports using the site simulation strategy in subsequent studies. As a brief side note, the energy of the two conformations is approximately equivalent (within 2 kcals) when the aqueous environment of the active site is -216- Table 25. Energetics for site MTX binary simulations: MTX movable, protein ignored. MTX-xtl. EvdW Ec1 NBs 28.53 E"' 3.17 9.37 -19.62 645 16.44 28.53 2.95 10.76 -20.45 641 8.16 21.96 24.75 3.67 10.54 -20.05 636 49.10 8.16 20.26 27.45 3.51 11.16 -21.83 637 48.34 8.19 19.42 27.32 3.33 10.46 -20.49 640 Time ETot Eb Es E,t, 0.5 49.17 8.69 19.03 1.0 45.99 7.75 1.5 49.09 2.0 AVG MTX-anti. 0.5 38.45 7.28 17.60 22.59 3.77 12.23 -25.02 608 1.0 40.58 6.21 15.20 25.70 3.79 13.60 -23.93 613 1.5 39.43 6.85 14.62 27.76 3.95 11.10 -24.85 608 2.0 41.21 9.19 14.75 26.59 3.46 10.14 -22.93 613 AVG 39.92 7.38 15.54 25.66 3.74 11.77 -24.18 611 -217- Table 26. Energetics for site MTX binary simulations: MTX and site region movable, remainder of protein ignored. MTX-xtl. Time ETot Eb Es Et/> Ew EvdW Ec1 NBs 0.5 -385.52 99.67 281.73 254.64 70.28 -278.68 -813.16 64275 1.0 -400.18 102.54 264.13 273.17 71.34 -276.84 -834.51 64058 1.5 -392.77 103.89 263.16 275.19 72.83 -278.42 -829.43 64734 2.0 -363.33 105.55 276.28 283.72 75.69 -266.88 -837.70 64747 AVG -385.45 102.91 271.33 271.68 72.54 -275.21 -828.70 64454 MTX-anti. 0.5 -385.84 98.02 255.10 272.43 69.21 -261.48 -819.11 64534 1.0 -364.80 94.73 261.31 276.48 69.36 -260.95 -805.73 64270 1.5 -392.19 96.14 260.90 273.90 68.67 -273.58 -811.22 64414 2.0 -368. 72 98.80 245.94 291.69 68.66 -259.85 -813.96 64099 AVG -377.89 96.92 255.81 278.63 68.98 -263.97 -812.51 64329 -218- added to the site complex (Table 27). Thus, as in the full structure simulations, the water solvent modulates the energetic differences between the xtl and the flipped-inhibitor protein complexes. -219- Table 27. Energetics for site MTX binary simulations: MTX and site protein movable, site solvent fixed. MTX-xtl. Time ETot Eb Es E,1, 0.5 -7831.65 99.67 281.73 1.0 -7887.31 102.54 1.5 -7944.78 2.0 AVG EvdW Ee1 NBs 254.64 E"' 70.28 -353.73 -8184.24 148527 264.13 273.17 71.34 -358.17 -8240.32 148464 103.89 263.16 275.19 72.83 -353.14 -8306.72 149359 -8004.96 105.55 276.28 283.72 75.69 -342.90 -8403.30 149359 -7917.18 102.91 271.33 271.68 72.54 -351.99 -8283.65 148927 MTX-anti. 0.5 -7806.45 98.02 255.10 272.43 69.21 -328.39 -8172.82 149147 1.0 -7920.65 94.73 261.31 276.48 69.36 -332.34 -8290.18 148869 1.5 -7964.63 96.14 260.89 273.90 68.69 -341.93 -8322.32 149288 2.0 -7969. 75 98.80 245.94 291.69 68.66 -324.87 -8349.97 148822 AVG -7915.37 96.92 255.81 278.63 68.98 -331.88 -8283.82 148782 -220- 6. Dihydrofolate Simulations Simulations were undertaken on the natural substrate ternary complex of E. coli Dihydrofolate Reductase. Because of the highly reactive nature of the ternary species, detailed experimental structural information on this native system is unavailable. Thus, molecular simulation provides some insights on the DHFR system that are not yet experimentally attainable. This new information includes the role( s) of specific amino acids in: (a) substrate binding, (b) product release, and/or (c) catalytic functionality. Also, the conformational preference of bound substrate, as described above for the methotrexate inhibitor, may be investigated. The purpose of these studies was twofold. First, we sought an atomistic understanding of the role DHFR plays in catalyzing the reduction of dihydrofolate to tetrahydrofolate. This picture includes the way the protein brings the two reacting moieties, i.e., DHF and NADPH, together for catalysis, the orientation of the substrate's pteridine ring, and the positions of key amino acids in the equilibrated active site. Second, these investigations served as controls for subsequent studies on mutant forms of the protein, the results of which are described more fully in Section 7. The simulations required complete ternary E. coli DHFR-DHF-NADPH complexes. These starting structures were obtained by: (a) modifying the E. coli binary crystallographic information to include the N ADPH cofactor; (b) altering the conformation of residues 17 to 22, at the NADPH binding site, to "hug" the cofactor ( as is the case for the analogous amino acids in the L. ca.,ei ternary complex); ( c) generating the bound DHF substrate from the coordinates of the MTX inhibitor; (d) protonating the aspartate residue at position 27; and (e) including additional water and counterions to the solvent. The details of these manipulations are discussed above in Section 4. Thus, the active site region of the protein -221- contained 101 amino acids (as listed in Table 28) and 408 water molecules. Two issues relevant to the simulations were: (a) the orientation of the DHF pteridine ring and (b) the site for protonation of Asp-27. With regard to the substrate conformation, two different forms were studied. These are analogous to those of the MTX discussed in the previous section. For the DHF simulations, the form of DHF structurally equivalent to the crystallographic MTX is referred to as DHF-xtl. This orientation of bound dihydrofolate does not give rise to the reduced tetrahydrofolate product, as discussed in Section 2.2. The other form of DHF, termed DHF-anti, is that conformation with the pteridine ring flipped 180 degrees relative to the DHF-xtl structure. It is this form that isotope studies show to be involved in catalysis. The concern associated with the protonation of Asp-27 focuses on identifying which of the carboxylate oxygens would carry the hydrogen. The issue becomes more complicated when alternate forms of the pteridine ring are involved; e.g., what may be best for the DHF-xtl system may not adequately accommodate the DHF-anti form. Thus, four different protein ternary complexes were simulated. These structures had: ( a) DHF in its xtl or anti form and (b) either Asp-27 OD1 or Asp-27 OD2 protonated. The simulation protocols used for the equilibration and production runs were those described above. The final molecular dynamics calculations were carried out for 10 ps of simulation time. The complexes were refined for structural and energetic analysis at 2 ps intervals. The results from the analyses are presented in Tables 29 to 33. The energetics of the two reactive small molecules, i.e., the DHF and NADPH, indicates that the structures derived from the anti form of DHF are ~10 kcal more stable than those from the DHF-xtl studies (see Table 29). This difference is primarily due to the energy difference between the forms of DHF -222- Table 28. Those DHFR amino acid residues within 8 A of bound DHF and NADPH. Ser-3, Leu-4, Ile-5, Ala-6, Ala-7, Leu-8, Ala-9, Val-10 Arg-12, Val-13, Ile-14, Gly-15, Met-16, Glu-17, Asn-18, Ala-19, Met-20, Pro-21, Trp-22, Asn-23, Leu-24, Pro-25, Ala-26, Asp-27, Leu-28, Ala29, Trp-30, Phe-31, Lys-32, Arg-33, Asn-34, Thr-35, Leu-36, Asp-37 Val-40, Ile-41, Met-42, Gly-43, Arg-44, His-45, Thr-46, Trp-47, Glu-48, Ser-49, Ile-50, Gly-51, Arg-52, Pro-53, Leu-54, Pro-55, Gly-56, Arg-57, Lys-58, Asn-59, Ile-60, Leu-62, Ser-63, Ser-64, Gln-65, Pro-66, Gly-67, Thr-68 Trp-74, Val-75, Lys-76, Ser-77, Val-78, Asp-79, Glu-80, Ala-81 Met-92, Val-93, Ile-94, Gly-95, Gly-96, Gly-97, Arg-98, Val-99, Tyr-100, Glu-101, Gln-102, Phe-103 Leu-110, Tyr-111, Leu-112, Thr-113, His-114, Ile-115, Asp-116 Val-119, Glu-120, Gly-121, Asp-122, Thr-123, His-124, Phe-125 Tyr-151, Cys-152, Phe-153, Lys-154, Ile-155 -223- Table 29. Energetics for wild-type DHFR: DHF and NADPH movable, protein ignored. DHF-anti Conformer; ODl protonated. Time 4.0 6.0 8.0 10.0 ETot 111.33 121.87 121.88 131.87 117.47 Eb 28.79 34.64 28.66 29.47 29.98 AVG 120.88 30.31 2.0 Es Ew 84.47 E"' 60.26 77.16 78.88 80.20 76.38 68.52 72.06 76.77 70.27 10.67 14.03 19.22 20.87 18.47 79.42 69.58 16.65 NBs EvdW 6.98 3.52 5.06 5.26 5.01 Ee1 -79.84 -76.00 -82.00 -80.69 -82.65 1853 1833 1855 1853 5.17 -80.24 1847 1843 DHF-anti Conformer; OD2 protonated. 2.0 4.0 6.0 115.15 130.84 133.29 31.05 36.94 35.12 85.44 93.87 95.67 73.13 73.12 71.22 14.36 12.82 14.82 8.72 8.30 10.42 -97.55 -94.22 -93.97 1863 1857 1857 8.0 37.34 83.15 72.32 13.63 36.85 87.89 69.81 12.69 7.42 7.14 -95.87 10.0 118.01 120.16 -94.22 1851 1861 AVG 123.49 35.46 89.20 71.92 13.66 8.40 -95.17 1858 -85.87 -90.79 -86.03 -90.03 1913 1905 1915 1906 DHF-xtl Conformer; ODl protonated. 2.0 115.54 29.41 4.0 6.0 133.32 137.00 33.63 29.12 8.0 127.12 10.0 AVG 7.72 80.24 84.88 89.37 72.94 83.22 80.53 11.12 14.30 15.73 83.66 80.20 13.87 138.18 31.72 32.93 8.09 8.29 7.72 93.09 84.50 13.00 7.15 -92.48 1906 130.23 31.36 86.25 80.28 13.60 7.79 -89.04 1909 1835 1840 1845 DHF-xtl Conformer; OD2 protonated. 62.83 12.08 9.89 -92.07 71.85 69.99 66.38 13.35 10.47 32.46 97.51 98.28 91.60 96.13 -89.74 -91.03 -90.40 136.75 37.00 94.84 68.87 11.46 11.76 10.88 12.07 13.57 11.94 -87.67 1837 133.20 36.23 95.67 67.98 11.82 11.67 -90.18 1841 2.0 126.68 4.0 6.0 8.0 143.54 129.45 129.60 10.0 AVG 36.43 38.92 36.35 1847 -224- (data given in Table 30), while the NADPH is essentially equivalent in the four cases (see Table 31). The stabilization gained from the two molecules interacting with each other, i.e., difference in energy between the two together and the sum of the individual energies, is greater for the ODl protonation scheme (4.17 kcals anti form and 5.03 kcals xtl form) than for the OD2 structures (2.23 and 3.20 kcals, respectively). With the addition of the active site protein, the energetic differences between the four cases split further (Table 32). The DHF-anti orientation with ODl protonated is 38 kcals lower in energy than the OD2 protonated form. This difference in energy is attributable primarily to the angle components (threebody) of the energy. The DHF-anti ODl system is also more stable than either of the DHF-xtl complexes by at least 15 kcals. Thus, energetically speaking, the ternary DHFR,DHF· NADPH complex favored is the DHF-anti ODl form. As found in the DHFR,MTX simulations, the DHFR active site will equilibrate to accommodate either the anti or xtl conformation of the substrate pteridine ring, as illustrated in Figure 15. After molecular simulation, a comparison of the binding of the D HF-anti and D HF-xtl forms indicates that: (a) the pteridine rings are essentially coplanar, unlike the results from the studies on the MTX binary complexes; (b) the phenyl rings have rotated only slightly and maintain a twist of~ 10°; and (c) the glutamate fragments possess quite similar structures. The difference seen between the two conformations of bound substrate and bound inhibitor, i.e., relative coplanarity or twisting of the pteridine ring systems, are most likely due to the occupation state of the NADPH site. In the DHFR-MTX binary simulations, the cofactor site contains solvent molecules that permit some :flexibility in the orientation of the inhibitor pteridine ring system. The cofactor cavities in the DHFR,DHF ternary studies, on the other hand, hold -225- Table 30. Energetics for wild-type DHFR: DHF movable, all else ignored. DHF-anti Conformer; ODl protonated. Time 2.0 4.0 6.0 8.0 10.0 AVG Eb ETot 31.27 46.07 42.44 56.62 45.45 44.37 5.06 5.75 5.58 5.86 Es 15.56 15.46 13.22 16.94 6.14 5.68 Ecf> 17.78 E,., EvdW 3.18 10.45 9.66 9.65 9.75 Ec1 -20.75 -16.50 -18.36 -16.77 10.19 -18.80 538 552 550 552 545 9.94 -18.24 547 7.24 13.54 24.47 21.68 28.70 24.02 10.67 12.13 10.37 14.94 23.33 8.72 NBs DHF-anti Conformer; OD2 protonated. 2.0 4.0 6.0 8.0 38.68 7.01 37.72 38.93 38.33 10.0 AVG 6.04 6.96 16.02 16.43 18.17 24.79 25.22 37.08 7.95 7.30 17.02 19.01 25.44 23.16 38.15 7.05 17.33 24.29 22.86 5.91 5.78 7.07 9.21 -24.25 542 5.80 8.07 8.28 7.20 540 547 544 4.87 6.87 -23.82 -24.41 -25.08 -24.12 5.89 7.93 -24.34 544 547 DHF-xtl Conformer; ODl protonated. 2.0 4.0 6.0 8.0 10.0 47.67 51.18 46.56 48.37 5.84 7.12 5.78 6.93 14.83 15.95 15.49 17.34 25.81 30.47 26.13 28.07 4.61 6.43 5.01 6.07 7.75 8.89 9.01 8.07 -11.16 -17.67 -14.87 -18.11 53.02 7.68 21.17 29.93 5.05 7.33 -18.13 561 562 565 561 560 AVG 49.36 6.67 16.96 28.08 5.43 8.21 -15.99 562 DHF-xtl Conformer; OD2 protonated. 2.0 49.56 10.31 4.0 6.0 8.0 10.0 55.50 53.91 51.91 49.36 7.85 7.51 6.99 6.75 AVG 52.05 7.88 14.78 12.57 11.86 12.86 20.24 29.47 29.87 26.37 6.42 6.12 4.33 4.90 13.18 13.60 15.27 15.58 -15.36 -14.11 -14.94 -14.79 551 566 566 566 10.96 26.42 4.36 14.99 564 12.61 26.47 5.23 14.52 -14.11 -14.66 563 -226- Table 31. Energetics for wild-type DHFR: NADPH movable, all else ignored. DHF-anti Conformer; ODl protonated. Time 2.0 4.0 6.0 8.0 10.0 AVG ETot Eb Es E,p Ew EvdW Ee1 82.32 80.27 23.73 68.91 61.70 42.48 44.05 7.48 6.79 -2.52 -3.65 -57.77 65.66 63.25 8.56 8.74 8.10 -2.25 -2.04 -2.48 -61.45 -61.72 -61.62 7.93 -2.59 -60.02 83.98 79.89 28.88 23.08 23.60 76.94 23.84 62.85 50.38 48.07 46.25 80.68 24.63 64.47 46.25 -57.52 NBs 807 806 813 813 810 810 DHF-anti Conformer; 0D2 protonated. 2.0 4.0 6.0 8.0 10.0 AVG 79.81 95.67 95.84 81.42 85.10 87.57 24.04 30.90 28.16 29.39 29.56 69.42 77.45 77.50 66.13 68.89 48.35 47.90 48.36 46.88 46.64 8.45 7.04 7.75 7.84 7.82 2.01 2.70 3.65 2.10 2.22 -74.46 -70.31 -69.58 -70.92 -70.03 829 821 28.41 71.88 47.63 7.78 2.54 -71.06 822 820 818 821 DHF-xtl Conformer; ODl protonated. 2.0 4.0 6.0 8.0 10.0 72.42 88.04 94.33 82.77 91.96 23.57 26.51 23.34 24.79 25.25 65.41 68.93 73.88 66.32 71.92 47.12 52.74 54.40 52.12 54.57 6.51 7.87 10.72 7.80 7.95 2.50 2.03 1.96 1.95 2.57 -72.69 -70.05 -69.96 -70.21 -70.30 826 824 822 826 826 AVG 85.90 24.69 69.29 52.19 8.17 2.20 -70.64 825 DHF-xtl Conformer; OD2 protonated. 42.59 5.66 -1.21 -75.06 820 7.23 79.74 83.27 42.38 40.11 40.01 6.14 6.56 -1.42 -1.90 -0.67 -74.01 -74.42 -73.68 823 826 827 30.26 83.88 42.45 7.40 -1.54 -71.99 824 28.35 83.07 41.50 6.60 -1.35 -73.83 824 80.84 90.97 26.12 31.07 82.73 85.72 78.51 80.97 28.84 25.47 10.0 90.45 AVG 84.35 2.0 4.0 6.0 8.0 -227- Table 32. Energetics for wild-type DHFR: DHF, N ADPH, and site movable, all else ignored. DHF-anti Conformer; ODl protonated. Time Es Et/> E.., 394.56 371.11 377.98 381.51 382.17 390.96 401.52 422.27 88.76 97.66 100.84 8.0 10.0 -793.08 Eb 145.88 153.92 148.51 150.98 -834.57 151.39 372.78 404.21 101.00 98.18 AVG -835.87 150.14 379.59 400.23 97.29 2.0 4.0 6.0 ETot -868.50 -854.83 -828.38 NBs EvdW -456.41 -447.77 -437.72 -438.79 Ec1 -1423.46 -1420.72 -1419.49 -438.13 -1422.98 105282 105411 -443.76 -1419.34 105293 -447.06 -442.72 -431.06 -421.25 -1421.04 -1422.65 -1433.73 -1437.35 104872 105031 105287 104854 -433.24 -1430.38 -1429.03 105257 105060 -1410.05 104998 105483 105291 DHF-anti Conformer; OD2 protonated. 2.0 4.0 6.0 -821.22 -796.61 -782.25 156.63 162.99 154.49 410.76 411.83 416.61 382.98 397.34 408.01 96.52 96.60 103.43 8.0 154.84 396.80 10.0 -791.61 -797.64 155.95 405.52 414.54 403.88 100.82 100.62 AVG -797.87 156.98 408.30 401.35 99.60 -435.07 DHF-xtl Conformer; ODl protonated. 2.0 4.0 6.0 -845.92 -811.21 -833.40 155.91 162.83 147.88 402.59 410.53 402.68 381.61 395.44 395.28 95.01 92.79 93.93 -442.77 -430.44 -440.26 -1438.26 -1442.35 -1432.91 106945 106736 106728 8.0 -799.28 152.92 422.61 400.91 95.46 -441.60 -1429.57 107149 10.0 -813.74 149.75 421.25 399.53 92.78 -440.71 -1436.34 106704 AVG -820.71 153.86 411.93 394.55 93.99 -439.16 -1435.89 106852 DHF-xtl Conformer; OD2 protonated. 