Mechanisms governing the visco-elastic responses of living cells assessed by foam and tensegrity models.

P Cañadas,V M Laurent,P Chabrand,D Isabey,S Wendling-Mansuy

doi:10.1007/bf02349982

Abstract

The visco-elastic properties of living cells, measured to date by various authors, vary considerably, depending on the experimental methods and/or on the theoretical models used. In the present study, two mechanisms thought to be involved in cellular visco-elastic responses were analysed, based on the idea that the cytoskeleton plays a fundamental role in cellular mechanical responses. For this purpose, the predictions of an open unit-cell model and a 30-element visco-elastic tensegrity model were tested, taking into consideration similar properties of the constitutive F-actin. The quantitative predictions of the time constant and viscosity modulus obtained by both models were compared with previously published experimental data obtained from living cells. The small viscosity modulus values (10(0)-10(3) Pa x s) predicted by the tensegrity model may reflect the combined contributions of the spatially rearranged constitutive filaments and the internal tension to the overall cytoskeleton response to external loading. In contrast, the high viscosity modulus values (10(3)-10(5) Pa x s) predicted by the unit-cell model may rather reflect the mechanical response of the cytoskeleton to the bending of the constitutive filaments and/or to the deformation of internal components. The present results suggest the existence of a close link between the overall visco-elastic response of micromanipulated cells and the underlying architecture.

Highlights

THERE EXISTS an increasing amount of experimental evidence suggesting that the mechanical behaviour of the cytoskeleton (CSK) interacting with the cellular environment may determine biological functions ofliving cells, such as adhesion, differentiation, spreading and apoptosis, and their role in the healing of wounds (CHICURELet al., 1998; HARRIS et al, 1980; THOUMINE et al, 1996; WANG et al, 1993; WANG and INGBER, 1994).The CSK is a complex, three-dimensional, 'solid' network that is mainly composed of three types of filamentous biopolymers, namely actin filaments or F-actin, microtubules and intermediate filaments
These predictions lead to viscosity modulus values in the 103-105 Pa. s range predicted by the open unit-cell model (6) and in the 10°-103 Pa.s range predicted by the tensegrity model (3)
It emerged that the values of the viscosity modulus measured using the microplate device (MD) (THOUMINE and OTT, 1997a), atomic force microscopy (AFM) (Wu et al, 1998) and micropipette manipulation (MM) (LAURENT et al, 2000; SATO et al, 1990; THOUMINE and OTT, 1997b) fall in the range predicted by the unit-cell model, whereas the values ofthe viscosity modulus measured by magnetic twisting cytometry (MTC) (LAURENT et al, 2002b; MAKSYM et al, 2000; WANG and INGBER, 1994; WANG, 1998), optical tweezers (OTs) (LAURENT et al, 2002b) and magnetic

Summary

Introduction

THERE EXISTS an increasing amount of experimental evidence suggesting that the mechanical behaviour of the cytoskeleton (CSK) interacting with the cellular environment may determine biological functions ofliving cells, such as adhesion, differentiation, spreading and apoptosis, and their role in the healing of wounds (CHICURELet al., 1998; HARRIS et al, 1980; THOUMINE et al, 1996; WANG et al, 1993; WANG and INGBER, 1994).The CSK is a complex, three-dimensional, 'solid' network that is mainly composed of three types of filamentous biopolymers, namely actin filaments or F-actin, microtubules and intermediate filaments. Structural models of the CSK have helped to elucidate the structural basis of the non-linear stress-strain relationship (i.e. strain hardening) systematically observed in adherent cells and the role of internal tension in the mechanical behaviour of the CSK (INGBER et al, 1993; SATCHER and DEWEY, 1996; STAMENOVIC et al, 1996; WENDLING et al, 1999; 2000b) These studies have made it possible to analyse the specific elastic properties of living cells, none of them has dealt, so far, with the cellular viscosity clearly found to play a role in many experimental studies (BAUSH et al, 1999; LAURENT et al, 2000; 2002b; MAKSYM et al, 2000; MATHUR et al, 2000; NEMOTO, 1982; SATCHER and DEWEY, 1996; SATO et al, 1990; THOUMINE and OTT, 1997a; b; VALBERG and ALBERTINI, 1985; VALBERG and FELDMAN, 1987; WANG et al, 1993;WANGandiNGBER, 1994;WANG, 1998;Wuetal., 1998; YAMADA et al, 2000)

Methods

Results

Conclusion