Theoretical Modeling On Mechanics Of Cell Adhesion By Considering Fully Coupled Interaction Between Media Deformation And Stochastic Molecular Reaction

The specific adhesion formed by adhesion molecules between cells and their microenvironments is a basic biological process in many physiological and pathological phenomena.This specific adhesion is usually composed of a cluster of molecular bonds that can rupture or rebind stochastically.Then,the stochastic processes of small molecules groups will be coupled with mechanical responses of the system.A quantitative study of how these bonds interact with cells and microenvironments is fundamental for many important processes in cell biology and engineering,such as cell growth,migration,differentiation,and propagation.Specifically,as a soft media,the deformability of cells and their microenvironments under mechanical stimuli is usually comparable with that of the bonds,making their rebinding events globally coupled with the deformation states of cells and their microenvironments.Unfortunately,this important principle of fully deformation-coupled effects between media and bonds is not realized or adopted in most conventional theoretical models for analyzing cellular adhesions,leading to the partial failure of conventional models for predicting cell experiments.Therefore,in order to fix this shortage,we considered a new theoretical model of a cluster of ligand-receptor bonds between soft elastic media or viscoelastic media,in which the rebinding rates of ligands to receptors are described,for the first time,by fully considering the coupling of deformability of the overall system with bonds reaction processes.On the basis of theory of continuum mechanics and statistical mechanics,we obtained a deformation-associated rebinding rate of open bonds,then applying this new rebinding rate to the strength measurement of molecular cluster.The innovative achievements of this paper are listed as follows:(1)In this study,we considered a new theoretical model of a cluster of ligandreceptor bonds between two soft elastic bodies,in which the rebinding rates of ligands to receptors are described,for the first time,by considering the fully coupled effects between deformations of elastic media and reaction processes of molecular bonds.On the basis of theory of continuum mechanics 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 not only depend on interfacial separation but relate to overall energy.This newly proposed rebinding rate along with the abovementioned new mechanisms may substantially improve our understanding of how cells adapt to their microenvironments by adjusting their mechanical properties through cytoskeleton remodeling.(2)The deformation of soft media generally involved the characteristic time scale for its duration,for instance,the creep and stress relaxation of cytoskeleton.In this case,only considering the coupling between elastic deformations of the soft media and the chemical reaction of molecular bonds will no longer fit.Based on this,we considered a new theoretical model of a cluster of ligand-receptor bonds between a soft elastic body and a viscoelastic body.In this model,we incorporated the deformation of viscoelastic media and its characteristic time scale into the bonds reaction processes.On the basis of theory of continuum mechanics and statistical mechanics,we obtained the deformation-associated and characteristic time dependent reactions rates of molecular bonds in a closed analytical form.We found that these reaction rates highly depend on the distributions and binding states of all other bonds,the overall deformation energy stored in the system,and the ratio between the reaction time and deformation characteristic time.On the basis of these deformation related and characteristic time associated reaction rates,we uncovered that the adhesion mechanisms between viscoelastic media and elastic media are significantly different.This finding may be helpful in understanding the interactions between cells and their viscoelastic microenvironments.(3)Due to the coupling between media deformation and bonds reaction rates,when we measured the strength of a cluster of molecular bonds by a deformable probe,the deformation of the probe may affect the measurement strength of bonds.Evans et al.extensively studied the sensitive force technique to probe the molecular adhesion and structural linkages at biological interfaces.Their group suggested that the low stiffness of a loading device may enhance the sensitivity of various interactions between the probe and the surface.Therefore,their work suggested the selection of a probe whose stiffness is comparable or even much smaller than that of the sample to be measured during the strength measurement of biological adhesion.However,when considered the coupling between bonds reaction rates and the probe deformation,their suggestion might not be suitable.Therefore,we consider an idealized theoretical model of a cluster of molecular bonds that are subjected to an applied tensile load.In this model,by deriving an exact expression of the rebinding rate and directly solving the master equation,we found that the measured adhesion strength of a molecular bond cluster exhibits strong dependence on the stiffness of the loading device and the bond number when the stiffness value is close to or smaller than the effective stiffness of the bond cluster.Thus,an improper selection of the stiffness value of the loading device may lead to measurement uncertainty.