The shape and differentiated state of many cell types are highly sensitive to the rigidity of the microenvironment. The physical mechanisms involved, however, are unknown. Here, we present a theoretical model and experiments demonstrating that the alignment of stress fibres within stem cells is a non-monotonic function of matrix rigidity. We treat the cell as an active elastic inclusion in a surrounding matrix, allowing the actomyosin forces to polarize in response to elastic stresses developed in the cell. The theory correctly predicts the monotonic increase of the cellular forces with the matrix rigidity and the alignment of stress fibres parallel to the long axis of cells. We show that the anisotropy of this alignment depends non-monotonically on matrix rigidity and demonstrate it experimentally by quantifying the orientational distribution of stress fibres in stem cells. These findings offer physical insight into the sensitivity of stem-cell differentiation to tissue elasticity and, more generally, introduce a cell-type-specific parameter for actomyosin polarizability.
Bibliographical noteFunding Information:
We thank R. De, R. Paul and N. Gov for many useful discussions. We are grateful to the Israel Science Foundation, the Clore Center for Biological Physics, the Schmidt Minerva Center and an EU Network grant for their support. F.R. gratefully acknowledges financial support through the Feodor Lynen fellowship of the Alexander von Humboldt Foundation. D.E.D. thanks NFS and NIH. A.E.X.B. was supported by a scholarship from the Natural Sciences and Engineering Research Council of Canada.