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.

References

References
1.
Janmey
,
P.
,
Euteneuer
,
U.
,
Traub
,
P.
, and
Schliwa
,
M.
,
1991
, “
Viscoelastic Properties of Vimentin Compared With Other Filamentous Biopolymer Networks
,”
J. Cell Biol.
,
113
(
1
), pp.
155
160
.
2.
Ingber
,
D.
,
1993
, “
Cellular Tensegrity: Defining New Rules of Biological Design That Govern the Cytoskeleton
,”
J. Cell Sci.
,
104
, pp.
613
627
.http://jcs.biologists.org/content/joces/104/3/613.full.pdf
3.
Huang
,
H.
,
Kamm
,
R.
, and
Lee
,
R.
,
2004
, “
Cell Mechanics and Mechanotransduction: Pathways, Probes, and Physiology
,”
Am. J. Physiol.-Cell. Physiol.
,
287
(
1
), pp.
C1
C11
.
4.
McGarry
,
J.
, and
Prendergast
,
P.
,
2004
, “
A Three-Dimensional Finite Element Model of an Adherent Eukaryotic Cell
,”
Eur. Cells Mater.
,
7
, pp.
27
33
.
5.
Bursa
,
J.
,
Holata
,
J.
, and
Lebis
,
R.
,
2012
, “
Tensegrity Finite Element Models of Mechanical Tests of Individual Cells
,”
Technol. Health Care
,
20
(
2
), pp.
135
150
.
6.
Bursa
,
J.
,
Lebis
,
R.
, and
Janicek
,
P.
,
2006
, “
FE Models of Stress-Strain States in Vascular Smooth Muscle Cell
,”
Technol. Health Care
,
14
(
4–5
), pp.
311
320
.https://content.iospress.com/articles/technology-and-health-care/thc00412
7.
Barreto
,
S.
,
Clausen
,
C.
,
Perrault
,
C.
,
Fletcher
,
D.
, and
Lacroix
,
D.
,
2013
, “
A Multi-Structural Single Cell Model of Force-Induced Interactions of Cytoskeletal Components
,”
Biomaterials
,
34
(
26
), pp.
6119
6126
.
8.
Xue
,
F.
,
Lennon
,
A.
,
McKayed
,
K.
,
Campbell
,
V.
, and
Prendergast
,
P.
,
2015
, “
Effect of Membrane Stiffness and Cytoskeletal Element Density on Mechanical Stimuli Within Cells: An Analysis of the Consequences of Ageing in Cells
,”
Comput Method Biomec
,
18
(
5
), pp.
468
476
.
9.
Ujihara
,
Y.
,
Nakamura
,
M.
,
Miyazaki
,
H.
, and
Wada
,
S.
,
2010
, “
Proposed Spring Network Cell Model Based on a Minimum Energy Concept
,”
Ann. Biomed. Eng.
,
38
(
4
), pp.
1530
1538
.
10.
Maurin
,
B.
,
Cañadas
,
P.
,
Baudriller
,
H.
,
Montcourrier
,
P.
, and
Bettache
,
N.
,
2008
, “
Mechanical Model of Cytoskeleton Structuration During Cell Adhesion and Spreading
,”
J. Biomech.
,
41
(
9
), pp.
2036
2041
.
11.
Stamenović
,
D.
, and
Coughlin
,
M.
,
1999
, “
The Role of Prestress and Architecture of the Cytoskeleton and Deformability of Cytoskeletal Filaments in Mechanics of Adherent Cells: A Quantitative Analysis
,”
J. Theor. Biol.
,
201
(
1
), pp.
63
74
.
12.
Stamenović
,
D.
,
Fredberg
,
J.
,
Wang
,
N.
,
Butler
,
J.
, and
Ingber
,
D.
,
1996
, “
A Microstructural Approach to Cytoskeletal Mechanics Based on Tensegrity
,”
J. Theor. Biol.
,
181
(
2
), pp.
125
136
.
13.
Coughlin
,
M.
, and
Stamenović
,
D.
,
1997
, “
A Tensegrity Structure With Buckling Compression Elements: Application to Cell Mechanics
,”
ASME J. Appl. Mech.
,
64
(
3
), pp.
480
486
.
14.
Coughlin
,
M.
, and
Stamenović
,
D.
,
1998
, “
A Tensegrity Model of the Cytoskeleton in Spread and round Cells
,”
ASME J. Biomech. Eng.
,
120
(
6
), pp.
770
777
.
15.
Volokh
,
K.
,
Vilnay
,
O.
, and
Belsky
,
M.
,
2000
, “
Tensegrity Architecture Explains Linear Stiffening and Predicts Softening of Living Cells
,”
J. Biomech.
,
33
(
12
), pp.
1543
1549
.
16.
Wang
,
N.
, and
Stamenović
,
D.
,
2000
, “
Contribution of Intermediate Filaments to Cell Stiffness, Stiffening, and Growth
,”
Am. J. Physiol.-Cell Physiol.
