An Ultracentrifugal Study of the Dissociation of Human Carboxyhemoglobin Citation Hutchinson, William Day (1957) An Ultracentrifugal Study of the Dissociation of Human Carboxyhemoglobin. Master's thesis, California Institute of Technology. doi:10.7907/W8JC-7T49. https://resolver.caltech.edu/CaltechTHESIS:04262010-094002832 Abstract The dissociation of human carboxyhemoglobin has been investigated by means of sedimentation velocity measurements. Sedimentation studies on this protein have been extended to concentrations as low as 0.002% by the use of absorption optics. Hemoglobin was observed to dissociate increasingly as the pH was changed from 7 to 5. Apparent dissociation constants at each pH have been calculated. Values of the apparent specific volume of human carboxyhemoglobin have been found. Item Type: Thesis (Master's thesis) 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): Vinograd, Jerome Rubin Thesis Committee: Unknown, Unknown Defense Date: 1 January 1957 Record Number: CaltechTHESIS:04262010-094002832 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:04262010-094002832 DOI: 10.7907/W8JC-7T49 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5742 Collection: CaltechTHESIS Deposited By: Tony Diaz Deposited On: 28 Jun 2010 15:31 Last Modified: 13 Oct 2023 19:40 Thesis Files Preview PDF - Final Version See Usage Policy. 984kB Repository Staff Only: item control page

AN ULTRACENTRIFUGAL STUDY OF THE DISSOCIATION OF HUMAN CARBOXYHEMOGLOBIN Thesis by William Day Hutchinson In Partial Fulfillment of the Requirements For the Degree of Master of Science in Chemistry California Institute of Technology Pasadena, California Abstract The dissociation of human carboxyhemoglobin has been investigated by means of sedimentation velocity measure- ments. Sedimentation studies on this protein have been extended to concentrations as low as 0.002% by the use of absorption optics. Hemoglobin was observed to dissociate increasingly as the pH was changed from 7 to 5. Apparent dissociation constants at each pH have been calculated. Values of the apparent specific volume of human carboxy- hemoglobin have been found. Acknowledgments I would like to express my sincere appreciation and sratitude to Doctor Jerome Vinograd, who not only sug- gested this research but showed great interest in its progress and outcome. I also wish to express my thanks to those people who have contributed the blood used in the hemoglobin prepara- tions. | For financial support during the course of this re- search I am indebted to the California Institute of Technology for granting me the Paul E. Lloyd Fellowship. TABLE OF CONTENTS PART TITLE PAGE I Introduction . . 2. 6. 2 2 6 6 ee we ee 1 IT Procedure . 6. ee ee eee ee ee 2 Til Experimental Methods . .... +... .« « IV Materials . 2... 1 ee ee ee we ew 8 Vv Results and Discussion ..... +. ees 17 VI Appendices . 6. 6 ee ee et ee ee ee 24, References . . 2. « «6 6 © © © we we ew ee tt lw le at INTRODUCTION The hemoglobins of several species of mammals have been revorted to dissociate into smaller molecules under the in- fluence of various conditions such as high urea concentra- tion, low pH, or low protein concentration. Burk and Greenburg reported that between pH 7.3 and 9, in 6.6 M urea, the molecular weight of horse carboxyhemoglobin, as deter- mined by osmotic pressure measurements, is half that found in the absence of urea (1). This finding was confirmed by Wu and Yang (2), who found,however, that the hemoglobins of the dog and sheep did not exhibit this behavior. Steinhardt, using the sedimentation and diffusion method, confirmed the earlier work on horse hemoglobin and effected recombination to a species having the original molecular weight by re- moving the urea by dialysis (3). A reported increase (4) in the diffusion coefficient of this protein, horse carboxy- hemoglobin, with dilution has been interpreted as a disso- ciation (5). Dissociation of horse carboxyhemoglobin by high salt concentrations (0.5-1.0 M) has been observed though no such behavior was found for human