Lin Yuan, Freund L B
Department of Mechanical Engineering, The University of Hong Kong, Hong Kong SAR, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 1):021909. doi: 10.1103/PhysRevE.78.021909. Epub 2008 Aug 19.
The strength of a bonded interface is considered for the case in which bonding is the result of clusters of discrete bonds distributed along the interface. Assumptions appropriate for the case of adhesion of biological cells to an extracellular matrix are introduced as a basis for the discussion. It is observed that those individual bonds nearest to the edges of a cluster are necessarily subjected to disproportionately large forces in transmitting loads across the interface, in analogy with well-known behavior in elastic crack mechanics. Adopting Bell's model for the kinetics of bond response under force, a stochastic model leading to a dependence of interface strength on cluster size is developed and analyzed. On the basis of this model, it is demonstrated that there is an optimum cluster size for maximum strength. This size arises from the competition between the nonuniform force distribution among bonds, which tends to promote smaller clusters, and stochastic response allowing bond reformation, which tends to promote larger clusters. The model results have been confirmed by means of direct Monte Carlo simulations. This analysis may be relevant to the observation that mature focal adhesion zones in cell bonding are found to have a relatively uniform size.
对于粘结界面强度的考虑，是基于沿界面分布的离散键簇形成粘结的情况。引入适用于生物细胞与细胞外基质粘附情况的假设，作为讨论的基础。据观察，与弹性裂纹力学中众所周知的行为类似，那些最靠近键簇边缘的单个键在通过界面传递载荷时必然承受不成比例的大力。采用贝尔关于力作用下键响应动力学的模型，开发并分析了一个导致界面强度依赖于键簇大小的随机模型。基于该模型，证明存在一个使强度最大的最佳键簇大小。这个大小源于键之间不均匀力分布（倾向于促进较小键簇）与允许键重新形成的随机响应（倾向于促进较大键簇）之间的竞争。模型结果已通过直接蒙特卡罗模拟得到证实。该分析可能与以下观察结果相关：在细胞粘结中发现成熟的粘着斑区域具有相对均匀的大小。
