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

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.