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Chiral processes that lack mirror symmetry pervade nature from enantioselective molecular interactions to the asymmetric development of organisms. An outstanding challenge at the interface between physics and biology consists in bridging the multiple scales between microscopic and macroscopic chirality. Here, we combine theory, experiments and modern inference algorithms to study a paradigmatic example of dynamic chirality transfer across scales: the generation of tissue-scale flows from subcellular forces. The distinctive properties of our microscopic graph model and the corresponding coarse-grained viscoelasticity are that (i) net cell proliferation is spatially inhomogeneous and (ii) cellular dynamics cannot be expressed as an energy gradient. To overcome the general challenge of inferring microscopic model parameters from noisy high-dimensional data, we develop a nudged automatic differentiation algorithm (NADA) that can handle large fluctuations in cell positions observed in single tissue snapshots. This data-calibrated microscopic model quantitatively captures proliferation-driven tissue flows observed at large scales in our experiments on fibroblastoma cell cultures. Beyond chirality, our inference algorithm can be used to extract interpretable graph models from limited amounts of noisy data of living and inanimate cellular systems such as networks of convection cells and flowing foams.