Using a top-down approach, an agent-based model was developed within NetLogo where cells and extracellular matrix (ECM) fibers were composed of multiple agents to create deformable structures capable of exerting, reacting to, and transmitting mechanical force. At the beginning of the simulation, long fibers were randomly distributed and cross linked. Throughout the simulation, imposed rules allowed cells to exert traction forces by extending pseudopodia, binding to fibers and pulling them towards the cell. Simulated cells remodeled the fibrous matrix to change both the density and alignment of fibers and migrated within the matrix in ways that are consistent with previous experimental work. For example, cells compacted the matrix in their pericellular regions much more than the average compaction experienced for the entire matrix (696% versus 21%). Between pairs of cells, the matrix density increased (by 92%) and the fibers became more aligned (anisotropy index increased from 0.45 to 0.68) in the direction parallel to a line connecting the two cells, consistent with the “lines of tension” observed in experiments by others. Cells migrated towards one another at an average rate of ∼0.5 cell diameters per 10,000 arbitrary units (AU); faster migration occurred in simulations where the fiber density in the intercellular area was greater. To explore the potential contribution of matrix stiffness gradients in the observed migration (i.e., durotaxis), the model was altered to contain a regular lattice of fibers possessing a stiffness gradient and just a single cell. In these simulations cells migrated preferentially in the direction of increasing stiffness at a rate of ∼2 cell diameter per 10,000 AU. This work demonstrates that matrix remodeling and durotaxis, both complex phenomena, might be emergent behaviors based on just a few rules that control how a cell can interact with a fibrous ECM.

References

References
1.
McLennan
,
R.
,
Dyson
,
L.
,
Prather
,
K. W.
,
Morrison
,
J. A.
,
Baker
,
R. E.
,
Maini
,
P. K.
, and
Kulesa
,
P. M.
,
2012
, “
Multiscale Mechanisms of Cell Migration During Development: Theory and Experiment
,”
Development (Cambridge, England)
,
139
(
16
), pp.
2935
2944
.10.1242/dev.081471
2.
Morales
,
T. I.
,
2007
, “
Chondrocyte Moves: Clever Strategies?
,”
Osteoarthr. Cartilage/OARS
,
15
(
8
), pp.
861
871
.10.1016/j.joca.2007.02.022
3.
Phan
,
S. H.
,
2012
, “
Genesis of the Myofibroblast in Lung Injury and Fibrosis
,”
Proc. Am. Thoracic Soc.
,
9
(
3
), pp.
148
152
.10.1513/pats.201201-011AW
4.
Grinnell
,
F.
,
1994
, “
Fibroblasts, Myofibroblasts, and Wound Contraction
,”
J. Cell Biol.
,
124
(
4
), pp.
401
404
.10.1083/jcb.124.4.401
5.
Bell
,
E.
,
Ehrlich
,
H. P.
,
Buttle
,
D. J.
, and
Nakatsuji
,
T.
,
1981
, “
Living Tissue Formed In Vitro and Accepted as Skin-Equivalent Tissue of Full Thickness
,”
Science N.Y.
,
211
(
4486
), pp.
1052
1054
.10.1126/science.7008197
6.
Weinberg
,
C. B.
, and
Bell
,
E.
,
1986
, “
A Blood Vessel Model Constructed From Collagen and Cultured Vascular Cells
,”
Science, New Ser.
,
231
(
4736
), pp.
397
400
.
7.
Meshel
,
A. S.
,
Wei
,
Q.
,
Adelstein
,
R. S.
, and
Sheetz
,
M. P.
,
2005
, “
Basic Mechanism of Three-Dimensional Collagen Fibre Transport by Fibroblasts
,”
Nat. Cell Biol.
,
7
(
2
), pp.
157
164
.10.1038/ncb1216
8.
Gabbiani
,
G.
,
Hirschel
,
B. J.
,
Ryan
,
G. B.
,
Statkov
,
P. R.
, and
Majno
,
G.
,
1972
, “
Granulation Tissue as a Contractile Organ. A Study of Structure and Function
,”
J. Exp. Med.
,
135
(
4
), pp.
719
734
.10.1084/jem.135.4.719
9.
Moulin
,
V.
,
Castilloux
,
G.
,
Jean
,
A.
,
Garrel
,
D. R.
,
Auger
,
F. A.
, and
Germain
,
L.
,
1996
, “
In Vitro Models to Study Wound Healing Fibroblasts
,”
Burns J. Int. Soc. Burn Inj.
,
22
(
5
), pp.
359
362
.10.1016/0305-4179(95)00167-0
10.
