Atomic force microscopy (AFM) studies of living biological cells is one of main experimental tools that enable quantitative measurements of deformation of the cells and extraction of information about their structural and mechanical properties. However, proper modelling of AFM probing and related adhesive contact problems are of crucial importance for interpretation of experimental data. The Johnson-Kendall-Roberts (JKR) theory of adhesive contact has often been used as a basis for modelling of various phenomena including cell-cell interactions. However, strictly speaking the original JKR theory is valid only for contact of isotropic linearly elastic spheres, while the cell membranes are often prestressed. For the first time, effects caused by molecular adhesion for living cells are analytically studied taking into account the mechanical properties of cell membranes whose stiffness depends on the level of the tensile prestress. Another important question is how one can extract the work of adhesion between the probe and the cell. An extended version of the Borodich-Galanov method for non-direct extraction of elastic and adhesive properties of contacted materials is proposed to apply to experiments of cell probing. Evidently, the proposed models of adhesive contact for cells with prestressed membranes do not cover all types of biological cells because the structure and properties of the cells may vary considerably. However, the obtained results can be applied to many types of smooth cells and can be used to describe initial stages of contact and various other processes when effects of adhesion are of crucial importance. This article is part of a discussion meeting issue 'A cracking approach to inventing new tough materials: fracture stranger than friction'.
Keywords: Johnson–Kendall–Roberts theory; adhesive contact; cell; prestress; probe; work of adhesion.