Chirality simultaneously exists at different length scales in many biological materials, e.g., climbing tendrils and bacterial flagella. It can transfer from lower structural levels to higher structural levels, which is tightly associated with the growth and assembly of biological materials. In this paper, a continuum mechanics model is presented for understanding the bottom–up transfer of chirality in fibrous biological materials. Basic physical mechanisms underlying the chirality transfer in biological world are revealed. It is demonstrated that the chirality of constituent elements at the microscale can induce the twisting of higher-level structures, which may further transfer into the macroscopic morphology in different manners, rendering the formation of hierarchically chiral structures in tissues or organs. The bottom–up transfer mechanism of chirality may provide a limit to the macroscopic size of biological materials through the accumulative contribution of twisting.

References

1.
Barry
,
E.
,
Hensel
,
Z.
,
Dogic
,
Z.
,
Shribak
,
M.
, and
Oldenbourg
,
R.
,
2006
, “
Entropy-Driven Formation of a Chiral Liquid-Crystalline Phase of Helical Filaments
,”
Phys. Rev. Lett.
,
96
(
1
), p.
018305
.
2.
Upmanyu
,
M.
,
Wang
,
H. L.
,
Liang
,
H. Y.
, and
Mahajan
,
R.
,
2008
, “
Strain-Dependent Twist-Stretch Elasticity in Chiral Filaments
,”
J. R. Soc. Interface
,
5
(
20
), pp.
303
310
.
3.
Gerbode
,
S. J.
,
Puzey
,
J. R.
,
McCormick
,
A. G.
, and
Mahadevan
,
L.
,
2012
, “
How the Cucumber Tendril Coils and Overwinds
,”
Science
,
337
(
6098
), pp.
1087
1091
.
4.
Ghafouri
,
R.
, and
Bruinsma
,
R.
,
2005
, “
Helicoid to Spiral Ribbon Transition
,”
Phys. Rev. Lett.
,
94
(
13
), p.
138101
.
5.
Schulgasser
,
K.
, and
Witztum
,
A.
,
2004
, “
The Hierarchy of Chirality
,”
J. Theor. Biol.
,
230
(
2
), pp.
281
288
.
6.
Aggeli
,
A.
,
Nyrkova
,
I. A.
,
Bell
,
M.
,
Harding
,
R.
,
Carrick
,
L.
,
McLeish
,
T. C. B.
,
Semenov
,
A. N.
, and
Boden
,
N.
,
2001
, “
Hierarchical Self-Assembly of Chiral Rod-Like Molecules as a Model for Petide β-Sheet Tapes Ribbons, Fibrils, and Fibers
,”
Proc. Natl. Acad. Sci. U. S. A.
,
98
(
21
), pp.
11857
11862
.
7.
Zhao
,
Z. L.
,
Zhao
,
H. P.
,
Wang
,
J. S.
,
Zhang
,
Z.
, and
Feng
,
X. Q.
,
2014
, “
Mechanical Properties of Carbon Nanotube Ropes With Hierarchical Helical Structures
,”
J. Mech. Phys. Solids
,
71
, pp.
64
83
.
8.
Qin
,
Z.
, and
Buehler
,
M. J.
,
2010
, “
Molecular Dynamics Simulation of the α-Helix to β-Sheet Transition in Coiled Protein Filaments: Evidence for a Critical Filament Length Scale
,”
Phys. Rev. Lett.
,
104
(
19
), p.
198304
.
9.
Srigiriraju
,
S. V.
, and
Powers
,
T. R.
,
2006
, “
Model for Polymorphic Transitions in Bacterial Flagella
,”
Phys. Rev. E
,
73
(
1
), p.
011902
.
10.
Zhao
,
Z. L.
,
Zhao
,
H. P.
,
Li
,
B. W.
,
Nie
,
B. D.
,
Feng
,
X. Q.
, and
Gao
,
H. J.
,
2015
, “
Biomechanical Tactics of Chiral Growth in Emergent Aquatic Macrophytes
,”
Sci. Rep.
,
5
, p.
12610
.
11.
Ye
,
H. M.
,
Wang
,
J. S.
,
Tang
,
S.
,
Xu
,
J.