carboxyhemo- globin (6). More recently, Field and O'Brien have reported a de- crease in the sedimentation coefficient with a concomitant rise in the diffusion coefficient of human carboxyhemo- globin in solutions of pH below 5 (7). Based upon compari- sons of the observed spreading of the boundary in the ultracentrifuge, Ogston and Field concluded that the equili- brium in the reaction was rapidly established (8). There have been no clear demonstrations of the adher- ence of any of these alleged dissociations to the law of mass action. A knowledge of the mass action expression, if any, would yield useful information about the group, or groups, involved in the reaction. A study of the effects of temperature on the equilibrium, if it is found to be a true equilibrium, would give useful information about the energy changes taking place. It has therefore been the purpose of this investigation to demonstrate whether or not one of these proteins, human carboxyhemoglobin, dissociates in accord with the law of mass action. PROCEDURE It may be shown that the measured sedimentation co- efficient, Ss, in a system in dissociation equilibrium is given by S dif {Se (1-e)S, where S, and S, are the sedi- mentation coefficients of the original species and the products of its dissociation respectively and e is the degree of dissociation. The quantity } 4 is the ratio of the molecular weight of the i°" species to that of the ginal species. Since & should be a function of the con- je or centration, a study of the sedimentation rate as a function * See avopendix I. -3- of protein concentration should reveal the effects of mass action. A judicious choice of analytical optics and cell depths makes it possible to study sedimentation behavior over a ten thousandfold range of concentration. The possibility of a change in the partial specific volume of the orotein in conditions favoring dissociation must be considered. The data of Field and O'Brien indicate that the appar- ent extent of dissociation is increased by the presence of urea in the solutions, and, contrary to the behavior of horse hemoglobin as was found earlier, the dissociation is unaffected by the presence of high salt concentrations. Since the presence of urea in protein solutions has been shown to increase the rate of protein denaturation (9) its effect in this instance is ambiguous. In this investiga- tion the extent of dissociation has been studied, therefore, as a function of the hydrogen ion and protein concentra- tions in solutions of single buffer salts. EXPERIMENTAL METHODS All sedimentation experiments were verformed in a Spinco Model E analytical ultracentrifuge. Most sedimen- tation coefficient determinations were made at the full speed of the instrument. This speed provided a conven- iently large movement of the boundary during a running time of about three hours. All the determinations using _le the cells of 30 mm. depth were performed at 50,740 RPM, the maximum speed of the rotor used with these cells. The sedimentation rate was followed in the concentration range of 2.00% to approximately 0.20% with the schlieren optical system of the instrument. This method records the refrac- tive index gradient between the solution and the solvent. At lower concentrations a more sensitive optical system based on light absorption was used. It was found that light of a wavelength of 546 mu was convenient in the con- centration range from 0.30% to 0.05%; ultraviolet light of a wavelength of 254 mu could be used from 0.12% to 0.02%. The absorption of the protein at 436 mu was such that con- centrations below 0.03% down to 0.002% could be studied. In the measurement of the sedimentation coefficients by absorption optics it was necessary to establish the relation between protein concentration and the plackening of the film. This relation is given by 0.D. (film) = ¥{ - 0.D.