Dual curvature sensing governs cell orientation and curvotaxis

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. SIGNIFICANCESubstrate surface curvature is a critical environmental cue that can influence multicellular organization and functions. Yet how cells collectively align and migrate on complex curved surfaces remains unclear. Here, we proposed a hydrodynamic theory of active nematic layers over curved surfaces for contractile theca cells (TCs), where we assume that the nematic directors of cells can respond to both the mean curvature and the Gaussian curvature of the underlying substrates. Our theory predicts distinct cell orientation patterns on hemicylindrical, hourglass- and dome-like substrates, consistent with experimental observations. Furthermore, by introducing curvature-induced active traction, our model recapitulates experimentally observed accumulation of TCs at the convex regions of hemicylindrical substrates as well as saddle-shaped regions of more complex geometries. Together, our study provides a simple theoretical framework to unify our understanding of curvature sensing across complex topology, providing insights into geometric control of tissue pattern formation.