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

Kinetic asymmetry is a key parameter describing non-equilibrium systems: it indicates the directionality of a reaction network under steady-state 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. First, we report the general expression of kinetic asymmetry for multi-cycle networks. Then, we specify it for a recently reported electrochemically controlled network comprising diffusion steps, which we used as a model system to reveal how key parameters influence directionality. In contrast with the current understanding, we establish that spatial separation—including compartmentalization—can enable autonomous energy ratchet mechanisms, with directionality dictated by thermodynamic features. Kinetic simulations confirm analytical findings and illustrate the interplay between diffusion, chemical, and electrochemical processes. The treatment is general, as it can be applied to other multi-cycle networks, facilitating the realization of endergonic processes across domains.