2.0 -810.77 167.30 413.26 367.30 109.42 -426.27 -1441.77 105359 4.0 6.0 -786.88 -807.75 164.73 166.28 397.55 403.92 399.98 397.33 103.78 100.24 -433.68 -447.39 106131 106504 8.0 10.0 -840.14 -819.40 162.33 397.79 411.05 376.35 94.74 AVG -812.99 366.48 381.49 103.06 102.25 -456.75 -452.48 -1419.23 -1428.12 -1414.61 -1417.33 -443.31 -1424.21 169.82 166.09 404.71 106842 107029 106373 -228- Figure 15. A. The DHF-anti and DHF-xtl equilibrated active site regions, indicating the subtle differences that arise in the catalytic pocket because of the altered conformation of substrate binding. Figure 15. B. The DHF binding site as the NADPH cofactor would see it. The nicotinamide ring of the NADPH, if shown, would be located just in front of the pteridine ring. This view clearly differentiates the two binding orientations of the substrate pteridine ring. -229- Figure 15. A. Figure 15. B. -230- the NADPH molecule and position its nicotinamide ring adjacent to the bound substrate, thus helping to maintain the conformation of the pteridine rings. The amino acid residues in the active site do adjust to accommodate the two binding modes of the substrate; however, the structural displacements are much smaller than those found for the MTX complexes. A structural analysis of the two NADPH cofactor positions shows that: (a) the nicotinamide rings adopt conformations that place the plane of the rings approximately perpendicular to each other; (b) the positions of the nicotinamide ribose rings and the diphosphate fragments are quite similar; and ( c) the adenosine units are slightly skewed. The altered conformations of the nicotinamide rings are most likely due to the change in binding orientation of the pteridine ring, as discussed above. The differences in conformation of the adenosine moieties appear at the solvent interface and hence do not disrupt the structural integrity of amino acids surrounding the bound cofactor. One key structural feature for the DHFR-DHF-NADPH ternary complex is the distance associated with the hydride transfer. NC4 of the cofactor nicotinamide ring holds the hydride prior to catalysis, while C6 of the dihydrofolate's pteridine ring is the sight for deposition. The results of examining this hydride transfer distance in the simulated structures are presented in Table 33. It is indeed the case that this distance is shorter for the substrate that began the simulations in the anti form. With ODl protonated, the wild-type hydride transfer distance is 3.63 A, while the separation increases to 4.42 when OD2 carries the proton. Based upon these studies, the ODl form is clearly favored for hydride transfer. For the xtl form of the substrate, the transfer distances are longer than those corresponding to the anti form (4.46 A for ODl and 5.55 A for OD2). This longer distance is consistent with the observation that only the anti form is -231- Table 33. Wild-type DHFR: hydride transfer distances. DHF-anti OD1 OD2 DHF-xtl ODl OD2 2.0 3.79 4.69 4.43 5.17 4.0 3.62 4.39 6.0 8.0 3.55 3.63 4.39 4.29 4.33 10.0 3.58 4.42 4.52 4.47 4.49 5.73 5.75 5.67 AVG 3.63 4.42 4.46 5.42 5.55 -232- catalytic. Both the energetic and distance analyses indicate that it is the 0D1 protonated DHF-anti ternary complex that is the reactive form for wild-type DHFR. These studies indicate that a distance of 3.6A separation of reaction centers in the equilibrated complex can lead to reactivity, whereas 4.4 A does not. -233- 7. Single-Site Mutations Two amino acid sites in the active site o{ Dihydrofolate Reductase were targeted for investigation by both experimental and theoretical site-directed mutagenesis. Both residues represent highly conserved amino acids when examining various sources of Dihydrofolate Reductase. The first is a phenylalanine located in the center o{ the pteridine-ring binding site, Phe-31 (E. coli numbering scheme; see Figure 3). The modification made and studied was that o{ a tyrosine mutant, i.e., the addition o{ a hydroxyl group. The second site for alteration is that o{ leucine at position 54, forming part o{ the benz-glutamate portion of the substrate cavity. This mutagenesis work involved both the deletion of the alkyl side chain, i.e., Leu-+Gly, and the re-positioning of a methyl substituent, i.e., Leu-+Ile. The Replace facility within BIOGRAF was used to make the mutations to the solvated wild-type protein ternary complex. In all cases, the new side chain was positioned to overlap, as best as possible, with the location of the native side chain. Details of generating the starting structure files are given above. The results of studying these single-site modifications are discussed below. 7.1 Phe-31-+Tyr-31 The Phe-31-+Tyr-31 mutation involves the addition of a hydroxyl substituent to the aromatic ring of residue 31. This modification introduces a hydrophilic moiety to the pteridine and benzyl binding regions of the active site, thus disturbing the hydrophobic nature of the catalytic pocket. The simulated equilibration, production runs, and structural refinements were handled in the same fashion as those of the wild-type complexes. The results are presented in Tables 34 to 38. -234- Table 34. Energetics for Tyr-31 mutant DHFR: DHF and NADPH movable, protein ignored. DHF-anti Conformer; OD1 protonated. Time E, 1.0 ETot 121.60 Eb 32.69 99.06 2.0 3.0 4.0 133.70 121.54 121.77 36.41 34.66 36.93 98.52 100.24 98.82 AVG 124.65 35.17 99.16 Eit> 57.93 61.09 55.42 54.08 57.13 Ew 12.50 9.45 9.77 8.19 EvdW 9.98 NBs 3.96 3.68 5.52 Ee1 -88.21 -75.73 -82.22 -81.78 1819 1819 1820 5.20 -81.99 1819 1877 1883 1867 1867 1874 7.64 1817 DHF-anti Conformer; OD2 protonated. 1.0 2.0 109.73 120.09 25.32 29.26 3.0 4.0 122.64 117.76 AVG 117.56 82.26 81.92 13.31 13.72 8.93 10.72 25.38 26.06 77.45 88.01 82.59 82.20 92.51 91.21 11.93 10.41 10.55 10.90 -97.54 -103.53 -100.32 -103.03 26.51 82.56 86.98 12.34 10.28 -101.11 Table 35. Energetics for Tyr-31 mutant DHFR: DHF movable, all else ignored. DHF-anti Conformer; OD1 protonated. Time 1.0 2.0 ETot 36.89 3.0 4.0 43.15 35.31 36.16 AVG 37.88 Eb 5.82 7.05 E,, E-,, 15.74 14.20 21.47 25.26 Ew 5.56 3.93 5.71 5.96 11.13 11.62 20.32 19.58 4.40 3.02 7.93 8.58 8.77 10.94 6.14 13.17 21.66 4.23 9.06 EvdW Ee1 -19.63 -15.88 NBs -15.02 -14.95 548 547 544 545 -16.37 546 DHF-anti Conformer; OD2 protonated. 19.30 18.45 14.81 12.24 25.86 30.79 36.74 37.42 5.73 8.21 5.69 3.90 11.32 9.74 11.55 11.24 -29.55 -29.13 -28.59 -30.03 556 39.10 4.23 5.22 4.59 4.33 41.02 4.59 16.20 32.70 5.88 10.96 -29.33 551 1.0 2.0 3.0 36.89 43.29 44.79 4.0 AVG 552 547 547 -235- Table 36. Energetics for Tyr-31 mutant DHFR: NADPH movable, all else ignored. DHF-anti Conformer; ODl protonated. Time 1.0 ETot 89.78 Eb 26.88 2.0 3.0 4.0 95.88 89.80 89.01 29.36 28.95 30.97 AVG 91.12 29.04 Es E,t, 83.32 84.32 36.46 NBs -2.03 -2.52 Ec1 -66.80 -57.93 -66.70 -66.32 -0.70 -64.44 813 EvdW 2.98 -1.22 89.11 87.20 35.84 35.10 34.51 E"' 6.93 5.52 5.38 5.17 85.99 35.48 5.75 810 810 817 813 DHF-anti Conformer; OD2 protonated. 1.0 2.0 3.0 4.0 76.92 81.97 82.74 21.09 24.04 83.67 20.79 21.73 AVG 81.33 21.91 58.15 69.55 67.78 56.41 51.13 1.03 5.03 -67.33 -73.29 69.96 55.77 53.79 7.58 5.51 6.23 6.51 2.75 3.57 -70.59 -71.89 820 827 825 826 66.36 54.28 6.46 3.10 -70. 78 825 Table 37. Energetics for Tyr-31 mutant DHFR: DHF, NADPH, and site movable, all else ignored. DHF-anti Conformer; ODl protonated. Time ETot 1.0 2.0 Es E,t, -790.98 -779.02 Eb 148.11 147.84 415.67 414.62 3.0 4.0 -800.61 -805.21 147.50 150.20 422.58 420.58 391.75 415.11 403.47 396.98 E"' 103.52 97.68 100.70 96.48 AVG -793.96 148.41 418.36 401.83 99.60 NBs -441.70 -442.23 Ec1 -1420.52 -1419.20 -1433.15 -1427.21 -437.13 -1425.02 104937 -455.98 -445.18 -445.34 -442.68 -1408.75 -1401.25 -1403.83 -1399.13 -447.30 -1403.24 106555 106740 106484 106700 106620 EvdW -429.52 -435.07 104693 104742 105498 104814 DHF-anti Conformer; OD2 protonated. 1.0 2.0 3.0 4.0 AVG -803.25 -773.14 -767.28 -750.78 -773.61 143.10 144.29 146.40 144.91 144.68 401.07 392.60 396.28 393.75 395.93 422.53 441.86 442.28 453.65 440.08 94.77 94.53 96.94 98.72 96.24 -236- The energies of the Tyr-31 DHF•NADPH complex are of the same magnitude as those of the wild-type protein. However, the OD2 protonated complex is ~7 kcals lower in energy than the corresponding ODl complex. Most of this difference in stability is due to the effect the mutation has on the energy of the bound NADPH cofactor (see Tables 31 and 36). The inclusion of the active site protein in the energetic analysis (results given in Table 37) indicate that the ODl protonated state is energetically favored by ~20 kcal. This preference parallels that found for the wild-type ternary complexes. The energy gap between the preferred ODl complex and the higher energy OD2 complex has dropped by ~50%. In the wild-type enzyme, the difference between the two DHF-anti structures was ~40 kcals, but in the Tyr-31 mutant the ODl form is now stabilized by ~20 kcal. The Tyr-31 mutant's incorporation of a hydroxyl group into the hydrophobic portion of the substrate pocket alters the structural character of the active site and introduces change in the binding orientation of DHF. The hydroxyl group disturbs the active site side chain packing, causing the aromatic ring to swing out toward the bound DHF. This structural change: (a) allows the hydroxyl group to hydrogen-bond to the carbonyl oxygen of Ile-94; (b) forces the side chain of Leu28 to adjust its equilibrium position; and (c) ultimately alters the conformation of bound DHF. Figure 16 illustrates the changes to substrate and active site side chain orientations produced by the Phe-31-+Tyr-31 mutation. A comparison of the active site surfaces mapped out by the wild-type and the Tyr-31 DHFR is shown in Figure 17. The change that is due to the "swinging" of the tyrosine's aromatic ring is apparent in the 3 o'clock position (with respect to the pteridine rings), while the adjustment to Leu-28's alkyl side chain is discernable in the 1-2 o'clock position. -237- Figure 16. Wire-frame comparison of the relaxed wild-type (red DHF and NADPH, yellow protein) and Tyr-31 mutant (light blue) DHFR ternary complexes. The hydroxyl group of Tyr-31 introduces a change in the binding orientation of the pteridine and benz-glutamate portions of the substate. Figure 17. The solvent surface comparison of wild-type (red DHF, NADPH, and Phe-31, orange site surface) and Tyr-31 mutant (light blue DHF, NADPH, Tyr-31, blue site surface) DHFR ternary complexes. The change that is due to Tyr-31 is visible to the immediate left of position 31, while the difference produced by Leu-28 is shown northeast of the pteridine ring. -238- Figure 16. Figure 17. -239- The hydride transfer distances for the simulated Tyr-31 DHF-anti ternary structures are given in Table 38. The NC4 to C6 distances differ by 1.0 A for the two states, with the OD2 form having the shorter hydride transfer distance of ~4.0 A. Thus, the energetically favored Tyr-31 DHF ternary complex leads to a NC4-C6 distance that is ~0.4A longer than for wild-type, leading to a slower rate for hydride transer. Experimentally, the Tyr-31 mutant protein has a kinetic profile different from that of the wild-type enzyme. 12 The product off-rate has increased, relative to the wild-type protein; fifty-fold and hydride transfer is now the rate-limiting step in the steady-state cycle. This change in the catalytic profile may be explained by two of the simulation results. First, the increase in product off-rate could be attained by the dissimilarity observed in the substrate binding. Presumably, this change in preferred DHF conformation between the wild-type and Tyr-31 proteins would carry over to a change in the orientation of bound product, thus leading to the measured increase in THF off-rate. Secondly, the slight increase in hydride transfer distance between the Tyr-31 and native forms of DHFR, ~4.0 vs. ~3.6 A, respectively, should have an effect on the rate for the transfer process, as experimentally observed. 7 .2 Leu-54--+Ile-54 The Leu-54--+Ile-54 mutation involves repositioning of one methyl substituent on the amino acid alkyl side chain. This rearrangement should alter the character of the pteridine binding pocket but not produce any void space requiring the inclusion of additional solvent molecules. The simulated equilibration, production runs, and structural refinements were done as described for the wild-type complexes and the results presented in Tables 39 to 43. -240- Table 38. Tyr-31 Mutant DHFR: hydride transfer distances. DHF-anti OD1 OD2 3.0 4.86 4.89 5.09 4.02 3.84 4.06 4.0 5.03 3.97 AVG 4.97 3.97 1.0 2.0 -241- The energetics of the DHF-NADPH complex indicate that the DHF-anti, OD1 system has the lowest energy (Table 39). The energy of the pair from this Ile-54 state is ~20 kcal lower than the analogous, reactive pair from the wildtype simulations. This decrease is due to an overall lower energy for the DHF in the Ile system (see Table 40). From these DHF-anti, ODl calculations, DHF's energy is ~23 kcals while the substrate's energy in the native ternary complex is ~44 kcals, a difference on the order of 20 kcals. The energy of NADPH from both forms of the enzyme, with the OD1 protonation and anti form of DHF, is comparable. The energetics for the DHF•NADPH pair from the DHF-anti, OD2 and DHF-xtl, ODl is ~7-8 kcals higher, while this energy from the DHF-xtl, OD2 complex has dropped by more than 20 kcals for the isoleucine at position 54, relative to the wild-type protein. These differences are due to changes in the individual energies for both the DHF and the NADPH (Tables 40 and 41). The addition of the active site protein to the energetic analysis indicates that, overall, the effect of moving the methyl group stabilizes the DHF-xtl forms of the ternary complex (Table 42). The active site energies for both of the DHFanti protonation states agree within ~2 kcals when comparing the Ile-54 with the Leu-54 enzyme. For the DHF-xtl conformations, the situation is quite different. This mutation has stabilized both protonation states, with respect to the wildtype DHFR, by more than 20 kcals. Thus, the relative population of states would be shifted toward the DHF-xtl form for this mutant protein and could alter the steady-state catalytic profile. The structural modifications at the active site, because of the repositioning of the Leu-54 -y-carbon, are illustrated by Figures 18 and 19. The conformation of Phe-31 's aromatic ring has twisted to accommodate the isoleucine side chain, introducing a change in the binding mode of the pteridine ring. Similarly, the -242- Table 39. Energetics for Ile-54 mutant DHFR: DHF and NADPH movable, protein ignored. DHF-anti Conformer; OD1 protonated. Time 2.0 4.0 6.0 ETot 99.43 Eb 31.84 Es 94.64 E<t> 56.67 34.65 30.89 10.0 108.73 30.74 35.87 93.04 88.77 87.94 58.05 55.74 8.0 96.06 88.27 97.76 AVG 98.05 32.80 92.21 56.35 59.78 91.32 57.32 E.., EvdW 10.77 6.71 9.52 9.38 8.79 6.90 6.61 8.26 9.11 9.51 Ec1 -101.21 NBs 1876 -106.09 -103.12 1888 1887 1884 9.67 -94.31 -97.91 7.63 -100.53 1885 -91.60 -99.91 -95.99 -98.15 -99.45 1904 -97.02 1902 -81.28 -80.98 -78.77 -78.55 1814 1804 1805 -77.58 1803 -79.43 1804 1891 DHF-anti Conformer; OD2 protonated. 2.0 4.0 6.0 8.0 10.0 126.45 125.27 135.81 141.14 127.59 36.06 34.82 38.12 40.75 38.23 96.40 103.15 101.08 106.93 95.18 65.86 65.89 71.44 69.61 73.21 11.28 14.26 12.18 14.22 12.72 8.45 7.05 8.99 7.78 7.70 AVG 131.25 37.60 100.55 69.20 12.93 7.99 1896 1904 1900 1905 DHF-xtl Conformer; OD1 protonated. 2.0 4.0 6.0 139.69 127.80 147.90 33.09 32.05 33.95 91.79 89.43 96.90 70.73 64.73 70.96 16.93 13.10 13.57 8.43 9.47 11.30 8.0 137.36 35.29 90.94 66.46 12.74 10.0 132.80 33.54 90.14 63.79 12.88 10.46 10.02 AVG 137.11 33.58 91.84 67.33 13.84 9.94 1796 DHF-xtl Conformer; OD2 protonated. 2.0 92.23 85.49 61.46 62.35 63.04 13.49 11.63 16.14 10.77 14.85 11.38 -88.86 -89.94 -96.57 1827 1827 1847 92.28 85.46 61.87 60.19 13.94 13.91 15.59 12.23 -95.15 1845 98.41 25.72 24.42 -97.79 1865 110.40 26.21 89.29 61.78 13.82 12.96 -93.66 1842 28.62 26.53 25.75 90.98 4.0 6.0 116.46 117.66 105.23 8.0 114.23 10.0 AVG -243- Table 40. Energetics for Ile-54 mutant DHFR: DHF movable, all else ignored. DHF-anti Conformer; OD! protonated. Time ETot Eb Es Eq, Ew EvdW Ee1 NBs 2.0 4.0 22.82 25.26 5.21 6.04 16.91 20.57 14.95 15.65 3.91 3.50 6.0 8.0 10.0 22.03 20.34 25.73 23.24 5.45 4.89 6.45 18.90 18.11 18.66 14.46 13.48 16.32 3.78 2.82 3.25 10.23 10.41 10.20 9.68 11.35 531 535 535 538 536 5.61 18.63 14.97 3.45 10.37 -28.38 -30.91 -30.75 -28.63 -30.30 -29.79 AVG 535 DHF-anti Conformer; OD2 protonated. 2.0 4.0 6.0 8.0 10.0 AVG 34.32 35.65 38.95 8.55 6.75 16.59 34.92 34.24 7.14 7.03 7.50 15.75 15.82 15.30 14.69 35.62 7.39 15.63 18.44 23.05 22.59 2.63 5.27 10.36 9.73 -22.25 -24.90 561 557 21.10 21.30 4.68 5.28 4.56 11.58 10.37 10.77 -22.86 -24.17 -24.59 564 563 561 21.30 4.48 10.56 -23.75 561 DHF-xtl Conformer; ODl protonated. 2.0 67.54 10.55 10.96 34.81 10.96 10.77 -10.50 575 4.0 62.17 9.02 12.59 29.97 8.02 11.61 -9.05 574 6.0 8.0 10.0 74.15 66.35 9.54 10.99 36.76 31.59 7.77 7.04 10.99 29.55 7.08 14.25 12.88 12.58 -7.92 -7.06 66.33 13.75 10.91 12.44 -6.31 570 570 573 AVG 67.31 10.22 12.13 32.54 8.17 12.42 -8.17 572 DHF-xtl Conformer; OD2 protonated. 2.0 57.16 9.16 15.07 23.95 8.49 14.64 -14.15 580 4.0 6.0 8.0 10.0 59.65 7.99 13.75 7.68 6.27 5.63 14.71 13.24 14.28 6.21 11.11 8.93 9.15 15.43 12.56 14.76 14.03 -10.86 -16.85 -15.86 -17.26 577 53.56 48.36 45.77 27.13 24.35 21.03 19.95 AVG 52.90 7.35 14.21 23.28 8.78 14.28 -14.99 581 581 583 583 -244- Table 41. Energetics for Ile-54 mutant DHFR: NADPH movable, all else ignored. DHF-anti Conformer; OD1 protonated. Time 2.0 4.0 ETot 81.36 75.84 Eb 26.64 28.60 Es 6.0 8.0 10.0 71.55 82.30 25.44 25.85 77.73 72.47 69.87 69.83 87.92 29.42 AVG 79.79 27.19 Eel> 41.73 42.39 Ew 73.55 41.29 42.88 43.47 6.86 6.02 5.60 5.97 5.86 72.69 42.35 6.06 EvdW 0.78 0.57 0.66 2.53 2.43 1.39 Ee1 -72.38 -74.22 NBs 829 834 -71.31 -64.76 837 834 -66.80 833 -69.89 833 DHF-anti Conformer; OD2 protonated. 2.0 97.88 27.51 79.80 4.0 6.0 96.05 28.07 30.98 87.41 85.26 33.72 10.0 112.24 99.60 30.73 91.63 80.49 AVG 101.70 30.20 84.92 8.0 102.73 47.42 42.84 48.85 48.51 8.66 8.99 7.50 51.90 8.94 8.16 47.90 8.45 1.55 0.70 -67.05 -71.96 -70.63 823 824 826 0.62 -71.25 -72.29 821 826 0.87 -70.64 824 -69.41 -71.07 798 795 -1.17 -69.80 -70.44 -70.00 798 793 796 -1.08 -70.14 796 -72.49 -76.92 -77.33 -77.38 -78.03 784 790 0.78 0.69 DHF-xtl Conformer; OD1 protonated. 