The value structure of metabolic states

To improve their metabolic performance, cells need to find compromises between high metabolic fluxes, low enzyme investments, and well-adapted metabolite concentrations. In mathematical models, such compromises can be described by optimality problems that trade metabolic benefit against enzyme cost. While many such modelling frameworks exist, they are often hard to compare and combine. To unify these modelling approaches, I propose a theory that characterises metabolic systems by a value structure, that is, a pattern of local costs and benefits assigned to all elements in the network. The economic values of metabolites, fluxes, and enzymes are interlinked by local balance equations. Formally defined as shadow values, the economic variables serve as local proxies for benefits that arise anywhere in the network, but are represented as local costs or benefits in the reaction of interest. Here I derive economic variables and their balance equations for kinetic, stoichiometric, and cell models. Metabolic value theory provides a new perspective on biochemical networks, defines concepts for comparing and combining metabolic optimality problems, and is useful for semi-automatic, layered, and modular modelling.