Mechanical Model Of Specific Adhesion Between Elastic Graded Substrate And Cell

Extracellular matrix(ECM)is a network structure composed of extracellular macromolecules and other substances distributed between cells.It widely exists in biological systems and is an important object for cells to exchange material,energy,and information.Experimental studies have observed that the mechanical heterogeneity of ECM can significantly regulate the directional migration of cells.For example,the uneven distribution of ECM stiffness in tumor tissue has been confirmed to affect the proliferation of cancer cells,and many other cells have also been found to have the characteristics of hardening.However,when cells migrate,they inevitably constantly adhere to and dissociate from the specific molecules of mechanical heterogeneity ECM.How cells perceive these mechanical signals at the molecular bond level in their adhesion to mechanical heterogeneity ECM remains unclear.In order to solve this problem,we combine continuum mechanics and statistical thermodynamics to describe the interfacial deformation of elastic graded substrates and the random dissociation and association of receptor-ligand adhesive molecular bonds,respectively.Based on the random elastic theoretical framework of cell adhesion,we established a theoretical model of cell elastic graded substrate adhesion mediated by ligand-receptor bond clusters,and used Monte Carlo simulation methods to computationally simulate the interaction between substrate and cell.The interfacial adhesion response between elastic graded substrate and cell regulated by receptor-ligand bonds under tensile loading was also explored.We found that:(1)During the process of stretching the cell elastic graded substrate adhesive interface,due to the large concentrated traction force near the stiff side edge of the adhesive region,crack first develops at the stiff side edge,and then propagates to another relatively soft adhesive edge until completed separation of the cell-substrate interface is achieved.This is completely different from the crack propagation from the two edges of the adhesive region to the center of the adhesive region when the uniform elastic solid-solid interface or solid-fluid interface is under tension;(2)The fracture evolution mechanism of cell elastic graded substrate was examined and its impact on the lifetime of adhesive molecular clusters was analyzed.It was found that when the external load was large,the unilateral crack expanded rapidly,resulting in a low lifetime of adhesive molecular clusters.However,when the external load was small,the lifetime of adhesive molecular clusters was higher than that of a flexible homogeneous adhesive interface;(3)The adhesive strength of the cell-elastic graded substrate adhesive structure was studied,and it was found that the adhesive strength increased with the increase of the loading rate.In summary,based on a specific adhesion model,this article has studied the effect of elastic graded substrate on adhesion interfaces.These findings will help us understand the detailed mechanism of adhesion interfaces responding to substrate mechanical heterogeneity at the molecular bond level.