A Theoretical Description of Elastic Pillar Substrates in Biophysical Experiments

Abstract

Arrays of elastic pillars are used in biophysical experiments as sensors for traction forces. The evaluation of the forces can be complicated if they are coupled to the pillar displacements over large distances. This is the case if many of the pillars are interconnected by elastic linkages as, for example, in fiber networks that are grown on top of pillars. To calculate the traction forces in such a network, we developed a set of nonlinear inhomogeneous equations relating the forces in the linking elements to the resulting pillar deflections. We chose a homogeneous, activated two-dimensional network of cytoskeletal actin filaments to illustrate that a pillar substrate is generally not a force sensor but a force-gradient sensor. In homogeneous networks the forces acting along the filaments can be approximated by analyzing only pillar deflections in the edge zones of the substrate and by integration over the corresponding force gradients.

A bio-chemo-mechanical model for cell contractility

“…When included, cell contractility has been modeled by simply prescribing a thermal strain to either a cell otherwise regarded as an isotropic elastic continuum (4) or a discrete set of elastic filaments representing the stress fibers (5). Such models neglect the biochemistry of the active apparatus of the cell that generates, supports, and responds to mechanical forces.…”

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

“…However, the model of Novak et al assumes that stress fibres form randomly at adhesion sites in proportion to the size of the adhesion and dissociate at a constant rate. Mohrdieck et al (2005) has developed a model for the actin cytoskeleton as a discrete set of fibres linking adhesion sites. However, this model assumes a predefined distribution of fibres which are subjected to a uniform prestrain and does not allow for changes in the cytoskeleton based on the underlying cell processes.…”

“…Previously, the contractile cytoskeleton has been included in computational models of biological gels as prepositioned passive filaments with prescribed shrinkage strains (Mohrdieck et al 2005;Storm et al 2005). However, these studies offer limited insight as they do not consider the underlying cellular processes.…”

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

“…The contractile properties of non-muscle cells due to the activity of stress fibres (SFs) have received increasing attention with the advent of experimental techniques such as micro-post arrays that allow the measurement of cellular forces (Elson and Genin, 2013). Computational models for SFs include networks models where filaments with prescribed shrinkage strains are specified (Mohrdieck et al, 2005). Such approaches neglect the biochemistry of the active apparatus of the cell that generates, supports and responds to mechanical forces.…”