The interactions between adherent cells and their extracellular matrix (ECM) have been shown to play an important role in many biological processes, such as wound healing, morphogenesis, differentiation, and cell migration. Cells attach to the ECM at focal adhesion sites and transmit contractile forces to the substrate via cytoskeletal actin stress fibers. This contraction results in traction stresses within the substrate/ECM. Traction force microscopy (TFM) is an experimental technique used to quantify the contractile forces generated by adherent cells. In TFM, cells are seeded on a flexible substrate and displacements of the substrate caused by cell contraction are tracked and converted to a traction stress field. The magnitude of these traction stresses are normally used as a surrogate measure of internal cell contractile force or contractility. We hypothesize that in addition to contractile force, other biomechanical properties including cell stiffness, adhesion energy density, and cell morphology may affect the traction stresses measured by TFM. In this study, we developed finite element models of the 2D and 3D TFM techniques to investigate how changes in several biomechanical properties alter the traction stresses measured by TFM. We independently varied cell stiffness, cell-ECM adhesion energy density, cell aspect ratio, and contractility and performed a sensitivity analysis to determine which parameters significantly contribute to the measured maximum traction stress and net contractile moment. Results suggest that changes in cell stiffness and adhesion energy density can significantly alter measured tractions, independent of contractility. Based on a sensitivity analysis, we developed a correction factor to account for changes in cell stiffness and adhesion and successfully applied this correction factor algorithm to experimental TFM measurements in invasive and noninvasive cancer cells. Therefore, application of these types of corrections to TFM measurements can yield more accurate estimates of cell contractility.

References

References
1.
Lauffenburger
,
D. A.
, and
Horwitz
,
A. F.
,
1996
, “
Cell Migration: A Physically Integrated Molecular Process
,”
Cell
,
84
(
3
), pp.
359
369
.10.1016/S0092-8674(00)81280-5
2.
Munevar
,
S.
,
Wang
,
Y.
, and
Dembo
,
M.
,
2001
, “
Traction Force Microscopy of Migrating Normal and H-ras Transformed 3T3 Fibroblasts
,”
Biophys. J.
,
80
(
4
), pp.
1744
1757
.10.1016/S0006-3495(01)76145-0
3.
Sheetz
,
M. P.
,
Felsenfeld
,
D. P.
, and
Galbraith
,
C. G.
,
1998
, “
Cell Migration: Regulation of Force on Extracellular-Matrix-Integrin Complexes
,”
Trends Cell Biol.
,
8
(
2
), pp.
51
54
.10.1016/S0962-8924(98)80005-6
4.
Trepat
,
X.
,
Wasserman
,
M. R.
,
Angelini
,
T. E.
,
Millet
,
E.
,
Weitz
,
D. A.
,
Butler
,
J. P.
, and
Fredberg
,
J. J.
,
2009
, “
Physical Forces During Collective Cell Migration
,”
Nat. Phys.
,
5
(
6
), pp.
426
430
.10.1038/nphys1269
5.
Nikkhah
,
M.
,
Edalat
,
F.
,
Manoucheri
,
S.
, and
Khademhosseini
,
A.
,
2012
, “
Engineering Microscale Topographies to Control the Cell-Substrate Interface
,”
Biomaterials
,
33
(
21
), pp.
5230
5246
.10.1016/j.biomaterials.2012.03.079
6.
Stevenson
,
M. D.
,
Sieminski
,
A. L.
,
McLeod
,
C. M.
,
Byfield
,
F. J.
,
Barocas
, V
. H.
, and
Gooch
,
K. J.
,
2010
, “
Pericellular Conditions Regulate Extent of Cell-Mediated Compaction of Collagen Gels
,”
Biophys. J.
,
99
(
1
), pp.
19
28
.10.1016/j.bpj.2010.03.041
7.
Boretti
,
M. I.
, and
Gooch
,
K. J.
,
2008
, “
Effect of Extracellular Matrix and 3D Morphogenesis on Islet Hormone Gene Expression by Ngn3-Infected Mouse Pancreatic Ductal Epithelial Cells
,”
Tissue Eng., Part A
,
14
(
12
), pp.
1927
1937
.10.1089/ten.tea.2007.0338
8.
Indra
, I
.
,
Undyala
, V
.
,
Kandow
,
C.
,
Thirumurthi
,
U.
,
Dembo
,
M.
