Effects of Contact Surface Shape on Dynamic Lifetime and Strength of Molecular Bond Clusters under Displacement- and Force-Controlled Loading Conditions.

Many experimental and theoretical studies have shown that the mechanical properties of cells and the extracellular matrix can significantly affect the lifetime and strength of the adhesion clusters of molecular bonds. However, there are few studies on how the shape of the contact surface affects the lifetime and strength of the adhesion clusters of molecular bonds, especially theoretical studies in this area. An idealized model of focal adhesion is adopted, in which two rigid media are bonded together by an array of receptor-ligand bonds modeled as Hookean springs on a complex surface topography, which is described by three parameters: the surface shape factor ß, the length of a single identical surface shape L, and the amplitude of surface shapes w. In this study, systematic Monte Carlo simulations of this model are conducted to study the lifetime of the molecular bond cluster under linear incremental force loading and the strength of the molecular bond cluster under linear incremental displacement loading. We find that both small surface shape amplitudes and large surface shape factors will increase the lifetime and strength of the adhesion cluster, whereas the length of a single surface shape causes oscillations in the lifetime and strength of the cluster, and this oscillation amplitude is affected by the surface shape amplitude and the factor. At the same time, we also find that the pretension in the cluster will play a dominant role in the adhesion strength under large amplitudes and small factors of surface shapes. The physical mechanisms behind these phenomena are that the changes of the length of a single surface shape, the amplitude of surface shapes, and the surface shape factor cause the changes of stress concentration in the adhesion region, bond affinity, and the number of similar affinity bonds.

Elasticity-associated rebinding rate of molecular bonds between soft elastic media.

A quantitative understanding of how cells interact with their extracellular matrix via molecular bonds is fundamental for many important processes in cell biology and engineering. In these interactions, the deformability of cells and matrix are usually comparable with that of the bonds, making their rebinding events globally coupled with the deformation states of whole systems. Unfortunately, this important principle is not realized or adopted in most conventional theoretical models for analyzing cellular adhesions. In this study, we considered a new theoretical model of a cluster of ligand-receptor bonds between two soft elastic bodies, in which the rebinding rates of ligands to receptors are described, by considering the deformation of the overall system under the influence of bond distributions. On the basis of theory of continuum and statistical mechanics, we obtained an elasticity-associated rebinding rate of open bonds in a closed analytical form that highly depends on the binding states and distributions of all other bonds as well as on the overall deformation energy stored in the elastic bodies and all closed bonds. On the basis of this elasticity-associated rebinding rate and by performing Monte Carlo simulations, we uncovered new mechanisms underlying the adhesion stability of molecular-bond clusters associated with deformable elastic bodies. Moreover, we revealed that the rebinding processes of molecular bonds is not only dependent on interfacial separation but is related to overall energy. This newly proposed rebinding rate may substantially improve our understanding of how cells adapt to their microenvironments by adjusting their mechanical properties through cytoskeleton remodeling.