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.
Issue Section:
Research Papers
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)81280-52.
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)76145-03.
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)80005-64.
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/nphys12695.
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.2012.03.0796.
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.2010.03.0417.
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.2007.03388.
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
.10.1088/1478-3975/8/1/0150159.
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.003347610.
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.003257211.
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.00108.201212.
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.2011.05.04013.
Wang
, J. H.
, and Lin
, J. S.
, 2007
, “Cell Traction Force and Measurement Methods
,” Biomech. Model. Mechanobiol.
, 6
(6
), pp. 361
–371
.10.1007/s10237-006-0068-414.
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)77386-815.
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
.10.1088/1478-3975/8/1/01500916.
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.2010.11.04417.
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-X18.
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)98041-719.
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.2006.05.00521.
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.00270.200122.
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.00169.200223.
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/s12195-009-0082-625.
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.090456510626.
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.153127.
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.106.10282228.
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
.10.1088/0953-8984/22/19/19411729.
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)00167-231.
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.9.060906.15192732.
Ananthakrishnan
, R.
, and Ehrlicher
, A.
, 2007
, “The Forces Behind Cell Movement
,” Int. J. Biol. Sci.
, 3
(5
), pp. 303
–317
.10.7150/ijbs.3.30333.
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
.10.1088/1478-3975/6/2/02500934.
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.00269.200135.
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.003976636.
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/BF0018037637.
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
.10.1063/1.292822938.
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.2004.11.00639.
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.00037.201140.
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.90688.200841.
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.2010.09.01242.
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-062910-10035143.
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/s10237-009-0175-0Copyright © 2013 by ASME
You do not currently have access to this content.
