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A Minimal Mechanosensing Model Predicts Keratocyte Evolution on Flexible Substrates

A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behavior of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and traveling waves in the lamellipodium leading edge (iii) response to mechanical stress externally applied to the substrate (tensotaxis), (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis) and (v) the configuration of substrate wrinkles induced by contractile forces applied by the keratocyte.