A viscoelastic-stochastic model of the effects of cytoskeleton remodelling on cell adhesion

Abstract

Cells can adapt their mechanical properties through cytoskeleton remodelling in response to external stimuli when the cells adhere to the extracellular matrix (ECM). Many studies have investigated the effects of cell and ECM elasticity on cell adhesion. However, experiments determined that cells are viscoelastic and exhibiting stress relaxation, and the mechanism behind the effect of cellular viscoelasticity on the cell adhesion behaviour remains unclear. Therefore, we propose a theoretical model of a cluster of ligand-receptor bonds between two dissimilar viscoelastic media subjected to an applied tensile load. In this model, the distribution of interfacial traction is assumed to follow classical continuum viscoelastic equations, whereas the rupture and rebinding of individual molecular bonds are governed by stochastic equations. On the basis of this model, we determined that viscosity can significantly increase the lifetime, stability and dynamic strength of the adhesion cluster of molecular bonds, because deformation relaxation attributed to the viscoelastic property can increase the rebinding probability of each open bond and reduce the stress concentration in the adhesion area.

Keywords: Monte Carlo simulation; cell adhesion; viscoelastic–stochastic model.

Figure 1.

Schematic of the cell–substrate adhesion system. An idealized theoretical model of adhesion between elastic and viscoelastic half spaces through a cluster of receptor–ligand bonds.

Figure 2.

Schematic of the geometrical relationships at position of (a) closed bond and (b) breaking bond. W(t) is the surface separation at infinity.

Figure 3.

Number of closed bonds as a function of the normalized time under constant force of F = 30 pN for total bonds N = 50 and different cell viscosity coefficient η_c = 1, 5 and 10 kPa s.

Figure 4.

(a) Average number of closed bonds as a function of normalized time for loading force 20 pN, total bond number N = 50 and viscosity η_c = 10 kPa s. (b) Distribution of the average force for varying cell viscosity.

Figure 5.

Schematic of the rebinding process of free receptor and ligand after breaking in single-bond level for viscoelastic model and elastic model of cell adhesion. The dash lines denote the cell and substrate surfaces at infinity.

Figure 6.

Mean normalized lifetime as a function of the applied force for varying cell viscosity and total bond number N = 20.

Figure 7.

Mean rupture force as a function of loading rate under displacement loading for varying cell viscosity and total bond number N = 50.

Figure 8.

Mean value of the normalized lifetime as a function of cluster size for varying cell viscosity under a fixed load of 0.53 kPa.