Geometry sensing by active flows

The development of an organism involves the self-organized formation of patterns and the generation of shape. Such morphogenetic processes often rely on flows of cells and molecules, driven by molecular force generation. Here, we investigate how the shape of an organism guides the orientation of such active flows and thereby contributes to the formation of chemical patterns. To address this question, we study active surfaces, i.e. active processes confined to a surface of complex geometry. We focus in particular on a simple active fluid model motivated by the cell cortex. We find that active cortical stresses can drive a rotation of the whole cell that aligns the chemical pattern of a stress regulator with the geometry of the cell. Specifically, this can explain how active tension in the cytokinetic ring can ensure that a cell divides along its longest axis, consistent with experimental observations in mouse and nematode embryos. In this process, the cytokinetic ring is aligned with the saddle of a prolate sphere. Notably, we find that even localized patches of isotropic active tension are advected towards such saddle geometries, even for non-spherical topologies. We find that such an advection of active particles towards certain points in a fluid film, characterized by their intrinsic surface geometry, is a generic consequence of viscosity. Thus, active surfaces generally exhibit a sense of their geometry, as surface geometry guides flows and thus patterns, which may contribute to the robustness of morphogenesis.