,
279
(
1
), pp.
C1881
C1894
.
17.
Cañadas
,
P.
,
Laurent
,
V.
,
Chabrand
,
P.
,
Isabey
,
D.
, and
Wendling-Mansuy
,
S.
,
2003
, “
Mechanisms Governing the Visco-Elastic Responses of Living Cells Assessed by Foam and Tensegrity Models
,”
Med. Biol. Eng. Comput.
,
41
(
6
), pp.
733
739
.
18.
Wang
,
N.
,
Naruse
,
K.
,
Stamenović
,
D.
,
Fredberg
,
J.
,
Mijailovich
,
S.
,
Tolić-Nørrelykke
,
I.
,
Polte
,
T.
,
Mannix
,
R.
, and
Ingber
,
D.
,
2001
, “
Mechanical Behavior in Living Cells Consistent With the Tensegrity Model
,”
Proc. Natl. Acad. Sci.
,
98
(
14
), pp.
7765
7770
.
19.
McGarry
,
J.
,
Klein-Nulend
,
J.
,
Mullender
,
M.
, and
Prendergast
,
P.
,
2005
, “
A Comparison of Strain and Fluid Shear Stress in Stimulating Bone Cell Responses—A Computational and Experimental Study
,”
Faseb J.
,
19
(
3
), pp.
482
484
.
20.
Prendergast
,
P.
,
2007
, “
Computational Modelling of Cell and Tissue Mechanoresponsiveness
,”
Gravit. Space Res.
,
20
(
2
), pp.
43
50
.http://gravitationalandspaceresearch.org/index.php/journal/article/view/415/410
21.
Nagayama
,
K.
,
Nagano
,
Y.
,
Sato
,
M.
, and
Matsumoto
,
T.
,
2006
, “
Effect of Actin Filament Distribution on Tensile Properties of Smooth Muscle Cells Obtained From Rat Thoracic Aortas
,”
J. Biomech.
,
39
(
2
), pp.
293
301
.
22.
Pillarisetti
,
A.
,
Desai
,
J.
,
Ladjal
,
H.
,
Schiffmacher
,
A.
,
Ferreira
,
A.
, and
Keefer
,
C.
,
2011
, “
Mechanical Phenotyping of Mouse Embryonic Stem Cells: Increase in Stiffness With Differentiation
,”
Cell Reprogram
,
13
(
4
), pp.
371
380
.
23.
Katchalsky
,
A.
,
1960
, “
Rheological Considerations of the Hemolysing Red Blood Cell
,”
Flow Properties of Blood and Other Biological Systems
,
Pergamon Press
,
New York
, pp.
155
171
.
24.
Mehrbod
,
M.
, and
Mofrad
,
R.
,
2011
, “
On the Significance of Microtubule Flexural Behavior in Cytoskeletal Mechanics
,”
PloS One
,
6
(
10
), p.
e25627
.
25.
Tsuda
,
Y.
,
Yasutake
,
H.
,
Ishijima
,
A.
, and
Yanagida
,
T.
,
1996
, “
Torsional Rigidity of Single Actin Filaments and Actin–Actin Bond Breaking Force Under Torsion Measured Directly by In Vitro Micromanipulation
,”
Proc. Natl. Acad. Sci. U. S. A.
,
93
(
23
), pp.
12937
12942
.
26.
Caille
,
N.
,
Thoumine
,
O.
,
Tardy
,
Y.
, and
Meister
,
J.
,
2002
, “
Contribution of the Nucleus to the Mechanical Properties of Endothelial Cells
,”
J. Biomech.
,
35
(
2
), pp.
177
187
.
27.
Charras
,
G.
,
Hu
,
C.
,
Coughlin
,
M.
, and
Mitchison
,
T.
,
2006
, “
Reassembly of Contractile Actin Cortex in Cell Blebs
,”
J. Cell Biol.
,
175
(
3
), pp.
477
490
.
28.
Charras
,
G.
, and
Paluch
,
E.
,
2008
, “
Blebs Lead the Way: How to Migrate Without Lamellipodia
,”
Nat. Rev. Mol. Cell Biol.
,
9
(
9
), p.
730
.
29.
Deguchi
,
S.
,
Ohashi
,
T.
, and
Sato
,
M.
,
2005
, “
Evaluation of Tension in Actin Bundle of Endothelial Cells Based on Preexisting Strain and Tensile Properties Measurements
,”
Mol. Cell Biomech.
,
2
(
3
), pp.
125
133
.http://www.techscience.com/doi/10.3970/mcb.2005.002.125.pdf
30.
Gittes
,
F.
,
Mickey
,
B.
,
Nettleton
,
J.
, and
Howard
,
J.
,
1993
, “
Flexural Rigidity of Microtubules and Actin Filaments Measured From Thermal fluctuations in Shape
,”
J. Cell Biol.
,
120
(
4
), pp.
