Biomechanical Heterogeneity of Living Cells: Comparison between Atomic Force Microscopy and Finite Element Simulation

Abstract

Atomic force microscopy (AFM) indentation is a popular method for characterizing the micromechanical properties of soft materials such as living cells. However, the mechanical data obtained from deep indentation measurements can be difficult and problematic to interpret as a result of the complex geometry of a cell, the nonlinearity of indentation contact, and constitutive relations of heterogeneous hyperelastic soft components. Living MDA-MB-231 cells were indented by spherical probes to obtain morphological and mechanical data that were adopted to build an accurate finite element model (FEM) for a parametric study. Initially, a 2Daxisymmetric numerical model was constructed with the main purpose of understanding the effect of geometrical and mechanical properties of constitutive parts such as the cell body, nucleus, and lamellipodium. A series of FEM deformation fields were directly compared with atomic force spectroscopy in order to resolve the mechanical convolution of heterogeneous parts and quantify Young's modulus and the geometry of nuclei. Furthermore, a 3D finite element model was constructed to investigate indentation events located far from the axisymmetric geometry. In this framework, the joint FEM/AFM approach has provided a useful methodology and a comprehensive characterization of the heterogeneous structure of living cells, emphasizing the deconvolution of geometrical structure and the true elastic modulus of the cell nucleus.

Spatially Resolved Correlation between Stiffness Increase and Actin Aggregation around Nanofibers Internalized in Living Macrophages

“…The correlation between the internalized nanofiber and the enhanced Young’s modulus is shown in Figure S1 in the Supplementary Material , acquired via simultaneous AFM and fluorescence microscopy. The contrast was also evidenced in the comparison of single force curves in Figure 3 d,h, selected on cell areas representing normal soft cell body (circles) and hard regions (triangles) representing nucleus in the control [ 40 ] and nanofiber inside the cell.…”

“…Interestingly, there are also other regions showing an increase in Young’s modulus, which can be ascribed to the influence of some out of focus nanofibers as well as organelles, especially the nucleus [ 40 ].…”

Structural models of the biological oxygen-evolving complex: achievements, insights, and challenges for biomimicry

“…, and NCO − ) further extended this class of complexes. 131,134,[136][137][138][139][140][141][142][143] Some of them, for example a compound reported by Wang et al, were also shown to mimic the S 1 to S 2 oxidation step. 142 An all-μ-oxo bridged Mn(III) 2 Mn(IV) 2 cubane complex was reported by Dismukes and co-workers ( Fig.…”

A Computational Framework to Model Mesenchymal Stem Cell Nucleus Mechanics Using Confocal Microscopy

“…Previous research described the nucleus's mechanical elasticity as either linear elastic or hyperelastic 27 . During our experiments we chose to model the nucleus as a linear elastic.…”

“…During our experiments we chose to model the nucleus as a linear elastic. As both homogenous and linear conversion models of nucleus #4 and #5 produced linear force-displacement curves, we have also implemented hyperplastic Mooney-Rivlin and Neo-Hookean material definitions 27 which again produced linear force-displacement relationship (Fig.S2). Suggesting that the shape of in silico loading curves were independent of the use of hyperelastic Mooney-Rivlin and Neo-Hookean models.…”