Chan, C.; Lin, S.-Z.; Tomida, K.; Ng, B. H.; Lee, C. H.; Lee, J. S.; Zhao, Z.; Eliza, F.

Cells lying in a curved environment can respond to the surface curvature by reorienting their shape. However, whether cells respond to the mean curvature and/or the Gaussian curvature remains largely unexplored. Here, inspired by experimental observations of how ovarian theca cells (TCs) orient themselves on substrates with different curvatures, we propose a theoretical framework for active nematic layers on curved surfaces. In this model, we assume that the nematic directors of the cells respond to both the mean curvature and the Gaussian curvature of the underlying substrate surface. Our theory predicts specific cell orientation patterns on hemicylindrical, hourglass- and dome-like substrates, consistent with experimental observations. In addition, by incorporating curvature-induced active traction, our model successfully recapitulates the experimental observation of TC accumulation at convex regions of hemicylindrical substrates as well as saddle-shaped regions of more complex geometries. Overall, our work reveals the unexpected role of cell curvature sensing in driving collective migration and pattern formation on various substrate curvature.