• Open Access

Geometrical Origins of Contractility in Disordered Actomyosin Networks

Martin Lenz
Phys. Rev. X 4, 041002 – Published 2 October 2014
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Abstract

Movement within eukaryotic cells largely originates from localized forces exerted by myosin motors on scaffolds of actin filaments. Although individual motors locally exert both contractile and extensile forces, large actomyosin structures at the cellular scale are overwhelmingly contractile, suggesting that the scaffold serves to favor contraction over extension. While this mechanism is well understood in highly organized striated muscle, its origin in disordered networks such as the cell cortex is unknown. Here, we develop a mathematical model of the actin scaffold’s local two- or three-dimensional mechanics and identify four competing contraction mechanisms. We predict that one mechanism dominates, whereby local deformations of the actin break the balance between contraction and extension. In this mechanism, contractile forces result mostly from motors plucking the filaments transversely rather than buckling them longitudinally. These findings shed light on recent in vitro experiments and provide a new geometrical understanding of contractility in the myriad of disordered actomyosin systems found in vivo.

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  • Received 14 April 2014

DOI:https://doi.org/10.1103/PhysRevX.4.041002

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

Martin Lenz*

  • Université Paris-Sud, CNRS, LPTMS, UMR 8626, Orsay 91405, France

  • *martin.lenz@u-psud.fr

Popular Summary

The movement of cells relies heavily on intracellular contractile structures made of actin filaments and myosin, a molecular motor. Some of these structures are very ordered (e.g., striated muscle), and their contractility arises straightforwardly from the geometrical arrangement of the filaments and motors, explaining how macroscopic movement arises from protein-scale interactions. It is often assumed that this mechanism accounts for more or less all actomyosin contractility. We show that this assumption is wrong in many disordered structures found in nonmuscle cells, such as the cell cortex.

Previous analyses of contractility treated the problem in one dimension; however, the literature remains divided as to what causes contraction in biologically important two- and three-dimensional situations. In nonmuscle cells, the molecular motors have no obvious propensity toward contractility and in fact have an equal probability of generating extension. There, contractility can only be understood by taking subtle geometrical effects into account. We identify and compare all such possible mechanisms theoretically, considering an ensemble of filament-motor systems embedded in a weakly deformed, linearly elastic medium. We find that actin deformation is essential for contractility, although our results are limited to deformations arising from small motor forces. Additional work is needed to analyze networks that undergo strong deformation and to study how motors might work collectively across a distance.

Our results are qualitatively supported by previous experiments, and our study paves the way for future in vivo quantitative analyses of contractility.

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Vol. 4, Iss. 4 — October - December 2014

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