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Living adherent cells change their orientation in response to substrate
stretching such that their cytoskeletal components reorganize in a new
direction. To study this phenomenon, we model the cytoskeleton as a
planar system of elastic cables and struts both pinned at their
endpoints to a flat flexible substrate. Tensed (pre-strained) cables
represent actin stress fibers, whereas compression - bearing struts
represent microtubules. We assume that in response to uniaxial substrate
stretching the model reorients and deforms into a new configuration that
minimizes its total potential energy. Using the Maxwell's global
stability criterion, we find global minima configurations during static
extension and compression of the substrate. Based on these results, we
predict reorientation during cyclic stretching of the substrate. We find
that in response to cyclic stretching cells either
reorient transversely to the direction of stretching, or exhibit
multiple configurations symmetrically distributed relative to the
direction of stretching. These predictions are consistent with
experimental data on living cells from the literature.
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