(sol'n} where the constant P is a function of the length of the light path and the extinction coefficient of the protein, and ¥ is the slope of the D-log E curve of the film for the conditions of development.” This equation is strictly valid only for systems in which Beer's law is obeyed and under conditions where the optical densities of the film fall on the linear part of the D-log E curve. * See appendix II. -5- The sedimentation coefficients were determined from the schlieren diagrams by measurements made on 20X enlarge- ments such that 1 cm. on the enlargement corresponded to an actual 0.05 cm. in the cell, thus simplifying the cal- culations. In view of the spreading of the boundary in solutions buffered at oH 5, the position of the boundary was determined in some instances from the second moment of the curve (10). The result differed from that obtained from the more conventional but less accurate zeroth moment by .02 cm. in the last picture of a run. It was estimated that this difference leads to errors no greater than the experimental error with normal spreading. The value of the sedimentation coefficients from ab- sorption runs were found from densitometer tracings. The optical densities of the film were measured on the Spinco Model R Analytrol using the microanalyzer attachment supplied with the instrument. The method used for de- termining the position of the boundary was that described by Shooter and Butler (11). The concentrations of the solutions were determined either refractometrically or spectrophotometrically. The value used for the specific refractive index increment for the 623 mu line of the mercury arc was 0.00181 (12) and Ble the value of the svecific extinction coefficient, Vem 3 540 mu, was 8.60 (13). The instruments used for the respec- tive measurements were a differential refractometer made _6- by the Phoenix Precision Instruments Company and a Beckman Model B spectrophotometer. For absorption runs with 254 mu light the chlorine- bromine filter supplied with the Spinco Model E ultra- centrifuge was used. At other wavelengths this filter was removed. An interference filter was substituted to pass light of 436 mu wavelength, and a Wratten #77A filter was used for 546 mu light. The lightsource used was the AH-4 low pressure mercury arc lamp. Except for the first few runs which were performed at 25°., all runs were performed at 20.0°C.; the sedimenta- tion coefficients, S720? thus correspond to velocities and equilibria at 20°, The density of the solution was used in the (1-V) (9) term which reduces the buoyancy factor to standard conditions. Since two analytical methods were used in this work the problem arose as to the equivalence of the results ob~ tained by the two methods. In order to check this unequi- vocally the sedimentation coefficients were measured by the two methods simultaneously in the same rotor employing two separate cells, thus avoiding the possibility of dif- ferent effects of temperature, denaturation, and methemo- globin formation in the comparison. To achieve reasonable sensitivity it was necessary to vary the cell thickness and the corresponding liquid layer thickness since the regions of equal sensitivity for the two methods do not overlap -7- for equal cell depths. For example a 12 mm. cell was used for the schlieren optical system, and a 3 mm. cell was used for the absorption system with 546 mu light. In order that one system would not conflict with the other, the cells were equipped with individual gelatin filters, and suitably sensitive photographic emulsions were employed. An example of the method is given in figure l. Figure 1 An Experimental Arrangement for Simultaneous Schlieren and Absorption Runs schlieren Absorption 103 F plate Royal Ortho Film #29 Wratten a a ae #61 Wratten (red) —— (green) 12 mm. cell -~-- tel : Sst 3 mm. cell #29 Wratten LL ol L.