A force based model of cell migration is presented which gives new insight into the importance of the dynamics of cell binding to the substrate. The main features of the model are the focus on discrete attachment dynamics, the treatment of the cellular forces as springs, and an incorporation of the stochastic nature of the attachment sites. One goal of the model is to capture the effect of the random binding and unbinding of cell attachments on global cell motion. Simulations reveal one of the most important factor influencing cell speed is the duration of the attachment to the substrate. The model captures the correct velocity and force relationships for several cell types.
Issue Section:
Research Papers
References
1.
Sonnemann
, K. J.
, and Bement
, W. M.
, 2011
, “Wound Repair: Toward Understanding and Integration of Single-Cell and Multicellular Wound Responses
,” Annu. Rev. Cell Dev. Biol.
, 27
, pp. 237
–263
.10.1146/annurev-cellbio-092910-1542512.
Krawczyk
, W.
, 1971
, “A Pattern of Epidermal Cell Migration During Wound Healing
,” J. Cell Biol.
, 49
(2
), pp. 247
–263
.10.1083/jcb.49.2.2473.
Tanner
, K.
, Ferris
, D.
, Lanzano
, L.
, Mandefro
, B.
, Mantulin
, W.
, Gardiner
, D.
, Rugg
, E.
, and Gratton
, E.
, 2009
, “Coherent Movement of Cell Layers During Wound Healing by Image Correlation Spectroscopy
,” Biophys. J.
, 97
(7
), pp. 2098
–2106
.10.1016/j.bpj.2009.06.0524.
Friedl
, P.
, and Wolf
, K.
, 2003
, “Tumour-Cell Invasion and Migration: Diversity and Escape Mechanisms
,” Nat. Rev. Cancer
, 3
(5
), pp. 362
–374
.10.1038/nrc10755.
Yilmaz
, M.
, and Christofori
, G.
, 2010
, “Mechanisms of Motility in Metastasizing Cells
,” Mol. Cancer Res.
, 8
(5
), pp. 629
–642
.10.1158/1541-7786.MCR-10-01396.
Keller
, R.
, Davidson
, L.
, Edlund
, A.
, Elul
, T.
, Ezin
, M.
, Shook
, D.
, and Skoglund
, P.
, 2000
, “Mechanisms of Convergence and Extension by Cell Intercalation
,” Philos. Trans. R. Soc. London, Ser. B
, 355
(1399
), pp. 897
–922
.10.1098/rstb.2000.06267.
Mammoto
, T.
, and Ingber
, D.
, 2010
, “Mechanical Control of Tissue and Organ Development
,” Development
, 137
(9
), pp. 1407
–1420
.10.1242/dev.0241668.
Rieu
, J.-P.
, Saito
, T.
, Delanoë-Ayari
, H.
, Sawada
, Y.
, and Kay
, R. R.
, 2009
, “Migration of Dictyostelium Slugs: Anterior-Like Cells may Provide the Motive Force for the Prespore Zone
,” Cell Motil. Cytoskeleton
, 66
(12
), pp. 1073
–86
.10.1002/cm.204119.
Holle
, A. W.
, and Engler
, A. J.
, 2011
, “More Than a Feeling: Discovering, Understanding, and Influencing Mechanosensing Pathways
,” Curr. Opin. Biotechnol.
, 22
(5
), pp. 648
–654
.10.1016/j.copbio.2011.04.00710.
Huttenlocher
, A.
, and Horwitz
, A. R.
, 2011
, “Integrins in Cell Migration
,” Cold Spring Harb. Perspect. Biol.
, 3
(9
), p. a005074
.10.1101/cshperspect.a00507411.
Izzard
, C.
, and Lochner
, L.
, 1976
, “Cell-to-Substrate Contacts in Living Fibroblasts: A Interference Reflexion Study With an Evaluation of the Technique
,” J. Cell Sci.
, 21
(1
), pp. 129
–159
.12.
Heath
, J.
, and Dunn
, G.
, 1978
, “Cell to Substratum Contacts of Chick Fibroblasts and Their Relation to the Microfilament System. A Correlated Interference-Reflexion and High-Voltage Electron-Microscope Study
,” J. Cell Sci.
, 29
(1
), pp. 197
–212
.13.
Lazarides
, E.
, and Burridge
, K.
, 1975
, “r,-actinin: Immunofluorescent Localization of a Muscle Structural Protein in Nonmuscle Cells
,” Cell
, 6
, pp. 289
–298
.10.1016/0092-8674(75)90180-414.
Gardel
, M. L.
, Schneider
, I. C.
, Aratyn-Schaus
, Y.
, and Waterman
, C. M.
