Duality, thermodynamics, and the linear programming problem in constraint-based models of metabolism

It is shown that the dual to the linear programming problem that arises in constraint-based models of metabolism can be given a thermodynamic interpretation in which the shadow prices are chemical potential analogues, and the objective is to minimize free energy consumption given a free energy drain corresponding to growth. The interpretation is distinct from conventional nonequilibrium thermodynamics, although it does satisfy a minimum entropy production principle. It can be used to motivate extensions of constraint-based modeling, for example, to microbial ecosystems.