Probabilistic and Maximum Entropy Modeling of Chemical Reaction Systems: Characteristics and Comparisons to Mass Action Kinetic Models

We demonstrate and characterize a first-principles approach to modeling the mass action dynamics of metabolism. Starting from a basic definition of entropy expressed as a multinomial probability density using Boltzmann probabilities with standard chemical potentials, we derive and compare the free energy dissipation and the entropy production rates. We express the relation between the entropy production and the chemical master equation for modeling metabolism, which unifies chemical kinetics and chemical thermodynamics. Subsequent implementation of an maximum free energy dissipation model for systems of coupled reactions is accomplished by using an approximation to the Marcelin equation for mass action kinetics that maximizes the entropy production. Because prediction uncertainty with respect to parameter variability is frequently a concern with mass action models utilizing rate constants, we compare and contrast the maximum entropy production model, which has its own set of rate parameters, to a population of standard mass action models in which the rate constants are randomly chosen. We show that a maximum entropy production model is characterized by a high probability of free energy dissipation rate, and likewise entropy production rate, relative to other models. We then characterize the variability of the maximum entropy production predictions with respect to uncertainties in parameters (standard free energies of formation) and with respect to ionic strengths typically found in a cell.