Thermodynamic and topological characterization of living systems

Abstract

Recent advances in microscopy techniques make it possible to study the growth, dynamics, and response of complex biophysical systems at single-cell and subcellular resolution, from bacterial communities and tissues to intra-cellular signaling and expression dynamics of genes. Despite such progress in data collection, major theoretical challenges remain to find structure and organizing principles in these data, which are often noisy and represent only a partial observation of the system. One such challenge is to estimate the rate at which a system is consuming free energy. All living systems must consume free energy to maintain or increase local order, and theoretical models can provide insights into the thermodynamic efficiency of important cellular processes. In experiments however, many degrees of freedom typically remain hidden to the observer, making thermodynamic inference challenging. Here, we introduce a framework to infer improved bounds on the rate of entropy production, by reformulating the problem of inference as a problem of optimization. We demonstrate the broad applicability of our approach by providing improved bounds on the energy consumption rates in a diverse range of biological systems including bacterial flagella motors, gene regulatory dynamics, and intracellular calcium oscillations. Another challenge is to distinguish two amorphous yet structurally different cellular materials, where in contrast to crystals, cellular structures are somewhat disordered. Here, we use information contained in the local topological structure to define a distance between disordered multicellular systems. Our metric allows an interpretable reconstruction of equilibrium and non-equilibrium phase spaces and embedded pathways from static system snapshots alone. Applied to cell-resolution imaging data, the framework recovers time-ordering without prior knowledge about the underlying dynamics, revealing that fly wing development solves a topological optimal transport problem, and enables comparisons across a wide range of different systems from zebrafish brains to bacterial colonies.