Adhesive models to understand the sensitivity of bio-molecules to environmental signals

Recently, contact mechanics has been widely used to get some understanding of the biological adhesion mechanisms, such as cell-cell adhesion, insects' adhesion and locomotion. JKR theory is usually adopted as a basis, in which the interaction of molecules is considered in contrast to the classical Hertz solution. In this paper, two problems are summarized, which may give some insights to cells or bio-molecules sensitivity to environmental signals: (1) cell reorientation on a stretched substrate; (2) spontaneous detachment between cells or bio-molecules under the variation of environmental signals. The intention here is only to illustrate the possibilities that contact mechanics may explain or predict some bio-phenomena using simple mechanical models. A complete analysis taking into account the full biological complexities is far beyond the scope of this paper. With this objective in mind, the sensitivity of bio-molecules to the environmental signals is described through the variation of adhesive contact area, which is affected by the external forces or deformations. In the first problem, two-dimensional generalized JKR model is used to explain why there exist three stages with two critical values of stretch amplitude controlling cells' reorientation. Three-dimensional adhesive model is used in the second problem, to analyze the spontaneous detachment between two adhering cells or bio-molecules, which may happen at a critical condition.