, 2010
, “Mechanical Integration of Actin and Adhesion Dynamics in Cell Migration
,” Annu. Rev. Cell Dev. Biol.
, 26
, pp. 315
–333
.10.1146/annurev.cellbio.011209.12203615.
Lauffenburger
, D.
, and Horwitz
, A.
, 1996
, “Cell Migration: A Physically Integrated Molecular Process
,” Cell
, 84
(3
), pp. 359
–369
.10.1016/S0092-8674(00)81280-516.
Dickinson
, R.
, 2000
, “A Generalized Transport Model for Biased Cell Migration in an Anisotropic Environment
,” J. Math. Biol.
, 40
(2
), pp. 97
–135
.10.1007/s00285005000617.
Sandersius
, S. A.
, and Newman
, T. J.
, 2008
, “Modeling Cell Rheology With the Subcellular Element Model
,” Phys. Biol.
, 5
(1
), p. 015002
.10.1088/1478-3975/5/1/01500218.
Keren
, K.
, Pincus
, Z.
, Allen
, G. M.
, Barnhart
, E. L.
, Marriott
, G.
, Mogilner
, A.
, and Theriot
, J. A.
, 2008
, “Mechanism of Shape Determination in Motile Cells
,” Nature
, 453
(7194
), pp. 475–U1
.10.1038/nature0695219.
Mogilner
, A.
, and Oster
, G.
, 2003
, “Force Generation by Actin Polymerization ii: The Elastic Ratchet and Tethered Filaments
,” Biophys. J.
, 84
(3
), pp. 1591
–1605
.10.1016/S0006-3495(03)74969-820.
Schreiber
, C. H.
, Stewart
, M.
, and Duke
, T.
, 2010
, “Simulation of Cell Motility That Reproduces the Force-Velocity Relationship
,” Proc. Natl. Acad. Sci. U.S.A.
, 107
(20
), pp. 9141
–9146
.10.1073/pnas.100253810721.
Paszek
, M. J.
, Boettiger
, D.
, Weaver
, V. M.
, and Hammer
, D. A.
, 2009
, “Integrin Clustering is Driven by Mechanical Resistance From the Glycocalyx and the Substrate
,” PLOS Comput. Biol.
, 5
(12
), p. e1000604
.10.1371/journal.pcbi.100060422.
Bottino
, D.
, and Fauci
, L.
, 1998
, “A Computational Model of Ameboid Deformation and Locomotion
,” Eur. Biophys. J.
, 27
(5
), pp. 532
–539
.10.1007/s00249005016323.
Herant
, M.
, and Dembo
, M.
, 2010
, “Form and Function in Cell Motility: From Fibroblasts to Keratocytes
,” Biophys. J.
, 98
(8
), pp. 1408
–1417
.10.1016/j.bpj.2009.12.430324.
Buenemann
, M.
, Levine
, H.
, Rappel
, W.-J.
, and Sander
, L. M.
, 2010
, “The Role of Cell Contraction and Adhesion in Dictyostelium Motility
,” Biophys. J.
, 99
(1
), pp. 50
–58
.10.1016/j.bpj.2010.03.05725.
Ionides
, E.
, Fang
, K.
, Isseroff
, R.
, and Oster
, G.
, 2004
, “Stochastic Models for Cell Motion and Taxis
,” J. Math. Biol.
, 48
(1
), pp. 23
–37
.10.1007/s00285-003-0220-z26.
Dallon
, J. C.
, and Othmer
, H. G.
, 2004
, “How Cellular Movement Determines the Collective Force Generated by the Dictyostelium discoideum Slug
,” J. Theor. Biol.
, 231
, pp. 203
–222
.10.1016/j.jtbi.2004.06.01527.
Mallet
, D. G.
, and Pettet
, G. J.
, 2006
, “A Mathematical Model of Integrin-Mediated Haptotactic Cell Migration
,” Bull. Math. Biol.
, 68
(2
), pp. 231
–253
.10.1007/s11538-005-9032-128.
Ulrich
, F.
, and Heisenberg
, C.-P.
, 2009
, “Trafficking and Cell Migration
,” Traffic
, 10
(7
), pp. 811
–818
.10.1111/j.1600-0854.2009.00929.x29.
Gumbiner
, B. M.
, 1996
, “Cell Adhesion: The Molecular Basis of Tissue Architecture and Morphogenesis
,” Cell
, 84
(3
), pp. 345
–357
.10.1016/S0092-8674(00)81279-930.
Uchida
, K.
, and Yumura
, S.
, 2004
, “Dynamics of Novel Feet of Dictyostelium Cells During Migration
,” J. Cell Sci.
, 117
(8
), pp. 1443
–1455
.10.1242/jcs.0101531.
