An original homogenization method was used to analyze the nonlinear elastic properties of epithelial cells probed by magnetic twisting cytometry. In this approach, the apparent rigidity of a cell with nonlinear mechanical properties is deduced from the mechanical response of the entire population of adherent cells. The proposed hyperelastic cell model successfully accounts for the variability in probe-cell geometrical features, and the influence of the cell–substrate adhesion. Spatially distributed local secant elastic moduli had amplitudes ranging from 10 to 400 Pa. The nonlinear elastic behavior of cells may contribute to the wide differences in published results regarding cell elasticity moduli.
1.
Davies
, P. F.
, Robotewskyj
, A.
, and Griem
, M. L.
, 1993
, “Endothelial Cell Adhesion in Real Time. Measurements In Vitro by Tandem Scanning Confocal Image Analysis
,” J. Clin. Invest.
, 91
(6
), pp. 2640
–2652
.2.
Forgacs
, G.
, 1995
, “Biological Specificity and Measurable Physical Properties of Cell Surface Receptors and Their Possible Role in Signal Transduction Through the Cytoskeleton
,” Biochem. Cell Biol.
, 73
(7–8
), pp. 317
–326
.3.
Ingber
, D. E.
, 1997
, “Tensegrity: The Architectural Basis of Cellular Mechanotransduction
,” Annu. Rev. Physiol.
, 59
, pp. 575
–599
.4.
Hamill
, O. P.
, and Martinac
, B.
, 2001
, “Molecular Basis of Mechanotransduction in Living Cells
,” Physiol. Rev.
, 81
(2
), pp. 685
–740
.5.
Ricci
, D.
, Tedesco
, M.
, and Grattarola
, M.
, 1997
, “Mechanical and Morphological Properties of Living 3T6 Cells Probed Via Scanning Force Microscopy
,” Microsc. Res. Tech.
, 36
, pp. 165
–171
.6.
Pourati
, J.
, Maniotis
, A.
, Spiegel
, D.
, Schaffer
, J. L.
, Butler
, J. P.
, Fredberg
, J. J.
, Ingber
, D. E.
, Stamenovic
, D.
, and Wang
, N.
, 1998
, “Is Cytoskeletal Tension a Major Determinant of Cell Deformability in Adherent Endothelial Cells?
” Am. J. Physiol.
, 274
(5
Pt 1), pp. C1283–C1289
C1283–C1289
.7.
Ingber
, D. E.
, with Heidemann
, S. R.
, Lamoureux
, P.
, and Buxbaum
, R. E.
, 2000
, “Opposing Views on Tensegrity as a Structural Framework for Understanding Cell Mechanics
,” J. Appl. Physiol.
, 89
(4
), pp. 1663
–1670
.8.
Rahman
, A.
, Tseng
, Y.
, and Wirtz
, D.
, 2002
, “Micromechanical Coupling Between Cell Surface Receptors and RGD Peptides
,” Biochem. Biophys. Res. Commun.
, 296
(3
), pp. 771
–778
.9.
Choquet
, D.
, Felsenfeld
, D. P.
, and Sheetz
, M. P.
, 1997
, “Extracellular Matrix Rigidity Causes Strengthening of Integrin–Cytoskeleton Linkages
,” Cell
, 88
(1
), pp. 39
–48
.10.
Sato
, M.
, Ohshima
, N.
, and Nerem
, R. M.
, 1996
, “Viscoelastic Properties of Cultured Porcine Aortic Endothelial Cells Exposed to Shear Stress
,” J. Biomech.
, 29
(4
), pp. 461
–467
.11.
Thoumine
, O.
, and Ott
, A.
, 1997
, “Time Scale Dependent Viscoelastic and Contractile Regimes in Fibroblasts Probed by Microplate Manipulation
,” J. Cell. Sci.
, 110
(Pt 17), pp. 2109
–2116
.12.
Wang
, N.
, Butler
, J. P.
, and Ingber
, D. E.
, 1993
, “Mechanotransduction Across the Cell Surface and Through the Cytoskeleton
,” Science
, 260
(5111
), pp. 1124
–1127
.13.
