Non-Gaussian and anisotropic fluctuations mediate the progression of global cellular order: a data-driven study

The dynamics of cellular pattern formation are crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in orientational alignment over time, accompanied by cell proliferation, under the influence of the weak guidance of a molecularly aligned substrate. However, a comprehensive understanding of how this order arises remains largely unknown. This knowledge gap may be attributed, in part, to a scarcity of mechanistic models that can capture the temporal progression of the complex nonequilibrium dynamics during the cellular alignment process. To fill in this gap, we develop a hybrid procedure that utilizes statistical learning approaches to select individual-level features for extending the state-of-art physics models. The maximum likelihood estimator of the model was derived and implemented in computationally scalable algorithms for model calibration and simulation. By including these features, such as the non-Gaussian, anisotropic fluctuations, and limiting alignment interaction only to neighboring cells with the same velocity direction, this model is able to reproduce system-level parameters: the temporal progression of the velocity orientational order parameters and the variability of velocity vectors. Unlike other data-driven approaches, we do not rely on a loss function to tune model parameters to match these system-level characteristics. Furthermore, we develop a computational toolbox for automating model construction and calibration that can be applied to other systems of active matter.