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Size-dependent transition from steady contraction to waves in actomyosin networks with turnover

Nature Physics volume 20, pages 123–134 (2024)Cite this article

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Abstract

Actomyosin networks play essential roles in many cellular processes, including intracellular transport, cell division and cell motility, and exhibit many spatiotemporal patterns. Despite extensive research, how the interplay between network mechanics, turnover and geometry leads to these different patterns is not well understood. We focus on the size-dependent behaviour of contracting actomyosin networks in the presence of turnover, using a reconstituted system based on cell extracts encapsulated in water-in-oil droplets. We show that the system can self-organize into different global contraction patterns, exhibiting persistent contractile flows in smaller droplets and periodic contractions in the form of waves or spirals in larger droplets. The transition between continuous and periodic contraction occurs at a characteristic length scale that is inversely dependent on the network contraction rate. These dynamics are captured by a theoretical model that considers the coexistence of different local density-dependent mechanical states with distinct rheological properties. The model shows how large-scale contractile behaviours emerge from the interplay between network percolation, which is essential for long-range force transmission, and rearrangements due to advection and turnover. Our findings thus demonstrate how varied contraction patterns can arise from the same microscopic constituents, without invoking specific biochemical regulation, merely by changing the system geometry.

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Fig. 1: Examples of continuous and periodic contraction patterns in actin networks with rapid turnover.
Fig. 2: Transition from continuous to periodic contraction depends on system size and contraction rate.
Fig. 3: Dynamics of droplets with changing actin turnover or contraction rates.
Fig. 4: Modelling the transition between continuous and periodic contraction.
Fig. 5: Transition from a global to a local contraction.

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Data availability

All the data used to support the findings of this paper are included in the plots and Supplementary Information. Any further details are available from K.K. upon request.

Code availability

The codes used for data analysis are publicly available as follows: Particle image velocimetry (PIV): https://github.com/nivieru/dropletsRhoV; Optical flow: https://ars.els-cdn.com/content/image/1-s2.0-S0006349516300339-mmc7.txt; Tracer bead tracking: https://site.physics.georgetown.edu/matlab/code.html; Spectral time-lapse (STL): https://zenodo.org/record/7663. The Matlab codes used for solving the 1D and 2D partial differential model equations as well as the the 1D discrete stochastic code are available at: https://github.com/mariyasavinov/SizeDependentWaves.git.

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Acknowledgements

We thank L. Garion for the help with extract preparation. We thank M. Piel, R. Voituriez and Juan Manuel García-Arcos for stimulating discussions and sharing unpublished results. We thank J.-F.C. Joanny for the helpful advice on the modelling. We thank P. Lenart, G. Bunin, A. Tayar, A. Frishman and S. Ro for comments on the paper. This work was supported by a grant from the United States–Israel Binational Science Foundation to K.K. and B. Goode (grant no. 2017158). M.S. and A.M. are supported by National Science Foundation grants DMS 1953430 and DMS 2052515.

Author information

Authors and Affiliations

  1. Department of Physics, Technion – Israel Institute of Technology, Haifa, Israel

    Ashwini Krishna, Niv Ierushalmi & Kinneret Keren

  2. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Mariya Savinov & Alex Mogilner

  3. Department of Biology, New York University, New York, NY, USA

    Alex Mogilner

  4. Network Biology Research Laboratories and Russell Berrie Nanotechnology Institute, Technion – Israel Institute of Technology, Haifa, Israel

    Kinneret Keren

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  1. Ashwini Krishna
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Contributions

A.K., N.I. and K.K. designed the experiments. A.K. and N.I. performed the experiments. A.K., N.I. and K.K. analysed the data. A.M., M.S., K.K. and A.K. developed the model. A.K., M.S., A.M. and K.K. wrote the paper. All co-authors discussed the results and commented on the paper.

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Correspondence to Alex Mogilner or Kinneret Keren.

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The authors declare no competing interests.

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Nature Physics thanks Anne Bernheim-Groswasser, Patrick McCall and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1

Wave front propagation in a droplet with periodic contraction.

Extended Data Fig. 2

Periodic contraction in different geometries.

Extended Data Fig. 3

The movement of tracer beads in a droplet exhibiting periodic contraction.

Extended Data Fig. 4

Periodic contraction in the form of spirals.

Extended Data Fig. 5

Contraction rate depends on droplet size.

Extended Data Fig. 6

Numerical solution of the 1D model.

Extended Data Fig. 7

Modeling the dynamics of droplets with changing actin turnover or contraction rates.

Extended Data Fig. 8

Predicted wave period as a function of system size.

Extended Data Fig. 9

2D contractile ring model.

Extended Data Fig. 10

Different contractile behaviors obtained from simulations of a discrete agent-based model for different parameter values.

Supplementary information

Supplementary Information

Supplementary text, extended data fig. legends for Figs. 1–10 and supplementary video legends for Videos 1–16.

Reporting Summary

Supplementary Video 1

Size-dependent contraction patterns.

Supplementary Video 2

Continuous actomyosin network contraction.

Supplementary Video 3

Periodic actomyosin network contraction as concentric waves.

Supplementary Video 4

Periodic actomyosin network contraction in an elongated capillary.

Supplementary Video 5

Periodic actomyosin network contraction in a spherical droplet.

Supplementary Video 6

Global actomyosin network contraction in a very large droplet.

Supplementary Video 7

The movement of tracer beads in a droplet exhibiting periodic contraction.

Supplementary Video 8

Periodic actomyosin network contraction as a clockwise spiral.

Supplementary Video 9

Mixed contraction pattern in droplet with an off-centre contraction centre.

Supplementary Video 10

Periodic contraction with different actin-associated proteins.

Supplementary Video 11

Contraction with limited turnover.

Supplementary Video 12

Transition from continuous to periodic contraction.

Supplementary Video 13

Model simulations of the size-dependent contractile behaviour.

Supplementary Video 14

Model simulations of the transition from continuous to periodic contraction in a system characterized by a contraction rate that increases over time.

Supplementary Video 15

Local contractions in droplets with enhanced myosin activity.

Supplementary Video 16

Local contractions in droplets with enhanced filament capping.

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Krishna, A., Savinov, M., Ierushalmi, N. et al. Size-dependent transition from steady contraction to waves in actomyosin networks with turnover. Nat. Phys. 20, 123–134 (2024). https://doi.org/10.1038/s41567-023-02271-5

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