Structural Heterogeneity in Silk Fibers and its Effects on Failure
Mechanics and Supercontraction
ARCHIVES
MASSACHUSETTS
by
Tristan Giesa
Dipl.-Ing. Mechanical Engineering
RWTH Aachen University, 2011
JUL 02 2015
LIBRARIES
Submitted to the Department of Civil and Environmental Engineering in Partial
Fulfillment of the Requirements for the Degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2015
2015 Massachusetts Institute of Technology. All rights reserved.
Signature of Author
Signature redacted
Department of C il nd Environmental Engineering
May 21, 2015
Certified by
Signature redacted
___
Markus J. Buehler
Professor of Civil and Environmental Engineering, Department Head
Thesis Supervisor
Accented by
_ __ _ _
Signature redacted,
idi Nepf
Donald and Martha Harleman Professor of Civil and Environmental En neering
Chair, Graduate Program Committee
1
INISTITUTE
OF TECHNOLOLGY
2
Structural Heterogeneity in Silk Fibers and its Effects on Failure Mechanics
and Supercontraction
by
Tristan Giesa
Dipl.-Ing. Mechanical Engineering
RWTH Aachen University, 2011
Submitted to the Department of Civil and Environmental Engineering
on May 21, 2015 in partial fulfillment of the requirements for the degree of
Doctor of Philosophy in the Field of Mechanics and Materials
Abstract
Spider dragline silk is a protein material that has evolved over millions of years
to become one of the strongest and toughest natural fibers known. Silk features a
heterogeneous structure that comprises P-sheet crystals embedded in an
amorphous matrix. However, it is not fully understood how the heterogeneity of
silk affects its mechanical properties.
First, the origin of the nanoscale heterogeneity during the Nephila Clavipes
dragline silk assembly is investigated. Using molecular dynamics simulations, a
shear flow at natural pulling speeds is modelled and the secondary structure
transitions as well as shear stresses in the silk protein chains are determined. It is
shown that under shear stresses beyond the elastic regime, silk undergoes an
a - P-transition in the spinning duct. The stability of the assembled P-sheet
structure seems to arise from a close proximity of the a-helices in the silk
solution. The smallest molecule size that might give rise to a silk-like structure is
determined to comprise four to six repeats of the silk sequence. Establishing the
3
molecular details of the assembly can guide the design of microfluidic devices
and the synthesis of bioinspired protein materials.
Second, it is shown how the heterogeneity of silk fibers, specifically its crystalline
phase, relates to its fracture mechanical properties: strength and toughness.
Analytical fracture mechanical arguments are presented to illustrate the relation
between fracture strength and heterogeneity in silk and other biopolymers.
Nanoconfinement and flaw tolerance are presented as natural strategies to
increase the mechanical performance of the entire material system. It is shown
that the consideration of interatomic interactions alone cannot explain the
fracture strength observed in biological fibers. Instead, structures at multiple
length-scales must be considered to explain the remarkable mechanical
performance and resilience of silk.
Third, the interaction of water with silk's heterogeneous nanostructure is
investigated. At high humidity, some spider dragline silks will shrink up to 50%,
a phenomenon known as supercontraction. The molecular origin of dragline silk
supercontraction is explored using a full-atomistic model and molecular
dynamics supported by in situ Raman spectroscopy and mechanical testing
performed at the Max Planck Institute in Potsdam, Germany. Tyrosine and
Arginine are identified as the key residues in the Nephila Clavipes silk sequence
that control supercontraction. A genetic engineering strategy to alter silk's
behavior to industrial requirements is proposed, where sequence mutations
reduce or even reverse the supercontraction mechanism.
Thesis Supervisor: Markus J. Buehler
Title: Professor and Department Head of Civil and Environmental Engineering
4
Acknowledgements
I would like to take this opportunity to express my gratitude to those who have
supported me throughout my graduate studies at MIT. I would like to thank my
advisor, Prof. Markus
J.
Buehler, for his mentorship, advice, and for the
opportunity to work and learn in such a great collaborative and inspiring
environment. I am grateful for the advice and support of my committee
members, Prof. Oral Buyukozturk, Prof. Pedro Reis, and Prof. Niels HoltenAndersen. I am indebted to my amazing collaborators with whom I had the
pleasure working on a diverse set of exciting research topics: Dr. David Spivak,
Prof. Carole Perry, Prof. David Kaplan, Prof. Joyce Wong, Prof. Nicola Pugno,
Dr. Admir Masic, and Dr. James Weaver.
I am very grateful to Leon Dimas, Dieter Brommer, and Francisco Martinez, for
their friendship and everlasting support, even in most difficult times. Many
thanks also to my past and present colleagues from the Laboratory for Atomistic
and Molecular Mechanics at MIT: Talal Al-Mulla, Melis Arslan, Laura Batty,
Graham Bratzel, Shu-Wei Chang, Chun-The Chen, Chia-Ching Chou, Steve
Cranford, Baptiste Depalle, Nina Dinjaski, Davoud Ebrahimi, Andre Garcia,
Alfonso Gautieri, Greta Gronau, Grace Gu, Kai Jin, Gang-Seob Jung, Shangchao
Lin, Shengjie Ling, Flavia Libonati, Reza Mirzaeifar, Arun Nair, Seunghwa Ryu,
Max Solar, Anna Tarakanova, Olena Tokareva, Steve Palkovic, and Zhao Qin.
Finally, I express my deepest gratitude to my family and friends who have
supported and encouraged me in all my endeavors.
This research was funded by grants by NSF, ARO, BASF-NORA and NIH. Their
support is greatly appreciated.
Cambridge, United States, June 2015
5
6
List of Journal Publications
I am the author of all the work presented in this thesis. Research was conducted
in the Department of Civil and Environmental Engineering at the Massachusetts
Institute of Technology. Part of the work presented here has been published in
peer-reviewed journal papers and book chapters (chronological):
1. T. Giesa, M. Arslan, N.M. Pugno, M.J. Buehler, Nanoconfinement of Spider
Silk Fibrils Begets Superior Strength, Extensibility and Toughness. Nano
Letters 11 (11), 5038-5046, 2011
2. D.I. Spivak, T. Giesa, E. Wood, M.J. Buehler, Category Theoretic Analysis of
HierarchicalProtein Materials and Social Networks. PLoS One 6 (9), e23911,
2011
3. T. Giesa, D.I. Spivak, M.J. Buehler, Reoccurring Patterns in Hierarchical
Protein Materials and Music: The Power of Analogies. BioNanoScience 1 (4),
153-161, 2011
4. T. Giesa, G. Bratzel, M.J. Buehler, Modeling and Simulation of Hierarchical
Protein Materials. In: Nano and Cell Mechanics: Fundamentals and
Frontiers, John Wiley & Sons, Ltd, 389-409, 2012
5. G. Gronau, S.T. Krishnaji, M.E. Kinahan, T. Giesa, J.Y. Wong, D.L. Kaplan,
M.J. Buehler, A review of combined experimental and computational procedures
for assessing biopolymer structure-process-propertyrelationships. Biomaterials
33 (33), 8240-8255, 2012
6. T. Giesa, D.I. Spivak, M.J. Buehler, Category Theory Based Solution for the
Building Block Replacement Problem in Materials Design. Advanced
Engineering Materials 14 (9), 810-817, 2012
7. T. Giesa, N.M. Pugno, M.J. Buehler, Natural Stiffening Increases Flaw
Tolerance of Biological Fibers. Physical Review E 86 (4), 041902, 2012
7
8. T. Giesa, M.J. Buehler, Spidermans Geheimnis. Physik in unserer Zeit 44 (2),
72-79, 2013
9. T. Giesa, M.J. Buehler, Nanoconfinement and the Strength of Biopolymers.
Annual Reviews of Biophysics 42, 651-673, 2013
10. L.S. Dimas, T. Giesa, MJ Buehler, Coupled Continuum and Discrete Analysis
of Random Heterogeneous Materials: Elasticity and Fracture. Journal of the
Mechanics and Physics of Solids 63, 481-490, 2014
11. T. Giesa, N.M. Pugno, J.Y. Wong, D.L. Kaplan, M.J. Buehler, What's Inside
the Box? - Length Scales that Govern Fracture Processes of Polymer Fibers.
Advanced Materials 26 (3), 412-417, 2014
12. L.S. Dimas, D. Veneziano, T. Giesa, M.J. Buehler, Random Bulk Propertiesof
Heterogeneous Rectangular Blocks with Lognormal Young's Modulus: Effective
Moduli. Journal of Applied Mechanics 82 (1), 011003, 2015
Journal papers in submission or revision:
13. T. Giesa, R. Schuetz, P. Fratzl, A. Masic, M.J. Buehler Molecular Origin of
Supercontraction in Spider Dragline Silk Revealed by
Simulation and
Experiment. In submission, 2015.
14. T. Giesa, C.C. Perry, M.J. Buehler, Secondary Structure Transition and
CriticalStress during the Assembly of Spider Silk Fibers. In submission, 2015.
15. L.S. Dimas, D. Veneziano, T. Giesa, M.J. Buehler, ProbabilityDistributionof
Fracture Elongation, Strength and Toughness of Notched Rectangular Blocks
with Lognormal Young's Modulus. In revision, 2015.
16. T. Giesa, R. Jagadeesan, D. I. Spivak., M.J. Buehler, A Python Library for
MaterialsArchitecture. In submission, 2015.
8
Table of Contents
A b stra ct ..............................................................................................................................
3
Acknowledgements .....................................................................................................
5
List of Journal Publications........................................................................................
7
Table of Contents .......................................................................................................
9
1
In trod u ction .............................................................................................................
1.1
Biological Materials as Template for Structural Design .........................
13
1.2
Spider Silk as Model Material ...................................................................
20
1.2.1
Properties of Silk Fibers .....................................................................
21
1.2.2
Tensile Behavior of Silk Dragline Fibers...........................................
23
1.2.3
Defects and Flaws in Silk Fibers ........................................................
25
1.3
2
Research Hypothesis....................................................................................
Meth od s....................................................................................................................
2.1
Atomistic Modeling .....................................................................................
26
29
30
2.1.1
Classical Molecular Dynamics ..........................................................
31
2.1.2
Quantities determined from Molecular Dynamics .............
32
2.1.3
Steered Molecular Dynamics.............................................................
34
2.1.4
Molecule Shape Calculation ...............................................................
34
2.1.5
Replica Exchange Molecular Dynamics.............................................
35
2.1.6
Entropy calculation...............................................................................
35
2.1.7
Free Energy of Solvation......................................................................
37
2.1.8
Simulated Raman and Infrared Spectrum.........................................
38
2.1.9
Data Analysis........................................................................................
41
Analytical approaches to materials failure/ fracture..............................
41
2.2
3
13
2.2.1
Linear elastic fracture mechanics......................................................
41
2.2.2
Polymer fracture mechanics ...............................................................
42
Creation of Heterogeneity - Silk Assembly....................................................
45
9
3.1
Backgrou nd ...................................................................................................
46
3.1.1
Fiber formation- spinning from solution..............................................
47
3.1.2
Silk structure after spinning ...............................................................
50
3.1.3
Simulation Setup .................................................................................
52
3.2
Size Dependence of Structural Transition ...............................................
58
3.3
Structural Stability of the Assembled Silk Molecules .............................
62
3.4
Molecular Details of the Transition Mechanism......................................
65
3.5
Layered Structures ......................................................................................
70
3.6
C onclu sion ....................................................................................................
72
4 Heterogeneity and Nanoconfinement of Fibrils to Increase Strength and
Tou gh n ess .......................................................................................................................
4.1
Background ...................................................................................................
74
4.1.1
Nanoconfinement Strategy ..................................................................
75
4.1.2
Confinement of Polymers ....................................................................
80
4.1.3
Strength of Polymers ..........................................................................
82
4.1.4
The Relation between Confinement and the Strength of Polymers .87
4.1.5
Nanoconfinement in Silk ....................................................................
94
Fracture Mechanics Analysis......................................................................
98
4.2
5
73
4.2.1
Importance of the Process Zone.........................................................
99
4.2.2
Derivation of the Process Zone Size ....................................................
100
4.2.3
Fracture Length Scales in Silk Fibers...................................................106
4.2.4
Continuum Fracture Mechanics Analysis ...................
108
4.3
The Importance of Heterogeneity in Silk Fibers.......................................
110
4.4
C on clu sion ......................................................................................................
113
Supercontraction - Silk's Interaction with Water ............................................
115
5.1
Back grou nd ....................................................................................................
116
5.1.1
Mechanism of Supercontraction ..........................................................
5.1.2
Combined Simulation and Experimental Approach........................117
5.1.3
Molecular Dynamics Setup...................................................................
10
117
119
Supercontraction of the silk wildtype ........................................................
5.2
120
5.2.1
Silk Supercontraction in Simulation and Experiment ...................... 120
5.2.2
Secondary Structure Change during Supercontraction ................... 123
Molecular Origin of Supercontraction .......................................................
5.3
124
5.3.1
Raman Spectroscopy and Hydrogen Bonding ..................................
124
5.3.2
Simulated Infrared Spectrum and Vibrational Density of States .... 127
5.3.3
Energy Balance and Supercontraction Stress.....................................129
5.3.4
Conformational Changes ......................................................................
5.3.5
Hydrogen Bonding of Tyrosine and Arginine...................................148
5.3.6
Key Residues for Supercontraction.....................................................
136
152
5.4
Controlling Supercontraction......................................................................
153
5.5
C on clu sion ......................................................................................................
157
6
Summary and Outlook ........................................................................................
159
7
A p p en d ix ...............................................................................................................
163
7.1
Secondary Structure and Shear Stress Trajectories ..................................
7.2
Probability for the a-p-Transition...............................................................167
7.3
N omenclature ................................................................................................
172
7.4
R eferences .......................................................................................................
177
7.5
List of Figu res ................................................................................................
197
7.6
List of Tables ..................................................................................................
211
11
163
12
1
Introduction
Parts of the review presented in this chapter have been published in:
" T. Giesa, M. Arslan, N.M. Pugno, M.J. Buehler, Nanoconfinement of Spider
Silk Fibrils Begets Superior Strength, Extensibility and Toughness. Nano
Letters, 11, 11, pp. 5038-5046, 2011
" T. Giesa, G. Bratzel, M.J. Buehler, Modeling and Simulation of Hierarchical
Protein Materials. In: Nano and Cell Mechanics: Fundamentals and
Frontiers, John Wiley & Sons, Ltd, pp. 389-409, 2012
*
T. Giesa, M.J. Buehler, Spidermans Geheimnis. Physik in unserer Zeit 44 (2),
72-79, 2013
*
T. Giesa, M.J. Buehler, Nanoconfinement and the Strength of Biopolymers.
Annual Reviews of Biophysics, 42, pp. 651-673, 2013
1.1
Biological Materials as Template for Structural Design
Most biological materials are organized in complex hierarchical structures [1],
some of which have already been mimicked by engineers using synthetic
pathways
such
as
transcription,
synergetic
assembly,
morphosynthesis
(including chemical transformations in confined geometries to produce complex
structures), and integrative synthesis. Latter combines all previously mentioned
methods to produce materials with complex morphologies [2]. Due to advances
in observation methods during the last few centuries, scientists have gained
deeper insight into the way structures and materials are fabricated in nature.
