In this study, we examine the outstanding issue of how surface topology affects the adhesion between cells and the extracellular matrix (ECM). Specifically, we showed that the adhesive contact can be well described by treating the attraction as continuous along the interface if the wavelength of surface undulations is larger than a few microns. On the other hand, the discrete nature of cell–ECM interactions, i.e., adhesion is achieved through the formation of individual receptor–ligand bonds, must be taken into account for wavy surfaces with a much smaller characteristic length. Interestingly, it was found that, due to the interplay between substrate elasticity and stochastic breakage/reformation of molecular bonds, the strength of cell–ECM adhesion will reach its maximum when the surface roughness is of the order of 20–40 nm, in quantitative agreement with recent experiments. In addition, because of the bonding kinetics involved, the apparent adhesion energy was predicted to be strongly rate-dependent with increasing detaching speed between surfaces leading to a rapidly elevated work of separation, a phenomenon that has been widely observed in bio-adhesion.

References

References
1.
Engler
,
A.
,
Sen
,
S.
,
Sweeney
,
H.
, and
Discher
,
D.
,
2006
, “
Matrix Elasticity Directs Stem Cell Lineage Specification
,”
Cell
,
126
(
4
), pp.
677
689
.
2.
Geiger
,
B.
, and
Bershadsky
,
A.
,
2002
, “
Exploring the Neighborhood: Adhesion-Coupled Cell Mechanosensors
,”
Cell
,
110
(
2
), pp.
139
142
.
3.
Harris
,
A.
,
Wild
,
P.
, and
Stopak
,
D.
,
1980
, “
Silicone Rubber Substrata: A New Wrinkle in the Study of Cell Locomotion
,”
Science
,
208
(
4440
), pp.
177
179
.
4.
Komnick
,
H.
,
Stockem
,
W.
, and
Wohlfarth-Bottermann
,
K.
,
1973
, “
Cell Motility: Mechanisms in Protoplasmic Streaming and Amoeboid Movement
,”
Int. Rev. Cytol.
,
34
(
1973
), pp.
169
249
.
5.
DiMilla
,
P.
,
Barbee
,
K.
, and
Lauffenburger
,
D.
,
1991
, “
Mathematical Model for the Effects of Adhesion and Mechanics on Cell Migration Speed
,”
Biophys. J.
,
60
(
1
), pp.
15
37
.
6.
Palecek
,
S.
,
Loftus
,
J.
,
Ginsberg
,
M.
,
Lauffenburger
,
D.
, and
Horwitz
,
A.
,
1997
, “
Integrin-Ligand Binding Properties Govern Cell Migration Speed Through Cell-Substratum Adhesiveness
,”
Nature
,
385
(
6616
), pp.
537
540
.
7.
Lin
,
Y.
,
2010
, “
A Model of Cell Motility Leading to Biphasic Dependence of Transport Speed on Adhesive Strength
,”
J. Mech. Phys. Solids.
,
58
(
4
), pp.
502
514
.
8.
Lodish
,
H.
,
2000
,
Molecular Cell Biology
,
W.H. Freeman
,
New York
.
9.
Fan
,
Y.
,
Cui
,
F.
,
Hou
,
S.
,
Xu
,
Q.
,
Chen
,
L.
, and
Lee
,
I.
,
2002
, “
Culture of Neural Cells on Silicon Wafers With Nano-Scale Surface Topography
,”
J. Neurosci. Methods
,
120
(
1
), pp.
17
23
.
10.
Taylor
,
R.
,
Verran
,
J.
,
Lees
,
G.
, and
Ward
,
A.
,
1998
, “
The Influence of Substratum Topography on Bacterial Adhesion to Polymethyl Methacrylate
,”
J. Mater. Sci.: Mater. Med.
,
9
(
1
), pp.
17
22
.
11.
Dalby
,
M.
,
Riehle
,
M.
,
Johnstone
,
H.
,
Affrossman
,
S.
, and
Curtis
,
A.
,
2002
, “
Polymer-Demixed Nanotopography: Control of Fibroblast Spreading and Proliferation
,”
Tissue Eng.
,
8
(
6
), pp.
1099
1108
.
12.
Gentile
,
F.
,
Tirinato
,
L.
,
Battista
,
E.
,
Causa
,
F.
,
Liberale
,
C.
,
di Fabrizio
,
E.
, and
Decuzzi
,
P.