____. #77A Wratten (red) (green schlieren light-____J ie --_. Absorption source lightsource _8- While it was not possible in all cases to carry out such Simultaneous experiments because of the requirements of reasonable sensitivity, consecutive experiments, using cells of the appropriate thicknesses were carried out to achieve an overlapping in the ranges of the different methods. For instance, the same solution was studied in a 30 mm. cell by schlieren optics, a 12 mm. cell by UV light, and a 3 mm. cell by light of a wavelength of 436 mm. MATERIALS The samples of carboxyhemoglobin used in this investi- cation were prepared by the method of Drabkin (14) as it has been modified by Rhinesmith, Schroeder, and Pauling (15). The buffers used were prepared from reagent grade chemicals. The buffer of pH 7.09 was that of Kegeles and Gutter (16). The phosphate buffer of pH 6 was prepared by dissolving per liter of distilled water, 2.66 gms. of NajHPO,*7H50, 9.71 gms. of NaH5PO,-+H,0, and 8.77 ems . of NaCl. The acetate buffer of pH 5.06 was prepared by dis- solving in a liter of distilled water 8.19 gms. of NaAc, 2.4 ec. glacial acetic acid, and 9.71 gm. of NaCl. The phosphate-acetate buffer was prepared by adding 12.30 gm. NaAc per liter to the buffer of Kegeles and Gutter (16). Table I Sedimentation Coefficients and Calculated Equilibrium Constants for Carboxyhemoglobin in Acetate-NaCl Buffer, pH 5.060, p = 0.25 Run# cone.% Method Amp Sw 20 S30 Kx M 372 1.79 seh. 3.42 3.97 .88 337. 1.55 n 3.32 3.69 2,28 353. 1.5 n 3.52 3.89 1.03 371 1.16 " 3.61 3.90 .76 786 1.00 tt 3.65 3.90 £65 3555.75 n 3.70 3.88 51 786 15 " 3.74 3.93 AY 338° 72 i 3.71 3.86 £50 379° -.60 " 3.56 3.71 281 767 2535 " 3.74 3.87 40 767 -490 " 3.67 3.77 AY 768 32 i 3.52 3.60 .48 768 27 " 3.44 3.50 74 748 226 " 3.32 3.38 1.06 865 .22 " 3.60 3.65 238 342 219 tt 3.37 3.42 1.18 870 .13 abs. 546 3.37 3.34 256 871 066 " " 3.34 3.35 —— .30 65S 027 tt 426 2.99 2.99 48 611 . 026 it " 3.03 3.03 239 614 .026 r " 3.00 3.00 AY 575 025 " " 2.57 577 020 " " 2.93 2.53 ae) 689 0043 " " 2.91 2.81 625 * These runs were made at 25.0°C., all others at 20.0°C. IT Manor % ‘NOILVYLNIONOD 00'| OOS’ ool’ OSO° OIO’ Soo’ 100° 1 | perro [od i J prrer yd | 7 prerry 7 | P+ €G° 4O LNVLSNOD WNINSITINO’ 3HL JO 3NIWA V ONINNSSY GALVINOIVS SVM 3AUNND IWOILSYOSHL 3HL | sp G2‘O=7 ‘90'S =Hd ‘Y344NG IOON- 31VL39V NI NIGOTSONSHAXOGYVD 4O LN319144909 NOILVLNAWIG3S O2'Mc Sedimentation Coefficients and Calculated Equilibrium -ll- Table II Constants for Carboxyhemoglobin in Phosphate-NaCl Buffer, Run# 41a 415 796 pH 6.00, m= 0.25, T 20.09C. Cone. % 2.11 1.05 77 -75 258 255 53 Method sehi. abs. abs. schl. abs. abs. abs. abs. abs. X ny 436 436 254 436 w,20 A el 4.31 428 4.18 4 40 435 434 44d 448 423 AAS 3.88 3.38 3.11 3.21 KxM Oo OO ODO O OC .0315 0194 .098 6222 2154 III #unoTd % ‘NOILVYLNSONOD O'| GO ‘oO 0OSO’' O10" SOO' 100° ; t | | | ptt LJ i ee | 62:0 =7 ‘00°9=Hd 'Y344N 1DON-3LVHdSOHd NI — Se NIGOTSOWSHAXOBHV) JO LN3I0I349090 NOILVLNSWIG3S / 4o¢ 5 O/ O Ke) O 02M -13- Table III Sedimentation Coefficients and Calculated Equilibrium Constants for Carboxyhemoglobin in Phosphate Buffer, pH 7.09, w= 0.10 Run # Cone. & Method Amp Sy 20 KxM 385" 1.52 schl. 4.16 396" 1.52 " 409 397" 1.14 " 4.20 386" 75 i 431 387" £38 i" 4.20 734a 6239 schl. 446 734d ~239 abs. 546 AAS 726 £229 ft n" 1.37 056 0985 schl. HAT 957 0985 abs 436 A UT 961 0985 " " AAO 571 0413 " " 4,4 0145 674 0324 i " AOL 0133 669 .028 " " 4,00 20119 673 .016 " " 3.55 - 0373 966 .0105 " " 3.04 215 951°" . 0087 " " 3.14 .083 675 .0065 " " 3.35 0295 686 00605 " " 3.27 .036 968 0043 " " 2.56 676 0032 tt tt 2.94, O42 * xxruns 385-397 were performed at 25.0°C., all others at 20.0°C. The actual pH of the solution in this case was 6.95. ~T4- AT WUnold %° NOILVYLNJONOD O'l 00S’ ool Oso: 010° Soo: 100: y a | { pour ryeret ii prrrry t | 4192 O1'0 =7 ‘602 =Hd‘'Yad4N@ ALVHdSOHd NI NIGOTOOWSHAXOSHVO JO LN3I9143309 NOILVLNAWIGAS Q —“40O0¢ & —1S'¢ TN - _O — Sb OZ'Mc A Synord % ‘NOILVYLNIONOD 00'2 OG'| 00'l OS’ | | ! | | NOILVYLNADNOD ON3Z LV JINOIION TIWNWYON 3HL 4OS 9° MS 40 ANIVA GSLVIOdVYLX] 3SHL ONIMOHS JONVY NOILVYLNJONOD HOIH SHL NI NIGOTISOWSHAXOSHVO 4O LN3IDI144909 NOILVLNAWIGSS © or ?—~o ~~ O—~p D 00'2=Hd°H344NG FLVL30V 3LVHdSOHd = Uy, CO) 60'2=Hd'N344NG JLVHdSOHd =(_) Il ob 02'Mc Run # 16- Table IV Comparison of Results Obtained by Different Methods Date 385 5/12/56 396 5/18/56 798a = 2/6/57 7o8b 2/6/57 A16 5/30/56 796a = 2/6/57 7396p ©=— 2/6/57 355 4/30/56 786 1/29/57 768b 748 A/T /5T 436 with 436, 659 11/7/56 611 10/1/56 614 10/2/56 675 11/19/56 686 11/28/56 546 with 546, 734b 12/28/56 726 1sen/ee S76 5/2/57 O77 5/2/57 734a 12/28/56 734b 12/28/56 956 4/25/57 O57 4/25/57 961 4/28/57 schlieren with schlieren, Cone .