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Optimal matrix rigidity for stress-fibre polarization in stem cells


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.

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Figure 1: Actomyosin stress-fibre alignment in hMSCs sparsely plated on 2D substrates of different elasticities.
Figure 2: Cell adhesion and polarization represented by a 1D spring model.
Figure 3: Cell polarization as a function of the ratio of Young’s modulus of the matrix, Em, and the cell, Ec, in both our 2D and 3D models.
Figure 4: The effect of axial cell elongation on stress-fibre polarization and experimental values of the order parameter S for different elastic substrates.


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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.

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A.Z. and S.A.S. developed the theory. F.R., A.E.X.B. and D.E.D. designed the experiments; F.R. carried out the experiments; A.E.X.B. wrote the image analysis algorithm. All authors analysed the data and wrote the paper.

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Correspondence to A. Zemel.

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Zemel, A., Rehfeldt, F., Brown, A. et al. Optimal matrix rigidity for stress-fibre polarization in stem cells. Nature Phys 6, 468–473 (2010).

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