Evaluating the nucleus effect on the dynamic indentation behavior of cells

Mechanical complexity of living cells can be mapped onto simple homogeneous equivalents

Biological cells are built up from different constituents of varying size and stiffness which all contribute to the cell's mechanical properties. Despite this heterogeneity, in the analysis of experimental measurements one often assumes a strongly simplified homogeneous cell and thus a single elastic modulus is assigned to the entire cell. This ad-hoc simplification has so far mostly been used without proper justification. Here, we use computer simulations to show that indeed a mechanically heterogeneous cell can effectively be replaced by a homogeneous equivalent cell with a volume averaged elastic modulus. To demonstrate the validity of this approach, we investigate a hyperelastic cell with a heterogeneous interior under compression and in shear/channel flow mimicking atomic force and microfluidic measurements, respectively. We find that the homogeneous equivalent cell reproduces quantitatively the behavior of its heterogeneous counterpart, and that this equality is largely independent of the stiffness or spatial distribution of the heterogeneity.

Modeling stem cell nucleus mechanics using confocal microscopy

Nuclear mechanics is emerging as a key component of stem cell function and differentiation. While changes in nuclear structure can be visually imaged with confocal microscopy, mechanical characterization of the nucleus and its sub-cellular components require specialized testing equipment. A computational model permitting cell-specific mechanical information directly from confocal and atomic force microscopy of cell nuclei would be of great value. Here, we developed a computational framework for generating finite element models of isolated cell nuclei from multiple confocal microscopy scans and simple atomic force microscopy (AFM) tests. Confocal imaging stacks of isolated mesenchymal stem cells were converted into finite element models and siRNA-mediated Lamin A/C depletion isolated chromatin and Lamin A/C structures. Using AFM-measured experimental stiffness values, a set of conversion factors were determined for both chromatin and Lamin A/C to map the voxel intensity of the original images to the element stiffness, allowing the prediction of nuclear stiffness in an additional set of other nuclei. The developed computational framework will identify the contribution of a multitude of sub-nuclear structures and predict global nuclear stiffness of multiple nuclei based on simple nuclear isolation protocols, confocal images and AFM tests.

Nonlinear compliance of elastic layers to indentation

Thin samples adherent to a rigid substrate are considerably less compliant to indentation when compared to specimens that are not geometrically confined. Analytical corrections to this so-called substrate effect exist for various types of indenters but are not applicable when large deformations are possible, as is the case in biological materials. To overcome this limitation, we construct a nonlinear scaling model characterized by one single exponent, which we explore employing a parametric finite element analysis. The model is based on asymptotes of two length scales in relation to the sample thickness, i.e., indentation depth and radius of the contact area. For small indentation depth, we require agreement with analytical, linear models, whereas for large indentation depth and extensive contact area, we recognize similarity to uniaxial deformation, indicating a divergent force required to indent nonlinear materials. In contrast, we find linear materials not to be influenced by the substrate effect beyond first order, implying that nonlinear effects originating from either the material or geometric confinement are clearly separated only in thin samples. Furthermore, in this regime the scaling model can be derived by following a heuristic argument extending a linear model to large indentation depths. Lastly, in a large indentation setting where the contact is small in comparison with sample thickness, we observe nonlinear effects independent of material type that we attribute to a higher-order influence of geometrical confinement. In this regime, we define a scalar as the ratio of strains along principal axes as obtained by comparison with the case of a point force on a half-space. We find this scalar to be in quantitative agreement with the scaling exponent, indicating an approach to distinguish between nonlinear effects in the scaling model. While we conjecture our findings to be applicable to other flat-ended indenters, we focus on the case of a flat-ended cylinder in normal contact with a thin layer. The analytical solution for small indentation associated with this problem has been given by Hayes et al. (J Biomech 5:541-551, 1972), for which we provide a convenient numerical implementation.

Study of morphological and mechanical features of multinuclear and mononuclear SW480 cells by atomic force microscopy

This article studies the morphological and mechanical features of multinuclear and mononuclear SW480 colon cancer cells by atomic force microscopy to understand their drug-resistance. The SW480 cells were incubated with the fullerenol concentrations of 1 mg/ml and 2 mg/ml. Morphological and mechanical features including the height, length, width, roughness, adhesion force and Young's modulus of three multinuclear cell groups and three mononuclear cell groups were imaged and analyzed. It was observed that the features of multinuclear cancer cells and mononuclear cancer cells were significantly different after the treatment with fullerenol. The experiment results indicated that the mononuclear SW480 cells were more sensitive to fullerenol than the multinuclear SW480 cells, and the multinuclear SW480 cells exhibited a stronger drug-resistance than the mononuclear SW480 cells. This work provides a guideline for the treatments of multinuclear and mononuclear cancer cells with drugs.