The stability of a bond cluster upon oscillated loads under physiological conditions is strongly regulated by the kinetics of association and dissociation of a single bond, which can play critical roles in cell–matrix adhesion, cell–cell adhesion, etc. Here, we obtain a simplified analysis for the bond association process of a constrained receptor to an oscillating ligand due to its diffusion-independence, which can facilitate the potential multiscale studies in the future. Based on the analysis, our results indicate that the mean passage time for bond association intriguingly saturates at high oscillating frequencies, and there can also surprisingly exist optimal bond elasticity for bond association. This work can bring important insights into understanding of the behaviors of bond cluster under cyclic loads at the level of a single bond.

References

References
1.
Erdmann
,
T.
, and
Schwarz
,
U. S.
,
2004
, “
Stochastic Dynamics of Adhesion Clusters Under Shared Constant Force and With Rebinding
,”
J. Chem. Phys.
,
121
(
18
), pp.
8997
9017
.
2.
Erdmann
,
T.
, and
Schwarz
,
U. S.
,
2004
, “
Stability of Adhesion Clusters Under Constant Force
,”
Phys. Rev. Lett.
,
92
(
10
), p.
108102
.
3.
Kramers
,
H. A.
,
1940
, “
Brownian Motion in a Field of Force and the Diffusion Model of Chemical Reactions
,”
Physica
,
7
(
4
), pp.
284
304
.
4.
Bell
,
G. I.
,
1978
, “
Models for the Specific Adhesion of Cells to Cells
,”
Science
,
200
(
4342
), pp.
618
627
.
5.
Evans
,
E.
, and
Ritchie
,
K.
,
1997
, “
Dynamic Strength of Molecular Adhesion Bonds
,”
Biophys. J.
,
72
(
4
), pp.
1541
1555
.
6.
Erdmann
,
T.
, and
Schwarz
,
U. S.
,
2006
, “
Bistability of Cell–Matrix Adhesions Resulting From Nonlinear Receptor-Ligand Dynamics
,”
Biophys. J.
,
91
(
6
), pp.
L60
62
.
7.
Filippov
,
A.
,
Klafter
,
J.
, and
Urbakh
,
M.
,
2004
, “
Friction Through Dynamical Formation and Rupture of Molecular Bonds
,”
Phys. Rev. Lett.
,
92
(
13
), p.
135503
.
8.
Kong
,
D.
,
Ji
,
B.
, and
Dai
,
L.
,
2008
, “
Stability of Adhesion Clusters and Cell Reorientation Under Lateral Cyclic Tension
,”
Biophys. J.
,
95
(
8
), pp.
4034
4044
.
9.
Mao
,
Z.
,
Chen
,
X.
, and
Chen
,
B.
,
2015
, “
Stability of Focal Adhesion Enhanced by Its Inner Force Fluctuation
,”
Chin. Phys. B
,
24
(
8
), p.
088702
.
10.
Dartsch
,
P.
,
Hämmerle
,
H.
, and
Betz
,
E.
,
1986
, “
Orientation of Cultured Arterial Smooth Muscle Cells Growing on Cyclically Stretched Substrates
,”
Cells Tissues Organs
,
125
(
2
), pp.
108
113
.
11.
Kemkemer
,
R.
,
Neidlinger-Wilke
,
C.
,
Claes
,
L.
, and
Gruler
,
H.
,
1999
, “
Cell Orientation Induced by Extracellular Signals
,”
Cell Biochem. Biophys.
,
30
(
2
), pp.
167
192
.
12.
Buck
,
R. C.
,
1980
, “
Reorientation Response of Cells to Repeated Stretch and Recoil of the Substratum
,”
Exp. Cell Res.
,
127
(
2
), pp.
470
474
.
13.
Greiner
,
A. M.
,
Chen
,
H.
,
Spatz
,
J. P.
, and
Kemkemer
,
R.
,
2013
, “
Cyclic Tensile Strain Controls Cell Shape and Directs Actin Stress Fiber Formation and Focal Adhesion Alignment in Spreading Cells
,”
PLoS One
,
8
(
10
), p.
e77328
.
14.
Jungbauer
,
S.
,
Gao
,
H.
,
Spatz
,
J. P.
, and
Kemkemer
,
R.
,
2008
, “
Two Characteristic Regimes in Frequency-Dependent Dynamic Reorientation of Fibroblasts on Cyclically Stretched Substrates
,”
Biophys. J.
,
95
(
7
), pp.
3470
3478
.
15.
Freund
,
L.
,
2009
, “
Characterizing the Resistance Generated by a Molecular Bond as It is Forcibly Separated
,”
Proc. Natl. Acad. Sci. U.S.A.
,
106
(
22
), pp.
8818
8823
.
16.
Freund
,
L.
