A model for the contractility of the cytoskeleton including the effects of stress-fibre formation and dissociation

Vikram S Deshpande, Robert M McMeeking, Anthony G Evans

Abstract

A model for the contractility of cells is presented that accounts for the dynamic reorganization of the cytoskeleton. It is motivated by three key biochemical processes: (i) an activation signal that triggers actin polymerization and myosin phosphorylation, (ii) the tension-dependent assembly of the actin and myosin into stress fibres, and (iii) the cross-bridge cycling between the actin and the myosin filaments that generates the tension. Simple relations are proposed to model these coupled phenomena and a constitutive law developed for the activation and response of a single stress fibre. This law is generalized to two- and three-dimensional cytoskeletal networks by employing a homogenization analysis and a finite strain continuum model is developed. The key features of the model are illustrated by considering: (i) a single stress fibre on a series of supports and (ii) a two-dimensional square cell on four supports. The model is shown to be capable of predicting a variety of key experimentally established characteristics including: (i) the decrease of the forces generated by the cell with increasing support compliance, (ii) the influence of cell shape and boundary conditions on the development of structural anisotropy, and (iii) the high concentration of the stress fibres both at the focal adhesions and at the sites of localized applied tension. Moreover, consistent with the experimental findings, the model predicts that multiple activation signals are more effective at developing stress fibres than a single prolonged signal.

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Footnotes

  • Electronic supplementary material is available at http://dx.doi.org/10.1098/rspa.2006.1793 or via http://www.journals.royalsoc.ac.uk.

  • In contrast to non-muscle cells, the cytoskeleton in muscle cells is relatively static and comprises a regular array of filament bundles called sarcomeres.

  • The Hill (1938) equation adequately models the cross-bridge dynamics in the low-frequency domain and readers are referred to Rice et al. (1999) for a discussion on more sophisticated models that capture the cross-bridge dynamics over a large frequency range. Since cell contractility is a relatively slow process, it suffices to use the simple Hill-type description to model the tension versus velocity relationship of the stress fibres.

  • Hill (1963) defined an RVE as a domain that is (i) structurally typical of the entire mixture (network of stress fibres) and (ii) sufficiently large compared with the micro-scale (say, the stress fibre radius).

  • ABAQUS (2004) User's Manual, v. 6.5. ABAQUS, Inc.

    • Received May 18, 2006.
    • Accepted November 14, 2006.
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