Depth-sensing indentation of spherical particles on corrugated substrates — An asymptotic model

Argatov, Ivan; Jin, Xiaoqing

doi:10.1016/j.ijengsci.2020.103349

Cited by 6 publications

(4 citation statements)

References 35 publications

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“…A generalization of the model for the case of conical [ 42 ] or monomial [ 43 ] indenters can be produced in a straightforward way, following the mathematical modelling approach outlined above. However, a special study is needed to account simultaneously for both the indenter shape effect [ 44 ] and the effect of spherical cell finite geometry [ 45 ].…”

Section: Discussionmentioning

confidence: 99%

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

Argatov

Jin

Mishuris

2023

J. R. Soc. Interface.

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A simple analytical model is built up to account for the interface deformation effect in a spherical atomic force microscopy (AFM)-based quasi-static indentation of a living cell covered with a pericellular brush. The compression behaviour of the pericellular coat is described using the Alexander–de Gennes model that allows for nonlinear deformation. An approximate second-order relation between contact force and indenter displacement is obtained in implicit form, using the Hertzian solution as a first-order approximation. A method of fitting the indentation brush/cell model to experimental data is suggested based on the non-dimensionalized version of the displacement–force relation in the parametric form and illustrated with a specific example of AFM raw data taken from the literature.

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Section: Discussionmentioning

confidence: 99%

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

Argatov

Jin

Mishuris

2023

J. R. Soc. Interface.

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“…Because the stress is accumulated predominantly in the top and side portions of the particle and because the side portion of the CCMV shell accounts for > 90% of the entire structure, the mechanical deformation of the CCMV capsid due to the particle-substrate interaction is essentially masked. For this reason, in the FNS model we did not explicitly consider the particle-substrate interactions [58] . The FNSmodel based theory can be used to describe the mechanical deformations of thick soft biological particles in the entire range of their dynamic regimes, i.e.…”

Section: Discussionmentioning

confidence: 99%

Fluctuating nonlinear spring theory: Strength, deformability, and toughness of biological nanoparticles from theoretical reconstruction of force-deformation spectra

et al. 2021

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“…[42]) then R = R 1 /2 = 4 μ m. If an elastic sphere (a cell) of radius R 1 is rested on a hard flat surface and it is compressed by a spherical AFM tip of radius R 2 then the total approach of the AFM tip and the sphere δ can be found as a sum δ = δ 1 + δ 2 , where δ 1 and δ 2 can be found by solving contact problems for spheres of effective radii R 1 and R 1 R 2 /( R 1 + R 2 ), respectively. The described contact configuration of a spherical particle resting on a rigid substrate has been recently discussed in detail [43].…”

Section: Specific Features Of Cells and Their Mechanical Modelsmentioning

confidence: 99%

Contact probing of prestressed adhesive membranes of living cells

Borodich

Galanov

Keer

et al. 2021

Phil. Trans. R. Soc. A.

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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’.

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Depth-sensing indentation of spherical particles on corrugated substrates — An asymptotic model

Cited by 6 publications

References 35 publications

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

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

Fluctuating nonlinear spring theory: Strength, deformability, and toughness of biological nanoparticles from theoretical reconstruction of force-deformation spectra

Contact probing of prestressed adhesive membranes of living cells

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