% 1. 252 258 255 253 TT 275 215 215 227 226 1 52 .026 027 026 0065 .00605 239 226 schlieren with absorption, ells -L17 2239 2239 ~0985 0985 .0985 WW WW hd FEE FE FE WW WW FEF FEE FE Wr AN VE £O B= tt nN NW © (o) Ne) bots no erm OW cog 6- 9G "00 235 227 43 A7 OIOT UW NON NOW NN “IN NN uw SINAN NN OO pH 0° 09 - 00 00 00 - 00 - 00 .06 06 06 .06 ~06 06 .06 OF 09 .00 - 00 OS 09 O09 09 «O09 20. 20. 25. 20. 20. 20, 20. 20. 20. 20. 20. 20. 20. 20, 20. 20. 20. 20. 20. 20, Temp.°C, 25. 25. 20, 20. 20. Oo Oo Oo Ooo Oo (exe) Oo OOo OOO Oo Oo Method mp. sechl. tt tt tt tt 37 tt tt tt tt tt abs. 426 abs. 426 abs. 436 abs. 436 abs. 426 abs. 546 abs. 546 abs. 254 schl. schl. abs. B46 schl. abs. 426 abs. 426 These runs were done simultaneously in the same rotor. -~1l7- ReSsULTS AND DISCUSSTON The results of the sedimentation coefficient determina- tions are compiled in tables IT, II, and TII, and the data of these tables are vlotted in figures 2, 3, lh, and 5. In table IV are shown the reproducibility of results obtained by the different methods. It was found that sedi- mentation coefficient determinations by schlieren optics agreed within +2 as is seen from the results of runs 385 and 396, 798a and b, 355 and 766, 768b and 748. With absorption optics using light of a wavelength of 436 mu the results agreed within + 2% as is seen in runs 659, 611, and 61L., and 675 and 686. The agreement among the results using light of a wavelength of 546 mu is given in runs 73kb and 726. The agreement between schlieren optics and absorption optics may be seen from the runs 73lLa and b, 976 and 977, and 956, 957, and 961. Of most significance in the plots of Sw, 20 versus c is the Pact that all curves are similar in their general appear- ance; the sedimentation rate appears to decrease ravidly at low concentrations at all pH values studied. Above 0.20% concentration at pH 6 and 7 the results of this study are slightly higher than the results of ovrevious workers; this is causec by the employing of solution densities insteac of solvent densities in reducing the measured sedimentation coefficients to standard conditions, Sy,29. Tne vaiue of the sedimentation coefficient of tne undissociated hemoglobin -18- molecule at zero concentration obtained by extrapolation of the data found at pH 6 and 7 is l..5 as opposed to the values i..3-l..4. found by others (16). The reason for this is not understood; the effect described above should have no effect on the value of the sedimentation coefficient at zero concentration. Apart from the effect described above, the sedimentation rate appears to be normal at pH 6 and 7 above a concentration of 0.20%, showing only the concentration dependence of the sedimentation coefficient of the unchanged hemoglobin mole- cule. For all protein concentrations studied at pH S, the values are low, indicating that at these concentrations in this buffer there is an appreciable degree of dissociation. This was also evident from the spreading and shapes of the schlieren peaks. Schumaker and Schachman (17) have recently reported that the sedimentation coefficient of numan carboxyhemoglobin at pH 7 is normal in concentrations as low as 0.005% in contra- diction to the present work. The reason for this difrerence is not understood. It is unlikely that errors in the concentration determinations can account for the diiference since a factor of approximately 10 in tne concentration would be required. It is not unreasonable for dissociation to occur at pH 7 if it occurs to the extents observed at pH S.and 6. It may be that the explanation Lies in the experimental method especially in view of the statement made by these authors that different values of the sedimentation ~19- coefficient for a cytocnrome preparation were found when ight of different wavelengtns was emoloyed. It snould be ft