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Thermodynamic irreversibility is a crucial property of living matter. Irreversible processes maintain spatiotemporally complex structures and functions characteristic of living systems. Robust and general quantification of irreversibility remains a challenging task due to 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 -- the Rho-GTPase system -- as well as complex Ginzburg-Landau dynamics. We show that our representations recover 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 framework leverages advances in deep learning to quantify the nonequilibrium and nonlinear behavior of complex living processes., 10 main pages, 10 supplementary pages, 4 main figures, 8 supplementary figures

A defining feature of living matter is the ability to harness energy to self-organize multiscale structures whose functions are facilitated by irreversible nonequilibrium dynamics. While progress has been made in elucidating the underlying principles, what remains unclear is the role that thermodynamics plays in shaping these structures and their ensuing functions. Here, we unravel how a fundamental thermodynamic connection between the physical energy dissipation sustaining a nonequilibrium system and a measure of statistical irreversibility (arrow of time), can provide quantitative insight into the mechanisms of nonequilibrium activity across scales. Specifically, we introduce a multiscale irreversibility metric and demonstrate how it can be used to extract model-independent estimates of dissipative timescales. Using this metric, we measure the dissipation timescale of a multiscale cellular structure - the actomyosin cortex - and further observe that the irreversibility metric maintains a monotonic relationship with the underlying biological nonequilibrium activity. Additionally, the irreversibility metric can detect shifts in the dissipative timescales when we induce spatiotemporal patterns of biochemical signaling proteins upstream of actomyosin activation. Our experimental measurements are complemented by a theoretical analysis of a generic class of nonequilibrium dynamics, elucidating how dissipative timescales manifest in multiscale irreversibility.

Biological functions rely on ordered structures and intricately controlled collective dynamics. This order in living systems is typically established and sustained by continuous dissipation of energy. The emergence of collective patterns of motion is unique to nonequilibrium systems and is a manifestation of dynamic steady states. Mechanical resilience of animal cells is largely controlled by the actomyosin cortex. The cortex provides stability but is, at the same time, highly adaptable due to rapid turnover of its components. Dynamic functions involve regulated transitions between different steady states of the cortex. We find that model actomyosin cortices, constructed to maintain turnover, self-organize into distinct nonequilibrium steady states when we vary cross-link density. The feedback between actin network structure and organization of stress-generating myosin motors defines the symmetries of the dynamic steady states. A marginally cross-linked state displays divergence-free long-range flow patterns. Higher cross-link density causes structural symmetry breaking, resulting in a stationary converging flow pattern. We track the flow patterns in the model actomyosin cortices using fluorescent single-walled carbon nanotubes as novel probes. The self-organization of stress patterns we have observed in a model system can have direct implications for biological functions., Alfred P. Sloan Foundation (Research Fellowship), Human Frontier Science Program (Strasbourg, France) (Career Development Award), Massachusetts Institute of Technology. Department of Physics