923
934
.
31.
Bertaud
,
J.
,
Qin
,
Z.
, and
Buehler
,
M.
,
2010
, “
Intermediate Filament-Deficient Cells Are Mechanically Softer at Large Deformation: A Multi-Scale Simulation Study
,”
Acta. Biomater.
,
6
(
7
), pp.
2457
2466
.
32.
Stricker
,
J.
,
Falzone
,
T.
, and
Gardel
,
M.
,
2010
, “
Mechanics of the F-Actin Cytoskeleton
,”
J. Biomech.
,
43
(
1
), pp.
9
14
.
33.
Rand
,
R.
,
1964
, “
Mechanical Properties of the Red Cell Membrane: II. Viscoelastic Breakdown of the Membrane
,”
Biophys J.
,
4
(
4
), pp.
303
316
.
34.
Miyazaki
,
H.
,
Hasegawa
,
Y.
, and
Hayashi
,
K.
,
2002
, “
Tensile Properties of Contractile and Synthetic Vascular Smooth Muscle Cells
,”
JSME Int. J. Ser. C-Mech. Syst. Mach. Elem. Manuf.
,
45
(
4
), pp.
870
879
.
35.
Nagayama
,
K.
, and
Matsumoto
,
T.
,
2008
, “
Contribution of Actin Filaments and Microtubules to Quasi-in Situ Tensile Properties and Internal Force Balance of Cultured Smooth Muscle Cells on a Substrate
,”
Am. J. Physiol.-Cell Physiol.
,
295
(
6
), pp.
C1569
C1578
.
36.
Ohara
,
Y.
,
Miyazaki
,
H.
, and
Hayashi
,
K.
,
2000
, “
Atomic Force Microscopy Measurement of the Mechanical Properties of Vascular Smooth Muscle Cell
,”
12th JSME Bioengineering Conference
, Kanazawa, Japan, Jan. 11–12, pp.
55
56
.
37.
Ohashi
,
T.
,
Ishii
,
Y.
,
Ishikawa
,
Y.
,
Matsumoto
,
T.
, and
Sato
,
M.
,
2002
, “
Experimental and Numerical Analyses of Local Mechanical Properties Measured by Atomic Force Microscopy for Sheared Endothelial Cells
,”
BioMed. Mater. Eng.
,
12
(
3
), pp.
319
327
.https://content.iospress.com/articles/bio-medical-materials-and-engineering/bme238
38.
Wang
,
N.
, and
Suo
,
Z.
,
2005
, “
Long-Distance Propagation of Forces in a Cell
,”
Biochem. Biophys. Res. Commun.
,
328
(
4
), pp.
1133
1138
.
39.
Guck
,
J.
,
Schinkinger
,
S.
,
Lincoln
,
B.
,
Wottawah
,
F.
,
Ebert
,
S.
,
Romeyke
,
M.
,
Lenz
,
D.
,
Erickson
,
H.
,
Ananthakrishnan
,
R.
,
Mitchell
,
D.
,
Kas
,
J.
,
Ulvick
,
S.
, and
Bilby
,
C.
,
2005
, “
Optical Deformability as an Inherent Cell Marker for Testing Malignant Transformation and Metastatic Competence
,”
Biophys. J.
,
88
(
5
), pp.
3689
3698
.
40.
Ofek
,
G.
,
Dowling
,
E.
,
Raphael
,
R.
,
McGarry
,
J.
, and
Athanasiou
,
K.
,
2010
, “
Biomechanics of Single Chondrocytes Under Direct Shear
,”
Biomech. Model. Mech.
,
9
(
2
), pp.
153
162
.
41.
Li
,
W.
,
Jiang
,
Y.
, and
Tuan
,
R.
,
2006
, “
Chondrocyte Phenotype in Engineered Fibrous Matrix Is Regulated by Fiber Size
,”
Tissue Eng.
,
12
(
7
), pp.
1775
1785
.
42.
Matsumoto
,
T.
,
Sato
,
J.
,
Yamamoto
,
M.
, and
Sato
,
M.
,
2000
, “
Smooth Muscle Cells Freshly Isolated From Rat Thoracic Aortas Are Much Stiffer Than Cultured Bovine Cells: Possible Effect of Phenotype
,”
JSME Int. J. Ser. C-Mech. Syst. Mach. Elem. Manuf.
,
43
(
4
), pp.
867
874
.
43.
Wang
,
N.
,
1998
, “
Mechanical Interactions Among Cytoskeletal Filaments
,”
Hypertension
,
32
(
1
), pp.
162
165
.
44.
Ujihara
,
Y.
,
Nakamura
,
M.
,
Miyazaki
,
H.
, and
Wada
,
S.
,
2012
, “
Contribution of Actin Filaments to the Global Compressive Properties of Fibroblasts
,”
J. Mech. Behav. Biomed. Mater.
,
14
, pp.
192
198
.
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