Data-driven irreversibility measurement for biological patterns

Thermodynamic irreversibility is a crucial property of living matter. Irreversible processes maintain spatiotemporally complex structures and functions characteristic of living systems. Robust and general qualifications of irreversibility remains a challenging task due to the nonlinearities and influences of many coupled degrees of freedom. Here we use deep learning to reveal tractable, low-dimensional representations of patterns in a canonical protein signaling process, Rho-GTPase system as well as complex Ginzburg-Landau dynamics. We show that our representation recovers the activity levels and irreversibility trends for a range of patterns. Additionally, we find that our irreversibility estimates serve as a dynamical order parameter, distinguishing stable and chaotic dynamics in these nonlinear systems. Our method leverages advances in deep learning to quantify the nonequilibrium and nonlinear behavior of general, complex living processes.