How can cells sense the elasticity of a substrate? An analysis using a cell tensegrity model

Abstract

A eukaryotic cell attaches and spreads on substrates, whether it is the extracellular matrix naturally produced by the cell itself, or artifi cial materials, such as tissueengineered scaffolds. Attachment and spreading require the cell to apply forces in the nN range to the substrate via adhesion sites, and these forces are balanced by the elastic response of the substrate. This mechanical interaction is one determinant of cell morphology and, ultimately, cell phenotype. In this paper we use a fi nite element model of a cell, with a tensegrity structure to model the cytoskeleton of actin fi laments and microtubules, to explore the way cells sense the stiffness of the substrate and thereby adapt to it. To support the computational results, an analytical 1D model is developed for comparison. We fi nd that (i) the tensegrity hypothesis of the cytoskeleton is suffi cient to explain the matrix-elasticity sensing, (ii) cell sensitivity is not constant but has a bell-shaped distribution over the physiological matrix-elasticity range, and (iii) the position of the sensitivity peak over the matrix-elasticity range depends on the cytoskeletal structure and in particular on the F-actin organisation. Our model suggests that F-actin reorganisation observed in mesenchymal stem cells (MSCs) in response to change of matrix elasticity is a structural-remodelling process that shifts the sensitivity peak towards the new value of matrix elasticity. This fi nding discloses a potential regulatory role of scaffold stiffness for cell differentiation.

Cellular contractility and substrate elasticity: a numerical investigation of the actin cytoskeleton and cell adhesion

“…The tensegrity model (Ingber 1993) has been used to investigate the response of contractile cells to substrate elasticity (De Santis et al 2011). This study also identifies the substrate stiffness over which the cell shows the greatest sensitivity to substrate elasticity.…”

Cooperative contractility: The role of stress fibres in the regulation of cell-cell junctions

“…Such approaches neglect the biochemistry of the active apparatus of the cell that generates, supports and responds to mechanical forces. The so-called tensegrity model (Ingber, 1993) has previously been used to simulate cells on elastic substrates (De Santis et al, 2011); however, the tensegrity model requires a predefined cytoskeleton. Furthermore, it has been shown experimentally that the disruption of microtubules results in an increase in the traction force generated by cells (Kolodney and Elson, 1995), contradicting the central assumption of the tensegrity model.…”

Biological Activity of Fibronectin at the Cell-Material Interface

“…These individual domains can be of hydrophobic, hydrophilic, positively, or negatively charged nature [49][50][51]. In solution, proteins rotate freely whereas on a surface each protein adopts a certain orientation determining which part of the molecule interacts with the surface and which part is exposed to the bulk solution.…”

“…In solution, proteins rotate freely whereas on a surface each protein adopts a certain orientation determining which part of the molecule interacts with the surface and which part is exposed to the bulk solution. The favored orientation of a protein on the surface is the one that minimize its free energy resulting from attractive coulomb and van-der-Waals interactions, hydrogen bonds, and the entropy gain of solvent molecules [49][50][51]. Therefore, its orientation and conformation will depend on the physico-chemical properties of the substrate surface, determining the accessibility of interaction domains with cell receptors.…”

“…Since cells must deform the substrate to sense it, and taking into account the range of forces cells can exert (which range from 1 to 5 nN/µm 2 ) [47][48], it would appear that cells are not able to deform so rigid substrates [4,[49][50] and, consequently, the family of materials investigated must be sensed as simply rigid substrates by cells.…”