1
|
Wohlrab S, Mueller S, Gekle S. Mechanical complexity of living cells can be mapped onto simple homogeneous equivalents. Biomech Model Mechanobiol 2024; 23:1067-1076. [PMID: 38411900 PMCID: PMC11101590 DOI: 10.1007/s10237-024-01823-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Accepted: 01/19/2024] [Indexed: 02/28/2024]
Abstract
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.
Collapse
Affiliation(s)
- Sebastian Wohlrab
- Theoretische Physik VI, Biofluid Simulation and Modeling, Universität Bayreuth, 95440, Bayreuth, Germany.
| | - Sebastian Mueller
- Theoretische Physik VI, Biofluid Simulation and Modeling, Universität Bayreuth, 95440, Bayreuth, Germany
| | - Stephan Gekle
- Theoretische Physik VI, Biofluid Simulation and Modeling, Universität Bayreuth, 95440, Bayreuth, Germany
| |
Collapse
|
2
|
Kennedy Z, Newberg J, Goelzer M, Judex S, Fitzpatrick CK, Uzer G. Modeling stem cell nucleus mechanics using confocal microscopy. Biomech Model Mechanobiol 2021; 20:2361-2372. [PMID: 34424419 PMCID: PMC8599651 DOI: 10.1007/s10237-021-01513-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2020] [Accepted: 08/14/2021] [Indexed: 11/24/2022]
Abstract
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.
Collapse
Affiliation(s)
- Zeke Kennedy
- Department of Mechanical and Biomedical Engineering, Boise State University, 1910 University Drive, MSd-2085, Boise, ID, 83725-2085, USA
| | - Joshua Newberg
- Department of Mechanical and Biomedical Engineering, Boise State University, 1910 University Drive, MSd-2085, Boise, ID, 83725-2085, USA
| | - Matthew Goelzer
- Department of Mechanical and Biomedical Engineering, Boise State University, 1910 University Drive, MSd-2085, Boise, ID, 83725-2085, USA
| | - Stefan Judex
- Biomedical Engineering, Stony Brook University, Stony Brook, USA
| | - Clare K Fitzpatrick
- Department of Mechanical and Biomedical Engineering, Boise State University, 1910 University Drive, MSd-2085, Boise, ID, 83725-2085, USA
| | - Gunes Uzer
- Department of Mechanical and Biomedical Engineering, Boise State University, 1910 University Drive, MSd-2085, Boise, ID, 83725-2085, USA.
| |
Collapse
|
3
|
Fessel A, Döbereiner HG. Nonlinear compliance of elastic layers to indentation. Biomech Model Mechanobiol 2017; 17:419-438. [PMID: 29094275 DOI: 10.1007/s10237-017-0969-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Accepted: 10/16/2017] [Indexed: 11/26/2022]
Abstract
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.
Collapse
Affiliation(s)
- Adrian Fessel
- Institut für Biophysik, Universität Bremen, Bremen, Germany.
| | | |
Collapse
|
4
|
Liu J, Qu Y, Wang G, Wang X, Zhang W, Li J, Wang Z, Li D, Jiang J. Study of morphological and mechanical features of multinuclear and mononuclear SW480 cells by atomic force microscopy. Microsc Res Tech 2017; 81:3-12. [PMID: 28990709 DOI: 10.1002/jemt.22950] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2017] [Revised: 07/22/2017] [Accepted: 09/26/2017] [Indexed: 12/22/2022]
Abstract
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.
Collapse
Affiliation(s)
- Jinyun Liu
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China.,Institute for Research in Applicable Computing, University of Bedfordshire, Luton, LU1 3JU, United Kingdom
| | - Yingmin Qu
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China
| | - Guoliang Wang
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China
| | - Xinyue Wang
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China
| | - Wenxiao Zhang
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China
| | - Jingmei Li
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China
| | - Zuobin Wang
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China.,Institute for Research in Applicable Computing, University of Bedfordshire, Luton, LU1 3JU, United Kingdom
| | - Dayou Li
- International Research Centre for Nano Handling and Manufacturing of China, Changchun University of Science and Technology, Changchun, 130022, China.,Institute for Research in Applicable Computing, University of Bedfordshire, Luton, LU1 3JU, United Kingdom
| | - Jinlan Jiang
- Scientific Research Centre of China-Japan Union Hospital, Jilin University, Changchun, 130033, China
| |
Collapse
|
5
|
Niu T, Cao G. Power-law rheology characterization of biological cell properties under AFM indentation measurement. RSC Adv 2014. [DOI: 10.1039/c4ra03111c] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
|