75.04 22.55 6.0 8.0 67.79 76.26 73.37 23.03 24.41 24.30 10.0 69.12 AVG 72.32 2.0 4.0 80.83 76.83 35.92 5.97 5.08 83.15 80.03 34.75 34.20 34.87 22.55 77.71 34.24 5.80 5.71 5.80 23.37 79.71 34.80 5.67 -0.81 -0.84 -1.48 -1.10 DHF-xtl Conformer; OD2 protonated. 2.0 4.0 6.0 8.0 10.0 AVG 64.05 62.70 57.02 70.37 58.61 62.55 19.45 18.54 18.07 19.45 18.79 18.86 75.92 78.48 70.78 79.03 71.18 37.51 35.23 38.68 40.84 40.24 5.00 5.42 5.03 5.01 4.76 75.08 38.50 5.04 -1.34 1.95 1.79 3.41 1.66 1.49 -76.43 794 792 800 792 -245- Table 42. Energetics for Ile-54 mutant DHFR: DHF, NADPH, and site movable, all else ignored. DHF-anti Conformer; OD1 protonated. Time Es 2.0 ETot -847.82 Eb 155.18 4.0 6.0 8.0 10.0 -845.50 -846.90 -844.77 -804.02 158.56 152.64 151.09 158.75 427.54 424.66 431.54 420.98 417.27 AVG -837.80 155.24 424.40 E.., EvdW 376.14 358.60 355.67 368.25 102.15 98.72 93.38 93.33 91.88 -468.24 -459.16 -464.12 -469.14 -449.95 Ec1 -1444.42 -1444.42 -1418.94 -1396.70 -1390.23 367.72 95.89 -462.12 -1418.94 105729 Erl> 379.96 NBs 105331 105475 105929 106032 105880 DHF-anti Conformer; OD2 protonated. 2.0 4.0 6.0 8.0 10.0 -830.46 -804.21 -771.73 -805.75 -786.64 151.85 152.09 153.14 414.74 406.36 419.00 151.17 157.60 AVG -799.76 153.17 409.01 397.22 358.55 389.72 412.81 402.22 412.36 87.63 97.22 97.46 97.96 95.90 -443.03 -426.48 -432.24 -428.28 -424.39 -1400.19 -1423.12 -1421.89 -1437.81 -1425.34 105660 105377 105768 105748 105572 409.27 395.13 95.23 -430.88 -1421.67 105625 DHF-xtl Conformer; OD1 protonated. 2.0 -859.10 162.46 394.27 369.34 373.46 378.46 93.47 -436.95 -1441.69 105595 4.0 6.0 -877.89 -887.96 158.85 160.15 8.0 10.0 -901.77 162.34 381.03 381.58 375.64 92.89 97.45 -445.01 -435.92 -1439.12 -1469.68 373.09 97.84 -442.54 -1468.14 105840 105796 105588 -902.62 159.69 379.49 370.69 95.42 -446.79 -1461.13 106006 AVG -885.87 160.70 382.40 373.01 95.41 -441.44 -1455.95 105765 103510 103876 103901 104527 104443 104051 DHF-xtl Conformer; OD2 protonated. 2.0 -854.04 152.07 376.90 373.28 92.49 -423.28 -1425.50 4.0 6.0 8.0 10.0 -837.71 -820.33 -815.76 -844.30 151.91 155.61 161.62 158.05 384.96 390.43 392.70 389.71 369.13 374.56 365.00 341.20 89.66 104.61 102.32 96.26 -422.21 -421.19 -419.37 -414.43 -1411.17 -1424.35 -1418.03 -1415.10 AVG -834.43 155.85 386.94 364.63 97.07 -420.10 -1418.83 -246- Figure 18. The equilibrated wild-type DHFR active site region with DHF-anti and NADPH bound (shown in red). Leu-54 (yellow) is shown to the right of the benz-glutamate portion of DHF, while Phe-31 is visible above the pteridine ring. Figure 19.The equilibrated Ile-54 mutant DHFR active site region with DHF- anti and NADPH bound (shown in green). Ile-54 (white) is shown to the right of the benz-glutamate portion of DHF, while Phe-31, slightly twisted relative to its position in the wild-type protein, is visible above the pteridine ring. -247- Figure 18. Figure 19. -248- substrate's benzyl ring position has been slightly twisted. The side chains of Met-42 and Ile-94 modify their positions in response to the mutation. The Ile substitution at position 54 produces changes in the hydride transfer distance between the nicotinamide and pteridine rings. The distance data are listed in Table 43. Both DHF-anti complexes have comparable distances for the Ile series, a carbon-carbon separation of ~3.9 A. This hydride transfer value is a bit longer than the 3.6 A calculated for the native enzyme complexes. The DHF-xtl species, however, have NC4 to C6 separations of ~5.4 A (ODl) and 4.8 A (OD2), values significantly longer than those calculated for the Anti forms. Experimentally, the steady-state kinetic profile for the Ile-54 mutant protein is different from that of the wild-type enzyme. 14 The hydride transfer rate is decreased by a factor of 30 and now competes for the rate-limiting step. This change in the catalytic profile can be understood on the basis of the increase in hydride transfer distance relative to the wild-type protein. As presented above, the transfer distance is ~3.6 A for the native protein while the value for the Ile-54 case is ~3.9 A. This slight change in transfer distance could be significant enough to account for the changes found experimentally. 7.3 Leu-54--+Gly-54 The Leu-54-+Gly-54 mutation involves removal of the leucine alkyl side chain. Such a deletion creates an empty region in the active site of the ternary complex. To fill this void cavity, two additional water molecules were substituted in each of the four starting structure files. The simulated equilibration, production runs, and structural refinements were handled in the same fashion as those of the wild-type complexes. The results are presented in Tables 44 to 48. The energetics of the Gly-54 DHF•NADPH complex is quite different from -249- Table 43. Ile-54 Mutant DHFR: hydride transfer distances. DHF-anti ODl OD2 DHF-xtl ODl OD2 2.0 4.06 3.79 5.36 4.86 4.0 6.0 8.0 3.93 3.87 3.86 3.79 3.87 3.77 5.47 5.05 5.28 5.40 4.74 4.91 10.0 4.03 3.90 5.36 4.31 AVG 3.95 3.82 5.37 4.77 -250- that found in the wild-type protein (Tables 44 and 29, respectively). The set from the DHF-xtl with OD2 protonated complex is the most stable form for the Gly-54 series, in contrast to the DHF-anti ODl set for the native protein. The energies of the DHF-anti OD2 and both DHF conformers with ODl protonated are ~20 kcals higher in the Gly-54 set than they are in the Leu-54 studies. These differences are attributable to the energy changes in the individual molecules (see Tables 45 and 46): ( a) the 15-20 kcal increase in energy of the DHF for both ODl species and (b) the 20 kcal change in NADPH from the DHF-anti OD2 complex. Including the active site protein in the energetic profile maintains the over- all stability of the DHF-xtl OD2 Gly-54 ternary complex (data given in Table 47). This form is ~30 kcal lower in energy than either of the ODl protonated complexes but only 16 kcal different from the DHF-anti OD2 state. Direct energetic comparisons of the Gly-54 series with the native set are not possible within the molecular mechanics framework because the two enzymes are composed of a different number of atoms. The structural changes resulting from the removal of the Leu-54 side chain are illustrated by Figure 20. The conformation of Phe-31 's aromatic ring has twisted to a much greater extent than in the Ile-54 structures, introducing a change in the binding of DHF's pteridine ring. The benzyl ring of the substrate has also been twisted slightly. The conformation of Ile-50's alkyl side chain exhibits the most pronounced change of any active site residue. The side chain re-orients itself, to substitute partially for the absent Leu group, by rotating its c1 carbon into the vacant site. This conformational change results in a ~3.5Achange of position for the 61 carbon of Ile-50! Less dramatic shifts are found for the side chain positions of Met-42 and Ile-94, similar to their changes in the Ile-54 mutant DHFR complexes. -251- Table 44. Energetics for Gly-54 mutant DHFR: DHF and NADPH movable, protein ignored. DHF-anti Conformer; OD1 protonated. Time 2.0 4.0 6.0 8.0 10.0 AVG ETot 131.31 Eb 36.34 136.12 141.32 147.14 37.78 40.42 148.66 45.73 140.91 40.46 42.02 Es Eif> 85.20 83.57 85.67 87.64 87.65 87.12 92.54 87.03 92.14 88.88 88.64 86.85 Ew EvdW 16.03 1.44 3.21 14.25 15.09 15.63 4.61 4.82 14.45 2.30 15.09 3.28 Ee1 -91.27 -92.44 -93.56 -94.92 -94.84 -93.41 NBs 1861 1864 1848 1848 1851 1854 DHF-anti Conformer; OD2 protonated. 2.0 42.58 41.72 46.80 43.78 49.38 109.01 4.0 6.0 8.0 10.0 131.35 133.28 140.02 137.66 155.65 9.70 11.54 11.23 12.18 13.34 5.40 111.08 119.88 118.50 123.88 58.20 62.52 57.30 59.34 63.46 5.88 3.88 4.73 5.57 -93.54 -99.46 -99.07 -100.86 -99.97 AVG 139.59 44.85 116.47 60.16 11.60 5.09 -98.58 1829 1824 1828 1823 1821 1825 DHF-xtl Conformer; OD1 protonated. 2.0 4.0 6.0 8.0 10.0 AVG 158.35 145.71 159.01 39.59 33.43 36.51 33.96 34.08 142.37 148.29 150.75 35.51 98.18 92.61 97.70 88.77 84.66 83.59 87.70 84.52 12.96 12.23 13.95 13.15 9.03 12.96 12.89 10.68 -86.07 -89.11 -89.73 -88.72 92.74 94.00 82.63 84.62 13.90 13.24 13.33 11.78 -88.39 -88.40 1891 1872 1878 1862 1863 1873 DHF-xtl Conformer; OD2 protonated. 2.0 116.77 29.35 91.22 74.88 11.50 6.16 -96.34 1927 4.0 6.0 124.27 113.35 29.90 27.48 84.82 87.99 79.84 68.77 12.16 11.72 8.52 6.26 -90.96 -88.87 1940 1923 8.0 122.97 116.99 84.52 85.44 75.54 69.95 10.05 10.69 8.07 8.01 -88.04 10.0 32.84 29.41 -86.51 1940 1932 AVG 118.87 29.80 86.80 73.80 11.22 7.40 -90.14 1932 -252- Table 45. Energetics for Gly-54 mutant DHFR: DHF movable, all else ignored. DHF-anti Conformer; ODl protonated. Time 2.0 4.0 Eb 8.23 6.57 9.00 9.97 Es Et/> 6.0 8.0 ETot 55.48 55.14 60.17 64.60 17.37 16.50 19.74 18.09 42.93 45.74 45.29 47.50 10.0 62.64 9.41 18.51 48.90 10.22 10.89 10.20 AVG 59.61 8.64 18.04 46.07 10.51 E.., 11.17 10.05 Ee1 -33.94 -33.55 EvdW 9.72 9.84 12.12 11.41 -36.20 -33.26 9.93 10.60 -34.30 -34.25 NBs 529 531 527 524 530 528 DHF-anti Conformer; OD2 protonated. 2.0 31.89 6.14 11.80 28.03 3.51 10.73 -28.33 4.0 7.97 14.33 10.48 -31.61 8.27 3.46 8.0 10.0 35.26 39.33 7.86 7.49 13.91 14.90 14.25 30.96 26.95 28.23 32.11 4.37 6.0 36.50 32.55 535 535 4.53 5.37 9.39 9.35 9.80 -29.42 -29.62 -29.70 5.34 536 535 AVG 35.11 7.55 13.84 29.26 4.25 9.95 -29.74 535 DHF-xtl Conformer; ODl protonated. 2.0 4.0 63.54 6.76 7.95 20.57 20.39 8.03 7.43 -16.32 -13.61 8.07 7.09 11.35 12.43 13.46 12.47 -15.59 -13.15 553 552 555 549 5.79 6.31 22.27 20.76 35.39 37.53 40.20 36.93 6.0 8.0 71.00 76.44 71.52 10.0 70.60 6.77 21.61 35.21 7.51 12.62 -13.12 552 AVG 70.62 7.39 21.12 37.05 6.95 12.47 -14.36 552 -14.99 -12.73 569 DHF-xtl Conformer; OD2 protonated. 8.70 4.0 42.92 53.04 7.35 6.89 13.05 14.10 24.65 30.04 4.16 4.72 6.0 8.0 10.0 46.20 51.39 50.34 6.25 6.09 7.42 14.54 14.36 15.57 23.03 28.73 23.92 4.58 3.72 4.15 10.02 9.96 10.69 10.14 AVG 48.78 6.80 14.32 26.07 4.27 9.90 2.0 -12.16 -12.20 -10.87 -12.59 571 572 566 568 569 -253- Table 46. Energetics for Gly-54 mutant DHFR: NADPH movable, all else ignored. DHF-anti Conformer; ODl protonated. Time 2.0 4.0 6.0 8.0 10.0 AVG Eb 28.11 31.21 ETot 83.05 88.32 87.70 88.73 Es 67.82 92.40 36.32 69.18 67.91 74.46 73.63 88.04 31.82 70.60 31.42 32.05 Erl> 40.64 41.90 41.83 39.53 40.78 39.98 E.., 4.86 4.20 4.87 4.74 4.25 4.58 Ec1 -55.02 -56.43 -54.77 -59.34 -58.25 -56.76 NBs -64.32 -67.41 797 794 -68.49 -70.22 -69.22 791 790 790 -67.93 792 811 4.87 -66.30 -71.79 -71.03 -72.28 -72.26 820 818 818 -70.73 817 0.88 -77.36 3.12 -76.08 0.56 -74.54 1.47 -72.80 1.85 -72.90 1.58 -74.74 824 827 EvdW -3.36 -1.75 -3.55 -2.71 -3.53 -2.98 808 808 805 798 802 804 DHF-anti Conformer; OD2 protonated. 36.44 33.75 97.21 30.16 4.0 103.92 100.80 96.75 6.0 8.0 10.0 112.69 106.93 120.62 38.54 35.92 41.88 AVG 108.99 37.31 2.0 -1.76 31.56 6.19 7.17 105.96 103.60 109.62 30.35 31.11 31.34 7.78 7.65 7.97 102.63 30.90 7.35 -1.44 -1.12 -0.99 -1.27 -1.02 DHF-xtl Conformer; ODl protonated. 2.0 103.00 32.83 77.61 72.22 49.27 46.06 7.17 5.92 4.0 82.76 25.48 6.0 8.0 90.07 78.59 10.0 AVG 2.42 75.43 68.02 71.13 47.50 47.60 47.43 5.88 6.06 84.65 28.48 26.53 27.30 6.39 3.82 2.67 4.66 87.81 28.12 72.88 47.57 6.28 3.69 817 DHF-xtl Conformer; OD2 protonated. 22.00 23.01 78.17 70.72 6.0 8.0 10.0 81.27 78.01 73.58 78.71 73.37 21.23 26.75 21.98 AVG 76.99 22.99 73.46 70.15 69.86 72.47 2.0 4.0 50.23 49.81 45.74 46.81 46.03 47.72 7.34 7.44 7.14 6.32 6.55 6.96 821 828 828 826 -254- Table 47. Energetics for Gly-54 mutant DHFR: DHF, NADPH, and site movable, all else ignored. DHF-anti Conformer; ODl protonated. Time 4.0 6.0 8.0 ETot -819.23 -783.71 -758.90 -724.10 10.0 -785.17 Eb 153.31 154.70 161.02 165.58 165.61 AVG -774.22 160.04 2.0 Es 400.25 410.49 416.63 423.64 416.08 413.42 E<I> 397.15 416.36 423.38 437.29 416.24 418.08 NBs 107.69 -445.56 -433.91 -429.77 -424.10 -433.80 Ee1 -1435.72 -1436.28 -1438.59 -1438.24 -1456.99 108.82 -433.43 -1441.16 104039 E"' 111.34 104.93 108.43 111.72 EvdW 104292 104227 104115 103723 103840 DHF-anti Conformer; OD2 protonated. 2.0 4.0 6.0 -829.44 -796.80 -801.45 166.13 162.25 169.43 433.78 428.75 430.91 403.58 427.24 412.79 95.08 98.88 97.31 -427.78 -437.52 -441.84 -1500.23 -1476.39 -1470.06 104388 104460 104688 8.0 10.0 -759.34 -750.65 168.23 177.13 444.10 449.58 427.41 438.59 -432.68 -437.68 -787.54 168.63 437.52 421.92 -1475.04 -1489.56 -1482.26 104335 104298 AVG 108.65 111.29 102.24 -435.50 104434 DHF-xtl Conformer; ODl protonated. 2.0 4.0 6.0 8.0 10.0 -765.84 -809.59 -779.65 -754.34 -751.83 162.84 155.50 166.95 163.30 429.03 404.00 423.97 437.11 418.07 105.10 98.57 105.05 109.25 107.16 -441.01 -434.41 -433.36 -439.11 -423.86 -1421.34 -1427.63 -1440.53 -1424.06 -1425.83 105414 106194 106484 106530 163.39 399.54 394.39 398.27 399.17 409.23 AVG -772.25 162.40 400.12 422.44 105.03 -434.35 -1427.88 106245 106603 DHF-xtl Conformer; OD2 protonated. 2.0 -819.65 147.37 387.62 434.44 109.67 -442.58 -1456.19 105608 4.0 6.0 8.0 -799.45 -790.73 -799.26 152.12 149.97 155.33 379.37 380.62 372.27 446.69 445.02 446.76 113.45 119.83 114.41 -431.03 -430.32 -435.26 -1460.04 -1455.85 -1452. 76 10.0 -808.51 148.18 374.82 438.92 115.34 -438.54 -1447.23 105627 105492 105.771 105460 AVG -803.52 150.59 378.94 442.37 114.54 -435.55 -1454.41 105592 -255- Figure 20. Equilibrated Gly-54 mutant DHFR active site region with DHF- anti and NADPH bound (shown in blue). Gly-54 (red) is shown to the right of the benz-glutamate portion of DHF, while Phe-31, slightly twisted relative to its position in the wild-type protein, is visible above the pteridine ring. The water molecules substituting for the removed side chain give rise to the "new" surface dots that appear between the residue 54 site and the DHF. Figure 21. A comparison of the substrate and cofactor from the equilibrated ternary complexes used for the Res-54 studies. - 256- Figure 20. Figure 21. -257- The hydride transfer distances for the simulated Gly-54 complexes are given in Table 48. The values for each of the four states are approximately equivalent; i.e., they are within 0.2 A of each other. Thus, for the Gly-54 DHFR enzyme, the calculated ground-state, hydride transfer distance is ~4.4 A. Figure 21 shows a comparison of the equilibrated DHF,N ADPH orientations from simulations of Res-54 mutants. Experimentally, the Gly-54 mutant protein has a kinetic profile different from that of the wild-type enzyme. 9 The rate of hydride transfer from the nicotinamide ring to C6 of the pteridine has dropped enough now to be the rate-limiting step in the steady-state cycle. This change in the catalytic profile may be explained on the basis of the difference in hydride transfer distance between the Gly-54 and native forms of DHFR. As indicated above, the simulated transfer distance in the wild-type protein is ~3.6 A, while the corresponding value for the Gly-54 case is ~4.4 A, an increase of 0.8 A! Clearly, that relatively large increase should have a substantial effect on the rate for the transfer process, as was experimentally observed. Another interesting insight comes from these Gly-54 calculations. For the wild-type protein, theory finds that the low energy and short hydride transfer distance both correspond to a DHF-anti conformation of bound substrate. This is in agreement with the isotope labeling studies, which showed that the reactive DHF does indeed have its pteridine ring in a conformation different from that of MTX when bound to DHFR. For the Gly-54 enzyme, however, simulation suggests that the substrate binds and reacts in a conformation similar to that of MTX. This conformation of DHF would yield THF product with the alternate stereochemistry at C6. Isotope studies on the Gly-54 produced THF will give a definitive indication of the nature of this product and hence will test these -258- Table 48. Gly-54 Mutant DHFR: hydride transfer distances. DHF-anti ODl OD2 DHF-xtl ODl OD2 2.0 4.0 4.47 4.33 4.29 4.28 4.26 4.61 6.0 8.0 4.42 4.53 4.38 4.27 4.43 4.48 4.29 4.25 4.44 4.38 10.0 4.48 4.25 4.67 4.18 AVG 4.45 4.29 4.49 4.31 -259- models of the DHFR ternary complex. The simulated ground-state hydride transfer distances for the mutant DHFR proteins investigated are summarized in Table 49. -260- Table 49. Summary of simulated ground-state hydride transfer distance for DHFR-DHF-NADPH ternary complexes. DHF-anti DHF-xtl ODl OD2 OD! OD2 Wild-type 3.6 4.4 4.5 5.6 Ile-54 4.0 3.8 5.4 4.8 Gly-54 4.5 4.3 4.5 4.3 Tyr-31 5.0 4.0 -261- 8. Segment Mutations The extension of the structure-sequence homology studies to include Chicken DHFR brought to light the possibility of modifying the bacterial enzyme in such a way as to incorporate some of the more typical mammalian properties, i.e., the ability to readily reduce folate (FOL) to 7,8-dihydrofolate. Bacterial forms of Dihydrofolate Reductase catalyze the transformation of FOL to DHF very slowly, while the Chicken enzyme more readily facilitates the reduction. 