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Research Papers

A Finite Element Bendo-Tensegrity Model of Eukaryotic Cell

[+] Author and Article Information
Yogesh Deepak Bansod

Faculty of Mechanical Engineering (FME),
Institute of Solid Mechanics, Mechatronics and
Biomechanics (ISMMB),
Brno University of Technology (BUT),
Technicka 2896/2,
Brno 61669, Czech Republic
e-mail: yogeshbansod@gmail.com

Takeo Matsumoto

Biomechanics Laboratory,
Department of Mechanical Engineering,
Nagoya Institute of Technology,
Gokiso-cho, Showa-ku,
Nagoya 466-8555, Japan
e-mail: takeo@nagoya-u.jp

Kazuaki Nagayama

Biomechanics Laboratory,
Department of Mechanical Engineering,
Nagoya Institute of Technology,
Gokiso-cho, Showa-ku,
Nagoya 466-8555, Japan
e-mail: kazuaki.nagayama.bio@vc.ibaraki.ac.jp

Jiri Bursa

Faculty of Mechanical Engineering (FME),
Institute of Solid Mechanics, Mechatronics and
Biomechanics (ISMMB),
Brno University of Technology (BUT),
Technicka 2896/2,
Brno 61669, Czech Republic
e-mail: bursa@fme.vutbr.cz

1Corresponding author.

Manuscript received September 15, 2016; final manuscript received April 30, 2018; published online June 21, 2018. Editor: Victor H. Barocas.

J Biomech Eng 140(10), 101001 (Jun 21, 2018) (9 pages) Paper No: BIO-16-1380; doi: 10.1115/1.4040246 History: Received September 15, 2016; Revised April 30, 2018

Mechanical interaction of cell with extracellular environment affects its function. The mechanisms by which mechanical stimuli are sensed and transduced into biochemical responses are still not well understood. Considering this, two finite element (FE) bendo-tensegrity models of a cell in different states are proposed with the aim to characterize cell deformation under different mechanical loading conditions: a suspended cell model elucidating the global response of cell in tensile test simulation and an adherent cell model explicating its local response in atomic force microscopy (AFM) indentation simulation. The force-elongation curve obtained from tensile test simulation lies within the range of experimentally obtained characteristics of smooth muscle cells (SMCs) and illustrates a nonlinear increase in reaction force with cell stretching. The force-indentation curves obtained from indentation simulations lie within the range of experimentally obtained curves of embryonic stem cells (ESCs) and exhibit the influence of indentation site on the overall reaction force of cell. Simulation results have demonstrated that actin filaments (AFs) and microtubules (MTs) play a crucial role in the cell stiffness during stretching, whereas actin cortex (AC) along with actin bundles (ABs) and MTs are essential for the cell rigidity during indentation. The proposed models quantify the mechanical contribution of individual cytoskeletal components to cell mechanics and the deformation of nucleus under different mechanical loading conditions. These results can aid in better understanding of structure-function relationships in living cells.

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Figures

Grahic Jump Location
Fig. 1

Sections of continuous elements and structural arrangement of cytoskeletal components with respect to the nucleus: (a) and (b) for suspended cell model and (c) and (d) for adherent cell model

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Fig. 2

Sectional views of the suspended cell model during consecutive steps in simulation of tensile test with micropipettes: (a) spherical cell and micropipettes, (b) compressing the cell against the fixed micropipette, and (c) stretching the cell with movable micropipette

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Fig. 3

Finite element model of an adherent cell in the indentation test, with displacement load applied at the tip pushing against the top of the cell and relevant constraints

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Fig. 4

Comparison of simulated force-elongation curve with the experimental curves taken from the study by Nagayama et al. [21], measuring the tensile properties of cultured aortic SMCs of diameter (D) using a cell tensile tester

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Fig. 5

Results of the tensile test simulation: (a) deformed shape of the cytoskeletal components and nucleus, distribution of axial stress in the discrete elements representing (b) MTs, and (c) AFs, distribution of axial strain in the discrete elements representing (d) IFs, and distribution of first principal strain in the continuous elements representing (e) nucleus

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Fig. 6

Sectional views comparing the contour plots of von Mises stress inside the cell during AFM simulation for indentation depth of 1 μm at (a) the apex and (b) a receptor; (c) comparison of simulated force-indentation curves with the experimental curves taken from the study by Pillarisetti et al. [22], measuring the stiffness of ESCs using AFM indentation

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Fig. 7

Contribution of the cytoskeletal components individually and in mutual combination to the response of cell models during (a) tensile test and (b) indentation test, highlighting their synergistic effect. The stiffness of the altered models is normalized with respect to that of the corresponding control model.

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Fig. 8

The effect of varying Young's modulus of individual cell components from the control values (Tables 1 and 2) on the stiffness of (a) suspended cell model in tensile test simulation and (b) adherent cell model in indentation test simulation. The stiffness calculated for each simulation is normalized with respect to that calculated for the corresponding control model.

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