Wang
, N.
, and Ingber
, D. E.
, 1994
, “Control of Cytoskeletal Mechanics by Extracellular Matrix, Cell Shape, and Mechanical Tension
,” Biophys. J.
, 66
(6
), pp. 2181
–2189
.14.
Wang
, N.
, and Ingber
, D. E.
, 1995
, “Probing Transmembrane Mechanical Coupling and Cytomechanics Using Magnetic Twisting Cytometry
,” Biochem. Cell Biol.
, 73
(7–8
), pp. 327
–335
.15.
Wang
, N.
, Planus
, E.
, Pouchelet
, M.
, Fredberg
, J. J.
, and Barlovatz-Meimon
, G.
, 1995
, “Urokinase Receptor Mediates Mechanical Force Transfer Across the Cell Surface
,” Am. J. Physiol.
, 268
(4
Pt 1), C1062–C1066
C1062–C1066
.16.
Wendling
, S.
, Planus
, E.
, Laurent
, V.
, Barbe
, L.
, Mary
, A.
, Oddou
, C.
, and Isabey
, D.
, 2000
, “Role of Cellular Tone and Microenvironment on Cytoskeleton Stiffness Predicted by Tensegrity Model
,” Eur. Phys. J.: Appl. Phys.
, 9
, pp. 51
–62
.17.
Laurent
, V. M.
, Henon
, S.
, Planus
, E.
, Fodil
, R.
, Balland
, M.
, Isabey
, D.
, and Gallet
, F.
, 2002
, “Assessment of Mechanical Properties of Adherent Living Cells by Bead Micromanipulation: Comparison of Magnetic Twisting Cytometry vs Optical Tweezers
,” J. Biomech. Eng.
, 124
(4
), pp. 408
–421
.18.
Laurent
, V. M.
, Fodil
, R.
, Canadas
, P.
, Fereol
, S.
, Louis
, B.
, Planus
, E.
, and Isabey
, D.
, 2003
, “Partitioning of Cortical and Deep Cytoskeleton Responses From Transient Magnetic Bead Twisting
,” Ann. Biomed. Eng.
, 31
(10
), 1263
–1278
.19.
Sato
, M.
, Theret
, D. P.
, Wheeler
, L. T.
, Ohshima
, N.
, and Nerem
, R. M.
, 1990
, “Application of the Micropipette Technique to the Measurement of Cultured Porcine Aortic Endothelial Cell Viscoelastic Properties
,” J. Biomech. Eng.
, 112
(3
), pp. 263
–268
.20.
Hubmayr
, R. D.
, Shore
, S. A.
, Fredberg
, J. J.
, Planus
, E.
, Panettieri
, Jr., R. A.
, Moller
, W.
, Heyder
, J.
, and Wang
, N.
, 1996
, “Pharmacological Activation Changes Stiffness of Cultured Human Airway Smooth Muscle Cells
,” Am. J. Physiol.
, 271
(5
Pt 1), pp. C1660–C1668
C1660–C1668
.21.
Potard
, U. S.
, Butler
, J. P.
, and Wang
, N.
, 1997
, “Cytoskeletal Mechanics in Confluent Epithelial Cells Probed Through Integrins and E-Cadherins
,” Am. J. Physiol.
, 272
(5
Pt 1), pp. C1654–C1663
C1654–C1663
.22.
Fabry
, B.
, Maksym
, G.
, Hubmayr
, R.
, Butler
, J.
, and Fredberg
, J.
, 1999
, “Implications of Heterogeneous Bead Behavior on Cell Mechanical Properties Measured With Magnetic Twisting Cytometry
,” J. Magn. Magn. Mater.
, 194
, pp. 120
–125
.23.
Fabry
, B.
, Maksym
, G. N.
, Butler
, J. P.
, Glogauer
, M.
, Navajas
, D.
, and Fredberg
, J. J.
, 2001
, “Scaling the Microrheology of Living Cells
,” Phys. Rev. Lett.
