Data-Driven Model Construction for Anisotropic Dynamics of Active Matter

The ability of cells to reorganize in response to external stimuli is important in areas ranging from morphogenesis to tissue engineering. Recently, we have discovered that flat substrates with nematic order can induce nematic alignment of dense, spindle-like cells, thereby influencing cell organization on the scale of the entire substrate. Remarkably, single cells are not sensitive to the substrate's anisotropy. Rather, the emergence of global nematic order is a collective phenomenon that requires both steric effects and molecular-scale anisotropy of the substrate. We develop new statistical learning approaches to extend state-of-the-art physics models for quantifying both effects by efficient feature selection that avoids fitting models by all combinations of features. By including these features, such as non-Gaussian, anisotropic fluctuations, and limiting interactions to only neighboring cells with similar velocity directions, this model reproduces the temporal progression of the velocity orientational order and the variability of velocity vectors, whereas models missing any of the features fail to recapitulate these temporally dependent properties. We found that the alignment order is facilitated by enhanced cell division along the substrate's nematic axis, and associated extensile stresses that restructure the cells' actomyosin networks. Our work provides a new understanding of cellular reorganization among weakly interacting cells.