ointed out that the method used by these authors was 'O different from the method cescribed in this paper in the respect that they modified the schlieren optical system and used it as an absorption system. The critical test of the adherence of the dissociation of carboxyhemoglobin to the law of mass action would be the calculation of an equilibrium constant for the reaction from the degrees of dissociation found from the sedimentation studies. In the calculation of degrees of dissociation it has been assumed that the cissociation reaction produces two new species having half the molecular weight of the normal hemoglobin molecule. The assumption of dissociation into equal fragments is in accord with earlier findings that the hemoglobins of various species dissociate into equal fragments and with the discovery that human carboxyhemogiobin molecule has symmetry about a diad axis (18). For a system undergoing dissociation into half mole- cules, the sedimentation coefficient is given by FOS Ht (1-0), 5 where So and Sy are the sedimentation coefficients or the original molecule and tne reaction product respectively. The value of the sedimentation coefficient of the intact hemo- globin molecule has been taken as 4.5 which is the extrapolat- ea value of the sedimentation coefficient of the normal molecule at zero concentration. The value ocr tne sedimentation coefficient of the half molecule has been taken as 2./{ wnich -20— is the value of the asymptote at zero concentration on the log plot of 37,20 against c for acetate buffer of pH 5. Since the exverimental curve of the sedimentation coefficient is the sum of two curves, the regular curve of the concentration dependence of 8, through its dependence on the frictional coefficient Ff, and the mass action cependence of Sw,202 the exoerimental data must be corrected to yield only the mass action devendence of Sy,29. Since dissociation occurs at high concentrations at pH 5 this correction has been applied to the data for tnis buffer; no correction was applied to the Sw ,20 values in buffers of oH 6 and 7 since dissociation is appreciable only at very low concentrations where the effects of concentration are negligible. The corrections applied in the case of the acetate bufYrered solutions were made on the basis tnat the concentration dependence of the secimentation coefficient of the half molecule was the same as for the whole molecule. The correc- tion made was 0.25 svedbergs per 1.00% »vrotein, as derived from a plot of S against c for the high concentration range in oH 7 buffer. Brom tables It, III, and IV the values for K x M are seen to be reasonably constant for the solutions cf pH 5 and 7. The corrected exverinental curve for oH 5 (figure II) is fitted by the constant 0.53. The best average value of the constant at pH 7.09 is 0.02h, deleting the high values 0.15 and 0.083 from the calculation of the average. The points corresponding to these high K values are designated by the -2]- crosses in figure IV. The data at pH 6 seem to be ambiguous for a calculation of the constant at this pH. Tf the values of K are taken as 0.53 at pH 5.06 and 0.024 at pH 7.09, the hydrogen ion concentration can enter the mass action expression only to some power less than the first power. To pinpoint the hydrogen ion dependence more accurately than this is beyond the scope of the data reported here. It is suggestec that more work be done at pH values 6 and 7 and l..5 to determine more closely the hydrogen ion dependence. The reactive group involved in the dissociation reaction is probably the histidine, for of all the acidic grouos in the protein, this would be expected to undergo most change in the pi range from 5-7. Tt has been observed that hemoglobin upon dissociation is converted more rapidly into methemoglobin. This qualita- tive observation is subject to a number of interpretations. It may be considered to be evidence for the position of the hemes in tre nemoglobin molecule. If the hemes are Located close to newly exposed surfaces of the two halves (and deeoly submerged within the