,
Feng
,
X. Q.
,
Guo
,
B. H.
,
Xie
,
X. M.
,
Zhou
,
J. J.
,
Li
,
L.
,
Wu
,
Q.
, and
Chen
,
G. Q.
,
2010
, “
Surface Stress Effects on the Bending Direction and Twisting Chirality of Lamellar Crystals of Chiral Polymer
,”
Macromolecules
,
43
(
13
), pp.
5762
5770
.
12.
Wada
,
H.
,
2012
, “
Hierarchical Helical Order in the Twisted Growth of Plant Organs
,”
Phys. Rev. Lett.
,
109
(
12
), p.
128104
.
13.
Wang
,
J. S.
,
Wang
,
G.
,
Feng
,
X. Q.
,
Kitamura
,
T.
,
Kang
,
Y. L.
,
Yu
,
S. W.
, and
Qin
,
Q. H.
,
2013
, “
Hierarchical Chirality Transfer in the Growth of Towel Gourd Tendrils
,”
Sci. Rep.
,
3
, p.
3102
.
14.
Hattne
,
J.
, and
Lamzin
,
V. S.
,
2011
, “
A Moment Invariant for Evaluating the Chirality of Three-Dimensional Objects
,”
J. R. Soc. Interface
,
8
(
54
), pp.
144
150
.
15.
Wang
,
J. S.
,
Cui
,
Y. H.
,
Shimada
,
T.
,
Wu
,
H. P.
, and
Kitamura
,
T.
,
2014
, “
Unusual Winding of Helices Under Tension
,”
App. Phys. Lett.
,
105
(
4
), p.
043702
.
16.
Wang
,
J. S.
,
Feng
,
X. Q.
,
Xu
,
J.
,
Qin
,
Q. H.
, and
Yu
,
S. W.
,
2011
, “
Chirality Transfer From Molecular to Morphological Scales in Quasi-One-Dimensional Nanomaterials: A Continuum Model
,”
J. Comput. Theor. Nanosci.
,
8
(
7
), pp.
1278
1287
.
17.
Claessens
,
M. M. A. E.
,
Semmrich
,
C.
,
Ramos
,
L.
, and
Bausch
,
A. R.
,
2008
, “
Helical Twist Controls the Thickness of F-Actin Bundles
,”
Proc. Natl. Acad. Sci. U. S. A.
,
105
(
26
), pp.
8819
8822
.
18.
Grason
,
G. M.
, and
Bruinsma
,
R. F.
,
2007
, “
Chirality and Equilibrium Biopolymer Bundles
,”
Phys. Rev. Lett.
,
99
(
9
), p.
098101
.
19.
Makowski
,
L.
, and
Magdoff-Fairchild
,
B.
,
1986
, “
Polymorphism of Sickle Cell Hemoglobin Aggregates: Structural Basis of Limited Radial Growth
,”
Science
,
234
(
4781
), pp.
1228
1231
.
20.
Turner
,
M. S.
,
Briehl
,
R. W.
,
Ferrone
,
F. A.
, and
Josephs
,
R.
, “
Twisted Protein Aggregates and Disease: The Stability of Sickle Hemoglobin Fibers
,”
Phys. Rev. Lett.
,
90
(
12
), p.
128103
.
21.
Fratzl
,
P.
,
Misof
,
K.
, and
Zizak
,
I.
,
1998
, “
Fibrillar Structure and Mechanical Properties of Collagen
,”
J. Struct. Biol.
,
122
(1–2), pp.
119
122
.
22.
Harris
,
A. B.
,
Kamien
,
R. D.
, and
Lubensky
,
T. C.
,
1999
, “
Molecular Chirality and Chiral Parameters
,”
Rev. Mod. Phys.
,
71
(
5
), pp.
1745
1757
.
23.
Grason
,
G. M.
,
2009
, “
Braided Bundles and Compact Coils: The Structures and Thermodynamics of Hexagonally Packed Chiral Filament Assemblies
,”
Phys. Rev. E
,
79
(
4
), p.
041919
.
24.
Guo
,
Q.
,
Chen
,
Z.
,
Li
,
W.
,
Dai
,
P.
,
Ren
,
K.
,
Lin
,
J.
,
Taber
,
L. A.
, and
Chen
,
W.
