Grand canonical Markov model: A stochastic theory for open nonequilibrium biochemical networks

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Abstract
In this paper we present the results of a stochastic model of reversible biochemical reaction networks that are being driven through an open boundary, such that the system is interacting with its surrounding environment with explicit material exchange. The stochastic model is based on the master equation approach and is intimately related to the grand canonical ensemble of statistical mechanics. We show that it is possible to analytically calculate the joint probability function of the random variables describing the number of molecules in each state of the system for general linear networks. Definitions of reaction chemical potentials and conductances follow from inherent properties of this model, providing a description of energy dissipation in the system. We are also able to suggest novel methods for experimentally determining reaction fluxes and biochemical affinities at nonequilibrium steady state as well as the overall network connectivity.