Time scale and other invariants of integrative mechanical behavior in living cells

Ben Fabry, Geoffrey N. Maksym, James P. Butler, Michael Glogauer, Daniel Navajas, Nathan A. Taback, Emil J. Millet, and Jeffrey J. Fredberg
Phys. Rev. E 68, 041914 – Published 27 October 2003
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Abstract

In dealing with systems as complex as the cytoskeleton, we need organizing principles or, short of that, an empirical framework into which these systems fit. We report here unexpected invariants of cytoskeletal behavior that comprise such an empirical framework. We measured elastic and frictional moduli of a variety of cell types over a wide range of time scales and using a variety of biological interventions. In all instances elastic stresses dominated at frequencies below 300 Hz, increased only weakly with frequency, and followed a power law; no characteristic time scale was evident. Frictional stresses paralleled the elastic behavior at frequencies below 10 Hz but approached a Newtonian viscous behavior at higher frequencies. Surprisingly, all data could be collapsed onto master curves, the existence of which implies that elastic and frictional stresses share a common underlying mechanism. Taken together, these findings define an unanticipated integrative framework for studying protein interactions within the complex microenvironment of the cell body, and appear to set limits on what can be predicted about integrated mechanical behavior of the matrix based solely on cytoskeletal constituents considered in isolation. Moreover, these observations are consistent with the hypothesis that the cytoskeleton of the living cell behaves as a soft glassy material, wherein cytoskeletal proteins modulate cell mechanical properties mainly by changing an effective temperature of the cytoskeletal matrix. If so, then the effective temperature becomes an easily quantified determinant of the ability of the cytoskeleton to deform, flow, and reorganize.

  • Received 7 May 2003

DOI:https://doi.org/10.1103/PhysRevE.68.041914

©2003 American Physical Society

Authors & Affiliations

Ben Fabry1,*, Geoffrey N. Maksym2, James P. Butler1, Michael Glogauer3, Daniel Navajas4, Nathan A. Taback5, Emil J. Millet1, and Jeffrey J. Fredberg1

  • 1Physiology Program, Harvard School of Public Health, 665 Huntington Avenue, Boston, Massachusetts 02115, USA
  • 2School of Biomedical Engineering, Dalhousie University, 5981 University Avenue, Halifax, Nova Scotia, Canada B3H 3J5
  • 3Faculty of Dentistry, University of Toronto, 150 College Street, Toronto, Ontario, Canada M5S 3E2
  • 4Unitat Biofísica i Bioenginyeria, Universitat de Barcelona–IDIBAPS, Casanova 143, 08036 Barcelona, Spain
  • 5Department of Biostatistics, Harvard School of Public Health, 665 Huntington Avenue, Boston, Massachusetts 02115, USA

  • *Email address: bfabry@hsph.harvard.edu

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Vol. 68, Iss. 4 — October 2003

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