Contact probing of prestressed adhesive membranes of living cells

Abstract

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’.

Atomic force microscopy-based indentation of cells: modelling the effect of a pericellular coat

“…Following [ 15 ], we can account for the effect of the cell prestress by modifying the elastic constant E *. We refer to papers [ 35 , 36 ] for more details.…”

“…It is important to highlight that equation ( 1.1 ) adopts the linearly elastic half-space approximation for evaluating the contact deformations of a cell in the region near the contact zone [ 11 ]. Moreover, when equation ( 1.1 ) is applied to the analysis of the AFM-based testing of living cells, it is tentatively assumed that cells have bare surfaces without being covered by any membrane protrusions or corrugations [ 14 , 15 ]. The latter simplifying assumption has been criticized for not being realistic enough for many types of living cells that are coated with pericellular brushes [ 14 ] and the so-called brush model has been introduced [ 16 ], which complements equation ( 1.1 ) by the model of entropic brush in the exponential form [ 17 , 18 ] for the relation between the contact force F and the separation distance, h , of the indenter tip from the brush grafting surface.…”

Atomic force microscopy in disease‐related studies: Exploring tissue and cell mechanics

“…q Large radius indenter, high adhesion and flexible sample. Short range surface forces in the contact area, ignoring adhesion outside the contact area Almeida et al, 2021;Borodich et al, 2021;Deng & Kesari, 2019;Fujinami et al, 2019;Korayem et al, 2020;Ren et al, 2021 DMT (Derjaguin-Muller-Toporov)…”

Choosing Nano medicine Stiffness using contact models, based on the atomic force microscopy with Analysis of the cancer cell elasticity modulus

“…Finally, they conclude that the AFM cantilever's geometry, mechanical property, and initial conditions affect nanomanipulation. Borodich et al [17] modeled the contact between the spherical AFM probe tip and a prestress cell membrane by relying on theoretical and experimental methods. Using contact theories that also consider the adhesion forces can produce more realistic results.…”