, 87
(14
), pp. 1481
–1502
.24.
Fabry
, B.
, Maksym
, G. N.
, Shore
, S. A.
, Moore
, P. E.
, Panettieri
, R. A.
, Butler
, J. P.
, and Fredberg
, J. J.
, 2001
, “Selected Contribution: Time Course and Heterogeneity of Contractile Responses in Cultured Human Airway Smooth Muscle Cells
,” J. Appl. Physiol.
, 91
, pp. 986
–994
.25.
Thoumine
, O.
, Ott
, A.
, Cardoso
, O.
, and Meister
, J. J.
, 1999
, “Microplates: A New Tool for Manipulation and Mechanical Perturbation of Individual Cells
,” J. Biochem. Biophys. Methods
, 39
(1–2
), pp. 47
–62
.26.
Svoboda
, K.
, and Block
, S. M.
, 1994
, “Biological Applications of Optical Forces
,” Annu. Rev. Biophys. Biomol. Struct.
, 23
, pp. 247
–285
.27.
Sheetz
, M. P.
, 1998
, “Laser Tweezers in Cell Biology. Introduction
,” Methods Cell Biol.
, 55
, pp. xi–xii
xi–xii
.28.
Henon
, S.
, Lenormand
, G.
, Richert
, A.
, and Gallet
, F.
, 1999
, “A New Determination of the Shear Modulus of the Human Erythrocyte Membrane Using Optical Tweezers
,” Biophys. J.
, 76
(2
), pp. 1145
–1151
.29.
Lenormand
, G.
, Henon
, S.
, Richert
, A.
, Simeon
, J.
, and Gallet
, F.
, 2001
, “Direct Measurement of the Area Expansion and Shear Moduli of the Human Red Blood Cell Membrane Skeleton
,” Biophys. J.
, 81
(1
), pp. 43
–56
.30.
Bausch
, A. R.
, Ziemann
, F.
, Boulbitch
, A. A.
, Jacobson
, K.
, and Sackmann
, E.
, 1998
, “Local Measurements of Viscoelastic Parameters of Adherent Cell Surfaces by Magnetic Bead Microrheometry
,” Biophys. J.
, 75
(4
), pp. 2038
–2049
.31.
Bausch
, A. R.
, Mo¨ller
, W.
, and Sackmann
, E.
, 1999
, “Measurement of Local Viscoelasticity and Forces in Living Cells by Magnetic Tweezers
,” Biophys. J.
, 76
, pp. 573
–579
.32.
Shroff
, S. G.
, Saner
, D. R.
, and Lal
, R.
, 1995
, “Dynamic Micromechanical Properties of Cultured Rat Atrial Myocytes Measured by Atomic Force Microscopy
,” Am. J. Physiol.
, 269
(1
Pt 1), pp. C286–C292
C286–C292
.33.
Dimitriadis
, E. K.
, Horkay
, F.
, Maresca
, J.
, Kachar
, B.
, and Chadwick
, R. S.
, 2002
, “Determination of Elastic Moduli of Thin Layers of Soft Material Using the Atomic Force Microscope
,” Biophys. J.
, 82
(5
), pp. 2798
–2810
.34.
Bausch
, A. R.
, Hellerer
, U.
, Essler
, M.
, Aepfelbacher
, M.
, and Sackmann
, E.
, 2001
, “Rapid Stiffening of Integrin Receptor–Actin Linkages in Endothelial Cells Stimulated With Thrombin: A Magnetic Bead Microrheology Study
,” Biophys. J.
, 80
(6
), pp. 2649
–2657
.35.
Laurent
, V. M.
, Planus
, E.
, Fodil
, R.
, and Isabey
, D.
, 2003
, “Mechanical Assessment by Magnetocytometry of the Cytosolic and Cortical Cytoskeletal Compartments in Adherent Epithelial Cells
,” Biorheology
, 40
(1–3
), pp. 235
–240
.36.
Stamenovic
, D.
, Ingber
, D. E.
, Wang
, N.
, and Fredberg
, J. J.