Sanchez et al. [2] state that new materials and systems produced by man must
aim at higher levels of sophistication and miniaturization, be recyclable and
reduce the environmental footprint, implying also increased reliability and
13
durability while consuming less energy in fabrication. By elucidating the design
and construction principles of living organisms,
new material synthesis
pathways become accessible. It has become possible to understand and even
imitate the superior performance, variability, and effectiveness seen in biological
systems. This development has culminated into the field of biomimetics [3]. By
controlling material
properties on the length scales of Angstroms and
nanometers through new processing methods, it is now possible to create
functional surfaces and polymer nanostructures with tailored mechanical,
optical, thermal, or electrical responses. Still, the understanding (and mimicking)
of the complex assembly
processes that form polymer-based/composite
biomaterials like bone, silk, collagen, and many biological tissues remains a
major challenge.
Protein materials are found in complex structures such as cells, organs, or
organisms. An analysis of their composition reveals universal basic constituents
(building blocks such as a-helices,
-sheets) but also highly specific features
(filament assemblies, nanocrystals in spider silk or tendon fascicles, etc.) [4].
These examples illustrate that the coexistence of universality and diversity is an
overarching feature in protein materials, as characterized by the UniversalityDiversity paradigm, wherein universality tends to dominate at smaller levels and
diversity is found predominantly at larger levels and used to create many
different functional properties [5].
Biological materials such as spider silk and diatom algae arrange in structural
hierarchies and optimize their behavior in regard to the environmental
requirements. Diatoms exhibit high structural stiffness combined with high
robustness to protect against predators, and spider webs show high energy
absorption and extensibility for catching prey while localizing web damage [6, 7].
Similarly, in the glassy sponge Eucleptella, silica nanospheres are arranged at
multiple levels of hierarchy to constitute a skeleton with high structural stability
14
at minimum cost [8]. The teeth of sea urchins and the lamellar structure of
mollusk shells are other examples for structural hierarchies in biomaterials that
lead to extremely strong and tough structures [9]. Earlier studies showed that in
materials like bone or wood, for example, the structural assembly of the basic
building blocks collagen, water, hydroxyapatite minerals, hemicelluloses, and
lignin governs the mechanical properties at different length scales with similar
mechanisms, despite the differences in the building blocks and the overall
material properties [10, 11]. Figure 1 shows the hierarchical structure of diatom
algae and glassy sponges as examples of complex assembled natural systems.
a
b
Figure 1 I Complex hierarchical structures found in natural materials. (a) Scanning electron microscopy
(SEM) pictures displaying the intricate hierarchical porous silica wall structure of diatoms. Figure adapted
from [12], with permission from Elsevier. (b) SEM pictures of the mineralized skeletal system of Eucleptella.
The caged structure consists of struts (bundled spicules) which themselves are a ceramic composite with
laminated silica layers and organic interlayers. Figure adapted from [8], copyright @ 2005, with permission
from the American Association for the Advancement of Science.
It is remarkable how the exceptionally complex functionality found in natural
biological systems is created despite (i) a limited number building blocks, e.g. the
20 amino acids in protein materials, (ii) constraints in available material volume
and energy for synthesis, and (iii) only a handful of simple chemical interactions,
generally referred to as interaction rules [5, 13-17]. The manipulation of single
building blocks has fundamental influences on the overall system behavior. A
single point-mutation in a DNA strand can make the difference between health
15
and disease [18]. On the other hand, the localized failure of larger structural
elements does not influence the total system behavior, in accordance with the
robustness of hierarchical systems. This is related to a high redundancy within
the structure.
Computational modeling and simulation of materials seeks to bridge analytical
theory and experimental observation in order to both explain these phenomena
and predict materials behavior. The computational tools available for multiscale
simulation and engineering of protein materials now cover a similar length scale
range as experimental tools (see chapter 0) and can provide crucial insights to
deformation
mechanisms,
particularly
at
the
nanoscale.
As
computer
performance continues to advance, multiscale computational modeling of
synthetic
and biological
materials will further enable
to improve
the
understanding of processes and provide a rigorous basis for the bottom-up
design of advanced materials, coupled with multiscale experiment. This
comprehensive view of structures and materials forms the foundation to a new
field of study, biomateriomics [19].
Biomateriomics aims at elucidating the basic components and building principles
selected by evolution to propose more reliable, efficient and environmentally
benign materials and requires a multidisciplinary approach. Within this
framework, the most important and interesting features of biological materials
are:
*
Reuse of structural constituents
Protein materials can be found in vastly complex structures such as cells,
organs or organisms. The coexistence of universality and diversity is an
overarching feature in protein structures, where universality tends to
dominate at smaller levels whereas diversity is found predominantly at
16
larger, functional levels [5]. The universal building blocks can be defined
depending on the depth of analysis, e.g., the 20 amino acids, the chemical
elements, or quantum level elements like strings.
*
Multi-constituent hierarchical build-ups
Many materials and structures engineered by humans bear a conflict
between strength and toughness; strong materials are often fragile, while
robust materials tend to be soft
[4]. In extreme conditions, only high
safety factors and thus bigger amount of resources can guarantee the
strength
of engineered materials.
This can
be overcome
by the
arrangement of structures at multiple scales. One of nature's remarkable
features is its ability to combine (bio)organic and inorganic components at
the nanoscale [20]. In materials like bone, universal patterns form a nanocomposite of strong but brittle minerals (hydroxyapatite) and soft but
ductile biopolymers (collagen) through the assembly into complex shapes
on seven levels of hierarchy, giving rise to improved mechanical
properties. Figure 2 shows the hierarchical build-up of two prominent
natural materials, spider silk and bone. The strength and toughness
observed in these materials serves as model to engineering composites.
Advances in 'soft chemistry' during the past ten years have produced
original hybrid materials with controlled
porosity and/or texture
resulting in easy-to-process materials [2]. These offer many advantages
such as tunable physical properties, high photochemical and thermal
stability, chemical inertness and negligible swelling, both in aqueous and
organic solvents with applications to smart devices, sensors and catalysis.
17
Silk
1PM
n-m
15
Fiber
Heteronanocomposite
Fibril
f-sheet and semiamorphous phase
Web
Bone
Amino acids
- A
Tropocollagen
- 300 nrn
Bone tissue
- 50 cm
Mineralized collagen fibrils
-mm
Osteons and Harvesian canals
- 100mm
Fibril arrays
- 10 MM
Fiber pattems
-50mm
Figure 2 Hierarchical structures of biological materials such as spider silk and bone. Biological materials
are designed bottom-up to overcome fundamental strength limits at the nanoscale. Spider dragline silk,
specifically the protein MaSpi, consists of -sheet nanocrystals embedded in an amorphous phase. These are
aligned along the fiber axis to form fibrils of size 20-150 nm. Hundreds of fibrils are spun together in a fiber
that eventually forms the frame of an orb web. Compact bone is composed of osteons that surround and
protect blood vessels. Osteons have a lamellar structure. Each individual lamella is composed of fibers
arranged in geometrical patterns. These fibers are the result of several collagen fibrils, each linked by an
organic phase to form fibril arrays. Each array makes up a single collagen fiber. The mineralized collagen
2010,
fibrils are the basic building blocks of bone. Bone figure adapted from Reference [20], copyright
James
Dr.
of
courtesy
Annual Reviews. Web image courtesy of Charles J. Sharp. Silk figure composition
Weaver, Harvard University.
18
0
Self-assembly under moderate conditions
In order to control structure and shape below the scale where most
engineering techniques become unfeasible, structural self-assembly to
control the chemical synthesis of small-scale structures upwards provides
a promising bottom-up approach. Key to engineering applications is the
thorough understanding of how simple chemical complexes, i.e., building
blocks like amino acids, DNA, viruses, nanoparticles, or enzymes as
catalysts, interact under moderate conditions (room-temperature and
atmospheric pressure) to form complex 3D structures. Current models
cannot predict protein folding unambiguously [21].
Self-healing
Self-healing is the functional repair to mitigate damage, for example from
an impact event, thus progressing from a conventional damage tolerance
philosophy. It is mainly related to two biological mechanisms [22]: On the
molecular level, sacrificial bonds, such as hydrogen bonds, dynamically
break and reform giving rise to a quasi-plastic behavior without fracture
(related for example to spider silk's second deformation stage, see chapter
1.2.2). On the macroscale, cyclic replacement of material, for instance in
bone and plants by specialized cells or in tissues by intermediate tissues,
forms the governing repair mechanism.
*
Lightweight design
The density of biological materials such as silk is generally less than 3
g/cm 3 (compare to steel: 8 g/cm 3) due to the hierarchical structure that
strongly reduces the amount of needed resources [23].
19
0
High robustness and strength (damage tolerance)
In most applications, catastrophic failure needs to be avoided by using
strong and tough (fracture-resistant) materials. Hard materials tend to be
brittle because the high stresses at the crack tip cannot be dissipated,
whereas soft materials dissipate the stress by plastic deformation. Natural
materials rely on intrinsic and extrinsic toughening mechanisms (see
chapter 4.1.4.2). Intrinsic mechanisms (based on plastic deformation, e.g.,
fiber sliding) are usually originated from smaller length scales (akin to
dislocations in metal), whereas extrinsic toughening mechanisms (e.g. fiber
bridging) usually take place on micrometer scales [24].
1.2
Spider Silk as Model Material
Spider and silkworm silk are among the most studied natural protein materials,
since they exhibit most of the desired features of a composite material discussed
in the previous chapter. Silk is a hierarchically structured protein fiber with a
high tensile strength and great extensibility, making it one of the toughest
materials known [25-27], in spite of the material's simple protein building blocks
[28-30]. In contrast to synthetic polymers based on petrochemicals, silk is spun
into strong and totally recyclable fibers at ambient temperatures, low pressures,
and with water as the solvent. However, biomimetic reproductions of silk remain
a challenge because of silk's characteristic microstructural features that can only
be achieved by controlled self-assembly of protein polymers with molecular
precision [31, 32]. Unlike silkworms, some spiders can use different glands to
create up to seven types of silk, from the strong dragline to the viscoeleastic
capture silk and tough eggsack casing [27].
20
1.2.1 Properties of Silk Fibers
Dragline silk, containing a high fraction of densely hydrogen-bonded (Hbonded) domains, is used to provide the structural frame for the web and has an
elastic modulus of up to 10 GPa [25]. Capture silk, on the other hand, is a viscid
biofilament containing cross-linked polymer networks and has an elastic
modulus that is comparable to that of other elastomers [33]. A comparison of silk
to other composite and classical engineering materials is shown in the Ashby
plot in Figure 3.
10000
Engineering
Natural Polyrmers and
Polymer Composites
Ceramics
Engineering
1000
W
Alloys
100
Natural Cellular
Materials
BenOO
ineering
,0,
C
posites
Engir
P
CO
10
Natural
Ceramics and
Ceramic
Comnposites
1
Elastomers
0.1
0.01
0.1
1
10
Density [g/cm3I
Figure 3 1 Density vs. failure strength of synthetic and natural materials as Ashby plot. Adapted from
Reference [34].
While there are many types of silk with different properties, this thesis focuses
on the dragline silk (specifically the protein MaSpi) of orb-weaving spiders that
is known to be extremely strong, extensible and tough [35-38]. Silk fibers
21
typically feature an initial modulus up to 10 GPa, a high extensibility exceeding
50-60% strain at failure, and a tensile strength of 1-2 GPa [37-41], which results in
toughness values of several times that of KevlarTM [42]. In addition to the
relatively large ultimate strength of spider silk, comparable to that of steel, silk
features a strength-to-density ratio that is up to ten times higher than that of steel
because of the material's small density (-1.3 g/cm 3). As shown in Figure 4, silk
features a hierarchical structure, where the nanoscale geometry is characterized
by a network of silk repeat units that each consist of a P-sheet nanocrystal
embedded in semi-amorphous protein domains. The sequence of silk repeat
units (in one-letter amino acid codes, here as an example for Major Ampullate
Spidroin 1, MaSpi, of Nephila clavipes) is (GAGAAAAAAGGAGQGYGLGS
QGGRGLGGQ)a where the bolded 'A' (Alanine) identifies the region that forms
-sheet nanocrystals and the rest forms semi-amorphous domains.
poly-alanine region
P-sheet crystal
... QGAG AAAAAA GGAGQ...
semi-amorphous phase
-
* 0.2 nm
hydrogen bonding
20 - 150 nm
pm-sheet
10 nm
content
15-50
%
fiber
1
fibril
Figure 4 | Silk features a hierarchical structure, where P-sheet crystals play a key role in defining the
mechanical properties by providing stiff and orderly cross-linking domains embedded in a semi-amorphous
matrix that consists predominantly of less ordered structures. These f-sheet nanocrystals, bonded by means
of assemblies of H-bonds, have dimensions of a few nanometers and constitute roughly 15-50% of the silk
volume. Adapted from Reference [43].
22
While rubber is extensible, and KevlarTM is stiff and strong, silks feature a
combination of strength and toughness not typically found in synthetic
materials. It is known that
-sheet crystals at the nanoscale play a key role in
defining the mechanical properties of silk by providing stiff and orderly crosslinking
domains
embedded
in a
semi-amorphous
matrix
that consists
predominantly of less ordered structures [44, 45]. These P-sheet nanocrystals,
bonded by means of assemblies of H-bonds, have dimensions of a few
nanometers and constitute roughly 15-50% of the silk volume. When silk fibers
are stretched, the P-sheet nanocrystals reinforce the partially extended and
oriented macromolecular chains by forming interlocking regions that transfer the
load between chains under lateral loading, similar to their function in other
structural proteins [46]. The hierarchical network of spider draglines, contrasting
synthetic elastomers like rubber, enables quick energy absorption and efficiently
suppresses vibration during an impact [42]. Rubbers, composed of random
polymer chains, display an elasticity regime that is primarily due to the change
in conformational entropy of these chains. In contrast, the amorphous chains in
silk filaments are extended and held in partial alignment with respect to the fiber
axis in its natural dry state, resulting in remarkably different mechanical
behaviors from rubbers [45, 46]. In chapter 5, the transition of hydrated silk into a
rubbery state will be discussed (supercontraction effect).
1.2.2 Tensile Behavior of Silk Dragline Fibers
The mechanical behavior of silk is explained in detail in Reference [44, 47].
Molecular-level studies elucidated the structure and role of P-sheet nanocrystals
and semi-amorphous protein domains during deformation, and the mechanical
parameters for the behavior of a single repeat unit of silk were extracted [44, 48,
49]. The mechanical behavior of silk fibers under tensile stretching is highly
nonlinear. Beyond an initial high-stiffness regime spider silk softens at the so23
called 'yield point' where the stress-strain response gives way to a plateau,
eventually leading to a stiffening regime prior to failure [50]. These mechanisms
result in the characteristic softening-stiffening stress-strain response that is found
for many different types of silk [37-39].
