Specific adhesion of a soft elastic body on a wavy surface

Abstract

This paper aims at developing a stochastic-elastic model of a soft elastic body adhering on a wavy surface via a patch of molecular bonds. The elastic deformation of the system is modeled by using continuum contact mechanics, while the stochastic behavior of adhesive bonds is modeled by using Bell's type of exponential bond association/dissociation rates. It is found that for sufficiently small adhesion patch size or stress concentration index, the adhesion strength is insensitive to the wavelength but decreases with the amplitude of surface undulation, and that for large adhesion patch size or stress concentration index, there exist optimal values of the surface wavelength and amplitude for maximum adhesion strength.Most biological cells must adhere to an extracellular matrix (ECM) or other cells in order to perform normal physiological functions such as migration, spreading, differentiation, growth, and healing. 1 Cell adhesion involves coordinated actions of many biological molecules such as ECM proteins, cytoskeletal proteins and membrane receptors, and can be strongly influenced by the topographical structures of ECM and the basement membranes of many biological tissues. 2,3 Bozec and Horton 4 proposed that the topographic features of type I collagen monomers may enhance attachment and adhesion of mammalian cells. Bettinger et al. 5 found that nanogratings appear to enhance while nanoposts and nanopits tend to reduce cell adhesion strength. Sykaras et al. 6 showed that surface roughness can strongly affect the osseointegration of implants. Eisenbarth et al. 7 studied the adhesion of fibroblasts on Ti, Ti-6Al-4V, and Ti30Ta substrates, and found that cell alignment becomes more distinct as the surface roughness increases. These experimental findings suggest that surface topography may play important roles in cell adhesion.Cells usually adhere to a material surface through focal adhesions consisting of multiple transmembrane receptor-ligand bonds. 8-10 The random, discrete association/dissociation behaviors of these molecular bonds are an essential characteristic feature of cell adhesion. From a statistical point of view, a single molecular bond has only a finite lifetime, 11-14 but a cluster of bonds can survive for much longer time due to collective effects in a stochastical ensemble. Erdmann and Schwarz 15 showed that the lifetime of a cluster of bonds increases with the increase of cluster size. Wang and Gao 16 considered two elastic half-spaces joined together by diffusive molecular bonds and showed that a uniform bond disa) Corresponding author. tribution along the interface is intrinsically unstable. Qian et al. 17,18 performed Monte-Carlo simulations to investigate the adhesion lifetime and strength of a single or periodic arrays of bond clusters between two elastic media. Wang and Gao 19 and Rizza et al. 20 investigated the size-and shape-dependent pull-off force and adhesion lifetime of a bond cluster, and showed that strong and stable adhesion can be achieved by selecting an optimal surface shape, ...

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

“…Recently, Ju et al [40] investigated the two-dimensional receptor-ligand association kinetics, which was found to be transport regulated. By recognizing that the mechanical properties of the substrate are crucial in the formation and growth of FAs, Gao and his co-workers successfully developed a coupled stochastic-elastic model [41][42][43][44] to present insights into the biophysical behaviour in cell adhesion, such as stiffness and orientation-dependent lifetime of cluster bonds [42,[45][46][47][48][49], stable size of the molecular bond cluster for cell adhesion [41,45,50], shape-dependent strength of cell adhesion [51][52][53], enhancement of cell adhesion via pre-tension in the cytoskeleton [54,55] and cell adhesion under cyclic tension [56].…”

Probing the mechanosensitivity in cell adhesion and migration: Experiments and modeling

“…A growing body of evidence suggests that the mechanical cues play a central role in regulating cell adhesion and migration, similar to chemical environmental cues [15][16][17][18][19]. In fact, cells live in a mechanical environment and participate in numerous physical interactions with the world around them.…”

Wavelet method applied to specific adhesion of elastic solids via molecular bonds

“…16 Quantitative study on constitutive relations of multicellular biological systems will help us to understand the mechanism of the tumor growth, 14,15 in which cell adhesion plays a vital role. However, the governing equations of the specific adhesion model of cellular interactions proposed by Wang and Gao 12 and Wang et al 13 consist of one nonlinear integro-differential equation with singular Cauchy kernel and one strong nonlinear differential equation. Therefore, how to efficiently and precisely solve these equations becomes crucially important for the understanding of the adhesion behavior of the system.…”

“…This finding is consistent with the fact that cells may strongly respond to changes in cellular and environmental stiffness. To gain further insight into this issue, for a specific adhesion system with two elastic solids contacted via a molecular bond cluster, Wang and Gao 12 and Wang et al 13 have proposed an analytical model by considering the mean-field stochastic-elastic coupling to investigate the dependence of adhesion strength on the cluster size and interfacial shape. However, the above progress is still far from enough towards the fully understanding of mechanisms on cell adhesion.…”

“…18 For coupled nonlinear singular integro-differential equations, the power series based iterative algorithm has been adopted by Wang and Gao 12 and Wang et al 13 Applications of this method involves the calculation of a number of Cauchy type singular integrals, which usually needs sophisticated mathematical skills. In order to avoid this cumbersome situation and establish a generally efficient mathematical tool to solve a broad range of strong nonlinear mathematical problems arising from molecular and cellular biomechanics studies, we adopt a recently developed wavelet based numerical method for the solution of the adhesion problems in the present study.…”