Delanoë-Ayari
, H.
, Iwaya
, S.
, Maeda
, Y. T.
, Inose
, J.
, Riviere
, C.
, Sano
, M.
, and Rieu
, J.-P.
, 2008
, “Changes in the Magnitude and Distribution of Forces at Different Dictyostelium Developmental Stages
,” Cell Motil. Cytoskeleton
, 65
(4
), pp. 314
–331
.10.1002/cm.2026232.
Delanoë-Ayari
, H.
, and Rieu
, J. P.
, 2010
, “4d Traction Force Microscopy Reveals Asymmetric Cortical Forces in Migrating Dictyostelium Cells
,” Phys. Rev. Lett.
, 105
(24
), p. 248103.33.
Fray
, T. R.
, Molloy
, J. E.
, Armitage
, M. P.
, and Sparrow
, J. C.
, 1998
, “Quantification of Single Human Dermal Fibroblast Contraction
,” Tissue Eng.
, 4
(3
), pp. 281
–291
.10.1089/ten.1998.4.28134.
Wrobel
, L. K.
, Fray
, T. R.
, Molloy
, J. E.
, Adams
, J. J.
, Armitage
, M. P.
, and Sparrow
, J. C.
, 2002
, “Contractility of Single Human Dermal Myofibroblasts and Fibroblasts
,” Cell Motil. Cytoskeleton
, 52
, pp. 82
–90
.10.1002/cm.1003435.
Tymchenko
, N.
, Wallentin
, J.
, Petronis
, S.
, Bjursten
, L. M.
, Kasemo
, B.
, and Gold
, J.
, 2007
, “A Novel Cell Force Sensor for Quantification of Traction During Cell Spreading and Contact Guidance
,” Biophys. J.
, 93
(1
), pp. 335
–345
.10.1529/biophysj.106.09330236.
Galbraith
, C. G.
, and Sheetz
, M. P.
, 1997
, “A Micromachined Device Provides a New Bend on Fibroblast Traction Forces
,” Proc. Natl. Acad. Sci. U.S.A.
, 94
(17
), pp. 9114
–9118
.10.1073/pnas.94.17.911437.
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)76145-038.
Brown
, R.
, Prajapati
, R.
, McGrouther
, D.
, Yannas
, I.
, and Eastwood
, M.
, 1998
, “Tensional Homeostasis in Dermal Fibroblasts: Mechanical Responses to Mechanical Loading in Three-Dimensional Substrates
,” J. Cell Physiol.
, 175
(3
), pp. 323
–332
.10.1002/(SICI)1097-4652(199806)175:3<323::AID-JCP10>3.0.CO;2-639.
Delvoye
, P.
, Wiliquet
, P.
, Leveque
, J. L.
, Nusgens
, B. V.
, and Lapiere
, C. M.
, 1991
, “Measurement of Mechanical Forces Generated by Skin Fibroblasts Embedded in a Three-Dimensional Collagen Gel
,” J. Invest. Dermatol.
, 97
(5
), pp. 898
–902
.10.1111/1523-1747.ep1249165140.
Kaiser
, J.-P.
, Reinmann
, A.
, and Bruinink
, A.
, 2006
, “The Effect of Topographic Characteristics on Cell Migration Velocity
,” Biomater.
, 27
(30
), pp. 5230
–5241
.10.1016/j.biomaterials.2006.06.00241.
Nenasheva
, T. A.
, Carter
, T.
, and Mashanov
, G. I.
, 2012
, “Automatic Tracking of Individual Migrating Cells Using Low-Magnification Dark-Field Microscopy
,” J. Microsc.
, 246
(1
), pp. 83
–88
.10.1111/j.1365-2818.2011.03590.x42.
Ricart
, B. G.
, Yang
, M. T.
, Hunter
, C. A.
, Chen
, C. S.
, and Hammer
, D. A.
, 2011
, “Measuring Traction Forces of Motile Dendritic Cells on Micropost Arrays
,” Biophys. J.
, 101
(11
), pp. 2620
–2628
.10.1016/j.bpj.2011.09.02243.
Jannatt
, 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.2011.05.04044.
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
–L60
.10.1529/biophysj.106.10282245.
Palecek
, S. P.
, Loftus
, J. C.
, Ginsberg
, M. H.
, Lauffenburger
, D. A.
, and Horwitz
, A. F.
, 1997
, “Integrin-Ligand Binding Properties Govern Cell Migration Speed Through Cell-Substratum Adhesiveness
,” Nature
, 385
(6616
), pp. 537
–540
.10.1038/385537a0Copyright © 2013 by ASME
You do not currently have access to this content.