Figure 5 displays schematically a typical stress-strain curve of spider silka dn
classifies its deformation regimes. Regime I is characterized by a linear-elastic
response dominated by homogenous stretching before protein unfolding begins.
The transition from Regime I to Regime II is marked by the beginning of the
rupture of hydrogen bonds (H-bond) in 3 1 0-protein helices that make up the
semi-amorphous domains, and the unraveling of these proteins continues until
all hidden length is exhausted. Regime II is the key to the extensibility of silk.
Regime III reflects the stiffening behavior that sets in after the exhaustion of
unfolding events and the alignment of polypeptide chains. This facilitates the
deformation of P-sheet nanocrystals that leads to a significant stiffening of the
material in Regime III. Regime IV involves a brief softening behavior as P-sheet
nanocrystals fail under stick-slip deformation leading to the breakdown of Psheet nanocrystal cross-links, and eventual material failure. The mechanical
stability of P-sheet nanocrystals is the key to the ultimate strength molecularlevel silk since they are the last molecular elements that break.
24
1500
- Experiment/Simulation
Quad-Linear Fit
1000
III
C 500
a''
0
0.1
0.2
0.4
0.3
Strain f;
0.5
0.6
Figure 5 | Stress-strain behavior for a defect-free silk fiber, noting the key transition points between the four
regimes marked by molecular events at the molecular scale. The transition from Regime I to Regime II
marks the onset of unfolding of the semi-amorphous phase of silk; the transition from Regime II to Regime
III marks the onset of stretching of the -sheet nanocrystal phase. In Regime IV (-sheet nanocrystals fail via
a stick-slip mechanism, eventually leading to failure. Figure adapted from Reference [431.
1.2.3 Defects and Flaws in Silk Fibers
At a much larger scale, experimental studies have shown that silk fibers contain
many defects that act as stress concentrators, including cavities, surfaces or tears
[51-53]. For example, Figure 6 shows images of crack-like cavities in Nephila
madagascariensis dragline silk [51]. These defects feature sizes that reach several
hundred nanometers and are crucial in the consideration of mechanical
properties as they serve as seeds for material failure through localized
deformation (in fracture mechanics defects are known to lead to local stress
concentrations) [54, 55]. Nevertheless, despite the presence of defects, silk fibers
display remarkable mechanical properties [56, 57].
25
Figure 6 1 Microscopic images of Nephila madagascariensis dragline silk fibers showing the skin-core
structure as well as flaws and cavities in the material. The white arrows point in the axial fiber direction,
and the red ellipses highlight some of the defects found in the structure. Pictures reprinted from [51], C
copyright 1998, with permission from John Wiley & Sons, Inc.
1.3 Research Hypothesis
As shown in the previous chapter, silk serves as a model fibrous material and has
the potential to replace expensive synthetic fibers in composites. Unfortunately,
silk has several disadvantages: it is very temperature sensitive and flammable, it
interacts strongly with water and the assembly process is quite complex. For
industrial purposes, silk has to be either modified (e.g., through genetic
engineering) to mitigate some of these problems or a new material has to be
created that contains silk's desirable features. To study the nanoscale
mechanisms that lead to silk's heterogeneity and that control silk's mechanical
properties, a multidisciplinary and multiscale approach is necessary. This work
focusses mainly on the computation of silk on the nanoscale using molecular
dynamics simulation. However, simulations complement and are validated with
experimental observations from literature and from collaborators.
First, the origin of the nanoscale heterogeneity during the Nephila Clavipes
dragline silk assembly is investigated. This is of interest since artificial spinning
of recombinant silk has not yet yielded fibers that compare in strength in
26
toughness to their natural counterparts. It is hypothesized, that shear stresses in
the spinning duct need to reach a critical value in order to allow the silk a - Ptransition from solution to fiber. Furthermore, it is hypothesized that the stability
of the crystal is determined by the size of the silk molecule in the solution and
that there is a minimum size that ensures this stability. Establishing the
molecular details of the assembly can guide the design of microfluidic devices
and the synthesis of bioinspired protein materials, even beyond silk.
Second, it is hypothesized that the heterogeneous structure during the assembly
is crucial to the mechanical performance
of the fiber. Specifically, the
nanoconfinement strategy employed in biomaterials leads to a flaw tolerant
structure. Structures at multiple length-scales must be considered to explain the
remarkable mechanical performance and resilience of silk. Understanding the
trigger of strengthening mechanisms has a tremendous impact on the design of
novel hierarchical materials.
Third, the interaction of water with silk's heterogeneous nanostructure is
investigated. At high humidity, some spider dragline silks will shrink up to 50%,
a phenomenon known as supercontraction. This effect is not necessarily
desirable. It is hypothesized that a detailed understanding and control over silk's
heterogenous nanostructure can help to identify the molecular origin of
supercontraction. Furthermore, a genetic engineering strategy (targeted sequence
mutations) can reduce or even reverse the supercontraction mechanism while
maintaining the mechanical properties.
27
28
2 Methods
In this chapter, molecular simulation is described as a multiscale method to
elucidate atomistic and molecular mechanisms
of protein assembly and
deformation. Figure 7 summarizes approximate length and time scale regimes of
the tools for multiscale engineering. Computational tools predict and explain
phenomena that are observed experimentally, but are limited to certain regimes
due to constraints on computational performance [18]. While mesoscale and
continuum modeling cannot capture atomistic details, they are trained by
atomistic results from Density Functional Theory (DFT) and Molecular Dynamics
(MD) simulations. They cover the same length scale range as experimental tools
(e.g.,
atomic
force
microscopy,
optical/ magnetical
electromechanical systems and nano-indentation.
29
tweezers,
micro-
0(300 nm. ps)
Nano
-
a
dentation
MEMS testing
>minr
Collagen
pnpette
nMicro
>m
fibril
C
Continuum
models
Meso.
scale
models
PSG
I
OpticalAnagnetic tweezers
-g
Nonreactive
Atomic force microscopy
Reactive
MD
iugraphy
PS
QM/DFT
Transmission eetron
NMR
diffraction
b
Length scale
pm
unm
diX-ray
I:
10
Nanopaticles
(nanowires.
carbon
nanotubes)
DNA
polypeptides
Secondary protein
structures (e.g. f-sheets,
a-helices)
Cells
Tissues
organs
organisms
Figure 7 1 Approximate length and time scale regimes of the tools for multiscale engineering.
to
Computational tools predict and explain phenomena that are observed experimentally, but are limited
continuum
and
mesoscale
While
certain regimes due to constraints on computational performance.
modeling (subpanel a) cannot capture atomistic details, they are trained by atomistic results from Density
scale
Functional Theory (DFT) and Molecular Dynamics (MD) simulations. They cover the same length
tweezers,
magnetical
optical/
b),
subpanel
(AFM,
microscopy
force
atomic
(e.g.
tools
range as experimental
classes
microelectromechanical systems (MEMS, subpanel c) and nano-indentation. The lower part indicates
[18],
from
reprinted
Figure
techniques.
or scales of protein materials that can be studied with the respective
Group.
Publishing
Nature
copyright 2009, with permission from the
2.1 Atomistic Modeling
Beginning from first principles, quantum mechanical methods such as the
Hartree-Fock Theory solve many-electron wave functions, based on the
Schr6dinger equation, to derive bond energies and chemical interactions, but are
limited to small molecules and describe processes lasting only femtoseconds [58].
Density functional theory (DFT) employs functionals based on the spatially30
dependent electron density to explore the electronic structure of atoms and
molecules such as the interactions of single peptides. For proteins, the energy
landscape,
the phonon modes (e.g., to capture dipole changes and the
polarization), and the distribution of charges within the molecule can be
determined. The current computational limit for these quantum methods is in
the order of a few thousand atoms. To capture the formation and interactions of
secondary structures of polypeptides (e.g., P-sheets and a-helices) and solventmediated processes on the order of nanoseconds, molecular dynamics (MD)
simulations use force fields trained by DFT results [59, 60].
Molecular dynamics was developed in the 1950's to describe multi-body motion
and fluid dynamics using first-principles calculations [61, 62]. Today, MD is
widely used to predict behavior and model various materials phenomena.
Simulations of proteins have experienced a significant advance in complexity
[59], from early reports of two-dimensional Monte Carlo Method folding
predictions of small polypeptides [63], to fully 3D atomistic molecular dynamics
simulations of a ribosome [64], the cellular component that reads RNA and
synthesizes proteins.
2.1.1 Classical Molecular Dynamics
In essence, molecular dynamics simulates systems in a thermodynamical
ensemble by solving a set of second order differential equations describing the
relative motion of particles in a system. For a pair interaction between atom i and
j, the equation of motion is given by Newtons law
dz
dtz
_
-
dU(r 1
d
)
d.
2.1
i,j=1..N,
drij
where mi is the mass of atom i, rij the distance between the atoms, U the
potential, and N the number of particles in the system. This equation is solved by
31
update schemes, e.g. the Verlet scheme using a timestep At. The motion (atomic
coordinates and velocity) is recorded and all other quantities are derived from it.
The key to molecular dynamics simulations is the determination of the potential
U(r). This quantity is determined from a prescribed force field. While reactive
forces fields such as ReaxFF are capable of capturing covalent bond chemistry,
molecular dynamics using non-reactive force fields such as CHARMM [65] can
simulate noncovalent interactions (e.g., electrostatics (hydrogen bonding), and
van der Waals forces) involved in secondary structure changes.
Since molecular dynamics is directly linked to statistical physics, state variables
in the simulated system can be set or calculated. For a thermodynamics ensemble
it is sufficient to specify three state variables. These variables can be for example
total energy E, number of particles N, volume V, temperature T, pressure p,
chemical potential M, enthalpy H. Simulations of proteins without chemical
reactions usually use the NVT (canonical), NPT (isothermal-isobaric) or NVE
(microcanonical) ensemble. MD software packages such as CHARMM, NAMD,
LAMMPS, or GROMACS are equipped with algorithms to calculate and control
these state variables.
2.1.2
Quantities determined from Molecular Dynamics
The statistical quantities that can be found from a molecular dynamics trajectory
are [66]:
*
Average potential energy U of a system with N particles and M
configurations
M
Ui
U = (U) =
2.2
j=1
32
Average kinetic energy K of a system with N particles and M
configurations
M
N
Imi
K = (K) =
2.3
-
"
j=1 -i=1
" Temperature T
2
T = yNk; (K)
2.4
" Pressure p
N
*
(rij
-
p = NkBT
1
dU
drj
2.5
Mean square displacement
N
(Ar 2 ) =
2.6
(r (t) - ri(to))2
i=1
Velocity autocorrelation function
(v(to)v(t)) =
111
i=1
*
2.7
vi(t)]
vitt.)
-
*
j=1
Virial Stress
(
- i7g
1
6
k1
N
+ 1
sil
mivikv,1 0 2
N
rirj dU(r)
r
=i,j,ii
33
dr
2.8
r rij
2.1.3 Steered Molecular Dynamics
Steered molecular dynamics (SMD), complements experimental Atomic Force
Microscopy (AFM) by using a virtual spring moving at a constant velocity or
maintaining a constant force to deform the protein [67]. SMD is a nonequilibrium simulation technique to simulate unfolding. Changes in secondary
structure, such as the strain-induced transitions to p-strands [68], and the rupture
of non-covalent interactions are especially important in solvated single-molecule
studies. In these studies energetic and chemical pathways are tracked while
whole or partial domains of proteins are unfolded. This method often uncovers
intermediate states during the unfolding process [69].
2.1.4 Molecule Shape Calculation
A common way to measure the shape of a molecule is the radius of gyration.
This second order tensor is calculated as the (mass or charge weighted) root
mean square distance of all the atoms from the center of mass of a molecule. It is
used here to quantify the size of the ensemble of atoms in the molecular
structure. The volume of the equivalent ellipsoid described by the gyration
tensor is V = (4/3)7rAxly, where Ai is the eigenvalue of the gyration tensor
associated with direction i. Usually, the tensor is calculated with respect to the
principal components of the system. If one of the principal components coincides
with the axis direction then the associated eigenvalue is the molecule size in that
direction. By comparing the change of radius for the same structure in two
different environmental conditions one can calculate the shape and volume
change of the structure. Alternatively, the average end-to-end distance of the
chains gives an estimate of the molecule size in axial direction.
34
2.1.5 Replica Exchange Molecular Dynamics
Replica exchange molecular dynamics (REMD) is a parallel tempering method
for improved conformational search introduced by Sugita et al. in 1999 [70].
Instead of performing a random walk in the multicanonical space, the system
performs a random walk in the temperature space. This is achieved by
simulating
NREMD
replicas of the same system at a range of initial temperatures
(usually 300K - 600K) and then performing Monte Carlo like acceptance checks
to exchange temperatures. This allows the system to escape from local energy
minima. Usually, the analysis is focused on the trajectory of the sample at 300 K
(most force fields are trained for this temperature) and the trajectories of the
higher temperatures are neglected after the simulation. They serve only to
overcome folding energy barriers. The optimum number of replicas (in a
canonical ensemble) is dependent on temperature range [Tmmi, Tmax] and system
size (number of atoms N) [71]
NREMD,Opt =
1 + 1.789 NV In
2.9
(rx
Usually, REMD is followed by an explicitly solvated equilibrium simulation and
can thus be run in implicit solvent. This reduces simulation time and the number
of required replica significantly. The output of REMD ois The analysis of the
clusters is performed using the MMTSB Toolset [72]. The REMD protocol is a
standard
tool of most molecular dynamics
software packages, such as
GROMACS and NAMD [65].
2.1.6 Entropy calculation
It is possible to estimate the total as well as relative entropy (or entropy change)
from the trajectory of a molecular dynamics simulation. The two most common
approaches are the quasi-harmonic method and Schlitter's method [73, 74]. Both
35
rely on the determination of the covariance tensor C of atomic fluctuations
(similar to a normal mode analysis) [75]. The components matrix of C is singular
in most cases. Multiplying C with the system mass tensor M yields a symmetric
semidefinite tensor that can be diagonalized.
The quasiharmonic method approximates the fluctuations using a Gaussian
probability distribution. First, the eigenfrequencies of the system are determined
by solving the eigenvalue problem
det M1/2 CM1
2
-
2.10
0.
kBT
These frequencies are then used to determine the entropy by calculating it as a
sum of harmonic oscillators
SQH
=
R
1
hwi/kBT In(hwi/kBT-1
-
e(hwi/kBT)
-_n(1
2.11
Schlitter showed that an estimate of the maximum system entropy is given by
Ssch= 0.5 R ln det 1+ (
2
)M1/2
C M1/2].
2.12
Generally, Ssch > SQH. Both quantities can be determined by finding and
diagonalizing the covariance matrix of the system fluctuations (after least square
fitting the trajectory to the average structure to remove rigid motion of the
molecule).
