Analysis of kinetic asymmetry in a multi-cycle chemical reaction network establishes the principles for autonomous compartmentalized molecular ratchets

Kinetic asymmetry is a key parameter describing non-equilibrium chemical systems: it indicates the directionality of a chemical reaction network under steady-state, non-equilibrium conditions. So far, kinetic asymmetry has been evaluated only in networks featuring a single cycle. Here, we have investigated kinetic asymmetry in a multi-cycle system using a combined theoretical and numerical approach. Inspired by the latest experimental developments, we selected a com-partmentalized redox-controlled network as a model system. We report the general analytical expression of kinetic asymmetry for multi-cycle networks, and specify it for the present system, which allows anticipating how key parameters influence directionality. We establish that compartmentalization can enable autonomous energy ratchet mechanisms, with directionality dictated by the system's thermodynamics. Kinetic simulations confirm analytical findings and illustrate the interplay between diffusion, chemical, and electrochemical processes. The presented treatment is general, as the same procedure can be used to assess kinetic asymmetry in other multi-cycle networks, facilitating the realization of en-dergonic processes across domains.