Open AccessStoichiometric network theory for nonequilibrium biochemical systems
Author(s) -
Qian Hong,
Beard Daniel A.,
Liang Shoudan
Publication year - 2003
Publication title -
european journal of biochemistry
Language(s) - English
Resource type - Journals
eISSN - 1432-1033
pISSN - 0014-2956
DOI - 10.1046/j.1432-1033.2003.03357.x
Subject(s) - non equilibrium thermodynamics , thermodynamics , stoichiometry , isothermal process , dissipation , physics , flux (metallurgy) , ohm's law , first law of thermodynamics , ohm , statistical physics , sigma , exergy , chemistry , quantum mechanics , organic chemistry
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 ℓ J ℓ =0 over a biochemical species, and potential law Σ ℓ μ 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.