Kim
,
A.
,
Lakshman
,
N.
, and
Petroll
,
W. M.
,
2006
, “
Quantitative Assessment of Local Collagen Matrix Remodeling in 3-D Culture: The Role of Rho Kinase
,”
Exp. Cell Res.
,
312
(
18
), pp.
3683
3692
.10.1016/j.yexcr.2006.08.009
11.
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
12.
Sieminski
,
A. L.
,
Hebbel
,
R. P.
, and
Gooch
,
K. J.
,
2004
, “
The Relative Magnitudes of Endothelial Force Generation and Matrix Stiffness Modulate Capillary Morphogenesis In Vitro
,”
Exp. Cell Res.
,
297
(
2
), pp.
574
584
.10.1016/j.yexcr.2004.03.035
13.
Zaleskas
,
J. M.
,
Kinner
,
B.
,
Freyman
,
T. M.
,
Yannas
,
I. V.
,
Gibson
,
L. J.
, and
Spector
,
M.
,
2004
, “
Contractile Forces Generated by Articular Chondrocytes in Collagen-Glycosaminoglycan Matrices
,”
Biomaterials
,
25
(
7–8
), pp.
1299
1308
.10.1016/j.biomaterials.2003.08.005
14.
Yamato
,
M.
,
Adachi
,
E.
,
Yamamoto
,
K.
, and
Hayashi
,
T.
,
1995
, “
Condensation of Collagen Fibrils to the Direct Vicinity of Fibroblasts as a Cause of Gel Contraction
,”
J. Biochem.
,
117
(
5
), pp.
940
946
.
15.
Mcleod
,
C.
,
Higgins
,
J.
,
Miroshnikova
,
Y.
,
Liu
,
R.
,
Garrett
,
A.
, and
Sarang-Sieminski
,
A.
,
2013
, “
Microscopic Matrix Remodeling Precedes Endothelial Morphological Changes During Capillary Morphogenesis
,”
ASME J. Biomech. Eng.
,
135
(
7
), p.
071002
.10.1115/1.4023984
16.
Katzberg
,
A. A.
,
1958
, “
The Mechanism of Traction Forces in Tissue Culture
,”
Ann. Surg.
,
150
(
1
), pp.
23
28
.10.1097/00000658-195907000-00002
17.
Ma
,
X.
,
Schickel
,
M.
,
Stevenson
,
M. D.
,
Sarang-Sieminski
,
A. L.
,
Gooch
,
K. J.
,
Ghadiali
,
S. N.
, and
Hart
,
R. T.
,
2013
, “
Fibers in the Extracellular Matrix Enable Long-Range Stress Transmission Between Cells
,”
Biophys. J.
,
104
, pp.
1
9
.10.1016/j.bpj.2013.02.017
18.
Tranquillo
,
R. T.
,
Durrani
,
M. A.
, and
Moon
,
A. G.
,
1992
, “
Tissue Engineering Science: Consequences of Cell Traction Force
,”
Cytotechnology
,
10
(
3
), pp.
225
250
.10.1007/BF00146673
19.
Dickinson
,
R. B.
,
Guido
,
S.
, and
Tranquillo
,
R. T.
,
1994
, “
Biased Cell Migration of Fibroblasts Exhibiting Contact Guidance in Oriented Collagen Gels
,”
Ann. Biomed. Eng.
,
22
(
4
), pp.
342
356
.10.1007/BF02368241
20.
Turturro
,
M. V.
, and
Papavasiliou
,
G.
,
2011
, “
Generation of Mechanical and Biofunctional Gradients in PEG Diacrylate Hydrogels by Perfusion-Based Frontal Photopolymerization
,”
J. Biomater. Sci.
, Polymer edition,
23
(7), pp. 917–939.10.1163/092050611X566450
21.
Hadjipanayi
,
E.
,
Mudera
,
V.
, and
Brown
,
R.
,
2009
, “
Guiding Cell Migration in 3D: A Collagen Matrix With Graded Directional Stiffness
,”
Cell Motility Cytoskeleton
,
66
(
3
), pp.
121
128
.10.1002/cm.20331
22.
Dallon
,
J. C.
,
Scott
,
M.
, and
Smith
,
W. V.
,
2013
, “
A Force Based Model of Individual Cell Migration With Discrete Attachment Sites and Random Switching Terms
,”
ASME J. Biomech. Eng.
,
135
(
7
), p.
071008
.10.1115/1.4023987
23.
Dokukina
,
I. V.
, and
Gracheva
,
M. E.
,
2010
, “
A Model of Fibroblast Motility on Substrates With Different Rigidities
,”
Biophys. J.
