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.

References

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-092910-154251
2.
Krawczyk
,
W.
,
1971
, “
A Pattern of Epidermal Cell Migration During Wound Healing
,”
J. Cell Biol.
,
49
(
2
), pp.
247
263
.10.1083/jcb.49.2.247
3.
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.2009.06.052
4.
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/nrc1075
5.
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-10-0139
6.
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.2000.0626
7.
Mammoto
,
T.
, and
Ingber
,
D.
,
2010
, “
Mechanical Control of Tissue and Organ Development
,”
Development
,
137
(
9
), pp.
1407
1420
.10.1242/dev.024166
8.
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.20411
9.
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.2011.04.007
10.
Huttenlocher
,
A.
, and
Horwitz
,
A. R.
,
2011
, “
Integrins in Cell Migration
,”
Cold Spring Harb. Perspect. Biol.
,
3
(
9
), p.
a005074
.10.1101/cshperspect.a005074
11.
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)90180-4
14.
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.011209.122036
15.
Lauffenburger
,
D.
, and
Horwitz
,
A.
,
1996
, “
Cell Migration: A Physically Integrated Molecular Process
,”
Cell
,
84
(
3
), pp.
359
369
.10.1016/S0092-8674(00)81280-5
16.
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/s002850050006
17.
Sandersius
,
S. A.
, and
Newman
,
T. J.
,
2008
, “
Modeling Cell Rheology With the Subcellular Element Model
,”
Phys. Biol.
,
5
(
1
), p.
015002
.10.1088/1478-3975/5/1/015002
18.
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/nature06952
19.
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)74969-8
20.
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.1002538107
21.
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.1000604
22.
Bottino
,
D.
, and
Fauci
,
L.
,
1998
, “
A Computational Model of Ameboid Deformation and Locomotion
,”
Eur. Biophys. J.
,
27
(
5
), pp.
532
539
.10.1007/s002490050163
23.
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.2009.12.4303
24.
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.2010.03.057
25.
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-z
26.
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.2004.06.015
27.
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/s11538-005-9032-1
28.
Ulrich
,
F.
, and
Heisenberg
,
C.-P.
,
2009
, “
Trafficking and Cell Migration
,”
Traffic
,
10
(
7
), pp.
811
818
.10.1111/j.1600-0854.2009.00929.x
29.
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)81279-9
30.
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.01015
31.
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.20262
32.
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.1998.4.281
34.
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.10034
35.
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.106.093302
36.
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.94.17.9114
37.
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
38.
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;2-6
39.
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.ep12491651
40.
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.2006.06.002
41.
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.x
42.
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.2011.09.022
43.
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.2011.05.040
44.
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.106.102822
45.
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
.10.1038/385537a0
You do not currently have access to this content.