, and
Beningo
,
K. A.
,
2011
, “
An In Vitro Correlation of Mechanical Forces and Metastatic Capacity
,”
Phys. Biol.
,
8
(
1
), p.
015015
.10.1088/1478-3975/8/1/015015
9.
Koch
,
T. M.
,
Munster
,
S.
,
Bonakdar
,
N.
,
Butler
,
J. P.
, and
Fabry
,
B.
,
2012
, “
3D Traction Forces in Cancer Cell Invasion
,”
PLoS One
,
7
(
3
), p.
e33476
.10.1371/journal.pone.0033476
10.
Kraning-Rush
,
C. M.
,
Califano
,
J. P.
, and
Reinhart-King
,
C. A.
,
2012
, “
Cellular Traction Stresses Increase With Increasing Metastatic Potential
,”
PLoS One
,
7
(
2
), p.
e32572
.10.1371/journal.pone.0032572
11.
Marinkovic
,
A.
,
Mih
,
J. D.
,
Park
,
J. A.
,
Liu
,
F.
, and
Tschumperlin
,
D. J.
,
2012
, “
Improved Throughput Traction Microscopy Reveals Pivotal Role for Matrix Stiffness in Fibroblast Contractility and TGF-Beta Responsiveness
,”
Am. J. Physiol. Lung Cell. Mol. Physiol.
,
303
(
3
), pp.
L169
180
.10.1152/ajplung.00108.2012
12.
Jannat
,
R. A.
,
Dembo
,
M.
, and
Hammer
,
D. A.
,
2011
, “
Traction Forces of Neutrophils Migrating on Compliant Substrates
,”
Biophys. J.
,
101
(
3
), pp.
575
584
.10.1016/j.bpj.2011.05.040
13.
Wang
,
J. H.
, and
Lin
,
J. S.
,
2007
, “
Cell Traction Force and Measurement Methods
,”
Biomech. Model. Mechanobiol.
,
6
(
6
), pp.
361
371
.10.1007/s10237-006-0068-4
14.
Dembo
,
M.
, and
Wang
,
Y. L.
,
1999
, “
Stresses at the Cell-To-Substrate Interface During Locomotion of Fibroblasts
,”
Biophys. J.
,
76
(
4
), pp.
2307
2316
.10.1016/S0006-3495(99)77386-8
15.
Kraning-Rush
,
C. M.
,
Carey
,
S. P.
,
Califano
,
J. P.
,
Smith
,
B. N.
, and
Reinhart-King
,
C. A.
,
2011
, “
The Role of the Cytoskeleton in Cellular Force Generation in 2D and 3D Environments
,”
Phys. Biol.
,
8
(
1
), p.
015009
.10.1088/1478-3975/8/1/015009
16.
Rape
,
A. D.
,
Guo
,
W. H.
, and
Wang
,
Y. L.
,
2011
, “
The Regulation of Traction Force in Relation to Cell Shape and Focal Adhesions
,”
Biomaterials
,
32
(
8
), pp.
2043
2051
.10.1016/j.biomaterials.2010.11.044
17.
Beningo
,
K. A.
, and
Wang
,
Y. L.
,
2002
, “
Flexible Substrata for the Detection of Cellular Traction Forces
,”
Trends Cell Biol.
,
12
(
2
), pp.
79
84
.10.1016/S0962-8924(01)02205-X
18.
Wang
,
Y. L.
, and
Pelham
,
R. J.
,
1998
, “
Preparation of a Flexible, Porous Polyacrylamide Substrate for Mechanical Studies of Cultured Cells
,”
Methods Enzymol
,
298
, pp.
489
496
.10.1016/S0076-6879(98)98041-7
19.
Pelham
,
R. J.
, and
Wang
,
Y. L.
,
1999
, “
High Resolution Detection of Mechanical Forces Exerted by Locomoting Fibroblasts on the Substrate
,”
Mol. Biol. Cell.
,
10
(
4
), pp.
935
945
.
20.
Yang
,
Z. C.
,
Lin
,
J. S.
,
Chen
,
J. X.
, and
Wang
,
J. H. C.
,
2006
, “
Determining Substrate Displacement and Cell Traction Fields—A New Approach
,”
J. Theor. Biol.
,
242
(
3
), pp.
607
616
.10.1016/j.jtbi.2006.05.005
21.
Butler
,
J. P.
,
Tolic-Norrelykke
, I
. M.
,
Fabry
,
B.
