Non-steady-state dynamics and growth optimization of scalable flux networks

Exponential growth naturally arises in many biochemical, cellular, ecological and economic flux networks. While the majority of mathematical models focus on balanced, steady-state growth, the general existence criteria for a stable long-term growth rate remains unclear. Here, we introduce a theoretical framework by connecting ergodic theory to the long-term behavior of flux networks. We investigate the convergence of exponential growth rate for a broad class of nonlinear flux networks, constructed by scalable flux functions.

Scalable networks expand our analytic tools for studying non-steady-state growing systems, including the cell cycle and oscillating ecosystems. We demonstrate how scalable networks facilitates the analysis of objective functions in flux optimization, and use them for characterizing the essential motif of autocatalytic flux networks. Overall, our theory allows systematic construction of nonlinear networks and investigate their growth rate under optimization, regulation and perturbation.