For N atoms, the covariance matrix has the shape 3N x 3N and hence 3N
eigenvalues and eigenvectors. The eigenvalues are decaying fast and for the
normal mode analysis only a fraction of them are contributing to the entropy.
This observation can speed up computation significantly when diagonalizing the
36
mass weighted covariance matrix and evaluating the entropy contributions of
each mode in equation 2.11.
2.1.7 Free Energy of Solvation
The free energy of solvation is the energy released or input when putting a solute
in solvent, e.g. silk in water. It can be computationally estimated by switching off
the interaction of the solute with the solvent and leaving only intra-molecular
interactions. The problem is that the free energy difference has to be calculated
from Monte Carlo probabilities of the transition from the solvated state to the
unsolvated state. In MD such events are too rare to be sampled within a
reasonable runtime. In order to estimate the free energy of solvation one can use
the so called A-method using the Bennett Acceptance Ratio (BAR) [76]. The idea
is to slowly decouple the solute from the solvent, using a parameter A e [0,1]. The
difference in free energy of each A-step is calculated by the Monte Carlo
transition probability P between state A and state B
PA-B
= ex
2.13
B-EA
where E = K + U is the total system energy. If the increments in A are small, the
transition energies are also small enough such that some of the phase space is
shared between the 'adjacent' simulations. Therefore, one can calculate the
Monte Carlo probabilities and the free energy difference between each state. For
expediency reasons it is common to decouple Coulombic and van-der-Waals
interactions simultaneously. In GROMACS, soft-core interactions prevent the
overlap of charges (meaning, although solute and solvent do not interact, they
cannot occupy the same space in the simulation box) without disturbing the freeenergy balance. Minimum increments of AA = 0.05 and a simulation time of 0.5
ns with a timestep of 0.5 fs and no holonomic constraints must be used. The cutoff scheme has to be changed to group cut-off, since GROMACS does not
37
support free energy calculations with the Verlet cut-off scheme. For very large
molecules with multiple chains, the solvent-solute decoupling does not work. In
this case, the free energy of solvation can be estimated directly from the solvent
accessible surface area of the molecule's residues [76, 77]. The surface accessible
area is calculated using the double cubic lattice method [78], and the relation to
the free energy of solvation is (18
2 cal/mol/A 2 ) [77].
2.1.8 Simulated Raman and Infrared Spectrum
The following introduction to dipoles, dipole moments, and polarization is
inspired by the excellent explanations in Reference [79]. In molecular dynamics
force fields, each atom is assigned a partial charge, reflecting the unequal
distribution of electrons within the molecule [80]. The phenomenon that strong
electronegative atoms pull electrons from less electronegative atoms is called
polarity and the resulting charge separation forms a so called dipole. The dipole
moment of a molecule is determined by the magnitudes and the distances
between the dipoles. For example, peptide bonds in the backbone of a protein
have large dipole moments. A molecule with a permanent dipole moment
creates a surrounding electrostatic field which induces a dipole moment in other
molecules located nearby. This effect is called polarization. Polarizability refers
to the ease with which electrons are shifted by this external electronic field.
Molecules that lack electrons are easier polarizable than molecules that have
many electrons.
When molecules vibrate it causes fluctuating dipoles. Hence, the dipole moment
fluctuates
also.
This coupling lets the
oscillation
of nearby
molecules
synchronize. The strength of the coupled fluctuation (dispersive interaction) is
related to the polarizability of the two molecules or atoms. The vibrations of
dipoles are experimentally directly determined by infrared (IR) spectroscopy. In
a material, certain frequency ranges are absorbed when shining electromagnetic
38
waves on it. Absorbing infrared laser light leads to the oscillation of molecule
bonds and are detectable in the reflected (not absorbed) spectrum. Each absorbed
frequency is characteristic for a certain type of bond, such that infrared
spectroscopy (IR) can detect material structures. A molecule is IR active only
when the molecule has a changeable or inducible dipole moment. A molecule is
IR inactive when the vibrations are symmetric to the center of the dipole. IR
spectra range from 4000 cm~ 1 to 400 cm-'. Each molecule has a typical pattern in
the spectrum, but at 1500 cm~' and below the origin of the spectrum cannot be
determined any more (fingerprint region).
For
solvated
spectroscopy
systems, IR spectroscopy
offers
the
possibility
to
cannot
be
investigate
used.
Here,
Raman
the crystallinity
and
composition of the material. This is especially important for biomaterials. Raman
spectroscopy requires the molecule to exhibit changes in polarizability during its
oscillations. A laser is shined at the material and the dispersed spectrum contains
additional frequencies. This is due to the material's interaction with the light by
transferring energy from or to the light. The additional lines in the spectrum are
called Stokes-Lines, and the shift in the spectrum is called Raman spectrum. The
quantity measured is therefore the fluctuation of the polarizability tensor. Since
the selection criteria for IR and Raman spectroscopy are different, they work as
complementary methods to characterize materials.
The IR spectrum can be found directly from molecular dynamics simulations.
Given the distribution of partial charges and the trajectory of all atoms, the
vibrations of the dipoles can be determined. The Fourier transform of those
vibrations generates the trajectory. This methodology is implemented as a
subroutine in VMD [81]. The condition for accurate results is a high output
frequency of atomic coordinates (to capture high frequency vibrations) and an
accurate partial charge distribution.
39
The Raman spectrum cannot directly be found from classical molecular
dynamics trajectories, since the partial charges are static on the atoms and
polarizability is not modeled. Certain core-shell models take the polarizability
into account and would allow the calculation of the Raman spectrum directly.
For large protein molecules, like silk, the CHARMM force field is preferred
which has fixed partial charges. An alternative route to the Raman spectrum is
via the vibrational density of states (VDOS). The VDOS is also called phonon
density of states or power spectrum. Under the Born-Oppenheimer assumption,
the fluctuations of the polarizability depend linearly on the atomic displacements
[82]. The VDOS is the Fourier transform of all molecule vibrations and its
measured intensities g (w) are related to the Raman intensity
IRaman(()
gR( )[n(o ) )
(0
'Raman(w)
by
2.14
+
where gR (W) is the convolution of the VDOS with the light-to-excitation coupling
factor C(w):
g R (_')
=
f C(w
C(w)g(w).
-
2.15
C(w) is a priori unknown and can be determined with an independent probe.
n(w) is the population of the vibrational mode at frequency w
n(w) = (ehw/kBT
-
2.16
)1 .
40
The intensities of the VDOS g (w) are found through the Fourier transform of the
velocity autocorrelation function [83]
g()=
*(v(t
_"o,
i2wt
0 )v(t))
(v(t0 )v(t0 ))
2.17
dt.
2.1.9 Data Analysis
Molecular dynamics simulations can produce large quantities of data when
storing atom positions, velocities, energies, forces, stresses (pressure), and system
temperature. The output frequency depends on the analysis type. For example,
an equilibrium simulation requires a less frequent output than the calculation of
vibrational spectra.
While there is a range of data analysis toolsets available, such as GROMACS
scripts, MMTSB [72], and VMD [81], most analyses have to be performed by
scripts specific to the task. An efficient programming language for processing
large data sets is Python. In this thesis, most analyses have been performed using
self-coded Python and MATLAB scripts. Visualization of molecules is performed
with VMD and data plotting with MATLAB and Origin.
2.2 Analytical approaches to materials failure/ fracture
2.2.1 Linear elastic fracture mechanics
One of the main interests in materials science is the study of flaw influences on
materials behavior and properties. The quantification of crack propagation is
based on Griffith's and Irwin's work from the early 19th century [84]. It assumed
that the energy needed to propagate a crack, the critical strain energy release rate
41
Gc, equals the surface energy of the two newly created surfaces along the crack
path
= Gc = _c-2 = 2ys ,2.18
9a
E
where Kc is the fracture toughness (mode III, III or mixed mode, a material
constant), E' the equivalent Young's modulus, and ys can be determined from
surface chemistry. Kc can be determined experimentally or analytically for
specific boundary conditions [85].
In linear elastic fracture mechanics analyses the stress intensity K scales with
aoV\F(), where uo is the stress applied on the specimen and F((a,Geometry))
a shape and boundary conditions dependent function. a is the crack length.
Linear elastic fracture mechanics predicts that the stress singularity at the crack
tip
scales
with
1/,fr
and
thus
the
yield
(also
known
as
process/plastic/damage/decohesion) zone 10 is given by
10 = F( ) 2 a
2.19
.
For the classical Griffith crack problem this simplifies to
)
1=
a
2.2.2
Polymer fracture mechanics
2.20
The fracture analysis of polymers is commonly addressed from two points of
view: a statistical, micromechanical (e.g., using Bell theory or atomic potentials)
[86, 87] or a continuum mechanical
(e.g., using phase field theory or
linear/nonlinear fracture mechanics based on Griffith's work) [88-91]. Both
42
approaches are well explored, but are yet to be unified in a comprehensive
framework.
In the nonlinear case including plasticity and irreversible damage before fracture,
the Griffith equation can be rewritten as [92]
Gc = Ys +
f
1 EijklEiiEkl dy,
2.21
where oui is the stress tensor, Eij the strain tensor,
Eijkl
the elastic tensor, and 10
the yield zone size in direction y.
Polymer and rubber materials are often modelled as homogeneous, nonlinear
elastic materials, where the strain energy release rate is given by the J-integral
[93]
W nk - ti
j = GC=
where W =
ui
uijdEj =
2.22
dr
E'
EijklEidcij
=
EijklEijEkl
is the internal strain energy
density, t = n - a the surface traction und u the displacement. In this convention,
the crack is oriented in the x1 direction.
To account for heterogeneity, Eshelby's expression can be applied [94-96]. For
heterogeneous, nonlinear elastic materials the strain energy release rate is given
by [97]
=FWnk -t
where
(Wk)expl
)GcdI-
(Wk)xdfl
2.23
is the derivative of the strain energy function in the
nonhomegenous material.
43
For the elastic solution, the size of the decohesion or process zone lo is given by
the Dugdale-Barenblatt yield-strip model, see Figure 8,
7r
Gc
8
cr2
10 = -E
2.24
where Gc is the critical energy release rate, a material parameter that quantifies
the amount of energy needed to drive a crack through a surface, E the elastic
modulus of the bonds, and
Ut
the theoretical strength of a chemical bond [98,
99]. This solution is often applied to the fracture of ductile materials.
a
. ..............
J-dominated
zone
Figure 8 1 Stress variation in the cohesive zone according to the Dugdale-Barenblatt model. Adapted from
Reference [100].
In view of Figure 8, for a nonlinear material, Gc can be generalized to [92].
Gc=
2.25
oa(r)dr,
where ro is the equilibrium lattice spacing of a cubic lattice on which the
molecules are arranged.
44
3 Creation of Heterogeneity - Silk Assembly
The research and review presented in this chapter will be published in:
*
T. Giesa, C.C. Perry, M.
J.
Buehler, Secondary Structure Transition and
Critical Stress during the Assembly of Spider Silk Fibers. In submission, 2015.
In this chapter, the following questions regarding silk assembly are answered:
" How is the heterogeneity of silk fibers created on the smallest scale?
" What is the importance of shear in the assembly process of silk fibers?
" What is the smallest molecule size that might give rise to a 'silk-like'
structure?
" What shear stresses are required for the secondary structure transition
from helical to sheet state?
" Which components/ parts of the silk sequence are crucial for the
secondary structure transition?
" How can these results be used towards the design of artificial spinning
devices?
Research strategy:
A model of the silk spidroin (solubilized silk before spinning) in equilibrium is
developed and the assembly process of Nephila Clavipes silk sequences is
computationally investigated. Using replica exchange molecular dynamics for a
total of 1 microsecond, the equilibrium structure of the spidroin is determined.
45
Using steered molecular dynamics at natural pulling speeds a shear flow is
modelled and the secondary structure transitions as well as shear stresses in the
silk protein chains are determined. Intra-chain interactions are studied for
structures having two, four or six poly-Alanine repeats. Additional inter-chain
interactions are studied for structures built from structures having four polyAlanine regions in a parallel and antiparallel configuration and compared to the
effect of a single molecule containing the same number of poly-Alanine regions.
After shearing, the assembled chains of different lengths are equilibrated to test
the stability.
3.1
Background
There is little doubt about the importance of shear stress facilitating secondary
structure transitions during the assembly process [101]. In fact, it has been
observed that without shear stress, silk fibers do not form, but maintain globular
shapes [102]. Surprisingly, given the current standing of the field, no one has
performed a detailed investigation of shear stress in the assembly mechanism.
The soluble spinning dopes stored in the glands of the spider is in a form that
enables spinning when the need arises. The material present in the spun fibers is
however, fundamentally different from the dope. While first attempts to
synthesize silk fibers have been successful, and industry-scale production of
recombinant silk has been made possible, the mechanical properties of the spun
fibers either do not currently compare with natural fibers or the assembly was
performed under non-ambient conditions
[103, 104].
Furthermore, many
synthesized fibers contain a substantial amount of regenerated silk, i.e. the
spinning dope originates from natural spider silk [104]. Using genetically
giLneered~ seqfILunc
prtiLLs a way
U ItUUc
11i1iatinLs1L!L UIL 101H suFpLy I11Im
spiders, but yields weaker and more brittle fibers [105]. The inferior quality of
46
the engineered fibers is mainly related to the selection of assembly process
parameters in industrial spinning devices, different rheological behavior and
molecular weights [105]. Even though much is understood about the molecular
structure of silk worm and spider silks, there is still ongoing debate about the
molecular structure [106].
3.1.1
Fiber formation- spinning from solution
Even though much is understood about the molecular structure of silk worm and
spider silks, there is still ongoing debate about the molecular structure [106]. The
spidroin (Figure 9 left) is water soluble while stored in the spider's abdomen, but
under certain conditions assembles into an insoluble fiber.
The dragline silk
spidroin consists mainly of two proteins, major ampullate spidroin 1 (MaSpi,
studied here) and major ampullate spidroin 1 (MaSp2) [107]. Spider dragline silk
after spinning could be described as comprising crystalline P-sheet crystals
embedded in an amorphous or poorly structured matrix (Figure 9 right). The
sequence is highly repetitive, where the number of repetitions a is in the order of
100's [35].
Recent studies using Raman microspectrophotometry have provided information
on all the distinct spidroins present in the glands of Nephila Clavipes, an orb
weaving spider that can be found in the south-east of the United States [108, 109].
These studies have shown that there are distinct types of spidroins, either totally
disordered or globular-like and natively folded with a high content of a-helices
[108]. Major Ampullate (MaSp dragline) and Minor Ampullate spinning dopes
were suggested to have an intermediate structure that contains some helices. The
presence of a-helices and left handed 3 10 -helices were both identified in MaSP
silks, while none of the spinning dopes were found to possess silk in P-sheet
conformation [109]. Interestingly, analysis of the silk sequences using prediction
software optimized for unfolded segments
47
(PONDR) suggested that all
sequences should be unfolded [108]. Likewise, secondary structure predictions
using the Porter algorithm predicted the structure of MaSP silk to comprise loops
and turns with helix being predicted for the (A)n region [108]. The MaSP
sequences were also shown to have no natural propensity for aggregation to give
-amyloid structures, clearly of importance to the use of silks in biomedical
applications.
