Measuring Irreversibility from Learned Representations of Biological Patterns

Thermodynamic irreversibility is a fundamental characteristic of living matter, crucial for maintaining the complex spatiotemporal structures and functions that define biological systems. However, accurately quantifying biologically relevant irreversibility remains challenging due to noise and nonlinear interactions among many degrees of freedom. Here, we employ deep learning techniques to identify tractable, low-dimensional representations of phase-field patterns in a canonical protein signaling process—the Rho-GTPase system—as well as in complex Ginzburg-Landau dynamics. We demonstrate that factorizing variational autoencoder neural networks can robustly extract informative pattern features despite noise. These neural-network-derived representations reveal signatures of mesoscopic broken detailed balance and time-reversal asymmetry in both Rho-GTPase and complex Ginzburg-Landau wave dynamics. By applying the compression-based Ziv-Merhav estimator to these representations, we successfully recover irreversibility trends across complex Ginzburg-Landau patterns, which vary widely in spatiotemporal frequency and noise level. Our irreversibility estimates also recapitulate cell-activity trends in Rho-GTPase patterns subjected to metabolic inhibition. Furthermore, our framework distinguishes between stable and chaotic dynamical phases in these nonlinear systems. By leveraging advances in deep learning, our approach provides robust, model-free measurements of nonequilibrium and nonlinear behavior in complex living processes. Published by the American Physical Society 2024