Nonequilibrium thermodynamic analysis of Michaelis-Menten kinetics

We developed a method of analysis of nonequilibrium steady states of chemical reaction system. The analysis is applied to systems of Michaelis-Menten type reactions. We focus our attention on the consequence of the quasi-steady-state approximation to the rate of entropy production. Under separation of time scale, the description of the complete kinetic system can be contracted to slow variables. We find that the resulting rate of entropy production can be written in a new and revealing way consisting of steady-state contribution, intermediate species-specific affinity production, and channel-mixing entropy terms. The species-specific term in entropy production is in the canonical form so that a thermodynamiclike description of far-from-equilibrium steady state becomes possible. Under the quasi-steady-state approximation, we find the rate of entropy production is first order. This applies also to more complicated models. Finally, we discuss the implications in stochastic fluctuations of the free energy of the system. The Michaelis-Menten type of reactions considered in this paper do not show the possibility in gains of power from fluctuating external environment.