From Dry to Wet Vertex Model Dynamics: Generating Sustained Flows

Complex tissue flows in epithelia are driven by intra- and inter-cellular processes that generate, maintain, and coordinate mechanical forces. There has been growing evidence that cell shape anisotropy, manifested as nematic order, plays an important role in this process. Here we extend a nematic vertex model by replacing substrate friction with internal viscous dissipation, of relevance to epithelia not supported by a substrate or the extracellular matrix, such as many early-stage embryos. When coupled to cell shape anisotropy, the internal viscous dissipation allows for long-range velocity correlations and thus enables the spontaneous emergence of flows with a large degree of spatiotemporal organisation. We demonstrate sustained flow in epithelial sheets confined to a channel, thus providing a link between the dynamical behaviour of continuum active nematics and the cell-level vertex model of tissue dynamics.