, 1996
, “A Microstructural Approach to Cytoskeletal Mechanics Based on Tensegrity
,” J. Theor. Biol.
, 181
, pp. 125
–136
.37.
Wendling
, S.
, Oddou
, C.
, and Isabey
, D.
, 1999
, “Stiffening Response of a Cellular Tensegrity Model
,” J. Theor. Biol.
, 196
(3
), pp. 309
–325
.38.
Stamenovic
, D.
, and Coughlin
, M. F.
, 2000
, “A Quantitative Model of Cellular Elasticity Based on Tensegrity
,” J. Biomech. Eng.
, 122
(1
), pp. 39
–43
.39.
Canadas
, P.
, Laurent
, V. M.
, Oddou
, C.
, Isabey
, D.
, and Wendling
, S.
, 2002
, “A Cellular Tensegrity Model to Analyze the Structural Viscoelasticity of the Cytoskeleton
,” J. Theor. Biol.
, 218
(2
), pp. 155
–173
.40.
Caille
, N.
, Thoumine
, O.
, Tardy
, Y.
, and Meister
, J. J.
, 2002
, “Contribution of the Nucleus to the Mechanical Properties of Endothelial Cells
,” J. Biomech.
, 35
(2
), pp. 177
–187
.41.
Charras
, G. T.
, and Horton
, M. A.
, 2002
, “Determination of Cellular Strains by Combined Atomic Force Microscopy and Finite Element Modeling
,” Biophys. J.
, 83
(2
), pp. 858
–879
.42.
Mijailovich
, S. M.
, Kojic
, M.
, Zivkovic
, M.
, Fabry
, B.
, and Fredberg
, J. J.
, 2002
, “A Finite Element Model of Cell Deformation During Magnetic Bead Twisting
,” J. Appl. Physiol.
, 93
(4
), pp. 1429
–1436
.43.
Bornert, M., Bretheau, T., and Gilormini, P., 2001, Homoge´ne´isation en Me´canique des Mate´riaux, Hermes Science Publications, Paris.
44.
Fodil
, R.
, Laurent
, V.
, Planus
, E.
, and Isabey
, D.
, 2003
, “Characterization of Cytoskeleton Mechanical Properties and 3D-Actin Structure in Twisted Adherent Epithelial Cells
,” Biorheology
, 40
(1–3
), pp. 241
–245
.45.
Schneider
, S. W.
, Pagel
, P.
, Rotsch
, C.
, Danker
, T.
, Oberleithner
, H.
, Radmacher
, M.
, and Schwab
, A.
, 2000
, “Volume Dynamics in Migrating Epithelial Cells Measured With Atomic Force Microscopy
,” Pfluegers Arch.
, 439
(3
), pp. 297
–303
.46.
Holzapfel, G. A., 2001, Nonlinear Solid Mechanics, Wiley, New York, p. 455.
47.
Costa
, K. D.
, and Yin
, F. C. P.
, 1999
, “Analysis of Indentation: Implications for Measuring Mechanical Properties With Atomic Force Microscopy
,” J. Biomech. Eng.
, 121
, pp. 462
–469
.48.
Yeoh
, O. H.
, 1990
, “Characterization of Elastic Properties of Carbon-Black-Filled Rubber Vulcaizates
,” Rubber Chem. Technol.
, 63
, pp. 792
–805
.49.
Shin
, D.
, and Athanasiou
, K.
, 1999
, “Cytoindentation for Obtaining Cell Biomechanical Properties
,” J. Orthop. Res.
, 17
, pp. 880
–890
.50.
Kamm
, R. D.
, McVittie
, A. K.
, and Bathe
, M.
, 2000
, “On the Role of Continuum Models in Mechanobiology
,” ASME International Congress—Mechanics in Biology
, 242
, pp. 1
–9
.51.
Mathur
, A. B.
, Collinsworth
, A. M.
, Reichert
, W. M.
, Kraus
, W. E.
, and Truskey
, G. A.
, 2001
, “Endothelial, Cardiac Muscle and Skeletal Muscle Exhibit Different Viscous and Elastic Properties as Determined by Atomic Force Microscopy
,” J. Biomech.
