Making models of cell sheets as active materials
Active or living materials are made out of agents that can move on their own, such as birds, fish, or artificial systems such as robots or active colloids. Cells are living materials, and the two-dimensional tissues known as epithelial cell sheets have a fundamental role in the developing embryo, and also in adult tissues including the gut and the cornea of the eye. Soft and active matter provides a theoretical and computational framework to understand the mechanics and dynamics of these tissues.
I will give an overview of the types of models that we have developed, in increasing order of included detail. In the simplest useful model, active Brownian particles, cells are self-propelled particles with uncoordinated activity. Due to mechanical interactions, this still leads to correlated, ’swirly’ flow fields as observed in experiment. We complement this activity mechanism with a vertex model, where the sheet is represented by a polygonal tiling, to develop a fully quantitative model of MDCK epithelial cell sheets. In this framework, we are also able to show that the ‘fingering instability’ at the edge of such sheets is more easily understood as large-scale, long lived fluctuations.
Finally, I will introduce catch bond style mechanochemical feedback on the cell junctions, as a model for the convergence-extension flows seen in gastrulation in early development. We are able to steer the material into making active T1 transitions against the applied stress, leading to a material with an effective negative viscosity.
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