  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.