Spinning Duct
Spinning Dope
FibrillFiber
-water
-
+
Ions
Shear
Figure 9 Molecular model of the silk fiber assembly process. Silk is processed from spidroin to a solid fiber
in the spinning duct under ambient conditions. The dragline silk spidroin consists mainly of MaSpl (studied
here) and MaSp2. The sequence is highly repetitive, a ~ 0(100). Shear stresses at the wall together with the
removal of water from the protein lead to the formation of a nano-composite having an aligned, #-sheet rich
crystalline phase. A change of ionic conditions during the spinning process is believed to lead to a
conformational change in the terminal regions of the silk protein.
The process for silk assembly and spinning into fibers is complex and there are a
variety of theories for the work-flow of the natural assembly process [110]. Shear
stresses at the wall together with the removal of water from the protein lead to
the formation of a nano-composite having an aligned P-sheet rich crystalline
phase. Spinning conditions including humidity, temperature, reeling speed and
ionic conditions are believed to control the assembly of silks. For that to be
possible, the protein needs to be protected from premature assembly which
would clog the spider's spinneret or the spinning device. Premature self48
assembly poses one of the issues involved with the synthetic production of silk
fibers. The importance of laminar flow in the spinning duct has been emphasized
with two theories being proposed by which the silk spidroin transitions to the
fiber form [111].
Firstly, the micelle theory states that in the spider's abdomen the silk dope is
stored in micelle form, where the hydrophobic terminal regions of the sequence
shield the interior a-helical structure from water [112]. This approach assumes a
low concentration of the spinning dope. During the spinning process, the applied
shear induces the formation of P-sheets, while a change in pKA and ionic
conditions mainly affects the structure of the terminal region [113]. The Cterminal is believed to shield the protein from premature assembly [108]. Due to
the pH-sensitivity of the terminal, the conformation changes in the spinning
duct, where a pH drop is induced through ion pumps [112]. Simulation studies
have confirmed that the terminal domains are critical in the initiation of
multimerization [114]. Although their sequence is highly preserved between
species, the N-terminal region is not present in all MaSpi silks [107]. Secondly,
the liquid crystal theory for spider and silkworm silk states that silk proteins are
stored in a nematic liquid-crystalline phase [41]. During assembly in the spinning
duct, the proteins organize in bilayered disks that elongate along the fiber axis
under shear flow. Under these conditions, random-coil and polyproline-II helixlike conformations transition to P-sheet-rich structures. This approach assumes a
rather high concentration of the spinning dope (-50%) [41].
Experimental studies to mimic the spinning process using engineered and
recombinantly produced spider dragline silk proteins from Araneus Diadematus
in microfluidic devices have confirmed that shear flow is essential for fiber
formation [115]. This experimental study generated results supporting the
micelle hypothesis of Jin and Kaplan [113]. The experiments were performed at
low-mid range concentrations and did not require liquid crystalline behavior for
49
fiber formation. Rather, high elongational flow rates of about 1000 s-1 in an in
vitro microfluidic device were essential, though the shear forces were not
measured. The high shear rates used were found to lead to significant increases
in viscosity and this was used as a marker for fiber formation. Also, an increase
in orientation of the crystallites in the fiber, shear thinning and an increase in
force along the spinning duct has been observed [41]. Higher draw rates also
lead to smaller crystals which increase stiffness and fracture resistance [49, 1001.
3.1.2
Silk structure after spinning
Once the MaSP silk has been spun there is experimental evidence that all
residual native-like structures are absent [116]. There is considerable information
about silk materials as formed by spiders (and silk worms) where numerous
experimental techniques including NMR (solution and solid state), X-ray
crystallography and Infrared and Raman spectroscopy have been used to study
the fibrous structures. As might be expected, there is more known about the
crystalline regions than the disordered regions owing to a paucity of methods to
study amorphous or poorly ordered materials. As examples of what is known for
N. Clavipes drag-line silk, X-ray diffraction studies have shown that the
fundamental crystalline unit has an orthogonal unit cell with the average size of
crystallites calculated to be ca. 2 x 5 x 7 nm [45] and the inter-crystalline length
along the fiber axis measured as 13 - 18nm [56]. The crystalline phase arises from
the organization of poly-Alanine segments of the silk protein sequence into Psheet structures although the precise P-sheet content reported varies according to
the measurement technique used. Analysis by Raman microspectroscopy
suggests levels of 30 - 40%, [117, 118], as opposed to about 20% identified by
XRD [119]. Computer simulations of the crystalline components of silk suggest
that the poly-Alanine sections line up anti-parallel in the H-bonding direction
50
with parallel stacking in the side-chain direction. This arrangement also leads to
stable P-sheets [48, 120].
The nanoconfined crystals are responsible for the high strength of silk materials,
while the amorphous part contributes to the elasticity of the material [44, 47,
121]. The non-crystalline regions are alternately described as amorphous, poorly
oriented or randomly coiled. They are not very well understood, although
analysis of silk fibers by NMR has provided significant detail on the likely
structures present in the less ordered domains [122, 123]. The presence of 3 1ohelical structures with GLGXQG motifs forming beta turns was proposed in the
late 90's [122, 124]. Later studies using
13
C labeling of materials and multipulse
NMR to measure backbone dihedral angles of Alanine and Glycine within silks
suggest that these amino acids are 'ordered'
on the NMR timescale of
microseconds - with poly-Alanine and GGX motifs probably located in
microcrystalline
domains and the remainder of the silk in a 3 10 -helix
arrangement [123]. Other structures including P-turn, (-spiral and helices have
been suggested with different views as to the structure adopted by GGX; both
less ordered helices/ distorted P-sheets have been proposed [109, 118, 123].
More recent studies have suggested that there are actually three distinct structure
types in silk: crystalline P-sheet, weakly ordered (-sheet, and amorphous or
disordered structures. The presence of the weakly ordered phase has been
suggested based on H/D exchange and NMR/ IR analysis and is described
variously as weakly oriented P-sheet [125, 126], or as oriented amorphous
regions [127, 128]. Molecular dynamics simulation studies of model silk
constructs built from bundles of silk fragments has shown that the density of Hbonds is lower in amorphous regions as compared to regions containing P-sheet
crystallites [48].
51
The observation that the primary sequence largely dictates which specific amino
acids and amino acid motifs are associated with particular structures is
particularly interesting in light of a long standing hypothesis from the Lewis
group which states that there are no redundant components of the spider silk
sequence [129]. They state that from a protein biochemistry standpoint, the
highly repetitive nature of the proteins makes it highly unlikely for any random
structure to be generated.
3.1.3 Simulation Setup
3.1.3.1
MaSpi Silk Model
The wildtype Nephila Clavipes silk MaSP1 sequence:
AAAAAAGGAGQGGYGGLGSQGAGRGGLGGQGAG
(accession number UniProt KB P19837) is used to study the assembly process.
Structures containing the 27 amino acids (Gly-rich semi-amorphous repeat, then
the poly-Alanine region followed by two, four, or six multiples of the whole
sequence to give the requisite number of poly-Alanine regions surrounded by
'amorphous/ less well ordered' material) are used as models, see Figure 9. The
structures differ from those in the studies by Keten and Buehler [48] and Bratzel
and Buehler [130] where bundles of polypeptide chains, each comprising a single
poly-Alanine region with an amorphous region at each end were studied by
REMD to replicate the P-sheet crystal dimensions and explore the length of the
poly-Alanine region to obtain maximum theoretical strength and toughness.
Multiple copies of the complete silk MaSP1 sequence are present within an
individual structure. Structures are initially built using the Biopolymer module
in Tripos Sybyl. Structures in random conformation with neutral ends are
minimized in vacuum before being exported for replica exchange calculation
(REMD) [70].
52
3.1.3.2
Replica Exchange MolecularDynamics
The REMD method is used to identify molecular structures. 48 replicas (see
equation 2.9) of strands with initial configuration and length schematically
shown in Figure 10a are simulated at temperatures between 300 and 800 K to
ensure coverage of conformational space. The REMD simulations are carried out
using the CHARMM force field [65] implemented in NAMD [131], using the
Generalized Born implicit solvent model (a-cutoff 12.0, ion concentration 0.3).
Solvent friction is added via a Langevin friction term (10 ps'). A cutoff of 15 A is
used for long range interactions and a timestep of 2 fs. REMD is run for 20 ns
/sample (total of 960 ns) and the temperatures exchanged every 0.2 ps.
Statistical analysis is performed using the MMTSB toolbox, [72] with a k-means
clustering algorithm (cluster distance 2
A).
Representative final ensemble
structures are chosen from the lowest temperature replica (300 K). The higher
temperatures are used for fast conformational search and overcoming kinetic
trapping in the REMD scheme. The simulations are run at Harvard's Odissey
cluster with 64-256 cores.
a
REMD + MD
a= 3
a =1
-
ips
b
a =5
SMD - 1Ons (0.5 m/s)
Inter-chain
Intra-chain
C
MD 50ns
Single-chain
Layer
GGQGGAGQGGYGGLGSQGAGRGGLGGQ
(GAGAAAAAAGGAGQGGYGGLGSQGAGRGGL)a
Figure 10 1 (a) Model of the silk spidroin in equilibrium. Using Replica Exchange Molecular Dynamics for a
total of 1 microsecond the equilibrium structure of the protein is determined for different chain lengths
(a = 1,3,5), here denoted as poly-Alanine regions (blue) and remainder of the intervening sequence (red). (b)
Model of the silk assembly process. Using Steered Molecular Dynamics at natural pulling speeds a shear
flow is modeled and the secondary structure transitions as well as shear stresses in the silk protein chains
are determined. Intra- as well as inter-chain interactions are investigated. (c) Model of the final fiber
structure. After shearing the assembled structure is simulated in solvent and vacuum to test the stability of
the structure as a single-chain or as layered structure, i.e. multiple stacked sheets after shear.
53
The center of the largest cluster, meaning the structure with minimum RMSD
(root mean squared deviation), is exported for analysis in explicit solvent. To
obtain more realistic molecular conformation and secondary and tertiary protein
structure, the structure is equilibrated for 20 ns using GROMACS (CHARMM27
forcefield) in a charge-neutralizing periodic waterbox of TIP3P containing 150
mM sodium chloride. To prevent image interactions, the waterbox pads the
protein by at least 10
A.
Equilibration is performed with Langevin dynamics in
an isothermal-isobaric ensemble (NPT: 300K, ibar) using the Nose-Hoover
thermostat and the Parrinello-Rahman barostat. Particle Mesh Ewald (PME)
electrostatics with 1.4 nm cut-off is used to more accurately capture solvent
interactions [132]. It is possible to use a 2 fs timestep because of holonomic
constraints (LINCS algorithm). The secondary structure of each structure is
determined using DSSP toolset and the STRIDE algorithm in VMD [81, 133].
3.1.3.3
Shear Flow and Steered MolecularDynamics
In order to simulate shear boundary conditions, SMD simulations are performed,
see chapter 2.1.3 [69]. Soft springs (stiffness k) are fixed to the symmetry points
of the equilibrated structures, as shown in Figure 11. The springs are set to
provide stiffness only in the pulling direction so that the structure is able to relax
in all other directions and hence no unnecessary constraints are enforced. An
isothermal ensemble in an explicitly solvated periodic waterbox is set up.
Isobaric constraints are enforced in the two directions that are perpendicular to
the pulling direction. The box size in pulling direction is constant and periodic,
but significantly larger than the molecule. A set of pulling speeds (0.5 - 5 m/s)
and spring stiffness's (100-2000 kcal/mol/A ) is used to probe the robustness of
the results.
54
(I)
(ii)
De
Figure 11 | Two different boundary conditions (i) and (ii), both shear, are tested to investigate the trajectory
of secondary structure and shear stress. The part of the sequence colored in blue is the Alanine rich region
and the part of the sequence colored in red is the Glycine-rich region. The pulling force is determined with
the steered molecular dynamics (SMD) algorithm.
Two shear boundary conditions, Figure 11 (i) and (ii), are tested to investigate the
trajectory of secondary structure and shear stress. The part of the sequence
colored in red is the Glycine-rich region and the part of the sequence colored in
blue is the Alanine-rich region. The symmetry positions of the sequence are held
by soft springs that acted only in the pulling direction to ensure that the
transition states could be captured during the simulation. The 'x' in Figure 11 (ii)
marks a fix at the alpha-carbon of the terminal amino acid. The pulling force is
determined and the diameter calculated at all points of the trajectory by the inplane radius of gyration of the structure and determining an equivalent molecule
diameter Deq.
Figure 12a shows the trajectory of secondary structure of the equilibrated
structures during the pulling experiment. The graph shown is one out of four
tests for a = 3 (with boundary condition (i)). All following graphs show averages
over the results of the two shear boundary conditions. The pulling speed is set to
0.5 m/s, well within the range of experimental drawing speeds, leading to a
simulation time of 10 ns. Higher pulling speeds have no significant influence on
the results (see Figure 13). This is in agreement with NMR experimental results
that state that the reeling speed has little effect on the secondary structure of the
fiber [134]. Similarly, the spring constant used in the SMD experiment has little
influence on the results. The average f-sheet content for each structure is
55
determined by averaging the P-sheet content for 1 ns around the maximum
content as indicated in Figure 12a. The transition shear stress, an example shown
in Figure 12b, is averaged in the same region as that taken to assess the P-sheet
content. In this case, after approximately 8 ns the stress exceeds the strength of
the material and the simulation results are valid only before this point. In all
cases, the structure transition happens prior to reaching this limit. There is most
likely an influence of the specific pulling residue positions on the behavior of the
molecule. It is also highly likely that the specific residue involved in particular
structures may be dependent on how the simulation is prepared. However, due
to variety of different chain lengths and simulation setups (all simulation are
repeated with different initial conditions) with different boundary conditions
and long equilibration times, general insights into the transition mechanism can
still be generated.
b
a
100
2500
max. P-sheet
-a-Helix
-P-sheet4
-Feq
2000
80 -Co
_TUM
rDeq
1500
60~
500
200
0
2
6
4
Time (ns
8
0
10
2
6
4
Time (ns)
8
10
Figure 12 1 Secondary structure transition and shear stress during the assembly of silk. (a) Secondary
structure trajectory during the pulling simulation in explicit solvent. The graph shown is one out of four
tests for a = 3 (with boundary condition (i)). Starting from the spidroin, a high a-helical and coil content and
no P-sheets can be found. During the shear induced assembly all helices and other structures transition into
P-sheets or are destroyed in agreement with experimental observations of the processes in the spinning
duct. The P-sheet content after pulling for each structure is determined by averaging the P-sheet content for
1 ns around the maximum content as indicated in the figure. (b) Shear stress associated with the secondary
structure transition. The transition shear stress is averaged in the same region as that taken to assess the Psheet content. In all cases, the structure transition happens prior to reaching the strength limit of the
material.