, and
Fredberg
,
J. J.
,
2002
, “
Traction Fields, Moments, and Strain Energy That Cells Exert on their Surroundings
,”
Am. J. Physiol.: Cell. Physiol.
,
282
(
3
), pp.
C595
605
.10.1152/ajpcell.00270.2001
22.
Tolic-Norrelykke
, I
. M.
,
Butler
,
J. P.
,
Chen
,
J.
, and
Wang
,
N.
,
2002
, “
Spatial and Temporal Traction Response in Human Airway Smooth Muscle Cells
,”
Am. J. Physiol.: Cell. Physiol.
,
283
(
4
), pp.
C1254
1266
.10.1152/ajpcell.00169.2002
23.
Landau
,
L. D.
, and
Lifshitz
,
E. M.
,
1986
,
Theory of Elasticity
,
Pergamon
,
New York
.
24.
Hur
,
S. S.
,
Zhao
,
Y.
,
Li
,
Y. S.
,
Botvinick
,
E.
, and
Chien
,
S.
,
2009
, “
Live Cells Exert 3-Dimensional Traction Forces on Their Substrata
,”
Cell. Mol. Bioeng.
,
2
(
3
), pp.
425
436
.10.1007/s12195-009-0082-6
25.
Maskarinec
,
S. A.
,
Franck
,
C.
,
Tirrell
,
D. A.
, and
Ravichandran
,
G.
,
2009
, “
Quantifying Cellular Traction Forces in Three Dimensions
,”
Proc. Natl. Acad. Sci. U.S.A.
,
106
(
52
), pp.
22,108
22,113
.10.1073/pnas.0904565106
26.
Legant
,
W. R.
,
Miller
,
J. S.
,
Blakely
,
B. L.
,
Cohen
,
D. M.
,
Genin
,
G. M.
, and
Chen
,
C. S.
,
2010
, “
Measurement of Mechanical Tractions Exerted by Cells in Three-Dimensional Matrices
,”
Nat. Methods
,
7
(
12
), pp.
969
971
.10.1038/nmeth.1531
27.
Smith
,
L. A.
,
Aranda-Espinoza
,
H.
,
Haun
,
J. B.
,
Dembo
,
M.
, and
Hammer
,
D. A.
,
2007
, “
Neutrophil Traction Stresses are Concentrated in the Uropod During Migration
,”
Biophys. J.
,
92
(
7
), pp.
L58
60
.10.1529/biophysj.106.102822
28.
Jannat
,
R. A.
,
Robbins
,
G. P.
,
Ricart
,
B. G.
,
Dembo
,
M.
, and
Hammer
,
D. A.
,
2010
, “
Neutrophil Adhesion and Chemotaxis Depend on Substrate Mechanics
,”
J. Phys. Condens. Matter
,
22
(
19
), p.
194117
.10.1088/0953-8984/22/19/194117
29.
Vincent
,
L. G.
,
Yong
,
T.
,
del Alamo
,
J.
,
Tan
,
L.
, and
Engler
,
A. J.
,
2011
, “
High Cell Aspect Ratio Alters Stem Cell Traction Stresses and Lineage
,”
Mol. Biol. Cell.
,
22
, Abstract 1587.
30.
Chan
,
B. P.
,
Bhat
, V
. D.
,
Yegnasubramanian
,
S.
,
Reichert
,
W. M.
, and
Truskey
,
G. A.
,
1999
, “
An Equilibrium Model of Endothelial Cell Adhesion via Integrin-Dependent and Integrin-Independent Ligands
,”
Biomaterials
,
20
(
23–24
), pp.
2395
2403
.10.1016/S0142-9612(99)00167-2
31.
Janmey
,
P. A.
, and
McCulloch
,
C. A.
,
2007
, “
Cell Mechanics: Integrating Cell Responses to Mechanical Stimuli
,”
Annu. Rev. Biomed. Eng.
,
9
, pp.
1
34
.10.1146/annurev.bioeng.9.060906.151927
32.
Ananthakrishnan
,
R.
, and
Ehrlicher
,
A.
,
2007
, “
The Forces Behind Cell Movement
,”
Int. J. Biol. Sci.
,
3
(
5
), pp.
303
317
.10.7150/ijbs.3.303
33.
Sunyer
,
R.
,
Trepat
,
X.
,
Fredberg
,
J. J.
,
Farre
,
R.
, and
Navajas
,
D.
