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It is shown that the dual to the linear programming problem that arises inconstraint-based models of metabolism can be given a thermodynamicinterpretation in which the shadow prices are chemical potential analogues, andthe objective is to minimise free energy consumption given a free energy draincorresponding to growth. The interpretation is distinct from conventionalnon-equilibrium thermodynamics, although it does satisfy a minimum entropyproduction principle. It can be used to motivate extensions of constraint-basedmodelling, for example to microbial ecosystems.Comment: 4 pages, 2 figures, 1 table, RevTeX 4, final accepted versio

Duality, Thermodynamics, and the Linear Programming Problem in Constraint-Based Models of Metabolism