,
98
(
12
), pp.
2794
2803
.10.1016/j.bpj.2010.03.026
24.
Schlüter
,
D. K.
,
Ramis-Conde
,
I.
, and
Chaplain
,
M. A. J.
,
2012
, “
Computational Modeling of Single-Cell Migration: The Leading Role of Extracellular Matrix Fibers
,”
Biophys. J.
,
103
(
6
), pp.
1141
1151
.10.1016/j.bpj.2012.07.048
25.
Sander
,
L. M.
,
2013
, “
Alignment Localization in Non-Linear Biological Media
,”
ASME J. Biomech. Eng.
,
135
(
7
), p.
071006
.10.1115/1.4024199
26.
Bauer
,
A. L.
,
Jackson
,
T. L
.
, and
Jiang
,
Y.
,
2009
, “
Topography of Extracellular Matrix Mediates Vascular Morphogenesis and Migration Speeds in Angiogenesis
,”
PLoS Comput. Biol.
,
5
(
7
), p.
e1000445
.10.1371/journal.pcbi.1000445
27.
Alberts
,
J. B.
,
2009
, “
Biophysically Realistic Filament Bending Dynamics in Agent-Based Biological Simulation
,”
PloS One
,
4
(
3
), p.
e4748
.10.1371/journal.pone.0004748
28.
Wilensky
,
U.
,
1999
,
NetLogo
, http://ccl.northwestern.edu/netlogo/,
Center for Connected Learning and Computer-Based Modeling
,
Northwestern University
,
Evanston, IL
.
29.
Fruchterman
,
E.
, and
Reingold
,
E. M.
, 1991, “Graph Drawing by Force-Directed Placement,”
Software- Practice and Experience
,
21
(11), pp. 1129–1164.
30.
Stéphanou
,
A.
,
Mylona
,
E.
,
Chaplain
,
M.
, and
Tracqui
P.
,
2008
, “
A Computational Model of Cell Migration Coupling the Growth of Focal Adhesions With Oscillatory Cell Protrusions
,”
J. Theor. Biol.
,
253
(
4
), pp.
701
716
.10.1016/j.jtbi.2008.04.035
31.
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
.10.1016/S0092-8674(00)81856-5
32.
Van den Akker
,
J.
,
Tuna
,
B. G.
,
Pistea
,
A.
,
Sleutel
,
A. J. J.
,
Bakker
E. N. T. P.
, and
Van Bavel
,
E.
,
2012
, “
Vascular Smooth Muscle Cells Remodel Collagen Matrices by Long-Distance Action and Anisotropic Interaction
,”
Med. Biol. Eng. Comput.
,
50
(
7
), pp.
701
715
.10.1007/s11517-012-0916-6
33.
Advani
,
S. G.
, and
Tucker
,
C. L. I.
,
1987
, “
The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites
,”
J. Rheol.
,
31
(
8
), pp.
751
784
.10.1122/1.549945
34.
Sander
,
E. A.
,
Stylianopoulos
,
T.
,
Tranquillo
,
R. T.
, and
Barocas
,
V. H.
,
2009
, “
Image-Based Multiscale Modeling Predicts Tissue-Level and Network-Level Fiber Reorganization in Stretched Cell-Compacted Collagen Gels
,”
Proc. Natl. Acad. Sci. U.S.A.
,
106
(
42
), pp.
17675
17680
.10.1073/pnas.0903716106
35.
Sander
,
E. A.
, and
Barocas
,
V. H.
,
2009
, “
Comparison of 2D Fiber Network Orientation Measurement Methods
,”
J. Biomed. Mater. Res. Part A
,
88
(
2
), pp.
322
331
.10.1002/jbm.a.31847
36.
Winer
,
J. P.
,
Oake
,
S.
, and
Janmey
,
P. A.
,
2009
, “
Non-Linear Elasticity of Extracellular Matrices Enables Contractile Cells to Communicate Local Position and Orientation
,”
PloS One
,
4
(
7
), p.
e6382
.10.1371/journal.pone.0006382
37.
Korff
,
T.
, and
Augustin
,
H. G.
,
1999
, “
Tensional Forces in Fibrillar Extracellular Matrices Control Directional Capillary Sprouting
,”
J. Cell Sci.
,
112
(Pt
1
), pp.
3249
3258
.
38.
Vernon
,
R. B.
, and
Sage
,
E. H.
,
1995
, “
Between Molecules and Morphology
,”
Am. J. Pathol.
,
147
(
4
), pp.
873
883
.
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