We provide a rigorous definition of free-energy transduction and its efficiency in arbitrary—linear or nonlinear—open chemical reaction networks (CRNs) operating at a steady state. Our method is based on the knowledge of the stoichiometric matrix and the chemostatted species (i.e., the species maintained at a constant concentration by the environment) to identify the fundamental currents and forces contributing to the entropy production. Transduction occurs when the current of a stoichiometrically balanced process is driven against its spontaneous direction (set by its force), thanks to other processes flowing along their spontaneous direction. In these regimes, open CRNs operate as thermodynamic machines. After exemplifying these general ideas using toy models, we analyze central energy metabolism. We relate the fundamental currents to metabolic pathways and discuss the efficiency with which they can transduce free energy.
For isobaric solutions, μi(z) must be regarded as the Gibbs free-energy content of species i.