A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks

• Published in: Journal of theoretical biology Vol. 292; no. 7; pp. 71 - 77
• Main Authors: Fleming, R.M.T., Maes, C.M., Saunders, M.A., Ye, Y., Palsson, B.Ø.
• Format: Journal Article
• Language: English
• Published: England Elsevier Ltd 07.01.2012
• Subjects: Biological Sciences; chemical reactions; Constraint-based modeling; Convex optimization; energy conservation; Entropy; Entropy function; Flux balance analysis; Genome; Humans; Metabolic Networks and Pathways - physiology; Models, Biological; system optimization; Systems Biology - methods; Thermodynamics; Thermodynamics; Flux balance analysis; Constraint-based modeling; Convex optimization; Entropy function
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2011.09.029

We derive a convex optimization problem on a steady-state nonequilibrium network of biochemical reactions, with the property that energy conservation and the second law of thermodynamics both hold at the problem solution. This suggests a new variational principle for biochemical networks that can be implemented in a computationally tractable manner. We derive the Lagrange dual of the optimization problem and use strong duality to demonstrate that a biochemical analogue of Tellegen׳s theorem holds at optimality. Each optimal flux is dependent on a free parameter that we relate to an elementary kinetic parameter when mass action kinetics is assumed. ► We derive a convex optimization problem that simultaneously enforces many constraints in genome-scale biochemical networks. ► Constraints enforced are steady state mass conservation, energy conservation and the second law of thermo-dynamics. ► We establish, in an exact manner, the duality relationship between reaction rates and chemical potentials. ► Efficient polynomial-time algorithms exist for solving such convex optimization problems based on interior point methods.