whole molecule), they would, upon fisseciation of the molecule, be exposed to oxidation. Another exolanation of this behavior may be that the groups wnich become acidic are the hemes themselves or other Ligands attached to the iron atom. Under these circumstances the iron atom may be perturbed upon acidification and more easily oxidized. -20- Measurement of Partial Specific Volume. To detect any change in the specific volume of the protein upon dissociation, measurements of the svecific volume were made. The quantity measured in this study was the apparent specific volume; it was assumed that it approximates the thermodynamically sig- nificant partial specific volume of the protein within the accuracy needed. The value of the apparent specific of hemoglobin in conditions favoring dissociation was found to be unchanged, within the accuracy of the determinations, from the value found in conditions where dissociation was negli- gible. The values found are given in table V. Table V Apparent Specific Volume of Human Hemoglobin 25.3°C. Solvent ml./gm. O.1 pp K phosphate O.747 + .001 pH 7.0 O.1 p Na Acetate 0.750 + .002 U.1l WM Urea pH 4.8 These values referred to 20.0°C. become 0.744 and 0.747 ml./fgm. Thus, it is seen that no appreciable change takes place in the specific volume on dissociation. During the course of the specific volume determinations it was found that there had been no other determinations of ~23- the partial specific volume of human carboxyhemoglobin; the value 0.749 ml./em. quoted in the literature is based on the conjecture that the values for horse hemoglobin and human hemoglobin are the same. -Oue APPENDICES I. In the ultracentrifuge, the flux due to sedimentation is: m 2 2 Be = ge, S.r = 234,00, w' Sir [e) Sy = Da 4018; where g is a function of the cell dimensions, r is the dis- tanee from the center of rotation of the plane through which sedimentation is occurring, and the c's are expressed in grams of solute per ml. of solution. For a dissociation of the type A =FB+C+.... , 1f we start with c, grams of A ver ml., when equilibrium is established we will have in the solu- tion co, (1-) grams of A and fice grams of the th product of dissociation. The quantity f. is the ratio of the mole- cular weight of the bh species to the molecular weight of the substance A. The total flux across a vlane in a cell con- taining such a system would be: limam _ 2 2 _ a AteO 4b ~ dc, (1- er) wy So + deol ai pByh =CoT W'S 0, (1-&)S, +34,85¢f yore Se, n| (1-)S, +f {S54 = In the case of a dissociation into fractional parts having molecular weights half that of the original species this ex- pression becomes: (1- &)S, + os, = 5 -25- II. On the straight line portion of the D log E curve of the film, the condition afo.p.(riim)}} _ a hice t] ¥ (1) a constant, is satisfied. For a solute obeing Beer's law then ty log =~ = Ke = 0.D. (sol'n) t log I, = log I, - 0.D. (soltn) (2) yg From (1), 0.D.(film) = (log t - log t ) (3) where log t* is the extrapolated value of log t when 0.D. (film) = 0. For a plane surface the amount of light reaching the surface is I = Kt, or log t = log I - log K (4) Substituting (4) into (3), * 0.D.(film) = ¥(-log K + log I - log t ) 0.D.(film) = ¥(log K + logeeI, - log t *), af IT=tT1 where @is a factor introduced to take account of G? the attenuation of the beam of light transmitted through the solution as it passes through the optical system of the ultracentrifuge. -26- —_ * O.D. (film) = Slog K + M(log & - log I, - log t ) Substituting in this equation the value of I, from equation 2, 0.D. (film) =Ylog K + Yloger- Yiog 6 + Y toe I, - §{0.D.(solm)]}. Combining terms so aS to include all constants in ® >» we Pind 0.D.(fiim) =8® - Y[o.D.(so1'n)] -27- REFERENCES 1. Burk, N. F., and Greenberg, D. M., J. Biol. Chem., 87, 197-238 (1930). 2, Wu, H., and Yang, E. F., Chinese J. Physiol., 6, 51 (1932). Steinhardt, J., J. Biol. Chem., 123, 543-575 (1°38). 4, Tiselius, A., and Gross, D., Kolloid Z., 66, 12 (1934). 5. Lamm, 0., and Polson, A., Biochem. 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