19 Molecular modeling/ docking studies, discussed in Section 3, suggest that the salient difference between bacterial and mammalian ease of FOL reduction is directly related to the size of the substrate binding pocket. It is possible that this explains the difference in chemistry, because a larger and/ or more flexible catalytic pocket could accommodate the pteridine ring conformation suitable for hydride transfer to the C7 position and thus catalyze the reduction of folate. The docking and comparison studies, discussed in detail in Section 3, illustrated two regions of dissimilarity between the E. coli and Chicken forms of DHFR that were appropriate segments to target for this protein-engineering effort. These sites are illustrated by Figure 22. Both regions involve sequence insertions in segments that are adjacent to the substrate binding pocket, as shown in Figure 23. The first targeted segment mutation incorporates the transformation of the E. coli residues Gly-51 through Asp-59 to the corresponding Chicken loop Pro-61 through Asn-72. In addition to altering the amino acid sequence, this mutation also increases the size of this loop region by three amino acid insertions. The second modification involves substituting the nine amino acid loop Ser-39 to Gln-4 7 from the Chicken for Leu-36 E. coli. The molecular simulations used to investigate these modified proteins focused on the ability of the protein to facilitate folate reduction. To this end, -262- Figure 22. The docked E. coli (yellow protein backbone and red MTX) and Chicken (magenta protein backbone and green NADPH) DHFR crystal complexes depicting the agreement in overall protein fold. Figure 23. The active site region of the docked E. coli and Chicken complexes illustrating the two Chicken-loop regions identified for use in the hybrid mutation studies. -263- -264- simulation strategies were designed to permit insight on the structural and energetic stability of folate ternary complexes. The "assay" used to decide whether the enzymes should accommodate, and hence reduce, folate involves comparing the results from constrained and unconstrained simulation runs. The constraints employed for the calculations hold the substrate (either folate or dihydrofolate) and NADPH in a position suitable for reactivity. The protocols used in these loop hybrid investigations involved: (1) Generation of initial hybrid protein structures based upon the crystallographic structures of the E. coli and Chicken forms of DHFR. The coordinates from the docked Chicken structure were used for the substituted amino acid segments. (2) Completion of the starting structure files by adding substrate (either DHF or FOL), NADPH, and adequate solvent. (3) Incorporation of structural. constraints between the substrate and cofactor appropriate for catalytic reduction, if required by the calculations. (4) Relaxation of the full ternary complex via molecular dynamics simulations. ( 5) Comparison of the structures and energetic profiles from the corresponding constrained and nonconstrained simulations. Because of the nature and extent of the structural reorganization expected for these protein hybrids and folate ternary complexes, extended molecular dynamics simulations are required. Such studies might require a few months of elapsed time. Preliminary simulation runs were undertaken to determine: (a) if the simulation strategies are appropriate and (b) if the full theoretical. component of the project should be undertaken (post-PhD). The calculations were carried out on both loop substitution proteins as well as the native E. coli enzyme. The preliminary simulations, which include ini- -265- tial structure relaxation, and only 2 ps of full production equilibration, indicate subtle structural differences between the constrained and nonconstrained protein ternary complexes, as given in Table 50. The RMS deviations for the wild-type E. coli DHF ternary complexes are ~0.3, with all heavy atoms and only protein backbone atoms. The corresponding deviations for the FOL complexes are ~0.4, slightly higher than the DHF values. This difference may be due to the protein's catalytic properties. Its ability to reduce dihydrofolate requires the accommodation of bound DHF and NADPH in a reactive orientation. This enzyme's difficulty in transforming folate, however, suggests that an unfavorable situation may occur when FOL and NADPH are brought together in a reactive fashion. The difference in RMS deviations for the E. coli DHF and FOL ternary complexes support this hypothesis. The RMS comparisons indicate a decrease in the dissimilarity of the constrained versus nonconstrained complexes for the hybrid proteins. Loop hybrid 1, with its addition of 3 amino acids to the substrate binding pocket, exhibits RMS values for both DHF and FOL ternary complexes, slightly smaller than those of the wild-type protein. This decrease is even more pronounced for loop hybrid 2; the DHF RMS value is more than 0.1 lower, while the FOL deviation has dropped by ~0.2. The incorporation of eight additional residues at the back of the benz-glutamate pocket may be responsible for this improvement in structural integrity. Visual comparisons of ea.ch of the hybrid FOL ternary complexes (including constraints) with the E. coli wild-type FOL ternary complex are shown in Figures 24 and 25. The energetic comparisons from the hybrid protein simulations ( after only 2 ps) were inconclusive. The differences between the energies for the constrained -266- Table 50. RMS deviations of constrained and nonconstrained structures for full DHFR ternary complexes. Heavy Main Wild-type E. coli DHF 0.31 0.32 FOL 0.42 0.36 Hybrid 1 DHF 0.26 0.28 FOL 0.36 0.35 Hybrid 2 DHF 0.19 0.16 FOL 0.23 0.21 -267- Figure 24. Preliminary results from the reactive folate simulations on loop hybrid 1 (shown in blue) and wild-type E. coli (drawn in red). Figure 25. Preliminary results from the reactive folate simulations on loop hybrid 2 (shown in green) and wild-type E. coli (drawn in red). -268- Figure 24. Figure 25. -269- and the nonconstrained complexes were negligible. Additional simulation should allow for a differentiation of the constrained and nonconstrained energetic profiles from the wild-type, loop hybrid 1, and loop hybrid 2 DHF and FOL ternary complexes. Thus, these preliminary molecular dynamics simulations on the modified E. coli• Chicken loop hybrid materials indicate that the increase in substrate binding pocket allows for a higher degree of structural integrity when maintaining a reactive folate ternary complex. A more extensive series of theoretical investigations will be undertaken to further probe the structural and folate-reducing properties of these hybrid enzymes. -270- 9. Summary Investigations of the similarity in sequence, structure, and chemical homology of the E. coli and L. caJei forms of DHFR, using computer graphics with macromolecular docking in conjunction with chemical homology assignments, offer an explanation for the agreement in catalytic reactivity of these bacterial enzymes. The overall sequence homology between the E. coli and L. caJei proteins is ~27%, while the sequence homology for the active site region is ~35%. The chemical homology for the entire catalytic pocket, however, is ~70%! The extension of this structure-sequence study to include Chicken DHFR indicates only ~60% chemical homology with the bacterial forms, thus suggesting subtle differences in the character of the active site cavity. These sequence-structure comparisons between bacterial and Chicken DHFR also identified target sites for engineering E. coli• Chicken hybrid enzymes. The molecular simulations on the native form of E. coli Dihydrofolate Reductase indicate: (a) the energetically favored form of methotrexate's pteridine ring, when bound to the enzyme, is that found in the crystal studies; (b) the active site region will adjust to accommodate the xtl and the anti forms of both MTX and the natural substrate, dihydrofolate; and (c) the anti-DHF (with Asp-27 ODl protonated) ternary complex is the catalytically favored form with hydride transfer distance of ~3.6 A. The computational investigations on single-site mutants reveal structural insights that offer explanations for trends in the experimental kinetic data. Phe31-+ Tyr-31 introduces change in substrate, and presumably product, binding, thus increasing the product off-rate. The removal of the alkyl side chain associated with the Leu-54--+Gly-54 mutation produces a dramatic increase in separation between the nicotinamide and pteridine reaction centers (from ~3.6 A -271- to ~4.3 A), which parallels the mutant protein's increase in hydride transfer rate. Similarly, the repositioning of a methyl group (Leu-54 --+ Ile-54) alters the hydride transfer distance and rate, as summarized in Table 49. Preliminary molecular simulations on the engineered E. coli• Chicken hybrid materials suggest that the increase in the substrate binding pocket, resulting from the loop insertions, allows for a higher degree of structural integrity when maintaining a reactive folate ternary complex. -272- 10. Conclusions The combination of theory and experiment on the mechanistic properties of wild-type and mutant complexes of Dihydrofolate Reductase provides complimentary information that together has led to new insights and understanding not accessible on the basis of either alone. As the predictions on these systems are tested via experimentation, and as the reliability of the predictions increases, these techniques will become true design tools for the development of new biological systems. -273- Notes and References (1.) J.E. Greatly. Adv. Pharm. Chemotherapy 1980, 17, 37. (2.) L. F. Kuyper, B. Roth, D. P. Baccanari, R. Ferone, C.R. Beddell, J. N. Champness, D. K. Stammers, J. G. Dann, F. E. Norrington, D. J. Baker, P. J. Goodford. J. Med. Chem. 1985, 28, 303. (3.) D. A. Matthews, R. A. Alden, J. T. Bolin, D. J. Filman, S. T. Freer, R. Hamlin, W. G. J. Hol, R. L. Kisliuk, E. J. Pastore, L. T. Plante, N.-H. Xuong, J. Kraut. J. Biol. Chem. 1978, 259, 6946. (4.) D. A. Matthews, R. A. Alden, S. T. Freer, N.-H. Xuong, J. Kraut. J. Biol. Chem. 1919, 254, 4144. (5.) J. T. Bolin, D. J. Filman, D. A. Matthews, R. C. Hamlin, J. Kraut. J. Biol. Chem. 1982, 257, 13650. (6.) D. J. Filman, J. T. Bolin, D. A. Matthews, J. Kraut. J. Biol. Chem. 1982, 257, 13663. (7.) D.R. Smith, J.M. Calvo. Nuc. Acida Rea. 1980, 8, 2255. (8.) J.-T. Chen, R. J. Mayer, C. A. Fierke, S. J. Benkovic. J. Cell Biochem. 1985, 29, 73. (9.) R. J. Mayer, J.-T. Chen, K. Taira, C. A. Fierke, S. J. Benkovic. Proc. Natl. Acad. Sci. USA 1986, 83, 7718. (10.) E. E. Howell, J.E. Villafranca, M. S. Warren, S. J. Oatley, J. Kraut. Science 1986, 231, 1123. (11.) C. A. Fierke, K. A. Johnson, S. J. Benkovic. Biochemiatry 1987, 26, 4085. (12.) J. T. Chen, K. Taira, C. D. Tu, S. J. Benkovic. Biochemi&try 1987, 26, 4093. (13.) S. J. Benkovic, C. A. Fierke, A. M. Naylor. Science 1988, 239, 1105. (14.) D. J. Murphy, S. J. Benkovic. Biochemiatry 1989, in press. -274- (15.) S. J. Benkovic, J. A. Adams, C. A. Fierke, A. M. Naylor. PteridineJ 1989, m press. (16.) P. A. Charlton, D. W. Young, B. Birdsall, J. Feeney, G. C. K. Roberts. J. Chem. Soc., Chem. Commun. 1979, 922. (17.) S. R. Stone, J. F. Morrison. BiochemiJtry 1984, 23, 2753. (18.) Coordinates made available from D. A. Matthews in prerelease form. (19.) R. L. Blakely The Biochemidry of Folic Acid and Related PteridineJ, NorthHolland Puhl.: Amsterdam (1969). (20) BIOGRAF is the interactive molecular mechanics/graphics program from Molecular Simulations Inc. (BioDesign) , Pasadena, CA. All simulations were performed on DEC VAX 8650 and Alliant FXB/8 computers, and structures were displayed on Evans & Sutherland PS330 and PS390 series graphics systems. (21.) F. M. Richards. Ann. Rev. Biophya. Bioeng. 1911, 6, 151. (22.) M. L. Connolly. J. Appl. Cry.,t. 1983, 16, 548. (23.) A. M. Naylor, W. A. Goddard III. In Impact of Surface and Interfacial Structure on Enzyme Activity, J. D. Burrington and D. Clark, Eds. (ACS Symposium Series: Washington, DC, 1989) in press. (24.) S. J. Weiner, P.A. Kollman, D. A. Case, U. C. Singh, C. Ghio, G. Alagona, S. Profeta, Jr., P. Weiner. J. Am. Chem. Soc. 1984, 106, 765. (25.) L. Cocco, C. Temple, Jr., J. A. Montgomery, R. E. London, R. L. Blakley. Biochem. Biophya. Rea. Commun. 1981, 100, 413. (26.) W. L. Jorgenson. J. Amer. Chem. Soc. 1981, 103, 335. (27.) L. X. Dang, B. M. Pettitt. J. Phya. Chem. 1987, 91, 3349. (28.) J. Labanowski, I. Motoc, C. B. Naylor, D. Mayer, R. A. Dammkoehler. Quant. Struct.-Act. Relat. 1986, 5, 138. -275- Appendix I A variety of force-field methods have evolved in the last few years. 1 - 7 Their differences are based on the potential functions and parameter sets used for the calculations. Typically, the energy function is based upon the separation of internal coordinate and nonbond interaction terms. We will focus our discussion on the specific functions used in the AMBER force-field 2 , 3 • The total energy for the system, Etot, is given by: (AI - 1) where Eb, E9, Eq, and E"' are those contributions that are due to covalent terms and that correspond to bonds, angles, torsions, and inversions, respectively. The non-bond components of the energy are due to van der Waals, electrostatic, and hydrogen-bond interactions; these are represented in Equation ( AI-1) by EvdW, Ee1, and EHb, respectively. For many systems, it is reasonable to consider the molecule as a set of masses held together by springs. Hooke's Law may then be used to calculate the energy contribution involved with bond and angle distortions from their natural values (Eb and Ee, respectively): (AI - 2) (AI - 3) where N and M are the total number of bonds and bond angles, respectively, in the molecule. The kbs and k 9 s are the force constants determined empirically, -276the ri and Bij are the actual bond lengths and angles, and rf and 8~ are the natural bond lengths and angles for the unconstrained system. Rotational barriers must be built into the force field: (AI - 4) m This Fourier series describes the change in energy associated with change in torsion angle <p. The force constant, km¢, may be negative for a component, indicating a preference for the trans conformation of a group of substituents. The n's account for different rotational periodicities. Umbrella forces (inversions), E"', are incorporated to describe the nonplanar or planar arrangement of trigonally bonded atoms: 0 E"' = L ki.,(wi - wf )2. (AI - 5) i=l This supplement to the torsional potential provides a better description near the minimum energy geometry and is important for molecular dynamics analysis. The potential energy function used to describe the attractions of London dispersion forces and the repulsions as the atoms get too close together is the Lennard-Jones 12-6 potential: EvdW ~ Aij Bij = L) 12 - - 6- ) • SW• i<.i rij (AI - 6) rij Here, the Aij and Bij are constants derived from the position and depth of the minimum of the interaction potential, rij is the distance between atoms i and j, and SW is a switching function used to smoothly truncate nonbonded contributions. A Coulomb potential is used to account for the electrostatic interactions: Ee1 4i<li · SW, = L -----"-41reor·· i <j 1J (AI - 7) -277- where q; represents the charge on atomic center i, t"i is the dielectric constant, and rij is the distance between atoms i and j. Once again, a switching function is employed to truncate contributions smoothly to the electrostatic energy of the system. The contribution to the energy from hydrogen bonds, EHb, is determined via a 12-10 potential function of the form: EHb = nij ) m(BA-H-D ) · (lcij2 - IO° L H-bonds HA HA r r COS COS n(BAA-A-H ) · sw' · sw" · (AI - 8) The parameters CijandDij are determined, based upon the minimum of the interaction potential, and rHA is the distance between the hydrogen and its H-bond acceptor heteroatom. ()A-H-D represents the angle between the H-bond acceptor, hydrogen, and donor atoms, while ()AA-A-H describes that angle defined by the atom preceding the acceptor, the acceptor, and hydrogen atoms. As above, switching functions are used for smooth truncation. -278- References (1) B. R. Brooks, R. E. Bruccoleri, B. D. Olafson, D. J. States, S. Swaminathan, M. Karplus. J. Comp. Chem., 1983, 4, 187. (2) S. J. Weiner, P.A. Kollman, D. A. Case, U. C. Singh, C. Ghio, G. Alagona, S. Profeta, Jr., P. Weiner. J. Am. Chem. Soc., 1984, 106, 765. (3) S. J. Weiner, P.A. Kollman, D. T. Nguyen, P.A. Case. J. Comp. Chem., 1986, 7, 230. (4) U. Burkert, N. L. Allinger. Molecular Mechanic&, ACS Monograph 177, 1982, Washington, D. C. (5) A. Hagler, E. Euler, S. Lifson. J. Amer. Chem. Soc., 1974, 96, 5319. (6) F. Momany, R. McGuire, A. Burgess, H. Scheraga. J. Phy&. Chem., 1975, 79, 2361. (7) BIOGRAF Reference Manual, BioDesign, Inc. Pasadena, CA 91101. -279- Appendix II The text of this appendix is a communication coauthored with William A. Goddard III, Garry E. Kiefer, and Donald A. Tomalia and has been submitted to the Journal of the American Chemical Society. -280- Starburst Dendrimers V: Molecular Shape Control Adel M. Naylor and William A. Goddard III* Contribution No. 7786 from the Arthur Amo., Noye& Laboratory of Chemical Phy&ic&, California Imtitute of Technology, Pa&adena, California 91125 and Garry E. Kiefer and Donald A. Tomalia* Functional Polymer& Re&earch Dow Chemical U.S.A., Midland, Michigan 48640 Molecular simulation studies show that starburst dendrimers may be shapedesigned to produce a continuum of morphologies ranging from open hemispherical domes to closed spheroids possessing internal hollows and channels. Carbon13 spin-lattice relaxation times (T1) of various guest molecules parallel these morphological developments, supporting the notion of unimolecular encapsulation. -281The recently reported "starburst dendrimer" 1 , 2 and "arborol" 3 systems are unimolecular prototypes that allow for both endo-receptor and exo.mpramolecular controlled molecular morphogenesis. This present communication describes the use of molecular simulation and reiterative generation development as a means for controlling molecular size and topology. In a previous communication 2 where the initiator core (I) = NH 3 and the interior branch segments are ,8-alanine units such as (2), .JV" .;\i / ' CH.,CH., - X - - CH-.CH., . . -X (1) (2) * = branch juncture it was presumed that these symmetrical junctured dendrimers were expanding three-dimensionally to produce regular spheroids as a function of generation (see Figure 1). Detailed experimental structural data were not available on these materials due to the fractal nature of the polymers. Hence, in order to provide information on the overall shape of these dendrimers and on the presence and character of internal guest/host sites, we carried out molecular mechanics simulations of generations 1 through 7. 