Machine Learning and Optimal Control of Enzyme Activities to Preserve Solvent Capacity in the Cell

Experimental measurements or computational model predictions of the post-translational regulation of enzymes needed in a metabolic pathway is a difficult problem. Consequently, regulation is mostly known only for well-studied reactions of central metabolism in various model organisms. In this study, we utilize two approaches to predict enzyme regulation policies and investigate the hypothesis that regulation is driven by the need to maintain the solvent capacity in the cell. The first predictive method uses a statistical thermodynamics and metabolic control theory framework while the second method is performed using a hybrid optimization-reinforcement learning approach. Efficient regulation schemes were learned from experimental data that either agree with theoretical calculations or result in a higher cell fitness using maximum useful work as a metric. Model predictions provide the following novel general principles: (1) the regulation itself causes the reactions to be much further from equilibrium instead of the common assumption that highly non-equilibrium reactions are the targets for regulation; (2) regulation is used to maintain the concentrations of both immediate and downstream product concentrations rather than to maintain a specific energy charge; and (3) the minimal regulation needed to maintain metabolite levels at physiological concentrations also results in the maximal energy production rate that can be obtained at physiological conditions. The resulting energy production rate is an emergent property of regulation which may be represented by a high value of the adenylate energy charge. In addition, the predictions demonstrate that the amount of regulation needed can be minimized if it is applied at the beginning or branch point of a pathway, in agreement with common notions. The approach is demonstrated for three pathways in the central metabolism of E. coli (gluconeogenesis, glycolysis-TCA and Pentose Phosphate-TCA) that each require different regulation schemes. It is shown quantitatively that hexokinase, glucose 6-phosphate dehydrogenase and glyceraldehyde phosphate dehydrogenase, all branch points of pathways, play the largest roles in regulating central metabolism.

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