56
3.1.3.4
Post Shear Equilibration and Stability
After exposing the structures to shear, a representative structure with a high
amount of P-sheet (in the domain, that has not been pulled) is further
equilibrated for 50 ns both in vacuum and in explicit (TiP3P) water containing
salt at 150 mM to measure the stability of the secondary structures induced by
shearing. In vacuum, an isothermal-isochoric ensemble is used with cut-off for
Coulombic and van-der-Waals interactions (3 nm), velocity-rescale thermostat
and dispersion correction (accounting for the cut-off van-der-Waals scheme). The
secondary structure is tracked using the DSSP algorithm.
In addition to the different length spidroins, stacked sandwich structures are
analyzed for stability. 2-layer and 3-layer sandwiches are formed in parallel and
anti-parallel stacking from chains with a = 3 taken from the result of the SMD
simulation (within the barred area in Figure 12). These sandwich structures are
then equilibrated in water with 150mM NaCl for 50 ns.
3.1.3.5
Transition Probabilities
In order to obtain a better understanding of the secondary structure transitions
from helix/turn to sheet, the probability of being either in a helical/turn
(spidroin) or in a sheet structure (after pulling and after further equilibration) is
calculated residue by residue. The probability for the initial equilibration,
-
defined as the percentage of frames each residue is part of a a-helix or turn/310
helix divided by the total number of frames, is calculated from the last 10 ns (out
of 30 ns) of the equilibration trajectory. Similarly, during the pulling simulation
the probability is calculated from the 1 ns that also defined the P-sheet content,
see above. The probability from the equilibration after pulling is calculated from
the last 10 ns (out of 50 ns) of the simulation. The joint probability for each
residue is calculated as the product of the three probabilities. This allows us to
track exactly which amino acid residues and which geometric relations are key to
57
the transition. The relative location of the residues appearing in all three
structures is compared using the Sybyl Tripos Biopolymer module and VMD.
3.2
Size Dependence of Structural Transition
The spider silk dope is stored in the abdomen of the spider in globular form to
prevent premature assembly and clogging of the spinning duct. In the
simulation, the general form of the simulated protein structure is largely
independent of the size of the molecule (left hand column, Table 1). The spidroin
remains unassembled and predominantly contains helical shapes (a-helices,
turns and 3 10 -helices) as observed in the deconvolution of Raman spectra [109,
135]. Similar evidence has been found for S. Cynthia Ricini silk, where the polyAlanine regions form a helical structure when dried as a film but P-sheet in fibers
[136]. The helices towards the beginning of the sequence are arranged at an angle
to one another typically of 60 degrees.
58
is stored in the
Table 1 1 Model structures of the stages during the assembly process. The spider silk dope
peptide/
simulated
the
of
abdomen of the spider in globular form. In the simulation, the general form
remains
It
column).
hand
(left
molecule
the
of
protein structure is largely independent of the size
a
column)
(second
process
shearing
the
During
turns.
and
helices
unassembled and predominantly contains
in
structure
the
of
equilibration
Subsequently,
structures.
1-sheet
into
transitions
structure
large part of the
column
vacuum or explicit water in the presence of ions, the silk relaxes again (third and fourth
In
fl-sheets.
their
retain
and
stable
are
respectively). In vacuum, irrespective of simulation size, all structures
original
their
to
return
3)
=
a
1,
=
a
stretches;
poly-Alanine
four
water, the smaller silk structures (two and
a = 5)
largely disordered 'spidroin-like' state and only the larger structure (six poly-Alanine stretches;
and
hydrated
fully
between
intermediate
an
be
to
assumed
be
can
condition
natural
The
remains stable.
vacuum due to the removal of water and ions from the silk as it is spun into air.
+
1. Equilibration
Replica Exchange
MD Water + Ions
Ius
2. Shear Flow
Steered Molecular
Dynamics
1Ons
3a. Equilibration
MD
Vacuum
50ns
3b. Equilibration
MD
Water + Ions
50ns
~4-~-
1 Loop
(a
3 Loops
5 Loops
~y
f~i
(a = 5)
During the shear induced assembly (second column, Table 1) all helices and
other structures transition into P-sheets or are destroyed, i.e., they transition into
random coil, in agreement with experimental observations of the processes in the
spinning duct [135]. Figure 12b and Figure 12c show the simulation results from
the shear simulation for a chain with a = 3. Secondary structure transitions and
associated shear stress results for other chain lengths can be found in the
Appendix, section 7.1. The amount of P-sheet is insensitive to the pulling speed,
Figure 13. This is in contrast to the results of experimental measurements which
have shown that the faster silk is reeled, the higher the P-sheet content. In
addition, at higher reeling speeds, smaller crystals are formed which positively
59
affects the toughness and ultimate strength of the fibers [56, 137]. Subsequently,
after equilibration of the structure in vacuum or explicit water in the presence of
ions, the silk relaxes again (third and fourth column respectively, Table 1). This is
discussed in the next chapter.
500
__O0
Spring Stiffness [kca/mol/A
1500
1000
2500
2000
45
40
35
30
0
CO'
25
3
VA
20
15
1015
0
I
0.2
I
0.4
I
0.6
i
i
I
1.2
1
0.8
Pulling Speed [m s
I
I
I
1.4
1.6
1.8
2
Figure 13 1 P-sheet content versus pulling speed for a set of spring stiffnesses. The observed P-sheet content
after shear is insensitive to the simulation parameters.
Figure 12a and Figure 12b provide further valuable insights into the assembly
mechanism of silk structures. The initial unfolding of the spidroin solution takes
place under very low shear stress. The stress drop (at -7 ns, see chapter 7.1) is a
phenomenon also observed when measuring forces during in vivo silking [138].
For the first time, a link is established between the drop in stress to the point
where a high P-sheet content in the structural transition is reached. This also
60
indicates that the creation of the crystal brings the molecule into a low energy
state with the force providing the energy to overcome the barrier for state
transition. The secondary structure transition from a-helical agglomerations to Psheet structures is ubiquitous and independent of the number of chain repeats a
and also very robust with respect to the simulation setup, Figure 13.
Figure 14a shows the average and maximum P-sheet content attained after the
shear flow experiment (determined by the methodology described on the
previous section, Figure 12a). The attained structure content is well within the
range of experimental observation (20-25%, [33]; 36%, [117]). Figure 14b shows
the associated transition shear stresses (determined by the methodology
described in the previous section, Figure 12b). For all chain lengths, the stress is
above the elastic limit of assembled silk fibers (150-300 MPa). This agrees with
experimental observation that reorganization of silk requires significant shear
stresses and the average force during silking is higher than the conventional
yielding force [139]. The transition shear stress for silk assembly is determined to
be between 300 and 700 MPa. Initial secondary structure transitions take place at
lower stresses already, -20% of the breaking stress. In order to reach the highest
P-sheet content, the stress needs to be increased to up to 50% of the breaking
stress. Experimental observations made by measuring the in vivo silking force
directly on the spun fiber, put the transition stress at 20-60% of the breaking
stress (i.e., 300-850 MPa for N. Clavipes silk) [138]. Interestingly, predictions from
flow simulations show that a much smaller pressure gradient is needed to push
the solution through the gland [140, 141]. However, such studies neglect the need
for secondary structure transition and investigate the process solely from a fluidmechanical point of view.
61
a
b
50
max.
1400
#-sheet
material stren-th
0ii'1200
40
21000
30
Experiment
10
~20
0 --
Expednment
I
20
__
3
a
a
5
Figure 14 1 (a) The P-sheet content attained after the shear flow experiment is independent of the chain
length and well within the range of experimental observation. (b) The transition shear stress for the silk
assembly is calculated to be between 300 and 700 MPa, whereas experimental observations put it between
20-60% of the breaking stress (300-850 MPa). This agrees with the observation that the reorganization of silk
requires significant shear stresses.
3.3 Structural Stability of the Assembled Silk Molecules
Structural stability, i.e. the stability of the equilibrium after the force-induced
state transition, of the pulled protein is determined by equilibrating it for 50
nanoseconds in explicit water and also in vacuum, see third and fourth column
in Table 1. The initial structure of this 'post-pulling' equilibration is a P-sheet rich
structure after the transition. The structures are considered stable, if the P-sheet
content does not change significantly during the simulation either in vacuum or
in water.
In vacuum, irrespective of the chain size a, all structures are stable and retain
their P-sheets, though the amorphous ends of all of chains show some
compaction during the equilibration stage. In solvent (water with ions present at
150mM), the smaller silk structures (two and four poly-Alanine stretches;
a = 1, a = 3) essentially return to their original largely disordered 'spidroin-like'
state and only the larger structure (six poly-Alanine stretches; a = 5) remain
relatively stable, Figure 15.
62
Figure 16 summarizes the secondary structure content of the spidroin and the
simulated structures after equilibration in explicit solvent (data taken from 40-50
nanoseconds of the simulation). While the shorter chains start to form 3 10-helices
again and retain only a low percentage of P-sheets, the larger structure is stable
and shows the secondary structure composition expected from the assembled
dragline silk fibers [135]. Specifically, a low helical content (310- and a-helices)
and a high
P-sheet and P-turn content are expected. This suggests that the
assembly mechanism proposed here may work similarly for a much larger
number of repeats. Figure 17 shows the same analysis for the relaxation in
vacuum, where all structures are stable.
50
-I
-3
-5
40
LOOP
Loops
Loops
30
'20
10
20
30
40
50
Simulation Time [ns]
Figure 15 1 Stability of the silk chains (P-sheet content) after shearing and a further equilibration in explicit
solvent. The shorter chains (a = 1, a = 3) cannot retain the P-sheet crystal and the structure returns in its
spidroin state; the larger structure a = 5 remains relatively stable.
63
45-
I
35[
30
T
[
I
40-
3pidroin
I Loop
I Loops
i Loops
I
20[
[
15
I
10
I
T
I
5
Y
01
L
Beta-sheet
Bend
Turn
Alpha-Helix
310 Helix
Figure 16 | Stability in water. Summary of the secondary structure content of the spidroin and the simulated
structures after equilibration in explicit solvent. While the shorter chains start to form 3 10 -helices and retain
only a low percentage of P-sheets, the larger structure is stable and shows the secondary structure
composition of final assembled dragline silk fibers.
rn.
I
;pidroin
Loop
45
II
Loops
Loops
40[
35[
I
I
30-
25
T
2015-
-
10
5
0
Beta-sheet
Bend
Turn
Alpha-Helix
310 Helix
Figure 17 1 Stability in vacuum. Summary of the secondary structure content of the spidroin and the
simulated structures after equilibration in vacuum. All chains remain stable independent of the chain
length.
64
In summary, a measure for the stress required to convert a largely disordered
structure into a P-sheet structure, 300-850 MPa, has been obtained by simulation.
Furthermore, the minimum size of structure that is required to stabilize the
formed p-sheet structures has been determined. This minimum size for a stable
structure is a = 5 for single chain and a = 3, for multi-chain. This result is
supported by studies of genetically engineered silk repeat units without
terminals, where the minimum number of repeats was a = 2 to form
indistinguishable nanofibrils, and with higher a the P-sheet content increased
and fibril growth was facilitated [142]. How this transition is effected, i.e.
whether there is a rationale as to which residues undergo the transition and why
structures remain, has remained one of the unanswered questions. Can the
molecular details found here be taken forward into the design of other polymer
materials?
3.4
Molecular Details of the Transition Mechanism
To gain a more detailed understanding of the transition mechanism, the
representative structures before pulling, after pulling and after relaxation in
vacuum and in solvent are compared to investigate how a largely helical
structure might transform into a stable P-sheet containing structure. The
probability of these structures containing helical or sheet content is computed for
each individual residue, see section 0, and the joint probability is plotted (blue
line) for the residue to transition. Figure 18 shows the probability for the
structure with a = 5 to transition from a-helix to P-sheet. Figure 19 shows the
probability for the structure with a = 5 to transition from 3 10 -helix/turn to
1-
sheet. The key residues of the transition are identified in Table 2. For comparison,
this analysis has been performed for all structures (a = 1,3,5 as well as interchain and layered structures) and the results are compiled in the Appendix,
chapter 7.2.
65
1.5
-REMD
-SMVD
a-helix- n-sheet
- Equilibration
-Joint
Probability
1
.0
0.5
0
0
100
AA [#]
50
Figure 18 2Transition probabilities for a -5 from a-helix to
each of the 206 residues of the structure with a
=
150
200
P-sheet. The graph shows the probability for
5 to be in a-helical state after REMD, in 1-sheet state after
SMD and in in 1-sheet state after Equilibration. The dark blue line is the joint probability defined as the
product of the three probabilities and indicates the residues that transition from helical to sheet structure
with high probability.
66
-REMD
- SMD
3 10-helix/turn -> n-sheet
- Equilibration
-- Joint Probability
1i[
-.
0.5[
0
AL I
50
150
100
AA [#J
200
Figure 19 1 Transition probabilities for a = 5 from turn/3 10 -helix to P-sheet. Probability for each of the 206
residues of the structure with a = 5 to be in 3 1 0-helical/tum state (after REMD) and in P-sheet state (after
SMD/after Equilibration).
Table 2 | Residues involved in the structural transition of silk chains with length a = 5 (206 residues). From
the transition probabilities (a-helices - bold, 3 10 -helices/turns - italicized) the residue numbers are identified
whose joint probability to transition is higher than 10%. These residue groups are the potential key players
in the silk assembly mechanism of the core structure.
I AO
M
mva.
1kT%
I RAair
vamp
I A
I - -
I R Q.Q()
I J(i1-14
I L3U
I 172
I V
67
- -
. .
.
I
.........
..
..........
...........
......
Figure 20 shows structure snapshots (a = 5) with highlighted residues identified
from Table 2 of the four transition stages, depicted in Table 1. Only the sections
with larger structural segments (> 4 residues) are shown. Blue represents
Alanine, white represents Glycine, brown represents Glutamine and aqua-color
represents Arginine. In spidroin state, Figure 20(i), the structure consists
principally of a-helices (in this example, 93/206 residues), turns and a small
number of residues in 3 10-helices. This 'exemplar' structure contains four long
helices (10-17 amino acids in length) and nine shorter helical sections. During the
shear simulation, the structure comprises three principal sections of P-sheet
structure (55/206 residues, 13-16 amino acids in length) plus two smaller (four
amino acids) regions as well as three extensive coiled/ open structured sections,
Figure 20(ii). The P-sheet sections all align antiparallel to one another within a
layer and also between layers.
