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

TL;DR

This paper introduces a convex optimization framework for calculating steady-state fluxes and potentials in biochemical networks, ensuring thermodynamic consistency and providing a new variational principle for analyzing nonequilibrium systems.

Contribution

It develops a novel convex optimization approach with a dual formulation that enforces thermodynamic laws in biochemical network analysis.

Findings

The optimization problem is convex and thermodynamically consistent.

A dual formulation reveals a biochemical analogue of Tellegen's theorem.

Optimal fluxes depend on free parameters related to kinetic parameters.

Abstract

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.