A Tensegrity Structure With Buckling Compression Elements: Application to Cell Mechanics

Abstract

A tensegrity structure composed of six slender struts interconnected with 24 linearly elastic cables is used as a model of cell deformability. Struts are allowed to buckle under compression and their post-buckling behavior is determined from an energy formulation of the classical pin-ended Euler column. At the reference state, the cables carry initial tension balanced by forces exerted by struts. The structure is stretched uniaxially and the stretching force versus axial extension relationships are obtained for different initial cable tensions by considering equilibrium at the joints. Structural stiffness is calculated as the ratio of stretching force to axial extension. Predicted dependences of structural stiffness on initial cable tension and on stretching force are consistent with behaviors observed in living cells. These predictions are both qualitatively and quantitatively superior to those obtained previously from the model in which the struts are viewed as rigid.

Symmetrical reconfiguration of tensegrity structures

“…resist shape distortion (Ingber, 1993(Ingber, , 1998. Results of static numerical analysis using a tensegrity structure to model a cell's static properties which were in agreement with biological experimental measurements have been reported (see Stamenovic et al, 1996;Coughlin and Stamenovic, 1997).…”

Tensegrity I. Cell structure and hierarchical systems biology

“…A more recent formulation of the model includes, for example, semiflexible struts analogous to microtubules, rather than rigid compression struts, and incorporates values for critical features of the individual cytoskeletal filaments (e.g. volume fraction, bending stiffness and cable stiffness) from the literature (Coughlin and Stamenovic, 1997;Stamenovic and Coughlin, 1999). This more refined model is qualitatively and quantitatively superior to that containing rigid struts.…”

“…Largely through the work of Stamenovic and co-workers, this oversimplified micromechanical model continues to be progressively modified and strengthened over time (Coughlin and Stamenovic, 1997;Coughlin and Stamenovic, 1998;Stamenovic and Coughlin, 1999;Stamenovic and Coughlin, 2000;Stamenovic and Ingber, 2002). A more recent formulation of the model includes, for example, semiflexible struts analogous to microtubules, rather than rigid compression struts, and incorporates values for critical features of the individual cytoskeletal filaments (e.g.…”

A Cellular Tensegrity Model to Analyse the Structural Viscoelasticity of the Cytoskeleton

“…Such a behavior has been attributed to the structural properties of the CSK considering that the overall mechanical properties of the CSK are strongly related to the spatial rearrangement of the CSK-filaments (Ingber & Folkman, 1989;Ingber, 1997Ingber, , 1998Ingber & Jamieson, 1985;Ingber & Karp, 1991;Wang & Ingber, 1994) and thus can be advantageously explained by the tensegrity concept (Ingber, 1993(Ingber, , 1998Ingber et al, 1994Ingber et al, , 1995Wang & Ingber, 1994;Wendling et al, 1999Wendling et al, , 2000a. Theoretical descriptions of tensegrity structure at the cellular level have been initially given by Stamenovic's group (Coughlin & Stamenovic, 1997Stamenovic et al, 1996), whereas other theoretical studies have provided normalized predictions of the mechanical behavior which all confirmed the expected nonlinear and pre-stress-dependent behaviors (Wendling et al, 1999(Wendling et al, , 2000a. Noteworthy, the tensegrity models proposed up to now to describe the CSK response have only been studied in terms of pure elastic behavior, i.e.…”