(III)
(I)
9549
IO(v)
((IV)
Figure 20 I Structure snapshots (a =5) with highlighted residues identified from Table 2 of the four
transition stages (i - iv), in agreement with Table 1. Only the sections with larger structural segments (2 4
residues) are shown. Blue represents Alanine, white represents Glycine, brown represents Glutamine and
aqua-color represents Arginine, compare to Table 2. Stability of the P-sheet structure (iii, iv) arises from a
close proximity in space of the helices in the spidroin (i). Relaxation in solvent (iv), far from destroying the
structures, leads to an apparent stabilisation of shorter strands of P-sheet that can be mostly poly-Alanine
but may also arise from other parts of the sequence using a range of amino acids.
68
. ....
....
....
.....
..
..
..
..
..
.. ....
.............
...
....
....
In the vacuum equilibration after pulling, the structure comprises four sections
of P-sheet (56/206 residues, six to seven amino acids in length) as well as four
sections three to four amino acids in length and seven sections with two amino
acids in length, Figure 20(iii). Additionally, the structure has a helix (six amino
acids) and turn structures, particularly towards the beginning of the sequence.
The structure now has two coiled/ open structured sections. The P-sheet sections
all align antiparallel to one another within a layer and also between layers.
In the fully solvated structure after equilibration (post-pulling) there are
numerous short sections of P-sheet (48/206 residues), though with some residues
in turns/ 3 10 -structures, Figure 20(iv). A helix has formed from residues towards
the start of the sequence and the 'loops' between the 'pulled' regions have
compressed somewhat, this leading to development of some of the additional Psheet structuring that is observed. The structure now comprises P-sheet that is
largely formed by the poly-Alanine regions (although usually not the whole
length of the (Ala)6 regions)
and also has several extensive regions of 'new/
induced' P-sheet that forms after the relaxation involving Glycine, Alanine and
Glutamine residues. There are still unfolded regions that sit on the outside of the
structure. The P-sheet region is not as centered (symmetrical in terms of the
surrounding amorphous structure) as in the vacuum relaxed structures though
the P-sheet sections still all align anti-parallel to one another within a layer and
also between layers. Some H-bonding can be observed between poly-Alanine Psheet regions for those sections that lie virtually parallel to one another. Note,
whereas Tyrosine can be found in either helical or turn structures, it shows no
propensity for involvement in the generation of P-sheet under conditions where
the resultant structure is able to relax as in 'post-equilibration' in solvent case.
This seems to be the sole domain of the Alanine, Glycine, Leucine and Glutamine
with only a single Arginine involved.
69
Considering the probability data, Figure 18/Figure 19, in conjunction with the
specific amino acids involved, it can be concluded that the structures that are
constantly as either 'helices' or 'p-sheet' in the initial equilibrated ('post-REMD')
structures, the 'post-pulled' structures and the structures equilibrated in solvent
(joint probability, blue line) largely arise from the more compact part of the
initial structure. The sequences (four amino acids or longer) represented in the
probability data, i.e. parts of the sequence that are most likely to transition, are
the second half of the first large helix, the second half of the second large helix
and the first half of the third large helix. The additional 'smaller common'
segments are either close in sequence position to the longer helices/ P-sheet
sections or are physically close in space when the 3D structure of the protein is
considered. An exception to this is Arginine, which seems to sit 'between' several
helices in the initial structure but is then close in space to the P-sheet structured
elements after pulling and relaxation. This is the point in the sequence from
which regions of P-sheet develop in the relaxed solvated structure that were not
present in the post-pulled structure.
In conclusion, stability of the P-sheet structure seems to arise from a close
proximity in space of the helices in the first place. Interestingly, relaxation in
solvent, far from destroying the structures completely leads to an apparent
stabilisation of shorter strands of P-sheet that can be mostly poly-Alanine but
may also arise from other parts of the sequence using a range of amino acids.
3.5
Layered Structures
To understand the formation of larger crystals in silk, composite structures with
two or three P-sheet layers (see Figure 10c and description in section 0), are
LrtdLU
Uy staLcing two or three chains of the a
= 3 sLrULLUr. Fig6
U
sMYWs U M
P-sheet content of the layered structures. 10-15% of the structure stabilizes as P-
70
sheets in solvent, 25-30% in vacuum, almost independent of the number of layers
or the orientation. The transition probabilities and associated residues are
presented in the appendix, chapter 7.2. Again, predominantly poly-Alanine
regions form the stable crystals. The anti-parallel stacked crystal forms hydrogen
bonds within the sheet and also in between sheets. The parallel oriented layers
('2 layer parallel') form in-plane anti-parallel sheets, but initially out of plane
parallel sheets that are not connected by hydrogen bonds. This suggests that
although the structure is stable, it would not transmit significant shear stresses
under loading. Therefore, reorganization to anti-parallel P-sheets is required.
4U I
I
Water
Vacuum
35
0
4.'
25-
0)
4-'
C
0
0 200)
0)
U)
15
10
5
0
InterChain
2Layer piradel
2Layer
3 Layer
Figure 21 | P-sheet content of sandwich structures after equilibration in vacuum and solvent. Layered
10-15%
structures are formed from chains with a = 3. Independent of the amount of layers or the orientation
vacuum.
in
20-30%
and
solvent,
in
of the structure stabilize as P-sheets
71
3.6 Conclusion
The shear induced secondary structure transition process of the core sequence
during the spider dragline silk assembly is investigated through molecular
dynamics analysis. Robust results are found where a shear stress of the order of
20-50% of the failure stress induced an a - P-transition in the poly-Alanine
region. The results are in agreement with the experimentally determined
secondary structure and pulling forces of spider dragline silk. While the
transition stress is independent of the chain length, the crystal is stable only in
larger configurations. This minimum size for a stable structure is shown to be six
poly-Alanine regions for a single chain and four poly-Alanine regions for
multiple chains. This marks the smallest molecule size that gives rise to a 'silklike' structure. While the poly-Alanine region plays a key role in the transition
from helix to sheet, other parts of the sequence (Glutamine, Arginine) may also
be involved in the stabilization of the molecules. In general, the stability of the Psheet structure seems to arise from a close proximity in space of the helices in the
spidroin state. This study emphasizes the role of shear in the assembly process of
silk and can guide the design of microfluidic devices that attempt to mimic the
natural spinning process. Establishing the molecular details of the assembly
process can guide the synthesis of bioinspired protein materials by designing
sequences that transition with high probabilities to stable P-sheet structures.
72
4 Heterogeneity
Nanoconfinement
and
of
Fibrils to Increase Strength and Toughness
The research and review presented in this chapter have been published in:
" T. Giesa, M.J. Buehler, Nanoconfinement and the Strength of Biopolymers.
Annual Reviews of Biophysics, 42, pp. 651-673, 2013
" T. Giesa, N.M. Pugno, J.Y. Wong, D.L. Kaplan, M.J. Buehler, Mhat's Inside
the Box? - Length Scales that Govern Fracture Processes of Polymer Fibers.
Advanced Materials, 26, 3, pp. 412-417, 2014
In this chapter, the following questions regarding silk's fracture mechanical
properties are answered:
" How is the heterogeneity of silk fibers related to its fracture mechanical
properties: strength and toughness?
" How does nanoconfinement relate to the process zone size of fibers and
ultimately increase their strength?
" How is flaw tolerance achieved in silk and other biopolymer fibers?
" What other strengthening mechanisms can be observed in biopolymer and
bio-composites?
" How is the nanoconfinement related to the silk assembly?
73
Research strategy:
The first part of this chapter is a review of size effects observed in the mechanical
strength
of biopolymers,
specifically spider silk, that are organized
in
microstructures such as fibrils, layered composites or particle nanocomposites.
Two natural strategies are emphasized: confined mineral platelets that transfer
load through a biopolymer interface in nanocomposites and confined fibrils as
part of fibers. The application of confinement as a mechanism to tailor specific
material properties in biological systems is discussed. Furthermore, it is shown
how nanoconfinement of basic material constituents at critical length scales
relates to the mechanical performance of the entire material system (elastic
modulus, strength, extensibility, and robustness). Analytical fracture mechanical
arguments are presented to illustrate the relation between fracture strength and
heterogeneity. The concept of flaw tolerance on multiple hierarchical levels is
connected to nanoconfinement. It is shown that the considerations of interatomic
interactions alone cannot explain the fracture strength observed in biological
fibers. Instead, the fracture strength of a fiber depends strongly on the lengthscale of observation, and structures at multiple length-scales must be considered
to explain their remarkable mechanical performance and resilience, including a
fiber's sensitivity with respect to cracks (and other flaws).
4.1
Background
Many manmade materials and structures bear a conflict between strength and
robustness; strong materials are often fragile whereas robust materials tend to be
soft [4, 24]. In nature, this conflict is resolved by the arrangement of structures at
multiple scales and the confinement of the constituents (building blocks) at
critical length scales. One of the remarkable
u.'etes
natural material
is thr
ability to combine organic and inorganic components at the nanoscale [20]. In
74
materials like bone, universal patterns form a nanoscale composite of strong but
brittle nanoscale
minerals (hydroxyapatite)
and softer but more ductile
biopolymers (collagen) through assembly into complex shapes on seven or more
levels of hierarchy, giving rise to dramatically enhanced mechanical properties
compared with those anticipated from the basic constituents. The exploitation of
nanoconfinement design principles reviewed here may pave the way for a wide
range of tailored properties in biomaterials, outperforming the design space of
classical engineering materials and providing a powerful paradigm to scale up
molecular properties to the macroscopic world.
4.1.1 Nanoconfinement Strategy
Nanoconfinement is one of the most important mechanisms that control the
properties of biopolymers and polymer composites. Its exploitation defines a
potent mechanism to create specific material properties in biological systems.
When the characteristic dimensions of a polymer-based material approach
molecular sizes, properties such as chain structure, chemical reactivity, and
thermodynamic behavior change significantly
[143]. This effect arises in
biological systems with limited space, such as cells, shell nanocomposites, and
thin fibers. The thorough understanding of fundamental confinement paradigms
is especially important in view of the vast range of applications of such polymer
structures as sensors, actuators, transistors, surface layers, filler matrices, and
many others [144].
The thermodynamics of confined polymers and the strength of biopolymers are
two intensively studied fields, but have never been thoroughly connected. The
quantities that determine the strength of a material are elastic modulus, strain at
failure, and failure strength (stress), as well as fracture toughness. Fracture
toughness is a material parameter that indicates the ability of a material to
withstand fracture. The influence of confinement on these quantities is not well
75
understood. Figure 22 shows the effect of the system dimension D (in the case of
a fiber, its diameter; in the case of a thin film, its thickness) on the elastic
modulus E and on the fracture strength a for a selection of materials. The
quantities are normalized by their respective bulk value (bulk modulus Eb and
bulk strength ab), see Table 3.
76
a
4.5
# Silk-elastin nanofibers (exp.)
a Okra nanofibers (exp./sm.)
a Polystyrene thin film (exp.)
thin fim (sim.)
* Polyethylene nanofiber (sim.)
V
4
3.5 F
V
o
o
a Polystyrene
3
e
+
*
A
2.5
2
1.5 F
0
?I
a
.......
I
I
age
0.5 F
"0
0.5
1.5
D/D
1
2
2.5
3
b
-
W
* Nylon 6.Ar anofibers (exp.)
A Polypyrrole nanotubes (exp.)
v PAMPS nan ofbers (exp.)
A
3
A Bombyx Mod silk (exp.)
v Polycaprolactone nanofiber (exp.)
2.5
-
2
-
1.5
4
*
Okra nanofiber (explsim.)
- -sbeet nanocrystal (sim.)
* MaSpI silk nanofiber (sim.)
* Polystyrene thin film (exp.)
YNA
.4
......#.......................
-----------
1
00
0.5
0
1
2
3
D/D
4
5
6
Figure 22 | Relative elastic modulus and strength of polymer materials as a function of size. (a) In most
nanofibers, the relative elastic modulus, as compared with the bulk modulus Eb, increases dramatically at a
critical diameter D*. This behavior is explained by the role of spatial confinement on entropy and the
dominance of intermolecular interactions in thin nanofibers. Thin polymer films with free surfaces tend to
display a decrease in the relative modulus due to the formation of highly mobile surface layers. (b) The
alignment of crystalites and the degree of crystallinity in the fiber also improve with smaller diameter,
leading to greater strength and toughness, sometimes even exceeding the bulk properties. The data for the
fracture strength of thin films show a decrease of the material strength. (The references, critical length scales,
and bulk values are summarized in Table 3.) Figure reprinted from Reference [121].
77
Table 3 1 Bulk modulus, bulk strength, and critical length scales for polymer materials. Taken from
Reference [1211.
Eb [MPa]
D* [nm]
References
70
[146, 147]
20
35,000
[149]
160
18
6b [MPa]
Polypyrrole nanofiber 500
Silk-elastin fiber
1,500
Polyethylene nanofiber 800-2,750
MaSpl silk fiber
-11,400
Polystyrene thin film
5,200
1[1511
120-80
50
20
[47, 48,
153]
1[155, 156]
The most important aspects that relate nanoconfinement of biopolymers to their
performance as materials are:
" Change
in conformational
behavior.
Confinement
influences
the
equilibrium shape and can lead to increased alignment of the polymer
chains. On free surfaces, thin films display increased mobility due to a
smaller interaction strength. In turn, this decreases the modulus of thin
polymer films.
" Increase in effective surface area. Splitting a fiber into n fibrils yields an
increase in surface area by a factor of V, giving rise to surface effects
such as increased chain mobility, less packing frustration, and increased
diffusion. Furthermore, the effective adhesion area increases (van der
Waals interactions). This is relevant in the context of critical length scales
for nanosized fibrillar structures (e.g., gecko adhesion).
" Change in elastic properties. Depending on the shape and environment of
the polymer, the modulus and glass transition temperature can increase or
decrease dramatically.
78
*
Change in failure mode. Below a critical size, beam-like systems tend to
fail in a shear rather than in a beam bending deflection. This has been
shown to be advantageous for systems that are sensitive against tensile
stresses. For instance, P-sheet nanocrystals are confined below 2-4 nm to
avoid a tensile stress-induced bending, which facilitates the intrusion of
water into the system, resulting in the breakdown of the crystal.
*
Additional fracture mechanisms.
Structure-splitting induces fracture
mechanisms such as crack deflection on interfaces, fiber bridging, crack
branching, and others. Paired with a composite structure of a weak,
ductile phase and a strong, brittle phase-as found in many natural
systems (e.g., bone, nacre, silk)-this design dramatically increases the
fracture toughness, robustness, and damage tolerance of the whole
system. An extreme case is the repeating patterns of brittle phases with
structural holes, i.e., gas. This arrangement, found, e.g., in the silica
structure of diatom algae, gives rise to improved strength, extensibility,
and robustness.
*
Homogeneous deformation. Confinement below a critical size forms a
potent design strategy to map nanoscale properties to the macroscale
despite system imperfections such as cracks and tears.
Confinement is not the only mechanism that contributes to the strength and
toughness of biopolymers and polymer-mineral composites. On various scales,
additional extrinsic mechanisms such as fiber bridging and grain bridging that
shield cracks, as well as plasticity-like intrinsic mechanisms [24], friction on the
scale of hundreds of nanometers [158], crack branching and microcracking in
composite structures [159], and many others increase the toughness of most
biomaterials.