4 The calculations used the AMBER force field 5 with the POLYGRAF molecular simulation programs. 6 These simulations indicate a dramatic change in morphology with generation, as indicated in Table I. Generations 1-3 are highly asymmetric (I 11 /Ix =:: 4.4 to 2. 7), whereas generations 5- 7 are nearly spherical (I 11 /Ix = 1.3), with the transition between the two forms (Iz /Ix = 1. 7) occur- -282- ring at generation 4. We find the average structures for the early generations to be very open, domed shapes, as shown in Figure 2. The latter generations are more dense, spheroid-like topologies (Figure 2c) with solvent-filled interior hollows connected by channels that run the entire length of the macromolecule (Figure 2d). Generations 4 through 7 seem quite capable of encapsulating host molecules. To experimentally investigate both the morphological changes as a function of generation and the predicted internal voids in the higher generation dendrimers, we carried out NMR studies of guest molecules in solution with carbomethoxy-terminated ,8-alanine dendrimers. Using the method of Menger and Jerkunica, 7 we found that 2,4-dichlorophenoxy acetic acid (3) or acetylsalicylic acid ( 4) exhibit behavior in the presence of dendrimer host molecules that supports the morphological changes predicted by molecular simulation. For example, adding ~12-68 mmol of (3) or ( 4) to 1 mmol of the starburst carbomethoxy-terminated dendrimers (A); (generations 0.5-5.5) in CDCh produced spin lattice relaxation times (T 1 's) for designated carbons that decrease from a maximum at generation 0.5 to a minimum at generation 3.5 (see Table II and Figure 3). The stoichiometries for guest:host were shown to be ~4:1 by weight and ~3:1 based on a molar comparison of dendrimer interior tertiary nitrogen:guest carboxylic acid moieties for generations = 2.5-5.5. Exceeding these guest:host ratios produces resonance signals with T 1 values characteristic of the guest molecules in bulk solvent phase in the absence of the dendrimeric hosts. The T 1 's for the small organic molecules reach a minimum at dendrimer generation 3.5, while the simulations show a. transition into a spheroid-like morphology between generations 3 and 4. This is indicated in Figure 3, where the maximum asymmetry (I./Ix) is plotted as a function of generation. We suggest -283- that this occurs because these macromolecules (generation 4 and above) are able to effectively encapsulate the smaller guest molecules and hence decrease the measured T 1 's. This minimization of T 1 's does not necessarily mean that the guest molecules are totally encapsulated; rather, they could be aggregated and congested at the surface of the polymer matrix. Thus we conclude that the suppressed T 1 values (G = 3.5-5.5) are supportive of the extensive channeling and presence of interior void space predicted by the molecular dynamics simulations. In conclusion, this work describes molecular simulations and physical measurements that suggest starburst branching strategies may be useful for controlling molecular morphogenesis. ACKNOWLEDGMENTS: We wish to gratefully acknowledge useful discussions with Drs. D. M. Hedstrand and L. R. Wilson. The simulations were funded by a contract from Energy Conversion and Utilization Technologies Program of the Department of Enerrgy. The computer equipment used was funded by a contract (No. N00014-86-K-0735) from Defense Advanced Research Projects Agency, Office of Naval Research, and by a grant (No. DMR-84-21119) from the Division of Materials Research of the National Science Foundation, Materials Research Groups. -284- REFERENCES AND NOTES (1) Tomalia, D. A.; Baker, H.; Dewald, J.; Hall, M.; Kallos, G.; Martin, S.; Roeck, J.; Ryder, J.; Smith, P. Polym. J. (Tokyo) 1985, 17, 117-132; Macromolecule& 1986, 19, 2466; Tomalia, D. A.; Berry, V.; Hall, M.; Hedstrand, D. M. Macromolecule& 1987, 20, 1164; Hall, H.; Padias, A.; McConnell, R.; Tomalia, D. A. J. Org. Chem. 1987, 52, 5305; Tomalia, D. A.; Dewald, J. R. U. S. Patent 4 507 466, 1985; U.S. Patent 4 558 120, 1985; U. S. Patent 4 568 737, 1986; U. S. Patent 4 587 329, 1986; U. S. Patent 4 631 337, 1986; U. S. Patent 4 694 064, 1987. (2) Tomalia, D. A.; Hall, M.; Hedstrand, D. M. J. Am. Chem. Soc. 1987, 109, 1601. (3) Newkome, G. R.; Yao, Z.-q.; Bak.er, G. R.; Gupta, V. K. J. Org. Chem. 1985, 50, 2003; Newkome, G. R.; Yao, Z.-q.; Bak.er, G. R.; Gupta, V. K.; Russo, P. S.; Saunders, M. J. J. Am. Chem. Soc. 1986, 103, 849; Newkome, G. R.; Baker, G. R.; Saunders, J. J.; Russo, P. S.; Gupta, V. K.; Yao, Z.-q.; Miller, J.E.; Bouillion, K. J. Chem. Soc., Chem. Commun. 1986, 752. (4) Naylor, A. M.; Goddard III, W. A., manuscript in preparation. (5) Weiner, S. J.; Kollman, P.A.; Case, D. A.; Singh, U.C.; Ghio, C.; Alagona, G.; Proteta, Jr., S.; Weiner, P. J. Am. Chem. Soc. 1984, 106, 765. (6) BioDesign, Inc., Pasadena, California, 91101. (7) Menger, F. M.; Jerkunica, J.M. J. Am. Chem. Soc. 1978, 100, 688. (8) Richards, F. Ann. Rev. Biophya. Bioeng. 1977, 6, 151. Table I. Moments of inertia for ,8-alanine starburst dendrimers from molecular dynamics simulation (x, y, and z are the principal axes). IT0T 11 % Ix 1 1.056 11.26 2 9.914 3 43.24 Generation % Iy % I. I./Ix 38.58 50.16 4.5 13.85 28.61 57.54 4.2 18.77 29.91 51.31 2.7 -- I 4 129.3 24.59 34.85 41.54 1.7 N 00 u, I 11 5 379.2 29.06 34.54 36.40 1.3 6 991.6 29.52 33.54 36.94 1.3 7 3131.0 29.88 31.16 38.96 1.3 Units: Dal tons x A2 • Table II. Carbon-13 spin lattice relaxation (T1, sec.) measurements for acetylsalicyclic acid (3) and 2,4dichlorophenoxy acetic acid ( 4) in the presence of dendrimers (A) where terminal groups are designated as in ( 1) with X = -CO2Me. Designated Carbons Dendrimer Generation 3 Guest Molecule ( 3) 5 6 3 Guest Molecule ( 4) 5 6 1.58 ± 0.04 (132.27)a 1.30 ± 0.03 (134.54) 1.76 ± 0.06 (123.81) 1.66 ± 0.10 (130.41) 2.70 ± 0.45 {127.66) 1.6 (114.15) 0.5 0.82 ± 0.01 (131.67) 0.60 ± 0.01 (133.08) 0.81 ± 0.01 (123.23) 0.74 ± 0.02 (129.67) 0.89 ± 0.01 (127.28) 0.74 ± 0.02 (114.48) 1.5 0.34 ± 0.01 (131.43) 0.30 ± 0.01 (132.41) 0.37 ± 0.02 (122.87) 0.47 ± 0.004 (129.70) 0.57 ± 0.01 {127.38) 0.049 ± 0.02 (114.58) 2.5 0.26 ± 0.01 (131.63) 0.24 ± 0.01 {132.52) 0.27 ± 0.01 {123.07) 0.38 ± 0.004 (129.79) 0.43 ± 0.01 (127.54) 0.35 ± 0.02 (114.78) 3.5 0.22 ± 0.02 (131.26) 0.22 ± 0.02 (132.13) 0.22 ± 0.01 (122.76) 0.34 ± 0.01 (128.64) 0.38 ± 0.01 (127.41) 0.35 ± 0.01 (114.66) 4.5 0.23 ± 0.01 (131.42) 0.25 ± 0.01 (132.28) 0.27 ± 0.02 (122.92) 0.40 ± 0.01 (129.57) 0.39 ± 0.01 (127.35) 0.32 ± 0.02 (114.63) 5.5 0.24 ± 0.01 (131.48) 0.24 ± 0.01 (132.51) 0.26 ± 0.01 (123.00) 0.34 ± 0.01 (129.38) 0.35 ± 0.01 (127.16) 0.31 ± 0.01 (114.39) acarbon-13 chemical shifts (ppm). I N 00 Q\ I -287- Figure Captions Figure 1. (A) Tri-dendron (tridirectional) dendrimer derived from ammonia where (I) = N and (B) are symmetrical branch junctured dendrons. (B) Monodendron (unidirectional) starburst branching patterns where X = amide linkages are derived from (1), Z = branch junctures as designated in (1) and (2) advanced to generation = 6. Figure 2. Orthogonal views of a ,8-alanine dendrimer. (a) and (b) illustrate the open, domed nature of the early generations (generation 3 shown), while (c) and ( d) show the spherical nature of the late generations (generation 6 shown). In (d) the character of the solvent-filled void spaces is depicted with the use of solvent-accessible surfaces. 8 • Figure 3. (Left Axis) Comparison of carbon-13 spin lattice relaxation times (T 1 , sec.) versus generation for designated carbons (3, 5, and 6; .A., □, and Q, respectively) in (3) with CHC1 3 solvent and various dendrimer generations. (Right Axis) Molecular asymmetry (- - - • (number of Z' groups). - - -) versus dendrimer generation -288- i:...i co _, -289- (a) (b) (c) (d) Figure 2. -290- Aspect Ratio ,. lz • 2.0 - 500 1.8 1.6 @]·carbon;@ 1.4 o= ffi] · carbon; @ O= ffiJ • carbon; {~) 1.2 400 3.00 10 0.8 - 2.00 0.6 0.4 - 0.2 - Generation: .5 Number of X groups: 3 Number of Z' groups: 10 1.5 2.0 3.0 12 6 3 2.5 6 3.5 4.0 24 12 4.5 5.0 Figure 3. 6.0 96 48 24 55 48 6.5 7.0 192 96 192 7.5 1.00 -291- Appendix III The text of this appendix is an article coauthored with Stephen J. Benkovic and Carol A. Fierke, which appeared in Science. -292- Insights into Enzyme Function from Studies on Mutants of Dihydrofolate Reductase s. J. BENKOVIC, C. A. FIERKE, A. M. ~AYLOR Kinetic analysis and protein mutagenesis allow the impor• tance of individual amino acids in ligand binding and catalvsis to be assessed. A kinetic analvsis has shown that the reaction catalyzed by dihydrofolate reductase is opti• mizcd with respect to product flux, which in tum is predetermined by the active-site hydrophobic surface. Protein mutagenesis has revealed that specific hydrophobic residues contribute 2 to 5 kilocalories per mole to ligand binding and catalysis. The extent to which perrurbations within this active-site ensemble mav affect catalvsis is discussed in terms of the constraints imposed by the energy surface for the reaction. D !HYDROFOJ..ATI REDUCTASE (5.6.7.8-TETRAHYDROFO· late: NADP oxidorcductase. E.C. 1.5. 1.3 I catah-zcs the :--:AD PH-dependent reduction of 7.8-dihnlrofolate iH 2F J ro 5,6. 7.8-retrah\'drofolate (H.F). The CllZ\'mc is ncccssarl' for maintaining imraccllular pools of H.F and its ·dcri\'ati,·es. which arc cssenoal cofactors in the biosynthesis of purines. th1mid\'late. and several amino acids. It is the target enzyme of a group of antifolate drugs. methotrcxm (MTXJ. rrunethopnm. and pmmcthamine. that are wide!\' used as anti rumor and antimicrobial agents \ 1 ). not been clarified. We have used site-directed mutag:encm to establish structure-function relations for the Es,hmchlll colt DHFR and in particular to evaluate the imponance of hydrophobic amino acids on the function of this cllZ\me and on the binding of inhibitors. The nature of the question posed presupposes two imponant sets of data (2 J: (i) an accurate structure that closeh· approximates the CllZ\me-H 2F·NADPH reactive tcrna.n· complex so that the kc,· amino acid comacrs are revealed and (ii) the elucidation of a complete kinetic pathway that can explain the stcad\'-Statc beha"ior of DHFR in terms of the rate-limiong steps in turno\'cr under a varim· of conditions and that allows for direct measurement nf the cataln:ic step at the CllZ\me-active me. Strucrure Visualization of the active-site amino acids was provided b\' the xra,· diffraction studies of Matthews a al.. (3) on rn·stals of the E. coli DHFR·MTX complex and of the !Aaobdus .ast1 DHFR· MTX·NADPH terna.n· complex (4. 5) refined to 1.7 A (6. 7). The two backbone structures are similar, despite less than 30% homologv for the rwo sequences; when the coordinates of 142 of the a· carbon atoms (out of 159) of the E. &di DHFR are matched to the 507.lcturallv cqui"alcnt carbons of the L. .asei DHFR. the rootmean-square dc\'iation is only 1. 07 A (6). The acti\'C site of both proteins is a cavity -15 A deep that is lined b,· hydrophobic side chains; the onlv polar side chain is the carboxl'I group of Asr 2" (E. roli) (Fig. l ). NADPH binds in an extended conformation "·ith the nicoonamidc moiety inscncd through the entrance of the ca,in· where it makes hvdrophobic and hydrogen-bonding interactions v.ith residues on the bottom and sides of the sire. Merhotrexate binds in an open conformation with the prcridine nng ncarll' perpendicular to the benz.01·l ring. The pyrimidine edge of the ptcridine ring is dccpll' buried in the acti\'e site, whereas the glutamate side chain extends out of the ca"iry to the surface. Selected kc\' hl'drophobic contacts are also illustrated in Fig:. I. The same interactions have been built into the proposed cllZ\me· NADPH·H 2F complex (6) but with the ptcridine ring rumed 0\'er with respect to the side chain by a 180' rotation about t h e ~ bond. as demanded bv the srcreochcmical course of the reduction (8). Howc\'cr, Naylor :and Goddard (9) hal'c suggested, with the use of molecular mechanics calculations. that the energetics of these alternate forms are nearly equal (\\;thin a few kilocalories / for both H 2F and MTX bound ro DHFR. The rwo complexes serve as the basis for our selection of residues for mutation. IATX (methotteute) The identities of the amino acids at the acti\'e site of dih\'drofolate rcductasc (DHFR) arc now known. but the function and relati"c unponancc of the amino acid residues in binding and catalvsis ha\'c 4 MARCH 1988 ARTICLES 110.< -293- Free Energy Profiles The detailed descriptions of reactions in terms of free energ, profiles have provided impressive insights into the coupling bcrn cen the overall thermcxhnarnic free energ,; change for the given rcactJon and specific steps in the kinetic sequence for ellZ\mc turnover (1-. 18). The free energy profiles provide a quanatative comparison between the ground and uansition stare lC\·els for ellZ\mc-Iigand complexes (19-21). Before we consider the effect of sire-specific mutations on the characteristics of DHFR. we C\'aluare the efficienc,; of this cllZ\nu, process. Given the definition of the kinetic seque~cc under phrnological conclitions (we introduce concentrations for 1'."H. K. H.F. and H 2F that approximate those of the E ro/1 cell). we can calculate the sreadv-srate turnover under these conclitions. A h,-potheacal maximum turnover is set bv having as the rate-limiting step the diffusional binding of H 2F to E·NH (22), because the lug:hcr concentration of NH would maintain the rcductasc in the E·KH form. Under these conditions the ellZ\me is opcranng at 15% of its h,-pothetical maximum turnover. slighch· limited by the d.issociaaon of H.F from E·NH·H.F. (This efficiency could be less if, under cellular conditions, channeling of H 2F to the ellZ\me occurred (23).] Consequently, the cli,·ision of the free energ\' change for the DHFR-catalvzcd reaction into the steps in Fig. 3 is a satisfactory Fig. 1. Carbon backbone strucrure of£. colt DHFR includmg bound ~gands solution to the problem of catal\7.ing this process intracellularh·. (MTX and ~ADPH I and the side chains for key amino acids [depicted with There are a number of pathwa,·s that efficiently solve the energetBIOGR..'