Accurate modeling of collagen molecules including their stiffness is essential for our understanding of mechanics of collagen fibers and tissues where these fibers play a prominent role. Studies of mechanical properties of collagen molecules employing various experimental methods and molecular dynamics (MD) simulations yield a broad range of values of the modulus of elasticity. The effect of nonlocal elasticity on the molecule stiffness derived from experiments and simulations is assessed in this brief. The estimate of the correction accounting for the nonlocal effect utilizes the exact solution of the nonlocal elasticity theory for one-dimensional elastic bars. It is demonstrated that the effect of nonlocal elasticity on the stiffness of collagen molecules can be neglected.

References

References
1.
Buehler
,
M. F.
,
2006
, “
Nature Designs Tough Collagen: Explaining the Nanostructure of Collagen Fibrils
,”
Proc. Natl. Acad. Sci. U.S.A.
,
103
(33), pp.
12285
12290
.10.1073/pnas.0603216103
2.
Fratzl
,
P.
, ed.,
2008
,
Collagen: Structure and Mechanics
,
Springer
,
New York
.
3.
Meyers
,
M. A.
,
Chen
,
P. Y.
,
Lin
,
A. Y. M.
, and
Seki
,
Y.
,
2008
, “
Biological Materials: Structure and Mechanical Properties
,”
Prog. Mater. Sci.
,
53
(
1
), pp.
1
206
.10.1016/j.pmatsci.2007.05.002
4.
Nordin
,
M.
,
Lorenz
,
T.
, and
Campello
,
M.
,
2001
, “
Biomechanics of Tendons and Ligaments
,”
Basic Biomechanics of the Musculoskeletal System
,
M.
,
Nordin
, and
V. H.
,
Frankel
, eds.,
Lippincott Williams & Wilkins
,
Baltimore, MD
, pp.
102
125
.
5.
Sasaki
,
N.
, and
Odajima
,
S.
,
1996
, “
Stress–Strain Curve and Young's Modulus of a Collagen Molecule as Determined by the X-Ray Diffraction Technique
,”
J. Biomech.
,
29
(
5
), pp.
655
658
.10.1016/0021-9290(95)00110-7
6.
Shayegan
,
M.
, and
Forde
,
N. R.
,
2013
, “
Microrheological Characterization of Collagen Systems: From Molecular Solutions to Fibrillar Gels
,”
PLoS ONE
,
8
(
8
), p.
e70590
10.1371/journal.pone.0070590.
7.
Gautieri
,
A.
,
Vesentini
,
S.
,
Redaelli
,
A.
, and
Buehler
,
M. J.
,
2012
, “
Viscoelastic Properties of Model Segments of Collagen Molecules
,”
Matrix Biol.
,
31
(
2
), pp.
141
149
.10.1016/j.matbio.2011.11.005
8.
Harley
,
R.
,
James
,
D.
,
Miller
,
A.
, and
White
,
J. W.
,
1977
, “
Phonons and the Elastic Moduli of Collagen and Muscle
,”
Nature
,
267
(5608), pp.
285
287
.10.1038/267285a0
9.
Cusack
,
S.
, and
Miller
,
A.
,
1979
, “
Determination of the Elastic Constants of Collagen by Brillouin Light Scattering
,”
J. Mol. Biol.
,
135
(
1
), pp.
39
51
.10.1016/0022-2836(79)90339-5
10.
Hofmann
,
H.
,
Voss
,
T.
,
Kühn
,
K.
, and
Engel
,
J.
,
1984
, “
Localization of Flexible Sites in Thread-Like Molecules From Electron Micrographs: Comparison of Interstitial, Basement Membrane and Intima Collagens
,”
J. Mol. Biol.
,
172
(3), pp.
325
343
.10.1016/S0022-2836(84)80029-7
11.
Sun
,
Y. L.
,
Luo
,
Z. P.
,
Fertala
,
A.
, and
An
,
K. N.
,
2002
, “
Direct Quantification of the Flexibility of Type I Collagen Monomer
,”
Biochem. Biophys. Res. Commun.
,
295
(
2
), pp.
382
386
.10.1016/S0006-291X(02)00685-X
12.
Lorenzo
,
A. C.
, and
Caffarena
,
E. R.
,
2005
, “
Elastic Properties, Young's Modulus Determination and Structural Stability of the Tropocollagen Molecule: A Computational Study by Steered Molecular Dynamics
,”
J. Biomech.
,
38
(
7
), pp.
1527
1533
.10.1016/j.jbiomech.2004.07.011
13.
Kröner
,
E.
,
1967
, “
Elasticity Theory of Materials With Long Range Cohesive Forces
,”
Int. J. Solids Struct.
,
3
(5), pp.
731
742
.10.1016/0020-7683(67)90049-2
14.
Eringen
,
A. C.
,
1987
, “
Theory of Nonlocal Elasticity and Some Applications
,”
Res. Mech.
,
21
(
4
), pp.
313
342
.
15.
Altan
,
S. B.
,
1989
, “
Uniqueness of Initial-Boundary Value Problems in Nonlocal Elasticity
,”
Int. J. Solids Struct.
,
25
(
11
), pp.
1271
1278
.10.1016/0020-7683(89)90091-7
16.
Pisano
,
A. A.
, and
Fuschi
,
P.
,
2003
, “
Closed Form Solution for a Nonlocal Elastic Bar in Tension
,”
Int. J. Solids Struct.
,
40
(1), pp.
13
23
.10.1016/S0020-7683(02)00547-4
17.
Li
,
R.
, and
Kardomateas
,
G. A.
,
2007
, “
Thermal Buckling of Multi-Walled Carbon Nanotubes by Nonlocal Elasticity
,”
ASME J. Appl. Mech.
,
74
(
3
), pp.
399
405
.10.1115/1.2200656
You do not currently have access to this content.