Structural constraints limit the regime of optimal flux in autocatalytic reaction networks

Autocatalytic chemical networks play a predominant role in a large number of natural systems such as in metabolic pathways and in ecological networks. In this work, we present a theoretical framework that identifies the thermodynamic conditions under which autocatalytic networks run optimally in a non-equilibrium stationary state. Our theory shows that the overall reaction associated with the network is aligned with the thermodynamic force that drives the system out of equilibrium. We also demonstrate that the thermodynamic force required to operate at a maximal flux obeys universal constraints that are independent of the kinetics, but solely determined by the stoichiometry of the overall process and by the structural properties of the underlying chemical reaction network.