\F 125J]. ics of the reduction within the thermodynamic constraints imposed by the overall reaction equilibrium and the diffusional barrier of Kinetics substrare-cllZ\me combination. All of these solutions have rwo The kinetic sequence for E. roli DHFR that predicts steadv-sme fearures in common: (i) the energy levels of the reaction inrermeclikinetic parameters and full-time course kinetics under a varict\' of ates are above that of the product ground scare and (ii I the substrate concentrations and pHs was established bv measuring the intermediate transioon state energy le\'els are below those for various ligand association and clissociation rare constants and pre- forming the E·1'.'H·H 1F complex. One solution is equivalent to stabilizing equally all of the stead\'-state reaction transients with the use of stopped-flow fluorescence and absorbance spectroscop,· (10). The scheme at 25 'C is inrermecliate ground and transition states rclati,·e to a prirrtitive sho"11 in Fig. 2, where NH = NADPH and N = NADP. Several reaction pathway, a process designated as urtiform binding I l .'O"). The kC\· fearurcs relevant is our cliscussion are: ( i I sread\'-statc turno,·cr is DHFR kinetic scheme conforms to within 1.6 kcal mol · 1 co the limited at pH 6 to i bv H.F release: 1ti I clissociatio~ of H.F is fastest predictions of the urtiform binding constraint. Moreover, the interfrom the mixed tern=· E·l'-<ri·H.F complex: consequenth· the nal stares. E·NH·H 2F and E·N·H.F, need not be at the same energy kinetic pathwav for srcad,·-srate rurno"cr at sarurating substrate level for high catalvtic efficiency (21, 24) because of the apparent conccnuations follows a specific, preferred pathway. in which H.F irreversibilin· of the overall conversion. Simulations preclict that this dissociation from DHFR occurs after NADPH rcpla.:es l'.ADP so internal equilibrium constant can vary bv 103 ,.;th less than a that the catalnic cvcles arc interlocked (heaw arrows): and (iii) the twofold change in turnover efficienC\' when the urtiform binding reaction suongh· fa,·ors H.F formation (o{·erall equilibrium con- constraint is maintained (201. An important consequence of the stam K 0 , = 104. pH iJ that is partially reflected in the internal high efficienC\· of the wild-n'f'C e~me is that mutations generall\' equilibrium E·!'sri·H 2F;: E·N·H.F (internal equilibrium constant will decrease the flux of the reducrase reaction under phvs,ological K,n, = 103• pH i) for the reactiYC rernat"\· complexes. conditions. Examination of the pH dependence of these reactions established an actiYe-sire group with an intrinsic pK. of 6.5 for the E·NH·H:F tern=· complex-a value that is the same for all forms of the Comparison of E. coli and L. CRSei DHFRs CI!Z\me: free. binarY. and rernar:,- complexes (11-13). Protonation We have studied rwo kinds of mutants, those that occur narurall,· of this group is required for the cherrtical step that involYes hvdride transfer from l\"H to H 2F. This active-site group is most lilceh· as in the comparison of the E roli and L. CRSei ellZ\mes and those 2 Asp '. Replacement of the Asp'- by Asn or Ser generates new generated through sire-specific mutagenesis at the active sire of the CI!Z\me forms that do nor haYe an acidic proton at their catalnic sire E. coli ellZ\me. and that require preproronated H 2F for acti,;n· (14). HowC\·er, The acri,·e-site amino acids of the two bacterial DHFRs were because of the location of the carbm.,·l of Asp 2'. its proton cannot o,·erlaid with MTX as a center for aligrui,ent; their solvent-accessible directlv transfer to !-15 of H 2F and requires a pathwa\' through surfaces were displa,·ed with BIOGRAF (Fig. 4 i (25) All of the interYerung water molecules or possibh· 04 ofH 2F (15). Although residues that contained anv atom within 5 Aof MTX were included the proton transfer component oi the reduction step is thermodY- The active-site amino acid.homologv was computed to be 55% from narrucallY unfavorable [pK. (Asp 2' I = 6.5; pK, (!'15 of H 2F) = 3.8 a base ensemble of 40 amino acids; those that were either identical 7 (]6)), the calculated proton transfer rare. 2 x 10 sec- 1, prondcs a or have only backbone interactions were deem_ed homologous. As a sufficient concentration of proronared H 2F so that the observed rare calibration point, the solvent-accessible surface of MTX in the for reduction (950 sec· 1 ) is nor rare-limiting. bin=· E. roli and tern=· L. CRSei complexes is identical (::: 2% I. Uo6 SCIENCE, VOL. 239 -294- t50 NC'_, 51,1,Al-1 .-c-1 Ei.2F 1.7NC- 1 E~~F 0.INC-1 -~ t ~ • J • 'c "~ Jsi i V • V 20 µAl_, eec-1 E 3.5Nc- 1 'i ~·- L~ ::~·~ v ~ ~£~:F 2 1,111- 1 Ne"" 1 ENH 1 . ~I";' ': ~;i I 1 ~ I C c• 2., uc;-1 E=,F 251,1A1- NC- EN ~ ,., a«_, ISMC- 1 ~ EH4F E 8ulf'- 1 aec-~ 25µ,W- 1 NC- 1 Fig. 2. Kmeric scheme for dihvdrofolate rcductas< at 25"C, MTE:--. buffer; N. NADP; l-.'H. NADPH; H,F, dihvdrofolatc; H.F, tctrahydrofolatc. Comparison of the total area of the solvcnt•accessible surfaces of the two proteins withm 5 A of the MTX revealed chat the £. coli area is 93% chat of L. casei (after deletion of the residues 15 to 20 in L. case, that arc positioned b\' NA.DP). The congruence in the protein surface in the region of MTX is remarkably similar; discernible differences occur, howc"er, near the glutamate and benzovl residues (Fig. 4). Consistent ,,.;th the apparent similarities in protein-substrate interactions arc the kinetic schemes of the two enz\'mcs, which arc near!\' identical and feature rapid, esscntiallv irreversible hydride transfer followed by rate-limiting H.F dissociation from E·NH·H.F, as described prcviouslv for the £. coli CllZ\me. A comparison of the reaction coordinate diagrams for the two cn~mes under phniological conditions is shown in Fig. 3 (26 J. The major difference observed is that the free cncrg'\· for binding NA.DPH to the l. casei ellZ\·mc is 2 kcal mo!· 1 more favorable than the £. coli c~mc. whcr~as the remainder of the free cnerg'\· differences arc less than l kcal mo!- 1. We presume that NA.D PH is positioned idcnticall,· on both ellZ\mes. We conclude char the cnerg'\· le,·cls of ground and transition state species arc predetermined b\' interactions between the substrate and the active•Site surface. which can be constructed bv a variable combination of amino acids. This anal,·sis docs not preclude specific transition state stabiliz.at1on (27, 281 that arises from changes on the protein surface as the reaction proceeds; obviouslv both the DHFR from E. col, and L. casei can respond similarh·. The design of speciesspecific inhibitors should exploit specific regions where ob,·ious differences arc manifest, that is Ilc 50 (f. coli) "ersus Phc 49 (L. casri). W c consider mutations at three smctl\' conserved amino acids (Phc:31 , Leu~, and Thr 113 ). Phc 31 resides ·in a hYdrophob1c pocket and intcraets with the pterovl mo1erv ofH 2F through van dcr Waals contacts such that the edge of the phenyl ring is oriented toward faces of both the ptcridinc ring and p-aminobenzovl group ( 71 in an edge-to-face: aromatic-aromatic interaction (35 ). The 1sobut\'I side chain of Leu~ is part of a hvdrophobic region around the benz.oyl glutamate: portion of the H 2F but is more than 10 A distant from the site of hydiide transfer. The hvdroxyl of Thr 113 forms a hvdrogen bond to the carboxylatc oxygen of Asp 27 and interact.< with the 2amino group of the ptcridine moic:t\' through a hYdrogc:n-bondcd water, 201. The effects of these mutations on kc\' rate steps m dihvdrofolatc reductase turnover arc exhibited in Table l. There arc a number of salient changes: (i I the dissociation constants for H 2F and H.F increase .,.;th a diminution in the bulk of the o substitucnt at Phc 31 and Leu~ as well as the loss of the hvdrogen-bonding interaction at Thr 113 ; (ii) the maximum vclocitY rM increases b\' a factor of 2 to 3 as a consequence of increasing k011 ( the dissociation rate constant ofH.F from E·J',.'H·TLF); (iii) the rate constant for the hydride transfer step (kH) decreases with the Gh.54 and the [Gh-' 4 , Val 31 ] mutants so that it is ratc-linuting for turnover; and 1i,·1 increases in the dissociation constants for MTX qualitam·clY parallel those for H 2F and H.F. Although these mutant c~mcs have larger VM values, the smaller binding constants for H 2F (l/KH,F' lower their turnover in a cellular milieu where the concentration of H 2F 1s estimated to be 0.3 µ.M. From a comparison of various mutants to the .,.;Jd-type protein one mav estimate the conmbution of a side chain group from the free energ'\' of substrate or inhibitor binding (36). For example. the replacement of Leu 54 ,,.;th Gl/4 , which is the closest approach to the: complete deletion of the isobutvl side chain. ma\' proYide an estimate of the hydrophobic binding encrg'\· of this side chain. A set of these free c:nerg:, changes is sho"n in Table 2. A difficult\' with this approach is that the deletion will most ccrtaml\' alter the architecture ,,.;thin the active site. For example. the effect of a glycine substitution is to increase the degrees of freedom of neigh• boring residues, and in addition, water molecules ma\' now begm to occupv the ca,ity. More rigorously, !er Gt: and G? be the free enc:rg\' of the c~me and the c~mc-subsrrate complex, respcCtI\'ch. for the equilibrium binding of A to wild-~'pc (N = Y) and mutant (N = H) DHFRs so that: Site-Specific Mutants In the study of designed mutant proteins, an important initial question to address is their structural integrity. Recent cl'\·stallographic studies indicate thar point mutations are in general accom· modarcd bv \'Cl'\' minor readjustments of the tertiarv protein structure with water molecules occup\'ing the space created bY a smaller amino acid o side chain (14, 29. 301. ln the case of the£. coli DHFR, x-ray crystallographic studies of the Asn" and Ser' mutants showed that neither the MTX binding geometry nor the derailed three-dimensional topography of the cllZ\mc was altered bv the mutation (14). A kinetic analvsis of the conformational states of various rcducrase mutants generated at the sites depicted in Fig. l established that the dismbution and rate of interconversion of the two conformational states of the free and mutant e~mcs were gcncrall\' unchanged (31-33). We conclude that our mutants have the same basic conformation as the wild rvpc and that changes in their binding and catal\'tic properties can be atmbuted primaril\' to the altered amino acid. but we note that substitution leads to localiz.ed conformational changes as the protein structure readjusts (34 I and thus requires a cautious interpretation of any data (\'ide infra). + MARCH 1988 15 10 \ 'i ! ~ 0 E+NH -5 -10 -15 ' - - - - - - - - - - - - - - - - - - - - Reaction coordIn1te Fig. 3. Gibbs free c:ncrg" coordinate diagrams for E. <D/1 ( - - ) and L. """ (- - -1 dihvdrofolat• rcductas< aligned at the substrate tcmar, compb. E·!\"H·H.F. calculated for conditioru approximaang a bacterial ceU: 1.0 m.lf 1':\DPH. 1.5 mM NADP. 0.3 ,.M H,F, 13 ,.M H.F. and 0.1M !',aCl.pH 7.o. 2s·c ARTICLES 110- -295- ( 1I AG: = G~ - Gt' - GA (2) The ground-state free energies of the ellZ\mes may or mav nor be identical (AGt"H 'f 0), nor is ir obvious when this term can be safeh· negkcted; thus AAGob, may not equal the 10trinsic bind.mg energ:; AGe'.-H contributed by group Y. A similar siruation prevails for the measurement of hydrogen bond strength. where one must distinguish between apparent and intrinsic bind.mg energies (37). In terms of apparent binding energies, Lcu 54 contributes 3.9 and 5.0 kcal mol- 1 to the respecove bind.mg ofH 2F and MTX to the E. coli DHFR. emphasizing the greater importance of hvdrophobic interactions in general (Table 2) (38) relative to salt bridge formation between the 2-arn100 group of MTX and Asp 2', which has been estimated ro be - 1.8 kcal mol- 1 (14). The same ordering, that is, hvdrophobic forces are greater than electrostatic forces, for MTX bind.mg emerges from free energy i;x:rrurbation calculations (39). The free cnergv changes for the Phe 3 and Val 31 mutant additionally include loss of the edge-to-face weakly polar interacoon between the aromatic side chain and the ligand. and in fact may be the major factor contributing to this AAG of 2 ro 3 kcal mol- 1. In the case of Tyr31 , the loss of bind.mg affinit\· ma)' reflect difficulties in solvating as weU as accommodating the hydroX\·l in the binarv complex. The fact that AAG for the double mutant is less than the swn of AAG for the rwo single mutants indicates the absence of large structural unfold.mg (40). Free Energy Relations Although these changes arc made at three spatiaUv separate loci on the surface of the active site, thev can be related bv means of a linear free energv Structure-function ~orrclation of then-pc k = that links thermod\'Ilamic \\ith kinetic changes. In parncular Fersht and his co-workers have applied these relations to mutants of tyrosvl-transfer R.>s;A (tR."IA) syntherase (41 ). In principle the free energy change berwecn the reactant ground stare and transition state (AAG·) is correlated ro the correspond.mg free energy change for the reactant-product equilibriwn (AAG), relative t0 a standard reactant. GencraUv such plots are linear \\ith slopes between zero and one. In the present case, however, the slope of a plot of log kH (the rate of hvdride transfer) versus log kH/k_H (the internal cquilibriwn) for a series ofDHFR mutants is ncarh· ,·errical (> > 1 ), suggesting that the transition state stabilirv is sensitive to the mutaoon (the values of kH decreased) but that the equilibriwn invoh·ing the ground states is not. This implies that the reactant and product ground stare arc pcrrurbed to the same extent-a manifesta• tion of the uniform bind.mg noted earlier. An alternate explanation that the perturbation is confined entireh· to a particular transition state stabiliution is ruled out b,· the effects of these mutations on the dissociation of H 2F and H.F. A variant on the classical free eoergv correlation relates changes in rate constants to changes in a second property of a common reactant. In the present case, plots of log kH versus log K H:r (Fig. 5) are linear with slopes of unit\· and suggest that the perturbation caused bv these mutations is Nice as important in altering the free energy of the transition state for hydride transfer as compared \\ith the ground state of the E · H 2F complex. The important point here is that the rate of hvdride transfer increases in direct proportion to an increase in the affinin· of the reducrase for H 2F, ,.;th the wildn-pc ellZ\me affinitv be~g maximal. An interpretation of the collective data is that the am,·e Sile 1s a reactive surface whose major funmon is to constram the SADPH and the H 2F into an optimal reaction space and oncntaaon. Th" " not a new concept; ccrtauilv the effect of extensi,·c mutations on tvrosvl-tR."IA s\'Ilthctase (42/. subtilisin (431, as well as alterations iii substrate structure (441, show that a.11 active-me group, conmb• utc to varving extents to selective bind.mg of substrate, and ro catalysis. These groups. that is, Leu~•, can be some dmance from the reaction site and stiU have a pronounced influence. Morem-er, the effects of the mutation should be more pronounced on the luneuc rather than the thermodynamic parameters since the former re9uires precise alignment of the 1':ADPH and H 2F, whereas the latter do not. EvenruaUv a situation can be reached when further increases m the bind.mg affirut\· for H 2F do not translate into an mcrea.sed rate (kH), hence the negative de\iation for the wild-n-pe DHFR from the correlation in Fig 5. A kev question. therefore, is the relation between the ener!!etics of the reaction path, in this case the transfer of a h,·dride 10n between C4 of the dihYdrop\'rid.me and C6 of H 2F, as a function of the distances and angles of the three parricipaong aroms (-C · • · H · · · C=). The construction of a molecular potenoal h,·per· surface defining the minimal energy path between the stable ground-state species either from experimental data or from theoreti• cal calculations remains a formidable task. Chemical reaction dmarnic information has been extracted from m·stallographic data; rwo notable examples are the hydrolrns of alkYlarvl acetals and the addition of nitrogen nucleophilcs to carbonyls. An increase of onJ,· 0.01 A in the ground-state length of the acetal bond to be clea,·ed 1s cqwvalent to a decrease of - 3 kcal mo]- 1 in the activation energv (45). For nucleophiles the angle of approach to the carbon\'! clusters is near 105° (46 J. Houk and co-workers have located the transition srates for hydride transfer from either methYlamine or 1,4-dihydro- a-e II08 Fig. 4, Supcrposiriorung of the active sites of the E. a,/i (gold: and L cam (blue I DHFRs v.1th MTX as a center for alignment. All residue, w1thrn 5 A of the MTX were included. Kev residues that are ,·isible lI1 the figure ,E co/1. L. casri) include Lcu 28 :Lcu'" · (up~r nght 1; Asp'":Asp" 11111ddk right . Ala: Ala 6 (lower right); Thr46 :Thr'' 1lower lefti; Ile"':Phc" 11111ddk left.: and Arg'':Lcu" (upper left:. Phe 31 can be seen rn the center of the \JC\\ [depicted with BIOGR:\F 1251]. SCIENCE, VOL. 2l9 -296- Fig. 5. Frtt cncrg\' correlation diagnm relating the rate constant for hydnde transfer to the K O for dissooanon of H,F from • saics of mutants rn the folatc binding site of DHFR Conclusions ! :-- • ~yr'' Wltd type v.,3, 3 Yal 113 - t, ~ ! • _, ~ ' - - - ' - -......