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’.

活生物细胞的原子力显微镜 (AFM) 研究是主要的实验工具之一，它能够定量测量细胞的变形并提取有关其结构和机械特性的信息。然而，AFM 探测和相关粘合剂接触问题的正确建模对于解释实验数据至关重要。Johnson-Kendall-Roberts (JKR) 粘附接触理论经常被用作各种现象建模的基础，包括细胞间相互作用。然而，严格地说，原始JKR理论仅适用于各向同性线弹性球体的接触，而细胞膜往往是预应力的。首次，考虑到细胞膜的机械特性，其刚度取决于拉伸预应力的水平，分析研究了分子粘附对活细胞造成的影响。另一个重要问题是如何提取探针和细胞之间的粘附功。提出了用于非直接提取接触材料的弹性和粘附特性的 Borodich-Galanov 方法的扩展版本，以应用于细胞探测实验。显然，所提出的带有预应力膜的细胞粘附接触模型并未涵盖所有类型的生物细胞，因为细胞的结构和特性可能会有很大差异。然而，

这篇文章是讨论会议题“一种新的坚韧材料的破解方法：断裂比摩擦更奇怪”的一部分。