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

Source: [A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks](<https://www.sota2.com/research/paper/68fa5ea21e209131ce9e402e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T18:54:48.646Z

Authors: Ronan M. T. Fleming, Christopher M. Maes, Michael A. Saunders, Yinyu Ye, Bernhard {\\O}. Palsson

Published: 2011-05-08T13:28:41.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1105.1513>)

[PDF](<https://arxiv.org/pdf/1105.1513.pdf>)