Predicting Cellular Regulation by Combining Statistical Thermodynamics, Control Theory, and Optimization*

Metabolic networks of biological cells can be viewed as dissipative structures. In particular, metabolic networks operate far from thermodynamic equilibrium, and are typically assumed to be near steady state. In that light, we present methods for inference of the distribution of flux through metabolic networks using the principle of maximum entropy production. Metabolism is governed by enzyme mediated reactions with fluxes that are subject to regulation through control of abundance of enzymes as well as control of their catalytic activities -- through for example post-translational regulation. On the time-scale of evolution natural selection will favor those cells with metabolic regulation that acts most efficiently in shifting environments and nutrient conditions, thus the environment will shape regulation. Therefore we assume regulation will be such that entropy production is maximized to the extent possible, subject to maintaining the physio-chemical viability of the cell while also directing flux to achieve a high rate of growth. From these principles we formulate methods for inferring regulation of metabolism in cells in response to environmental conditions as solutions of associated optimization problems that can additionally incorporate known information and available metabolomics and proteomics data. Critically, this approach allows for prediction of metabolic fluxes, concentrations, energetics, associated rate parameters and regulation/control that are extremely difficult to measure experimentally, while taking advantage of more readily available abundance data for metabolites and proteins in the cell.