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 sigma(l)J(l)=0 over a biochemical species, and potential law sigma(l) mu(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 deltamu = RT ln(J-/J+). The product -Jdeltamu 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 deltamu 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 deltamu can be established as the linear flux-force relation in irreversible thermodynamics, analogous to Ohm's law in electrical circuits.
Qian
Hong
H
Department of Applied Mathematics and Bioengineering, University of Washington, Seattle, USA. qian@amath.washington.edu
Beard
Daniel A
DA
Liang
Shou-dan
SD
D000818:Animals; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D013598:Systems Theory; D013816:Thermodynamics