Thermodynamics of Growth in Open Chemical Reaction Networks

We identify the thermodynamic conditions necessary to observe indefinite growth in homogeneous open chemical reaction networks (CRNs) satisfying mass action kinetics. We also characterize the thermodynamic efficiency of growth by considering the fraction of the chemical work supplied from the surroundings that is converted into CRN free energy. We find that indefinite growth cannot arise in CRNs chemostatted by fixing the concentration of some species at constant values, or in continuous-flow stirred tank reactors. Indefinite growth requires a constant net influx from the surroundings of at least one species. In this case, unimolecular CRNs always generate equilibrium linear growth, i.e., a continuous linear accumulation of species with equilibrium concentrations and efficiency one. Multimolecular CRNs are necessary to generate nonequilibrium growth, i.e., the continuous accumulation of species with nonequilibrium concentrations. Pseudounimolecular CRNs---a subclass of multimolecular CRNs---always generate asymptotic linear growth with zero efficiency. Our findings demonstrate the importance of the CRN topology and the chemostatting procedure in determining the dynamics and thermodynamics of growth.