Biocontrol of Biomolecular Systems: Polyhedral Constraints on Binding's Regulation of Catalysis from Biocircuits to Metabolism

Author: Xiao, Fangzhou

Year: 2022

Degree: Dissertation (Ph.D.)

Advisor: Doyle, John Comstock

Committee Members: Murray, Richard M.; Winfree, Erik; Phillips, Robert B.; Pachter, Lior S.; Doyle, John Comstock

Option: Bioengineering

DOI: 10.7907/rtwq-v497

Abstract

One eventual goal of bioengineering is to build complex biological machines that fully realize the unique potential of biotechnology, namely adaptation, survival, growth, and dominance. In order to do so, not only do we need theoretical understanding and reliable manufacturing of biological parts and components, we also need a systems theory that captures fundamental structures to obtain insight about the space of all possible behaviors when parts are put together. This enables us to understand what can and cannot be achieved. Examples from other engineering disciplines are Turing machines for computers, information channels for communication networks, linear input output systems for electrical circuits, and thermodynamics for heat engines. This work is an attempt at developing a systems theory tailored to biomolecular systems in cells. The results form the following statements.

Biomolecular systems are binding and catalysis reactions. Catalysis determines the direction of change, while binding regulates how the catalysis rates vary with reactant concentrations. Given a binding reaction network, the full range of regulatory profiles can be captured by the reaction orders of catalysis, which in turn is constrained in polyhedral sets determined by the stoichiometry of binding. This constitute a rule, that since cells control catalysis by binding, cells control catalysis rates by regulating reaction orders constrained in polyhedral sets. This rule has ramifications in several directions. On metabolism, by incorporating the constraint that reaction orders of metabolic fluxes, not the fluxes themselves, are controlled, we can predict metabolism dynamics directly from network stoichiometry, e.g. glycolytic oscillations and growth arrests. This is a fully dynamic upgrade of flux balance analysis, a popular constraint-based method to model metabolism. On systems biology, this rule derives a method of biocircuit analysis based on the full range of values that reaction orders can take. This allows discovery of necessary and sufficient conditions for a circuit to achieve a certain function, thus revealing regimes hidden by traditional methods of analysis. It also promotes holistic comparisons of different circuit implementations, e.g. activating versus repressing, thur enabling biocircuit design where we know when a design will work, and when a design will fail. On dynamics and control of biocircuits, reaction order can work as a robust basis for stability, perfect adaptation, multistability, and oscillations. Lyapunov functions and dissipative control theory tailored for biomolecular systems are constructed based on reaction orders. On the mathematics of biology, it relates bioregulation to convex polyhedra, log derivative operator decompositions, and fundamental rules of calculus for positive variables.

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