Stoichiometric network theory for nonequilibrium biochemical systems

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 Σ_ℓJ_ℓ=0 over a biochemical species, and potential law Σ_ℓμ_ℓ=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.