Specific Adhesion Mechanics Under The Coupling Effect Of Medium Deformation And Molecular Potential

As the basic unit of life,the interaction between cells and the extracellular biophysical environment is an indispensable link for the normal physiological function of cells.This interaction is formed through clusters of molecular bonds formed by adhesion molecules that can rupture or rebind stochastically.Then,molecular-level events such as molecular diffusion and stochastical chemical reactions of molecular bonds are coupled to the overall deformation of the system.Therefore,a quantitative study of the effects of mechanical properties of the system,such as elasticity,creep,relaxation,etc.,on molecular level events of adhesion molecules will help us to further understand the physiological and pathological processes of cells,such as,the effects of molecular diffusion and medium viscosity on the system lifetime and strength,and the theoretical explanations of the experiments of "negative rigidity",the adjustment of their own stiffness to match the hardness of the substrate through skeleton recombination,and the "catch to slip" conversion of cells.Specifically,we assumed that the molecule-level behaviors such as molecules diffusion and stochastic chemical reactions between molecules and binding sites are Markov processes,while the deformation of the medium was controlled by continuum mechanics.In the process of stochastic ruptur/rebind transitions of molecular bonds,one-dimensional energy landscape of molecules thermal fluctuation was given based on considering the effect of deformation energy of the whole system and the binding energy between molecules and binding sites on the molecular random thermal fluctuation.Based on this energy landscape,we gave the molecular bond reaction rate by considering the effect of molecular bond rebinding on the ruptur process and the effect of molecular bond re-breaking on the bind process.At the same time,on the basis of this energy landscape and theory of statistical thermodynamics,we gave the expression of free energy and strength of adhesion system.The specific research results of this paper are listed as follows:(1)In this study,we considered an adhesion system mediated by a cluster of receptor-ligand bonds formed via reactive and diffusive adhesion molecules between two viscoelastic half-spaces under force-controlled or displaecment-controlled loading,in which molecular diffusion and stochastic rupture/rebind transitions of receptor-ligand bonds are Markov stochastic processes,whereas the viscoelastic deformation of the adhesion media is given by continuum mechanics.We gave the master equations describing molecular diffusion and stochastic rupture/rebind transitions of receptor–ligand bonds and verified the new theoretical model by model degradation and Monte Carlo simulation.The results obtained using the proposed model reveal that the adhesion lifetime and strength are actually determined by competition between time scales of molecular diffusion,viscoelastic deformation,and stochastic rupture/rebind transitions of the receptor-ligand bonds.By using Monte Carlo simulation,we found that there is an optimal diffusion coefficient of adhesion molecules corresponding to the maximum adhesion lifetime and strength,which agrees with the experimentally determined range of diffusion coefficients for real cellular systems on receptors embedded in plasma membranes.In addition,the viscosity of the adhesive medium can significantly improve the adhesion lifetime and strength,because the deformation creep of the adhesive medium can effectively increase the probability of receptor-ligand bonds rebinding.(2)Considering that the deformation of the adhesive medium is comparable to that of the receptor-ligand bond,we established the adhesion system of a cluster of receptor-ligand bonds between two soft elastic bondies under displaecment-controlled loading.In this model,we gave one-dimensional energy landscape of the receptor thermal fluctuation by considering the effect of the deformation energy of the whole adhesion system and the binding energy between receptor and ligand on the thermal fluctuations of the receptor.It is found that the energy landscape is highly dependent on the state distribution of receptor-ligand bonds and the deformation energy stored in soft media and all receptor-ligand bonds,as well as the binding energy of receptor and ligand.On the basis of the newly obtained energy landscape of the receptor thermal fluctuation and theory of statistical thermodynamics,we derived the expression of free energy and strength of adhesion system,and verified the validity of the new strength theory by comparing with Monte Carlo simulation,Brownian dynamics simulation and existing strength theory.According to the new strength theory,we have a good explanation of the cellular experimental,such as: 1)how cells adapt to the extracellular biophysical environment by adjusting their mechanical properties through cytoskeleton remodeling,2)the “durotaxis” and “negative durotaxi” behavior of cells.In addition,we found that the effect of adhesion size on adhesion strength depends on the loading mode of the adhesion system.When the adhesion system is under force-controlled loading,it has an optimal size window to maximize the adhesion strength.When the adhesion system is under displacement-controlled loading,the adhesion strength increases monotonically with the adhesion size.(3)In order to understand the counterintuitive phenomenon of force-enhanced adhesion observed in cell biology,existing theoretical models are all based on the consideration that the configuration and/or rupture pathway of receptor-ligand bond change after mechanical force,which in turn increases the rupture energy barrier and results in force-enhanced adhesion.In our study,on the basis of the one-dimensional energy landscape of the receptor thermal fluctuation,we gave the receptor-ligand bond reaction rate by considering the effect of bond rebinding on the ruptur process and the effect of molecular bond re-breaking on the bind process.By using this reaction rate,we find that the adhesion lifetime firstly increases and then decreases with the external force.The variation of adhesion lifetime is a typical characteristic of the “catch to slip” transition in adhesion systems.Thus,without considering the influence of external forces on the intrinsic properties of receptoe-ligand bonds,we provide a new way to explain the “catch-to-slip” switching behavior observed in cell biology.