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 R ' J ' ¼ 0 over a biochemical species, and potential law R ' l ' ¼ 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 ¼ J + -J -, with chemical potential difference Dl ¼ RT ln(J -/J + ). The product -JDl 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 Dl 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 Dl can be established as the linear fluxforce relation in irreversible thermodynamics, analogous to Ohm's law in electrical circuits.

Dissipation and maintenance of stable states in an enzymatic system: Analysis and simulation

“…Kinetic constraints [16,17] are conditions under which the reaction establishes stable states. Thermodynamic constraints restrict the direction of the reactions [1,[11][12][13][14][15]. Although thermodynamic and kinetic constraints restrict different aspects of the reaction, they can be closely related.…”

“…Energy conservation and dissipation in biochemical networks are important aspects for understanding biological functions [1,[11][12][13][14][15]26]. In particular, in nonlinear autonomous and forced reaction systems, thermodynamic efficiency and dissipation have been systematically studied [23][24][25].…”

“…Those constraints restrict different aspects of the network. Specifically, stoichiometric constraints restrict the molar relation of reactants; thermodynamic constraints confine the direction of reactions [1,[11][12][13][14][15]; and kinetic constraints guarantee the formation of stable states that are necessary for implementing biological functions [16,17]. In a network, each enzymatic reaction is an essential component for constructing the network, and it also has a boundary at which substrate is supplied and product is removed.…”

“…The total dissipation of those elementary reactions represents the thermodynamic dissipation of the enzyme reaction. Furthermore, dissipation is closely associated with the concept of thermodynamic constraints [1,[11][12][13][14][15]. Is the maintenance of a stable state related to other properties of the system?…”

Finite time thermodynamic coupling in a biochemical network

“…It may also be intriguing to point out that Onsager in his famous paper on reciprocal relation had to cite the example of cyclic reaction A = B, B = C, C = A, without which he could not find example of coupling in chemical reactions. The coupling in Onsager approach is between the reduced flux descriptions and not by actual fluxes and forces, and similar definitions of stoichiometric networks depending on presence of reaction cycles, with dependent kinetic coefficients in which coupling had to be forcefully introduced have cited frequently in literature (Qian and Beard 2005;Qian et al 2003).…”