,
2010
, “
Cells Preferentially Grow on Rough Substrates
,”
Biomaterials
,
31
(
28
), pp.
7205
7212
.
13.
Johnson
,
K.
,
1995
, “
The Adhesion of Two Elastic Bodies With Slightly Wavy Surfaces
,”
Int. J. Solids Struct.
,
32
(
3–4
), pp.
423
430
.
14.
Guduru
,
P.
,
2007
, “
Detachment of a Rigid Solid From an Elastic Wavy Surface: Theory
,”
J. Mech. Phys. Solids.
,
55
(
3
), pp.
445
472
.
15.
Li
,
Q.
, and
Kim
,
K.
,
2009
, “
Micromechanics of Rough Surface Adhesion: A Homogenized Projection Method
,”
Acta Mech. Solida Sin.
,
22
(
5
), pp.
377
390
.
16.
Rabinovich
,
Y.
,
Adler
,
J.
,
Ata
,
A.
,
Singh
,
R.
, and
Moudgil
,
B.
,
2000
, “
Adhesion Between Nanoscale Rough Surfaces
,”
J. Colloid Interface Sci.
,
232
(
1
), pp.
10
16
.
17.
Rabinovich
,
Y.
,
Adler
,
J.
,
Ata
,
A.
,
Singh
,
R.
, and
Moudgil
,
B.
,
2000
, “
Adhesion Between Nanoscale Rough Surfaces
,”
J. Colloid Interface Sci.
,
232
(
1
), pp.
17
24
.
18.
Evans
,
E.
, and
Ritchie
,
K.
,
1997
, “
Dynamic Strength of Molecular Adhesion Bonds
,”
Biophys. J.
,
72
(
4
), pp.
1541
1555
.
19.
Freund
,
L.
,
2009
, “
Characterizing the Resistance Generated by a Molecular Bond as It Is Forcibly Separated
,”
Proc. Natl. Acad. Sci.
,
106
(
22
), pp.
8818
8823
.
20.
Lin
,
Y.
, and
Freund
,
L.
,
2008
, “
Optimum Size of a Molecular Bond Cluster in Adhesion
,”
Phys. Rev. E.
,
78
(
2
), p.
021909
.
21.
Qian
,
J.
,
Wang
,
J.
,
Lin
,
Y.
, and
Gao
,
H.
,
2009
, “
Lifetime and Strength of Periodic Bond Clusters Between Elastic Media Under Inclined Loading
,”
Biophys. J.
,
97
(
9
), pp.
2438
2445
.
22.
Gao
,
H.
,
Qian
,
J.
, and
Chen
,
B.
,
2011
, “
Probing Mechanical Principles of Focal Contacts in Cell-Matrix Adhesion With a Coupled Stochastic-Elastic Modelling Framework
,”
J. R. Soc. Interface
,
8
(
62
), pp.
1217
1232
.
23.
Erdmann
,
T.
, and
Schwarz
,
U.
,
2004
, “
Stability of Adhesion Clusters Under Constant Force
,”
Phys. Rev. Lett.
,
92
(
10
), p.
108102
.
24.
Erdmann
,
T.
, and
Schwarz
,
U.
,
2004
, “
Stochastic Dynamics of Adhesion Clusters Under Shared Constant Force and With Rebinding
,”
J. Chem. Phys.
,
121
(
18
), pp.
8997
9017
.
25.
Zhang
,
W.
,
Lin
,
Y.
,
Qian
,
J.
,
Chen
,
W.
, and
Gao
,
H.
,
2013
, “
Tuning Molecular Adhesion Via Material Anisotropy
,”
Adv. Funct. Mater.
,
23
(
37
), pp.
4729
4738
.
26.
Decuzzi
,
P.
, and
Ferrari
,
M.
,
2010
, “
Modulating Cellular Adhesion Through Nanotopography
,”
Biomaterials
,
31
(
1
), pp.
173
179
.
27.
Emsley
,
J.
,
Knight
,
C. G.
,
Famdale
,
R. W.
,
Barnes
,
M. J.
, and
Liddington
,
R. C.
,
2000
, “
Structural Basis of Collagen Recognition by Integrin α2β1
,”
Cell
,
101
(
1
), pp.
47
56
.
28.
Moursi
,
A. M.
,
Globus
,
R. K.
, and
Damsky
,
C. H.
,
1997
, “
Interactions Between Integrin Receptors and Fibronectin are Required for Calvarial Osteoblast Differentiation in vitro
,”
J. Cell Sci.
,
110
(
Pt. 158
), pp.