,
2014
, “
Brittle Crack Growth Modeled as the Forced Separation of Chemical Bonds Within a K-Field
,”
J. Mech. Phys. Solids
,
64
, pp.
212
222
.
17.
Saunders
,
T. E.
,
2015
, “
Aggregation-Fragmentation Model of Robust Concentration Gradient Formation
,”
Phys. Rev. E
,
91
(
2
), p.
022704
.
18.
Gambin
,
Y.
,
Lopez-Esparza
,
R.
,
Reffay
,
M.
,
Sierecki
,
E.
,
Gov
,
N.
,
Genest
,
M.
,
Hodges
,
R.
, and
Urbach
,
W.
,
2006
, “
Lateral Mobility of Proteins in Liquid Membranes Revisited
,”
Proc. Natl. Acad. Sci. U.S.A.
,
103
(
7
), pp.
2098
2102
.
19.
Rinko
,
L. J.
,
Lawrence
,
M. B.
, and
Guilford
,
W. H.
,
2004
, “
The Molecular Mechanics of P-and L-Selectin Lectin Domains Binding to PSGL-1
,”
Biophys. J.
,
86
(
1
), pp.
544
554
.
20.
Chen
,
X.
,
Li
,
D.
,
Ji
,
B.
, and
Chen
,
B.
,
2015
, “
Reconciling Bond Strength of a Slip Bond at Low Loading Rates With Rebinding
,”
Europhys. Lett.
,
109
(
6
), p.
68002
.
21.
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
.
22.
Chen
,
B.
,
Kemkemer
,
R.
,
Deibler
,
M.
,
Spatz
,
J.
, and
Gao
,
H.
,
2012
, “
Cyclic Stretch Induces Cell Reorientation on Substrates by Destabilizing Catch Bonds in Focal Adhesions
,”
PLoS One
,
7
(
11
), p.
e48346
.
23.
Chen
,
X.
, and
Chen
,
B.
,
2014
, “
Probing the Instability of a Cluster of Slip Bonds Upon Cyclic Loads With a Coupled Finite Element Analysis and Monte Carlo Method
,”
ASME J. Appl. Mech.
,
81
(
11
), p.
111002
.
24.
Chen
,
B.
,
2014
, “
Probing the Effect of Random Adhesion Energy on Receptor-Mediated Endocytosis With a Semistochastic Model
,”
ASME J. Appl. Mech.
,
81
(
8
), p.
081013
.
25.
Li
,
L.
,
Yao
,
H.
, and
Wang
,
J.
,
2015
, “
Dynamic Strength of Molecular Bond Clusters Under Displacement- and Force-Controlled Loading Conditions
,”
ASME J. Appl. Mech.
,
83
(
2
), p.
021004
.
26.
Jonsdottir
,
F.
, and
Freund
,
L. B.
,
2014
, “
Large Amplitude Thermal Fluctuations of Confined Semiflexible Biopolymer Filaments
,”
ASME J. Appl. Mech.
,
81
(
11
), p.
111006
.
27.
Seifert
,
U.
,
2002
, “
Dynamic Strength of Adhesion Molecules: Role of Rebinding and Self-Consistent Rates
,”
Europhys. Lett.
,
58
(
5
), p.
792
.
28.
Friddle
,
R. W.
,
Podsiadlo
,
P.
,
Artyukhin
,
A. B.
, and
Noy
,
A.
,
2008
, “
Near-Equilibrium Chemical Force Microscopy
,”
J. Phys. Chem. C
,
112
(
13
), pp.
4986
4990
.
29.
Friddle
,
R. W.
,
Noy
,
A.
, and
De Yoreo
,
J. J.
,
2012
, “
Interpreting the Widespread Nonlinear Force Spectra of Intermolecular Bonds
,”
Proc. Natl. Acad. Sci. U.S.A.
,
109
(
34
), pp.
13573
13578
.
30.
Li
,
D.
, and
Ji
,
B.
,
2014
, “
Predicted Rupture Force of a Single Molecular Bond Becomes Rate Independent at Ultralow Loading Rates
,”
Phys. Rev. Lett.
,
112
(
7
), p.
078302
.
31.
Li
,
D.
, and
Ji
,
B.
,
2015
, “
Crucial Roles of Bond Rebinding in Rupture Behaviors of Single Molecular Bond at Ultralow Loading Rates
,”
Int. J. Appl. Mech.
,
7
(
01
), p.
1550015
.
32.
Alsteens
,
D.
,
Pfreundschuh
,
M.
,
Zhang
,
C.
,
Spoerri
,
P. M.
,
Coughlin
,
S. R.
,
Kobilka
,
B. K.
, and
Müller
,
D. J.
,
2015
, “
Imaging G Protein-Coupled Receptors While Quantifying Their Ligand-Binding Free-Energy Landscape
,”
Nat. Methods
,
12
(
9
), pp.
845
851
.
You do not currently have access to this content.