,
2014
, “
Mechanics of Tunable Helices and Geometric Frustration in Biomimetic Seashells
,”
EPL
,
105
(
6
), p.
64005
.
25.
Helfrich
,
W.
,
1991
, “
Elastic Theory of Helical Fibers
,”
Langmuir
,
7
(
3
), pp.
567
568
.
26.
Neville
,
A. C.
,
1993
,
Biology of Fibrous Composites: Development Beyond the Cell Membrane
,
Cambridge University Press
,
Cambridge, UK
.
27.
Emons
,
A. M. C.
, and
Mulde
,
B. M.
,
1998
, “
The Making of the Architecture of the Plant Cell Wall: How Cells Exploit Geometry
,”
Proc. Natl. Acad. Sci. U. S. A.
,
95
(
12
), pp.
7215
7219
.
28.
Marklund
,
E.
, and
Varna
,
J.
,
2009
, “
Modeling the Effect of Helical Fiber
,”
Appl. Compos. Mater.
,
16
(
4
), pp.
245
262
.
29.
Yang
,
Y. S.
,
Meyer
,
R. B.
, and
Hagan
,
M. F.
,
2010
, “
Self-Limited Self-Assembly of Chiral Filaments
,”
Phys. Rev. Lett.
,
104
(
25
), p.
258102
.
30.
Lloyd
,
C.
, and
Chan
,
J.
,
2004
, “
Microtubules and the Shape of Plants to Come
,”
Nat. Rev. Mol. Cell Biol.
,
5
(
1
), pp.
13
23
.
31.
Li
,
Q.
,
Kang
,
Y. L.
,
Qiu
,
W.
,
Li
,
Y. L.
,
Huang
,
G. Y.
,
Guo
,
J. G.
,
Deng
,
W. L.
, and
Zhong
,
X. H.
,
2011
, “
Deformation Mechanisms of Carbon Nanotubes Fibres Under Tensile Loading by In Situ Raman Spectroscopy Analysis
,”
Nanotechnology
,
22
(
22
), p.
225704
.
32.
Cox
,
H. L.
,
1952
, “
The Elasticity and Strength of Paper and Other Fibrous Materials
,”
Br. J. Appl. Phys.
,
3
(
3
), p.
72
.
33.
Wu
,
X. F.
, and
Dzenis
,
Y. A.
,
2005
, “
Elasticity of Planar Fiber Network
,”
J. Appl. Phys.
,
98
(
9
), p.
093501
.
34.
Fu
,
S. Y.
, and
Lauke
,
B.
,
1996
, “
Effects of Fiber Length and Fiber Orientation Distributions on the Tensile Strength of Short-Fiber-Reinforced Polymers
,”
Compos. Sci. Technol.
,
56
(
10
), pp.
1179
1190
.
35.
Tu
,
Z. C.
,
Li
,
Q. X.
, and
Hu
,
X.
,
2006
, “
Theoretical Determination of the Necessary Condition for the Formation of ZnO Nanorings and Nanohelices
,”
Phys. Rev. B
,
73
(
11
), p.
115402
.
36.
Wang
,
J. S.
,
Ye
,
H. M.
,
Qin
,
Q. H.
,
Xu
,
J.
, and
Feng
,
X. Q.
,
2012
, “
Anisotropic Surface Effects on the Formation of Chiral Morphologies of Nanomaterials
,”
Proc. R. Soc. A
,
468
(
2139
), pp.
609
633
.
37.
Gray
,
D. G.
,
1989
, “
Chirality and Curl of Paper Sheets
,”
J. Pulp Pap. Sci.
,
15
(3), pp.
J105
J109
.
38.
Dionne
,
I.
,
Werbowyj
,
R. S.
, and
Gray
,
D. G.
,
1991
, “
Chiral Twisting Curl in Newsprint Sheets
,”
J. Pulp Pap. Sci.
,
17
(4), pp.
J123
J127
.
39.
Alvaa
,
M.
, and
Niskanen
,
K.
,
2006
, “
The Physics of Paper
,”
Rep. Prog. Phys.
,
69
(
3
), pp.
669
723
.
40.
Lakes
,
R.
,
2015
, “
Third-Rank Piezoelectricity in Isotropic Chiral Solids
,”
Appl. Phys. Lett.
,
106
(
21
), p.
212905
.
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