,
2009
, “
The Temperature Dependence of Cell Mechanics Measured by Atomic Force Microscopy
,”
Phys. Biol.
,
6
(
2
), p.
025009
.10.1088/1478-3975/6/2/025009
34.
Wang
,
N.
,
Tolic-Norrelykke
, I
. M.
,
Chen
,
J.
,
Mijailovich
,
S. M.
,
Butler
,
J. P.
,
Fredberg
,
J. J.
, and
Stamenovic
,
D.
,
2002
, “
Cell Prestress. I. Stiffness and Prestress are Closely Associated in Adherent Contractile Cells
,”
Am. J. Physiol.: Cell Physiol.
,
282
(
3
), pp.
C606
616
.10.1152/ajpcell.00269.2001
35.
Li
,
R.
,
Ackerman
,
W. E. T.
,
Mihai
,
C.
,
Volakis
,
L. I.
,
Ghadiali
,
S.
, and
Kniss
,
D. A.
,
2012
, “
Myoferlin Depletion in Breast Cancer Cells Promotes Mesenchymal to Epithelial Shape Change and Stalls Invasion
,”
PLoS One
,
7
(
6
), p.
e39766
.10.1371/journal.pone.0039766
36.
Schmidt
,
F. G.
,
Ziemann
,
F.
, and
Sackmann
,
E.
,
1996
, “
Shear Field Mapping in Actin Networks by Using Magnetic Tweezers
,”
Eur. Biophys. J.
,
24
(
5
), pp.
348
353
.10.1007/BF00180376
37.
Lin
,
L. A. G.
,
Liu
,
A. Q.
,
Yu
,
Y. F.
,
Zhang
,
C.
,
Lim
,
C. S.
,
Ng
,
S. H.
,
Yap
,
P. H.
, and
Gao
,
H. J.
,
2008
, “
Cell Compressibility Studies Utilizing Noncontact Hydrostatic Pressure Measurements on Single Living Cells in a Microchamber
,”
Appl. Phys. Lett.
,
92
(
23
), p.
233901
.10.1063/1.2928229
38.
Trickey
,
W. R.
,
Baaijens
,
F. P. T.
,
Laursen
,
T. A.
,
Alexopoulos
,
L. G.
, and
Guilak
,
F.
,
2006
, “
Determination of the Poisson's Ratio of the Cell: Recovery Properties of Chondrocytes After Release From Complete Micropipette Aspiration
,”
J. Biomech.
,
39
(
1
), pp.
78
87
.10.1016/j.jbiomech.2004.11.006
39.
Mihai
,
C.
,
Bao
,
S.
,
Lai
,
J. P.
,
Ghadiali
,
S. N.
, and
Knoell
,
D. L.
,
2012
, “
PTEN Inhibition Improves Wound Healing in Lung Epithelia Through Changes in Cellular Mechanics That Enhance Migration
,”
Am. J. Physiol. Lung Cell. Mol. Physiol.
,
302
(
3
), pp.
L287
299
.10.1152/ajplung.00037.2011
40.
Dailey
,
H. L.
,
Ricles
,
L. M.
,
Yalcin
,
H. C.
, and
Ghadiali
,
S. N.
,
2009
, “
Image-Based Finite Element Modeling of Alveolar Epithelial Cell Injury During Airway Reopening
,”
J. Appl. Physiol.
,
106
(
1
), pp.
221
232
.10.1152/japplphysiol.90688.2008
41.
Or-Tzadikario
,
S.
, and
Gefen
,
A.
,
2011
, “
Confocal-Based Cell-Specific Finite Element Modeling Extended to Study Variable Cell Shapes and Intracellular Structures: The Example of the Adipocyte
,”
J. Biomech.
,
44
(
3
), pp.
567
573
.10.1016/j.jbiomech.2010.09.012
42.
Kollmannsberger
,
P.
, and
Fabry
,
B.
,
2011
, “
Linear and Nonlinear Rheology of Living Cells
,”
Annu. Rev. Mater. Res.
,
41
, pp.
75
97
.10.1146/annurev-matsci-062910-100351
43.
Dailey
,
H. L.
, and
Ghadiali
,
S. N.
,
2010
, “
Influence of Power-Law Rheology on Cell Injury During Microbubble Flows
,”
Biomech. Model. Mechanobiol.
,
9
(
3
), pp.
263
279
.10.1007/s10237-009-0175-0
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