--J'---0---.J_J 1 -T -5 ◄ -3 Log Kc, (H2F) (M-,) -2 Table 1. Effect.< of mutations on kinetic and thcrmodynlJllic parameters charactcnsoc of E. col, DHFR (10, 12, 32. 48). E. col, DHFR Wild t\'pc va1~' Gh-" GI,-". Val" Val"' ..,ff. ·H• (S<:C- I) 950 400 14 0.9 120 (Ii.Fi (sec-') Ko Ko (Ii.Fi (H,F1 (µM, (µM) 0.06 0.3 >15 0.21 6.6 140 2000 30 VM• (S<:C-1) 12 26 14 0.9 32 12 > 20 >300 >300 60 4.0 Ko (MTXl (nM) 0.02 3.2 100 900 0.5 •pH-l!ld<pcndent \'aluc:, m MTE!'- buffer. 25"C Table 2. Free energ:,· changes associated "ith ligand binding to E. e,,li DHFR. The error for these "alucs (SEM1 IS !:0.5 kcal mol- 1 Mutation Phe" to TIT Phe" to \'al Leu" to Glv Phe" to \' al. Leu'' to Gil' to \'al Tor"' Change Ko iH,F, .UG (kcal mol- 1 1 K0 1MTX1 .J..l.G (kcal mol- 1) H \'drophobJC Hvdrophobic H \'drophobic Hvdrophobic 1.5 2.0 3.9 5.4 2.i H vdrogcn bond (2) 2.9 1.9 3.0 5.0 6.3 pvridine to the methl'liminiwn cation. In either case a svn transition state is favored ~ith a bent -C · · · H · · · 0c bond angle (150' to 160') (47). These conclusions may be transposed to the DHFR reaction subject to the restricnons imposed by stereochemical considerations, so that a model emerges as a possibility for the chemical reduction step. ";'-. f ul l ~ ~) ,,s• )-b~: 9'•CONM 1 From their theoretical calculations. the optimal carbon-carbon bond distance in this transition state is 2.6 A; extending this distance by 0 .1 or O.3 A causes increases in the energy of activation of O. 7 and 5.0 kcal mol- 1, respc:ctiveh· (48). These ener~· difference.< translate into a reduction in the rate of the hydride transfer step b\' factors of 3 to 5000. Thus the information gleaned from either experiment or thcor\' argues for the importance of small molecular changes on the order of < 1 A that can account for the observed changes caused b\' specific mutations. On the other hand, we cannot eliminate at present the possibilil'I· that the mutated CllZ\mes ha,·e allowed the formation of nonproducti\'e ground-state complexes. such as bound H 2F adopting the MTX conformation (9, 49/. + MARCH 1988 Insights into the importance of active-site residues in the binding of ligand!; and i.n catalysis have been obtained through the powerful combination of site-specific mutagenesis and complete kinetic anaJ,·sis of the ellZ}me-catalyzed transformaaon. Hvdrophobic intera~cions appear to dominant the binding of substrates or inhibaor, as wcU as catalysis. The disparate mutations studied to date fit scrucrurc-reacti\'ity correlations that linearly relate the rate of hl'dnde transfer to the binding of H,F. which is consistent with the hypothesis that the active-site residues act as an ensemble to create a particular surface for binding and catalvz.ing the reacaon The same swface can be constructed bv differing combinations of ammo acids. as illustrated by the E. roli and L. casti comparison. and can be unfavorably perturbed by single changes at kc\' residues. Consequent!\' there must be compensating changes. lnformation obtained from both theory and experiment document that sma!J changes m distance ma,· be translated into energy changes sufficient to account for our observations. These changes. on the order of < J A. most likely will not be detected by the present methods (x-ray and nuclear magnetic resonance) used to establish structure and these methods may only detect changes in mutated ellZ}mes largelv devoid of activity. Funhermorc, one can anticipate that linearit, in the structure-reactivity correlations will decay, since the correlation between the free ener~· of activation and reactant bond angle and distances must ultimately be nonlinear, and because the rcqwremcnts for ligand binding arc not as restrictive as those for catalysis. REFERENCES AND NOTES 1. R. L BlaklC\·, in Foi,,u, .,.,/ Prer,,u R L. BWr.d\· and S J. Bcnkos,.:. Eds IWiJC\·, Ne..- Yorl. i985 i. vol. 2. p. 191. · 2 J. R. l<.nrn,·lcs, Sama 236. 1252 I 1987). 3. D A. Matthews et Ill., iJnd 197. 452 I 1977). 4. D A Mttthe..-, et 111..J Bwl a-.. 253. 6946 (1978; 5. D A. Matth.,.·,. R. A. Alden. S T Frc:er, K Xuong. J Kraut. iJnd 25-f. 4144 (19791 6. J T Bohn. D J. Filman. D. A. Muth..... R C Hamlin. J. Kraut. t1n,1 25-, 13650 (19821 7. D. J. Filman, J. T. Bohn. D A. Matth.,.,. J Kraut. tln,I. p. 13663 8. P. A. Charlton. D W. Young. B Budsall J Fc:enC\. G. C K. Robert.>. 0,,,. C-,,,,, 1979. 922 119791. 9 A. M !'-avlor and W A Goddard III. unpubbsh<d rc:,ults 10 CA. F,crk KA Johnson. S. ). Benlr.m·,c.B"""-s:n 26. 4085 119~-, 11. S. R. Stone and). F. Mormon. Bi«ho,,. BitJtm!s A.a,, 745. 24- :1983, 12. J.-T. Chen. K. Taira.CD Tu. S J Bcnl.ovic, U.. 4-093 ,19g13. K. Tau-a, J.•T Chen, C. A. F1erk S J. Bcnl.O\ic, B•J1 S«.Jpn 60. 3025 (1987). 14. E. E. Howell, J.E. Villafnnca. M. S Wam:n, S. J Oat!C\·. ). KraUt. Sama 231. 1123 (1986) JS. ). E Gread\', B,oche,,,im,,y U. 4761 (19851. 16 M. Poe, J Bwl a,,,,, isl. 3724 <19~71 17. W. ). Al~· and J. R. Knowlc,, Bt«hnwutrr 15, 5631 (19761 18. w P Jenw,Airr E - i 43.219 (19751 19. J. Staahowc. K. P. Namb,u. J.) Burbaum. D. M Stauffer. S A Benner.I A'" a,,,,, S« 107. 2757 (1985). 20. C. A Fieri«. R. D. Kuchta. K. A Johnson. S. ) Bcn1.m·1c. Col,/ Sp,,"f' H.....,. ~ Q...u BiDI, m press 21 ). Chm,] A'" 0,,,,, S« 105. 6502 11983). 22. M. H. Penner and C Fnedcn.]. Bwl. a,,,,,. U.2. 15908 I 19871. 23. M Young, G. Wasscmw,, P. Benlr.O\ic. S. Benlr.om. m F',oc,a,"!I, o(rh, S«oNI W..-ehop.,. Folyl IINi A•nfoM PolJll;,,,-,,, I. Goldman, Ed (Praeger. i-;.,. Yort.. 1985 i. p 76. 24. A D. Ellmpon and S. A. Benner.]. Ti,_, Bwl., in press 2S. BIOGR.4.F i> an inttracm·e molccular mmulacon thn:c-dimcns100al p-aphics program from BlODESIGN, Inc .. Pasadena. CA. 26 ). Andn:w, and C. A. Fierte. unpublished n,suJts 2i L Pau!mg. 0-.. Efl!I N,.,, U. 1375 11946) 28. D. E. Koshland and K E. Nc:et. A""• &. B""'1mt. 37. 359 1196~1 29. S. Sprang et al., Sea,..,, 237. 905 1198 7 1 30 C Chotlw..]. MDI. Bw/. 105. I (19761 31. P. 1 CavlC\·, S. M. ). Dunn. R W King. B ~ 20. 874 , 1981' 32. R.).Maver.).-TChcn.K.Twa.C.A F1crke.S J Bcnl.onc,Pro.c /,'11ZIA"'" Sn U.S.A. 13, 7718 I 19861 33. J -T Chen, R. J. Maver. C A. Fu:rk S J. Benlr.mi<. J CdJ BIIKhno 29. -3 (l985i . 34 J A.Ger!LD.W Hibler.) A Wilde,P H Bokon,/'nf<""E"f"' 1.2331198-_1 35. S K. Burle\· and G. A. Pctsko. 5 = 229. 23 I1985 i B-.,,,, am.. ARTICLES 1109 -297- 36 A R. Fcnht. in £ ~ Sm.a,,,,. llnli M""""""' I Freeman. N"" Yori. ed 2. 1985,. p 311 TmwlJ B.,,J,,,,, Sa 12. 301 (198~1 38 K T.ura and S J Bcnkovic. J Mt1i 0,,,.. 111 press 39 C Sinp, and 5 J. Benko"'· unpub!Jshcd r,sulrs 40 P. J. Carter. G W111m. A J Willuruon. A R Fcnht. Celi 38. 835 , 19841 41 D M Lowe. G Winter. A R FonhL Bt«hmr.,,,.. 26.60381198', -l2 A R Fmht. R ]. Lcamcrbarro". T N C. Wells. TmwlJ Broch,,. Sa 11. 321 (19%, 43 D A Emli tt al .. Samu 233. 659 , I 9861 44 C A F,m, and W P. Jenda./ B,c/ a,,.,, 261. 7603 119%1 r --· mo 45 A J Bngp t1 al. J Am Ch"" S0< 106. 6200 '1984, 46 H B Burg, .nd J D Dun,tz. A" Ch"" Res 16. 153 , I 983 47 Y. D Wu and K !',;. Houle J Am c;,,,. S« 109. 2220 c198-, 48 _ _ person.al communJC3tmn 49 K T.ura. C -~ f1'rk J ·T Chen. K A Johruon. 5 J Benxom. Trmd: B00<hrm Sa ll. 2'5: 1987: SO We thmk J ·T Chen. R Maver. K Ta.J.n. K John~m. J ."i.ndrt'\\~ C Sin1rh K Houi.... and Y -D Wu for theu help and m,·olvement m th.J~ wort.. We- .a.1'-<; thanl W .-\. Goddard III for US(' of the computer graphics facWt:, for g-arhic~ J15;:-lJ,, Ton work w~ supported I.fl pant,, :---:JH grant GM14129 and DOE. ELlJ 49 l42-E0403-0 3550 C.A.F ,s a ~1H postdoctoral folio" SCIENCE. VOL. 2<9 -298- Figure 1. Figure 4. -299- Appendix IV The text of this appendix is an article coauthored with Stephen J. Benkovic, Joseph A. Adams, and Carol A. Fierke. It has been submitted to Pteridine~ and is currently in press. -300- Insights into Enzymic Catalysis from Studies on Dihydrofolate Reduct.ases Stephen J. Benkovic*, Joseph A. Adams:, Carol A. FierkeJ and Adel H. Naylor~ Department of Chemistry The Pennsylvania State University University Park, Pennsylvania 16802 * The Pennsylvania State University, to whom colflllunication should be addressed. * The Pennsylvania State University J Duke University Medical Center California Institute of Technology -301- Introduction Dihydrofolate reductase (5,6,7,8-tetrahydrofolate: NADP+ oxidoreductase, ECl.5.1.3) catalyzes the NADPH-dependent reduction of 7,8-dihydrofolate (H 2F) 0 HN I:::,.. H N~ N Z pteridyl moiety NJf:~H·z~H~COiNHCHCHzCHzCOOH s1: ~- l , COOH . N H i : i : i bridge i benzorc acrd morery 1 : iglutamic acrd more ry NHz HzN 'Hl :X N A N I N r C H z N - o ~ CONHCHCHzCHzCOOH ~ COOH I ~ N MTX (methotrc:ate) to 5,6,7,8-tetrahydrofolate (H 4F). The enzyme is essential for both eucaryotes and procaryotes to avoid depletion of H F owing to its oxidation by 4 thymidylate synthetase and thus directly influences pyrimidine biosynthesis. It has long been the target enzyme for chemotherapeutic agents and its inhibition by methotrexate (HTX) is mainly responsible for the mechanism of action of this drug (Blakley, 1985). Because of its biological and pharmacological importance, dihydrofolate reductase (DHFR) has been the subject of extensive structural and mechanistic investigations. In particular the X-ray crystallography has provided the structures of the HTX and HTX·NADPH enzyme -302- complexes for the E.coli and L.casei species respectively (Matthews et al., 1978 and 1979;Bolin et al., 1982; Filman et al., 1982). Stereochemistry has traced the course of the reduction and established that H F must be bound in a 2 conformation in which the pteridine ring is rotated lSO• relative to the C6-C9 bond of the side chain in HTX (Charlton et al., 1979). With the development of the protocols for site specific mutagenesis, it has become possible to pursue several novel lines of inquiry: i) to evaluate the role of hydrophobic residues in catalysis and in substrate and drug binding; ii) to ascertain the importance of proximal and distal residues on the acidity and function of the unique active site carboxylate; and iii) to determine the influence of multiple amino acid changes on the thermodynamic and kinetic characteristics of the active site by comparing the E.coli and L.casei enzymes. Structural and Kinetic Features of Native DHFR The active site structure of the E.coli DHFR•methotrexate·NADPH complex along with several conserved amino acid residues that have been altered by mutagenesis is depicted in Fig. 1. The NADPH has been positioned based on analogy to its observed locus in the L.casei complex. The active site is a cavity some 15 A deep lined by hydrophobic side chains with the only acidic function present being the carboxyl of Asp-27. NADPH binds in an extended conformation with the nicotinamide moiety inserted through the entrance of the cavity and the pyrophosphoryl linkage making strong ionic and hydrogen bonding contacts (Arg-44, His-45). HTX, and by inference H F, lies towards the back 2 of the site where the pteridine and benzoyl rings are surrounded by hydrophobic residues (e.g. Ile-5, Phe-31, Ile-SO, and Leu-54). The Asp-27 interacts with the N2 and N3 nitrogens of the pyrimidine ring and does not make a direct hydrogen bonded contact with NS, despite the fact that protonation of NS is -303- required to complete the reduction of the N5-C6 imine upon hydride transfer to C6. The kinetic sequence for E.coli DHFR that predicts accurately the observed steady-state kinetic parameters and full-time course kinetics under a variety of substrate concentrations and as a function of pH was established by measuring the various ligand association and dissociation rate constants and pre-steady-state reaction transients employing stopped-flow fluorescence and absorbance spectroscopy (Fig. 2) (Fierke et al., 1987a). The enzyme has an intrinsic fluorescence that is quenched by the binding of ligands, particularly HTX. Independent measurements of the equilibrium binding for the various ligand combinations to form the binary and ternary reactant and product complexes gave dissociation constants in satisfactory agreement with those calculated from kinetic measurements of individual rate constants implying that the kinetic scheme is self consistent. Several features of the kinetic sequence germane to our considerations are: i) steady-state turnover is limited by H F release; ii) the nonequilibrium binding of H F and NADPH 4 2 becomes ordered owing to the fact that the rate constant for H F dissociation 4 is greatest from the mixed ternary E·NADPH·H F complex rather than either of 4 the two possible product complexes; and iii) the overall reaction strongly favors H F formation (K 4 ov = 10 11 ) that is partially reflected in the internal 3 equilibrium, E·NADPH•H F~ E•NADP+ •H F (Kint= 10 ). 4 2 The Active Site Asp-27 Reasoning from chemical precedent, the mechanism of imine reduction is expected to favor preprotonation at NS followed by hydride transfer. However the absence of a proximal acid function calls into question this presumption and raises issues concerning the identity of the acidic residue and the rates of proton transfer steps to H F and medium. 2 -304- Examination of the pH dependence of the steady-state turnover showed that the rate limiting step is H F release at pH <7.S which changes to the chemical 4 step of hydride transfer at pH >8.5. The pH-VH transition is controlled by the ionization of an acidic residue with an apparent pK a = 8.1 (Fig.~). The rate constant for the isolated hydride transfer step is dependent on by an acidic active site group with a pK a = 6.5, a value that is the same for all forms of the enzyme: free, binary and ternary complexes. Although binding of H F/H F are pH independent, the rate of dissociation of H F is significantly 4 4 2 slower than the rate of hydride transfer up to pH 8.1 increasing the pK observed in VM by ca. 1.6 pKa units. a The identity of the acidic active site residue was clearly shown to be the remote Asp-27 by its replacement with Asn or Ser resulting in two mutant enzyme forms that require preprotonated H F for 2 activity (Howell, 1986). Several lines of evidence from wild-type and mutant enzymes suggest that despite its cloistered location at the back of the active site cavity, the proton on Asp-27 readily exchanges with solvent namely: deuterium kinetic isotope effects on VH/~ (H F) and VH that at high pH converge to the same 2 value of ca. 3 (Chen, 1987); and the VM/~ (H F) pH-rate prot"ile for the 2 Tyr-31 mutant that exhibits a "hollow" in the vicinity of the apparent pK (Taira, 1987a). a Similarly there is no sign that the proton transfer component of the chemical step becomes rate-limiting since i) the amplitude of the hydride transfer step in native DHFR, which is stoichiometric with enzyme, is not attenuated at a pH where the ternary complex exists equally in both protonated and nonprotonated forms and ii) the perturbed pK a (6pK a = 0-2) of Asp-27 in various mutants does not correlate with the rate of hydride transfer. Thus, despite its location the carboxyl of Asp-27 can effectively function to donate its proton to NS probably through a specific water channel -305- or via the periphery of the pterin ring(N3->04->N5) (Gready, 1985). There is also evidence from mutants of DHFR that the carboxyl can be repositioned, e.g. by substitution of an Asp for Thr-113 and a neutral replacement at position-27. However, the lower catalytic efficiency [VM/Km (H F)] cannot be 2 as yet unequivocally attributed to a decreased rate of proton transfer (Howell et al., 1987). Pressing our line of inquiry further, we questioned whether the pK a of Asp-27, and hence its interaction with H F and H F, might be coupled to events 4 2 in the NADPH binding site in order to rationalize the NAD~H assistance of H4F dissociation. Mutation of Arg-44 to Leu-44 (Perry et al., 1987) that effec- tively deletes the ionic interaction of this side chain with the 2'-phosphate and pyrophosphate moiety of the nicotinamide cofactor in the binary complex as well as to neighboring residues in the free enzyme (e.g. Pro-66 and Ser-63) has a profound unexpected influence on the pK and ternary enzyme complexes. units to 8.4 (Adams, 1987). a of Asp-27 in the free, binary, In all cases the pK a