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Large and reversible myosin-dependent forces in rigidity sensing

Nature Physics volume 15, pages 689–695 (2019)Cite this article

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Abstract

Cells sense the rigidity of their environment through localized pinching, which occurs when myosin molecular motors generate contractions within actin filaments anchoring the cell to its surroundings. We present high-resolution experiments performed on these elementary contractile units in cells. Our experimental results challenge the current understanding of molecular motor force generation. Surprisingly, bipolar myosin filaments generate much larger forces per motor than measured in single-molecule experiments. Furthermore, contraction to a fixed distance, followed by relaxation at the same rate, is observed over a wide range of matrix rigidities. Finally, stepwise displacements of the matrix contacts are apparent during both contraction and relaxation. Building on a generic two-state model of molecular motor collections, we interpret these unexpected observations as spontaneously emerging features of a collective motor behaviour. Our approach explains why, in the cellular context, collections of resilient and slow motors contract in a stepwise fashion while collections of weak and fast motors do not. We thus rationalize the specificity of motor contractions implied in rigidity sensing compared to previous in vitro observations.

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Fig. 1: Tension and relaxation dynamics observed through correlated pillar motion.
Fig. 2: Myosin-motor number quantification.
Fig. 3: Sketch of the model.
Fig. 4: Comparison between experiments and simulations with localized transition rates at the minimum of the energy profiles.
Fig. 5: Analytical description for the 2.5 nm step behaviour.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon request.

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Acknowledgements

J.-F.R., J.P. and M.S. are supported by the National Research Foundation, Prime Ministers Office, Singapore and the Ministry of Education under the Research Centres of Excellence programme. In addition, J.L. and M.S. were supported by NIH grant R01GM113022.

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Author notes

  1. These authors contributed equally: James Lohner, Jean-Francois Rupprecht.

Authors and Affiliations

  1. Department of Biological Sciences, Columbia University, New York, NY, USA

    James Lohner, Junquiang Hu, Nicola Mandriota, Ozgur Sahin & Michael P. Sheetz

  2. Mechanobiology Institute, National University of Singapore, Singapore, Singapore

    Jean-Francois Rupprecht, Diego Pitta de Araujo, Jacques Prost & Michael P. Sheetz

  3. Department of Biomedical Engineering, Columbia University, New York, NY, USA

    Mayur Saxena

  4. Droice Research, New York, NY, USA

    Mayur Saxena

  5. Department of Mechanical Engineering, Columbia University, New York, NY, USA

    James Hone

  6. Laboratoire Physico Chimie Curie, Institut Curie, PSL Research University, CNRS UMR168, Paris, France

    Jacques Prost

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Contributions

J.L., J.Hu, J.Ho. and M.P.S. designed the experimental study. J.-F.R. and J.P. designed the theoretical analysis. J.-F.R. performed the simulations. J.L. performed the experiments. J.L. and M.S. were involved in data analysis. J.Hu and J.Ho. developed the method for making dual rigidity pillars. N.M. and O.S. carried out measurements of pillar rigidity. D.P.A. implemented the 3D animations of pillar motion. J.-F.R., J.P. and M.P.S. wrote the manuscript.

Corresponding authors

Correspondence to Jean-Francois Rupprecht, Jacques Prost or Michael P. Sheetz.

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Supplementary information

Supplementary Information

Appendices A and B, Supplementary Figures 1–10, Supplementary Tables I–III and Supplementary References 1–15.

Reporting Summary

Supplementary Video 1

Mouse embryonic fibroblast cell spreading on dual-stiffness pillars. Cyan shading represents soft pillars (3 pN nm–1, marked with C343 dye). No shading represents stiff pillars (60 pN nm–1). Pillar displacements occur primarily at the leading edge of the lamellipodium, where they can be seen as red arrows. Contractile units are highlighted by green displacement arrows. The frequency of contractile units increases as the cell enters P2 spreading. Density of contractile units per unit of cell edge, contractile unit maximum pillar displacement, and contractile unit pillar displacement velocities are invariant across stiffness lines. Movie duration 8 min (1 frame s–1).

Supplementary Video 2

Stochastic simulation of the motor assembly, with transition rates localized around the minimum of the potential. Top panel: total pillar deflection as a function of time. The red cross indicates the current state of the assembly. Bottom panel: state of the motors assembly (colour symbols) cyclic position ξi = mod(xi, l) and energy of a particular motor (blue curve) potential W1 in state 1 as a function of the cyclic coordinate ξ (orange curve) transition rate ω1 from state 1 to state 2. Parameters are K = 10 pN nm−1 and N = 120 (other parameters are given in Supplementary Table III).

Supplementary Video 3

Analytical resolution for a constant total transition rate ω of main text equation (4), corresponding to the large number of motor limit. Top panel: total pillar deflection X(t) of the collective assembly as a function of time ωt. The red cross indicates the current value of the pillar deflection. Bottom panel: joint energy–density representation — (blue curve) energy profile in state 1 as a function of the cyclic coordinate ξ = mod(x, l), (grey curve) occupation density P1 in state 1. The occupation density in state 2 is given by P2 = 1/l − P1.

Supplementary Video 4

Animation showing the process of contraction, relaxation and disassembly (performed in Blender).

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Lohner, J., Rupprecht, JF., Hu, J. et al. Large and reversible myosin-dependent forces in rigidity sensing. Nat. Phys. 15, 689–695 (2019). https://doi.org/10.1038/s41567-019-0477-9

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