The structural origin of irreversible transitions in biological networks

Cellular processes often exhibit irreversible state transitions even after external signals responsible for a transition are withdrawn. Long-standing questions remain: Where does such irreversibility originate from and can it be reversed? Although positive-feedback circuits among cellular components are known to relate to irreversibility, which circuits hold the dynamical origin of such irreversibility within large complex molecular networks remains unknown. Moreover, identifying the structural origin of irreversibility opens the door for control approaches to manipulate irreversibility. Here, we present Revelation Of the Original circuit of irreversible Transition (ROOT), which identifies molecular components underlying irreversible transitions and their control from logical network models. Specifically, ROOT pinpoints feedback loops functionally responsible for irreversible transitions and proposes strategies either for restoring the system to a state prior to the irreversible transition while preserving irreversibility, or for eliminating irreversibility itself. Applied to diverse biological processes, ROOT identifies irreversibility kernels and reverse control strategies that are validated by biological literature and existing experiments, providing a quantitative basis for revealing the origin of irreversibility and leveraging it to modulate irreversible cellular processes.