Stoichiometric network theory for nonequilibrium biochemical systems

Abstract

We introduce the basic concepts and develop a theory for nonequilibrium steady-state biochemical systems applicable to analyzing large-scale complex isothermal reaction networks. In terms of the stoichiometric matrix, we demonstrate both Kirchhoff's flux law ΣlJl = 0 over a biochemical species, and potential law Σlμl = 0 over a reaction loop. They reflect mass and energy conservation, respectively. For each reaction, its steady-state flux J can be decomposed into forward and backward one-way fluxes J = J+ - J-, with chemical potential difference Δμ = RT ln(J-/J+). The product -JΔμ gives the isothermal heat dissipation rate, which is necessarily non-negative according to the second law of thermodynamics. The stoichiometric network theory (SNT) embodies all of the relevant fundamental physics. Knowing J and Δμ of a biochemical reaction, a conductance can be computed which directly reflects the level of gene expression for the particular enzyme. For sufficiently small flux a linear relationship between J and Δμ can be established as the linear flux-force relation in irreversible thermodynamics, analogous to Ohm's law in electrical circuits.