2187
2196
.
29.
Johnson
,
K.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
30.
Arnold
,
M.
,
Cavalcanti-Adam
,
E. A.
,
Glass
,
R.
,
Blümmel
,
J.
,
Eck
,
W.
,
Kantlehner
,
M.
,
Kessler
,
H.
, and
Spatz
,
J. P.
,
2004
, “
Activation of Integrin Function by Nanopatterned Adhesive Interfaces
,”
Chem. Phys. Chem.
,
5
(
3
), pp.
383
388
.
31.
Kunzler
,
T.
,
Huwiler
,
C.
,
Drobek
,
T.
,
Vörös
,
J.
, and
Spencer
,
N.
,
2007
, “
Systematic Study of Osteoblast Response to Nanotopography by Means of Nanoparticle-Density Gradients
,”
Biomaterials
,
28
(
33
), pp.
5000
5006
.
32.
Mitik-Dineva
,
N.
,
Wang
,
J.
,
Mocanasu
,
R.
,
Stoddart
,
P.
,
Crawford
,
R.
, and
Ivanova
,
E.
,
2008
, “
Impact of Nano-Topography on Bacterial Attachment
,”
Biotechnol. J.
,
3
(
4
), pp.
536
544
.
33.
Bell
,
G.
,
1978
, “
Models for the Specific Adhesion of Cells to Cells
,”
Science
,
200
(
4342
), pp.
618
627
.
34.
Marshall
,
B.
,
Sarangapani
,
K.
,
Wu
,
J.
,
Lawrence
,
M.
,
McEver
,
R.
, and
Zhu
,
C.
,
2006
, “
Measuring Molecular Elasticity by Atomic Force Microscope Cantilever Fluctuations
,”
Biophys. J.
,
90
(
2
), pp.
681
692
.
35.
Boal
,
D.
,
2002
,
Mechanics of the Cell
,
Cambridge University Press
,
Cambridge, UK
.
36.
Lekka
,
M.
,
Laidler
,
P.
,
Gil
,
D.
,
Lekki
,
J.
,
Stachura
,
Z.
, and
Hrynkiewicz
,
A.
,
1999
, “
Elasticity of Normal and Cancerous Human Bladder Cells Studied by Scanning Force Microscopy
,”
Eur. Biophys. J.
,
28
(
4
), pp.
312
316
.
37.
Hynes
,
R.
,
1992
, “
Integrins: Versatility, Modulation, and Signaling in Cell Adhesion
,”
Cell
,
69
(
1
), pp.
11
25
.
38.
Johnson
,
K.
,
Kendall
,
K.
, and
Roberts
,
A.
,
1971
, “
Surface Energy and the Contact of Elastic Solids
,”
Proc. R. Soc. A
,
324
(
1558
), pp.
301
313
.
39.
Yao
,
H.
,
Guduru
,
P.
, and
Gao
,
H.
,
2008
, “
Maximum Strength for Intermolecular Adhesion of Nanospheres at an Optimal Size
,”
J. R. Soc. Interface
,
5
(
28
), pp.
1363
1370
.
40.
Pähler
,
G.
,
Lorenz
,
B.
, and
Janshoff
,
A.
,
2013
, “
Impact of Peptide Clustering on Unbinding Forces in the Context of Fusion Mimetics
,”
Biochem. Biophy. Res. Commun.
,
430
(
3
), pp.
938
943
.
41.
Vajpayee
,
S.
,
Long
,
R.
,
Shen
,
L.
,
Jagota
,
A.
, and
Hui
,
C.
,
2009
, “
Effect of Rate on Adhesion and Static Friction of a Film-Terminated Fibrillar Interface
,”
Langmuir
,
25
(
5
), pp.
2765
2771
.
42.
Cao
,
X.
,
Lin
,
Y.
,
Driscoll
,
T. P.
,
Franco-Barraza
,
J.
,
Cukierman
,
E.
,
Mauck
,
R. L.
, and
Shenoy
,
V. B. A.
,
2015
, “
Chemo-Mechanical Model for Extracellular Matrix and Nuclear Rigidity Regulated Size of Focal Adhesion Plaques
,”
Biophys. J.
,
109
(
9
), pp.
1807
1817
.
You do not currently have access to this content.