, 34
, pp. 1545
–1553
.52.
Fabry
, B.
, Maksym
, G. N.
, Butler
, J. P.
, Glogauer
, M.
, Navajas
, D.
, Taback
, N. A.
, Millet
, E. J.
, and Fredberg
, J. J.
, 2003
, “Time Scale and Other Invariants of Integrative Mechanical Behavior in Living Cells
,” Phys. Rev. E
, 68
(4
Pt 1), p. 041914
041914
.53.
Maksym
, G. N.
, Fabry
, B.
, Butler
, J. P.
, Navajas
, D.
, Tschumperlin
, D. J.
, Laporte
, J. D.
, and Fredberg
, J. J.
, 2000
, “Mechanical Properties of Cultured Human Airway Smooth Muscle Cells From 0.05 to 0.4 Hz
,” J. Appl. Physiol.
, 89
(4
), pp. 1619
–1632
.54.
Doornaert
, B.
, Leblond
, V.
, Planus
, E.
, Galiacy
, S.
, Laurent
, V. M.
, Gras
, G.
, Isabey
, D.
, and Lafuma
, C.
, 2003
, “Time Course of Actin Cytoskeleton Stiffness and Matrix Adhesion Molecules in Human Bronchial Epithelial Cell Cultures
,” Exp. Cell Res.
, 287
, pp. 199
–208
.55.
Wozniak
, M.
, Fausto
, A.
, Carron
, C. P.
, Meyer
, D. M.
, and Hruska
, K. A.
, 2000
, “Mechanically Strained Cells of the Osteoblast Lineage Organize Their Extracellular Matrix Through Unique Sites of Alphavbeta3-Integrin Expression
,” J. Bone Miner. Res.
, 15
(9
), pp. 1731
–1745
.56.
Mathur
, A. B.
, Truskey
, G.
, and Reichert
, W. M.
, 2000
, “Atomic Force and Total Internal Reflection Fluorescence Microscopy for the Study of Force Transmission in Endothelial Cells
,” Biophys. J.
, 78
(4
), pp. 1725
–1735
.57.
Balaban
, N. Q.
, Schwarz
, U. S.
, Riveline
, D.
, Goichberg
, P.
, Tzur
, G.
, Sabanay
, I.
, Mahalu
, D.
, Safran
, S.
, Bershadsky
, A.
, Addadi
, L.
et al., 2001
, “Force and Focal Adhesion Assembly: A Close Relationship Studied Using Elastic Micropatterned Substrates
,” Nat. Cell Biol.
, 3
(5
), pp. 466
–472
.58.
Schwarz
, U. S.
, Balaban
, N. Q.
, Riveline
, D.
, Bershadsky
, A.
, Geiger
, B.
, and Safran
, S. A.
, 2002
, “Calculation of Forces at Focal Adhesions From Elastic Substrate Data: The Effect of Localized Force and the Need for Regularization
,” Biophys. J.
, 83
(3
), pp. 1380
–1394
.59.
Hu
, S.
, Chen
, J.
, Fabry
, B.
, Numaguchi
, Y.
, Gouldstone
, A.
, Ingber
, D. E.
, Fredberg
, J. J.
, Butler
, J. P.
, and Wang
, N.
, 2003
, “Intracellular Stress Tomography Reveals Stress Focusing and Structural Anisotropy in Cytoskeleton of Living Cells
,” Am. J. Physiol. Cell Physiol.
, 285
(5
), pp. C1082–C1090
C1082–C1090
.60.
Pommerenke
, H.
, Schreiber
, E.
, Durr
, F.
, Nebe
, B.
, Hahnel
, C.
, Moller
, W.
, and Rychly
, J.
, 1996
, “Stimulation of Integrin Receptors Using a Magnetic Drag Force Device Induces an Intracellular Free Calcium Response
,” Eur. J. Cell Biol.
, 70
(2
), pp. 157
–164
.Copyright © 2004
by ASME
You do not currently have access to this content.