is increased by ca. 2 pK a Fig. 4 traces the amino acid backbone from Arg-44 in the N terminal direction to Asp-27 and in the C-terminal direction to Arg-52 and Arg-57--the latter residues form salt bridges to the two glutamate carboxylate residues of MTX. The distance from Arg-44 to Asp-27 is ca. 25 A, suggesting subtle movement of the peptide chain is responsible for the pK change rather than an environmental effect. a If the effect were purely elec- trostatic, a simple coulombic calculation (6pK a • 244/Dr where Dis the effective dielectric constant and r is the charge separation distance in A) would require a dielectric constant of 5 (heptane= 4). This is far less than the range of 50-100 reported for the influence of mutations on the pK His-64 of subtilisin (Russell and Fersht, 1987). a of The Leu-44 mutant is also characterized by the absence of an accelerating effect by NADPH on the rate of -306- 1 H4F dissociation (2 s-l vs. 12 s- ) and a reduced rate for hydride transfer (SO s -1 and 950 s -1 ), although the deuterium kinetic isotope effect (NADPD) on the hydride step remains the same (Adams, 1987). Thus we conjecture that the molecular origin of the NADPH effect commences at Arg-44 and extends to either or both Asp-27 and Arg-52/57 acting to weaken all three ionic/hydrogen bonding interactions with H4F. The reduced rate of hydride transfer in this mutant, however, is not a result of an inadequate rate for proton transfer but is probably a consequence of alternate conformations for bound NADPH (Adams, 1987). Hydrophobic Effects In the study of designed mutant proteins whose purpose is to evaluate specific interactions, i.e. hydrogen bonds, ionic pairs or hydrophobic effects, a recurring question is their structural integrity versus the wild-type. Crystallographic studies on DHFR E.coli mutants (Asn-27 and Ser-27) showed that neither the MTX binding geometry nor the detailed three-dimensional topography of the enzyme was altered within± 0.2 A (Howell et al., 1986). However a substitution, be it a conservative deletion or replacement, will lead to conformational changes that may be localized or subtly propagated through the protein. Since in estimating the value of a side chain contribution to the free energy of binding the most relevant comparison is its deletion to a glycine, which because of its reduced volume, most certainly will be solvated differently at the active site. general 66G b 0 S Thus in may not be equated to the binding energy of the moiety in question, although this term may be the predominant contribution (Fersht, 1986). With that caveat one can still assess the apparent binding energy and the relative contribution of a given residue to the active site ensemble. -307- It has been particularly instructive to examine the effect of a mutation (Phe-31 to Val-31) on the binding of the drug HTX. HTX is an example of a slow binding inhibitor where the bimolecular association proceeds in two stages via an initial encounter complex that isometizes to the observed structure (Williams et al., 1979; Blakley, 1985). On the presumption that the free energies of the wild-type and mutant enzymes are equal, a free energy diagram has been constructed for the binding of HTX to the wild-type DHFR plus two mutants at Phe-31 (Taira et al., 1987b). Several salient results emerged: i) replacement of Phe-31 by Val-31 alters the accessibility -0f HTX to its binding pocket by reducing the bimolecular combination rate a hundred fold; ii) the value of edge to face aromatic-aromatic interactions estimated from the binding of HTX and 6,7-dimethylpteridine are ca. 3.0 kcal mol-l. Since the salt bridge formed between N-1 and N-2 of HTX and Asp-27 may contribute ca. 1.8 kcal/mol-l to the drugs binding affinity (Howell et al., 1986), hydrophobic interactions are at least as important determinants in the tight binding of HTX. The more complex question of the relationship between substrate/product binding and enzymic catalysis can also be scrutinized by mutagenesis. For at least five mutants including those at Phe-31, Leu-54, and Thr-113 there is a linear free energy relationship between the rate constant for hydride transfer and the dissociation constant for H F plotted logarithmically (Benkovic et 2 al., 1987). In essence there is.£!· a 2 kcal mol-l increase in the free energy of activation for the chemical step for every 1 kcal mol-l decrease in the free energy of H F dissociation. 2 In short the weaker ground state binding of the substrate translates into a slower rate of hydride transfer, an example of a loss in ground state as well as a greater loss in transition state stabilization (Jencks, 1975). The weaker binding of H F is also paralleled in 2 -308- weaker H4F binding so that the dissociation rate constant for this product no longer may be rate limiting. Particularly informative is the Leu-54 to Gly-54 mutation, ca. 18 A away from the locus of the hydride transfer, that decreases the rate of the chemical step from 950 s (ca. 4.0 kcal/mol -1 -1 to 14 s -1 and increases~ (H F) from 0.21 µM to 140 µH 2 ) (Mayer et al., 1986). If the Gly substituent is viewed as too extreme a deletion, replacement of Leu-54 with Ile surprisingly produces an analogous change in the rate of the hydride transfer step (30 s- 1 ) (Murphy, 1987). The exquisite sensitivity of the locus to· a single methyl group in the active site cannot at present be definitively rationalized; however an attractive hypothesis views bound H F as distributing between two 2 conformers, one of which may be an unproductive complex akin to bound HTX whose equilibrium position is tuned by various residues. Moreover ab initio calculations suggest the pathway for hydride transfer to be exquisitely sensitive to the distance and angle between the participating atoms, i.e. 2 3 changes on the order of less than 1 A can decrease rates by factors of 10 -10 (Wu and Houk, 1987). Comparison of Hutiple Active Site Changes (E.coli and L.casei DHFR) The detailed kinetic description of the E.coli DHFR catalyzed reaction provided an opportunity to evaluate the efficiency of this process. Given the definition of the kinetic sequence under physiological conditions (at concentrations for NADPH/NADP+ and H F/H F approximating those of the E.coli cell) 4 2 the turnover at steady state and its reciprocal the reaction flux were calculated (Fierke et al., 1987b). A maximum hypothetical catalytic turnover also can be computed after imposing H F diffusion to the E.NADPH complex (the 2 predominant form of the enzyme in the cell) as the only rate-limiting step. At physiological conditions the E.coli DHFR would be operating at ca. 157. -309- efficiency, suggesting that the free energy cost of the various steps has been well optimized (Benkovic et al., 1987). Yet computer simulation revealed that there were a large number of pathways that efficiently solve the energetics of the reduction within the thermodynamic constraints imposed by the overall reaction equilibrium and the diff·..isional barrier of the enzyme/substrate combination. For example, the internal equilibrium constant (E·NADPH·H F 2 3 E·NADP+·H F) can be varied by 10 with less than a two-fold change in turnover 4 maintaining the uniform binding constraint. Two related questions are prompt- ed by the above calculations: i) is the catalytic process exhibited by the E.coli DHFR also employed by DHFRs froc other species; ii) how many and what kinds of active site changes can be tolerated while still maintaining high catalytic efficiency? The X-ray crystallographic structure of the active site amino acids of the E.coli and L.casei DHFRs were overlaid using HTX as a center for alignment resulting in a base ensemble of 40 amino acids within 5 A of the drug. The active site equivalence was computed to be 55%; those amino acids that were either identical or have backbone interactions only were deemed equivalent. Despite these differences comparison of the total solvent accessible surfaces of the two proteins within this 5 A radius showed them to be within 7% of each other and the protein surfaces to be remarkably congruent. However, several prominant changes (E.coli:L.casei) Ala-29: His-20; Leu-36: Val-35; Ile-SO: Phe-49; and Arg-52: Lys-51 result in discernible differences in the positioning of the glutamate and benzoyl residues. A similar overlay was constructed for the NADPH binding site after positioning the NADPH in the E.coli site by analogy to its known position in the L.casei. In this case an active site ensemble of 58 amino acids 7 A from the cofactor were counted with a 727. equivalence based on the above criteria. The close similarity in this section -310- of the active site surface between the two species is shown in Fig. S despite the amino acid differences and the fact that the NADPH was modeled into the E.coli structure without changes in side chain positions. ElucidatiQn of the kinetic sequence for the L.'casei DHFR using the stopped-flow methods described earlier revealed the same features as reported for the E.coli (Benkovic, 1987; Andrews, 1988). Host importantly when the individual rate constants are expressed in terms of free energy the differences for each step (E.coli:L.casei) are within 1 kcal mol of the E.coli enzyme. -1 equivalent to that These free energy differences for.the two enzymes are depicted for the bound species in Fig. 6. It is apparent that an active site with multiple amino acid changes can result in similar kinetic sequences and catalytic efficiencies. Since single mutations can result in marked loss in catalytic activity, i.e. Leu-54 to Ile-54, it is reasonable to presume that some of these changes must be compensatory; others are probably neutral. One may hypothesize that the active site residues act as an ensemble to create a unique surface with the observed novel kinetic properties. The answer to the rhetorical question why this surface and not others may lie not only in the need for catalytic efficiency within the cell milieu but also in the stereochemical requirements of binding these substrates and in curtailing inhibition by others and the demands for stably folding a given primary sequence into this cavity shape. One may also specu- late that residues strictly conserved during evolution may not be changed because no compensatory mutation exists that satisfies all these three requirements within the cell. -311- References Ad~s, J. A. (1987) unpublished results. Albery, W. J., & Knowles, J. R. (1976) Biochemistry g, 5631-5640. Andrews, J. (1988) unpublished results. Benkovic, S. J., Fierke, C. A., & Naylor, A. M. (1987) Science, in press. Blakley, R. L. (1985) in Folates and Pterins pp. 191-253, Wiley, New York. Blakley, R. L., & Cocco, L. (1985) Biochemistry 24, 4772-4777. Bolin, J. T., Fil.man, D. J., Matthews, D. A., Hamlin, R. C., & Kraut, J. (1982) J. Biol. Chem. 257, 13650-13662. Charlton, P.A., Young, D. W., Birdsall, B., Feeney, J., & Roberts, G. C. K. (1979) J. Chem. Soc. Chem. Commun. 922-924. Chen, J. -T., Taira, K., Tu, C. D., & Benkovic, S. J. (1987) Biochemistry 26, 4093-4100. Fersht, A. R. (1987a) Trends Biochem. Sci. 12, 301-304. Fierke, C. A., Johnson, K. A., & Benkovic, S. J. (1987b) Biochemistry 26, 4085-4092. Fierke, C. A., Kuchta, R. D., Johnson, K. A., & Benkovic, S.J. (1987) Cold Spring Harbor Symp. on Quant. Biol. 52, in press. Filman, D. J., Bolin, J. T., Matthews, D. A., & Kraut, J. (1982) J. Biol. Chern. 257, 13663-13672. Gready, J. E. (1985) Biochemistry 24, 4761-4766. Howell, E. E., Villafranca, J.E., Warren, M. S., Oatley, S. J., & Kraut, J. (1986) Science 231, 1123-1128. Howell, E. E., Warren, H. S., Booth, C. L. J., Villafranca, J.E., & Kraut, J. (!987) Biochemistry, in press. Jencks, W. P. (1975) Advances in Enzymology 43, 219-410. -312- Matthews, D. A., Alden, R. A., Bolin, J. T., Filman, D. J., Freer, S. T., Hamlin, R., Hol, W. G. J., Kisliuk, R. L., Pastore, E. J., Plante, L. T., Xuong, N. -H., & Kraut, J. (1978) J. Biol. Chem. 253, 6946-6954. Matthews, D. A., Alden, R. A., Freer, S. T., Xuong, N., & Kraut, J. (1979) J. Biol. Chem. 254, 4144-4154. Mayer, R. J., Chen, J. -T., Taira, K., Fierke, C. A., & Benkovic, S. J. (1986) Proc. Natl. Acad. Sci. 83, 7718-7720. Murphy, D. J. (1987), unpublished results. Perry, K. M., Onuffer, J. J., Touchette, N. A., Herndon, C, S., Gittleman, M. S., Matthews, C.R., Chen, J. -T., Mayer, R. J., Taira, K., Benkovic, S. J., Howell, E. E., & Kraut, J. (1987) Biochemistry 26, 2674-2682. Russel, A. J., & Fersht, A. R. (1987) Nature 328, 496-500. Taira, K., Chen, J. -T., Fierke, C. A., & Benkovic, S. J. (1987a) Bull. Chem. Soc. Jpn. 60, 3025-3030. Taira, K., & Benkovic, S. J. (1987b) J. Med. Chem., in press. Williams, J. W., Morrison, J. F., & Duggleby, R. G. (1979) Biochemistry!.§_, 2567-2573. Wu, Y. D., & Houk, K. N. (1987), personal communication. -313- Acknowledgements We thank W.A. Goddard III for use of the computer graphics facility for graphical display. Footnote Abbreviations: DHFR, dihydrofolate reductase; H F, 7,8-dihydrofolate; H4F 2 5,6,7,8-tetrahydrofolate; HTX, methotrexate. *BIOGRAF* is an interactive molecular simulation 3-dimensional graphics program from BIODESIGN, Inc., Pasadena, CA. -314- Figure Legends Fig. 1. Carbon backbone structure of E.coli DHFR·MTX·NADPH and the side chains for key amino acids depicted using BIOGRAF*. Fig. 2. Kinetic scheme for DHFR at 25°C, HTEN buffer, N, NADP; NH, NADPH; Fig. 3. H2F, dihydrofolate; H4F, tetrahydrofolate. Observed rate constants for hydride transfer(-·-), H F dissociation 4 (---) and VH (-) as a function of pH. Fig. 4. Amino acid structure of E.coli from Arg-44 to Arg-57 (C-terminal direction) and Asp-27 (N-terminal direction) depicted using BIOGRAF*. Fig. 5. Superpositioning of the active sites of the E.coli (gold) and L.casei (blue) DHFRs with NADPH as a center for alignment. residues within 7 A were included. All Some key residues that are visible in the left hand panel (adenine portion) are (E.coli:L.casei); Gln-65: Gln-65 (top); Arg-44:Arg-43 (middle right); Arg-98:Gln-101 (bottom); and Ser-64:His-64 (middle left). In the right hand panel (nicotinamide portion) the key residues are (E.coli:L.casei); Ile-94:Ala-97 (upper right); Phe-31:Phe-30 (middle right); Asp-27:Asp-26 (lower right); and Ile-50:Phe-29 (upper left). * These residues are depicted using BIOGRAF. Fig. 6. Plot of 6~G (E.coli minus L.casei) calculated from equilibrium constants vs. various bound species that are identified in Fig. 2. E[TS) * represents the transition state for the chemical hydride transfer step calculated from the forward rate constant. All free energy values are pH independent and are measured using standard state concentrations of 1 H NADPH and H F. 2 T = 25°C. -315- Figure 1. Figure 4. 5µM-1,-1 E H2 F 40,.M-••-l '< 1.1,- 1 >, NH 950 s- 1 H F ' O.G 1 - E 2 20 .-, 1 40,.M-••-l 40 .-, ' N E H F 2.4s- 1 '> '25µM-ls-l N E 4 5,.M--1•-1200 •-• 13µM- 1,-1I 300 s- 1 I E 20µM-•s- 1 ... 3.5s-• ENH 2µM-•s-~ '- 12.5•- I NH E 85s-!.., ' 1s-i H4 F 8µM- Figure 2. 1 E 1.4 ,- ..,, H f 4 ' 25µM- 1,-1 E t,.:J f-' °' I -317- 3 2 en m 0 ·---·-........ ........ ·,. . '' ~------.c..:-~--,-------'· . ~. c,i 0 0 -I 5 6 7 8 pH Figure 3. 9 10 -318- Figure 5. left Figure 5. right -- 1.0 0 E -' 0 0 .JI! 0 ( !) <I <I I v-1 I-' ID I -1.0 ENH HzF E[TS]* EN H4 F E H4 F BOUND SPECIES Figure 6. ENH H4F ENH -320- Appendix V The solvent potential used for the molecular simulations is derived from tbe Jorgensen transferable, intermolecular, potential model1. This scheme is a pairwise additive site-site potential with the interaction sites positioned at the nuclear centers. The form of the intermolecular potential function is given by Equation AV-1. all sites u< 2 >(r 1, r 2 ) = ~ ~ ij Aij + Cij + 4i<lie 12 6 rij rij rij 2 (AV -1) Here, ri is the set of vectors defining the positions of the atoms in two different molecules, and rij is the distance between center i and center j. For the TIPS model,1 the constants have the values Aoo = 580,000 kcal A12 /mol, Coo = -525.0 kcal A6 /mol, and 4H = 0.40. The intramolecular potential is given by Equation AV-2. (AV - 2) Here, rij is the distance between atoms i and j within the single molecule, 8HoH is the angle between the two OH bonds, dij and tij are the equilibrium distance and angle for the isolated molecule, respectively. The TIPS model uses the experimental geometry for water. Thus, BHoH = 104.5° and roH = 0.96 A. For the Pettitt flexible modification 2 , the constants have the values a = 1059.2 kcal/mol/ A2 , b = 68.1 kcal/mol/radian2, and c = 76.5 kcal/mol/ A2 • -321References (1) W. L. Jorgensen. J. Amer. Chem. Soc., 1981, 103, 335. (2) L. X. Dang, B. M. Pettitt. J. PhyJ. Chem., 1987, 91, 3349. -322- Well, Bob, I won't have to 3pend the re3t of my life wondering ...