Here, the discussion is limited to two generic natural strategies (universally
observed in nature and representing critical mechanisms that play an important
79
role in developing a comprehensive understanding of biological materials):
confinement of the biopolymer interface in composites [quantitatively equal to
thin film structures [160]] and confinement of fibrils in fibers. Both these
mechanisms are ultimately important to understand the importance of spider
silk's nanostructure.
4.1.2
Confinement of Polymers
To understand the effects of confined system dimensions on the material
properties of a polymer, the basic thermodynamics and kinematics of the
polypeptide chains must be analyzed through experimentation and simulation.
The statistics of confined polymer materials can be studied by molecular
dynamics or Monte Carlo simulation [161-164]. The most important properties of
a spatially confined solution are: the nature of the confining surface, geometry of
the confining object [165, 166], and chain flexibility [167, 168]. Recent research,
e.g., by Zhou et al. [169], has explored the influence of spatial confinement or
macromolecular crowding on (re)folding, equilibria, shape, and entropy of
biomolecules in cells. The presence of a physical boundary reduces the accessible
volume of the chain and thus the entropic free energy by
SG = -kBT(ln(fconf) - n(fth)) ,
4.1
where T is the absolute temperature, kB is the Boltzmann constant, fconf is the
accessible volume fraction, and ft
is the theoretically allowed fraction of
configurations (with respect to the total system volume) [170, 171]. Hence, a
confinement provides a stabilization of the native state, decreases the folding free
energy, and increases the melting temperature. A mechanism similar to
confinement is macromolecular crowding [172, 173]. Close to thin film
boundaries in liquid-crystal polymers, the interfacial perturbations create various
types of new local organizations, such as an alignment along the surface (called
80
weak nematic ordering) [174-176]. The shape of the confined zone can critically
influence the rates of protein folding [166].
Therefore, confinement is a complex problem, highly dependent on boundary
conditions such as substrate, environment, and shape. It is thus of utmost
importance to include the ramifications of these effects into molecular studies
[177]. Much work has been done on the thermodynamics of confined polymer
and liquid-crystal materials. The influence of confinement on the glass transition
temperature has been intensively studied and comprehensively reviewed [178].
The behavior is complex and dependent on many variables, such that decades of
research still cannot provide consistent answers. A general review on the effect of
confinement on thermodynamic properties of glassy polymers by molecular
dynamics simulation can be found in Reference [179]. Recent studies include
experimental [180-183] and computational [184] investigations, also in the
context of nanocomposites [185, 186], many of which examine polystyrene as it
displays strong size effects [187].
Confinement dramatically changes the elastic properties of polymer materials.
Arinstein & Zussmann [146] reviewed the effect of reduced sizes and dimensions
on the mechanical and thermodynamical behavior of electrospun polymer fibers.
They identified critical length (nanometer) scales at which the material behavior
deviates significantly from the bulk behavior. This includes an increase in elastic
modulus with smaller diameters, and the temperature dependence of the elastic
modulus
[188].
For larger fibers, the modulus increases with elevating
temperatures, as predicted by rubber elasticity, whereas it decreases with rising
temperature for smaller-diameter fibers, similar to solid and crystalline materials.
This behavior is explained by the role of spatial confinement on entropy and the
dominance of intermolecular interactions in thin nanofibers. Also, the degree of
crystallinity and orientation of the crystallites increases with smaller diameters
[188], similar to thin films [189]. The crystallization of polymers in thin films
81
plays an important role in defining their mechanical response. Crystal
orientation is enforced in polymers with larger Kuhn lengths, and the polymer
can be modeled as a system of self-avoiding rigid rods (Onsager model). It can be
shown via the correlation length of a crystalline region in an amorphous domain
that the size of the oriented region is in the same order as the fiber diameter at
which the dramatic increase in elastic modulus is observed.
The experimental results for elastic modulus of confined thin films are
ambiguous as the measurements are often highly influenced by the stiff substrate
[190, 191]. The controversial discussion as to what extent surface effects and
supramolecular microstructure control the behavior of thin films and nanofibers
is still not settled. In materials for which surface effects dominate (amorphous
thin films), the modulus tends to decrease with confinement (in comparison with
the bulk behavior), whereas in materials with significant crystalline phases
(polymer fibers), the modulus can increase by up to a factor of 20. The confining
substrate and the molecular mass of the polymer influence the confinement
behavior, which is of great relevance to the analysis of composite materials [192].
4.1.3 Strength of Polymers
4.1.3.1
Strength of Hydrogen Bonds
The failure of hierarchically organized protein domains is governed by the
competing mechanisms of H-bond breaking and bond reformation. Such a
process can be modeled by statistical models based on Bell's theory or Kramer's
diffusion model [193]. In these frameworks the existence of a H-bond between a
donor and acceptor atom is treated as a random variable, where the number of
attempts to break or reform the bond per second is prescribed by the natural
vibration frequency wo ~ 10" s-'. Hence, w0 represents the attempts of each
bond to overcome an energy barrier Eb. An externally applied force f reduces
82
this energy barrier. The energy associated with the force is fxb cos(8), where Xb
is the distance between the equilibrated state and the transition state, and 0 is the
angle between the direction of the reaction pathway of bond breaking and that of
the applied load. The off-rate X is the product of the vibration frequency and the
probability to overcome the energy barrier and is given by:
Eb - fxbcos(6)
kBT
4.2
)
=
(
X woexp (
The off-rate is the reciprocal of the bond lifetime. Note that this equation is
related to the probability of state transition, see chapter 2.1.7. For complex
chemical reactions, a similar model can be developed that includes higher-order
correction terms [194].
4.1.3.2
Strength of Hydrogen Bond Clusters
The common basic secondary structures found in protein materials are a-helices,
-sheets, and P-coils. Recently, their mechanical performance has been elucidated
by atomistic simulation [195]. These structures can be understood as nanoscale
'brick-and-mortar' - a strong constituent (e.g., the polypeptide chain) is stabilized
by a weak glue-like matrix (e.g., clusters of H-bonds) [196]. To study the
unfolding of these structures, the hierarchical architecture that enhances H-bond
cooperativity must be correctly captured. Bond cooperativity is the ability of
hydrogen bond clusters to act synergistically to withstand failure; usually
enforced under shear deformation rather than bending deformation.
The rupture strength of H-bonded protein domains can be determined based on
the energetic analysis discussed above [197]. In an array of H-bonds, the optimal
number Ncr of cooperating bonds that fail simultaneously in a cluster is given by:
83
Ncr = kT
Eb (4(p
[(1
acr)2
+ 4acr - 1] - In
(UXO)I
4.3
where acr is the ratio between end-to-end length and contour length of the
polymer chain at failure and
4,
is the persistence length of the polypeptide. It
was found that for H-bond clusters Ncr ~ 4, in accordance with cluster sizes
found in nature (Figure 23) [157]. Protein materials such as spider silk, muscle
tissue, and amyloid fibers consist of arrangement of ordered and unordered
(amorphous) structures. An example of an ordered structure is the P-sheet,
composed of hierarchical assemblies of weak H-bonds (100-1,000 times weaker
than covalent bonds). Despite the intrinsic strength limitation of H-bonds, these
materials gain exceptional strength and robustness by clustering weak bonds in
groups of three to four that then break concurrently.
For hierarchical assemblies of H-bonded clusters Ackbarow et al. [195] devised a
model to capture the force distribution in a hierarchically organized network.
The off-rate for such a hierarchical network Xh is given by:
Xh
= wo exp
(
Nc~rEb + kBT In (Ncr) - fxbcos(6)
kN
4.4
where Ncr is given by equation and N is the total number of bonds in parallel.
They also defined a robustness index r(Ncr) = 1 + (kbT In Ncr - Eb)/(EbNcr).
Again, Nr
4 optimizes the robustness in the Pareto sense.
84
....
.............
. . ........
..
-2-F"
--
I
I--
I
10
12
200
-sheet
9150
100
50
0
2
6
4
8
#of residues
14
16
Predicted critical size
-sheet
Dimensions found in
several natural protein
secondary structures
P-helix
-*
a-helix'
Figure 23 I Rupture strength of H-bond clusters and critical sizes of some protein secondary structures. Top:
The intrinsic strength limit of H-bonds can be overcome by clusters of three to four H-bonds that then
interact synergistically to resist deformation and failure. The H-bond assemblies are loaded in parallel in ahelices, P-sheets, and P-helices. Note that the shear strength curve is derived for a single n-sheet in a pull-out
test. The natural load condition for an a-helix is tension, for which an unzipping effect is easily achieved.
Bottom: This result explains the cluster size found in natural protein secondary structures (a-helix: N = 3.5;
0-helix: N = 5; and 1-sheet: N = 2.5 - 8). Figure adapted with permission from [157] Copyright 2008
American Chemical Society.
4.1.3.3 Strength of Single Molecules
Many biopolymers, e.g., amyloids, spider dragline silk, and titin as part of the
muscle sarcomere, gain their strength through the arrangement of p-sheet rich
crystalline
regions and non-crystalline
(amorphous) regions
[198,
199].
Fundamental insights into their mechanical performance is gained by single
molecule experiments. The strength of single molecules can be tested
experimentally and computationally. Comprehensive reviews of single-molecule
experiments in biological physics can be found in References [69, 200]. Atomic
force microscopy thereby provides a tool for a variety of characterization tasks,
85
such as determining the surface morphology, the elastic modulus, and the yield
strength of small-scale samples [201-204]. On a similar length scale, the strength
of polymer complexes can be determined by a computational method called
steered molecular dynamics (see chapter 2.1.3) that simultaneously sheds light
on the (un)folding pathways of proteins under force, as well as their
corresponding intermediate states [205-207].
4.1.3.4
Nanoscale Surface Strength - Weak Interactions
Nanoscale biological surfaces feature properties of self-similar and self-affine
fractals, that can be treated by mathematical analysis. Self-similarity is the
property whereby an object's structure at a larger scale is equal to that at a
smaller scale and self-affinity is the property whereby a substantially different
amount of anisotropic scaling does not affect the morphology of an object's
surface. Splitting a fiber into n fibrils yields an increase in surface area by a factor
of Ni. Similarly, fractality increases the effective surface area dramatically, which
enhances adhesion and diffusion. On the other hand, increased chain mobility at
interfaces can decrease the interfacial strength [208]. For general fractal surfaces,
the effective adhesion yeff can be derived as a function of measurable surface
geometry properties and the van der Waals surface energy difference [209].
Hence, it is possible to calculate the interface strength of various materials,
including biological systems such as the gecko foot [209]. In hard solids, the area
of contact within the effective cutoff is extremely small, and additionally, they
store only limited elastic energy. Although gecko skin is primarily composed of
stiff keratin, the branching fibers and nanometer-sized spatulae lead to the
formation of a soft, elastic layer that can follow the profile of the substrate at all
length scales [210]. The gecko adhesion effect has been successfully mimicked,
but the efficiency of natural systems, i.e., the transmitted load per projected area,
still cannot be reached [211].
86
4.1.4 The Relation between Confinement and the Strength of Polymers
Most biological materials are hierarchically organized, i.e., they consist of
hundreds of nanoscale features that are copied many times, e.g., in a self-similar
way [1]. The protein constituents are often of molecular size, hence the abovediscussed changes in properties are relevant in these materials. The following
chapter outlines how the specific effects of confinement come to work in
biopolymers and biopolymer composites. The focus of this discussion is mainly
on the confinement of the final structure, as this is crucial to the actual
performance of the system, and not the effect of confinement during the growth
process. The question of how the confined systems are actually self-assembled is
of a different nature, as a detailed analysis of the growth process is needed.
Specifically, the growth of the crystals in polymer-mineral nanocomposites is
likely controlled by the free surface energy provided by the surrounding
polymer matrix (i.e., a nucleation problem), whereas the size of silk fibers, for
example, is controlled by the conditions during the spinning process (e.g.,
channel size, shear rate, and pH). This is discussed in chapter 3.
4.1.4.1
Thin Films
Nanoconfined thin films (on a substrate, but with a free surface) tend to decrease
their fracture strength relative to their bulk strength, which has been confirmed
experimentally [1561 and computationally [2121, see Figure 22. Furthermore, it
has been reported that their strain at failure increases with confinement [213].
This can be explained by the decrease in intermolecular entanglement density
near the free surface leading to increased segmental mobility but reduced
strength of the intermolecular forces [156, 208]. Thin biopolymer films with freestanding surfaces are relevant in many applications, for example, as sensors and
coatings. Thus, their low mechanical performance at small scales is not
necessarily a performance issue.
87
4.1.4.2
Biopolymer and Mineral Composites
Composite biomaterials consist of multiple distinct materials (e.g., organic and
inorganic as in brick-and-mortar) or multiple phases (e.g., crystalline and
random-coil)
and feature
enhanced characteristics
constituents
alone
215].
[214,
Their
applications
with respect to their
and
properties
in
nanotechnology have been reviewed in Reference [216, 217]. For example,
polymer-layered silicate nanocomposites are much lighter than a bulk polymer
material of equivalent strength and stiffness, are easier to recycle, and do not
suffer from the 'one-dimensionality' of fiber-reinforced materials [218]. The
mechanisms that play a key role in these materials rely on the transfer of shear
stresses across the polymer-mineral interface. The stiff boundaries of the mineral
phase diminish the potentially negative surface effects (e.g., high chain mobility)
and rather enhance the strengthening effects (e.g., an increased shear transfer
capability).
In most applications, catastrophic failure can be avoided by using strong and
tough (fracture-resistant) materials that fail gradually. Hard materials tend to be
brittle because the high strain energy due to stresses at the crack tip cannot be
dissipated, whereas soft materials dissipate the energy by plastic deformation.
Composites rely on a synergistic interplay of crack arrest, stress delocalization,
and dissipation, see Figure 24. Specifically, natural composite materials rely on
intrinsic and extrinsic toughening mechanisms [24]. Intrinsic mechanisms (based
on plastic deformation, e.g., platelet sliding) usually originate from smaller
length scales (akin to dislocations in metal), whereas extrinsic toughening
mechanisms (e.g., fiber bridging) usually take place on micrometer scales. Nacre,
for example, features a brick-and-mortar structure, where the soft phase allows
small movements between the strong aragonite platelets. As the movement is
limited to -1 pm due to a friction mechanism, this constitutes a toughening
mechanism. Crack deviation and platelet pullout provide further contributions to
88
a fracture toughness of an order of magnitude higher than either of its
constituent phases [24]. These mechanisms have been applied to synthetic bioinspired ceramic materials made of aluminum bricks and a polymeric lubricant
with toughness values exceeding 30 MPa Vi (for comparison, the value for
aluminum is -20 MPa Viii, and for the polymer it is -1 MPa
V). Furthermore,
the repeating patterns in a hierarchical material contributed to an improved
redundancy; i.e., a partially flawed system maintains its mechanical functionality
through a load bypass.
b
a
40
Intrinsic toughening
Brick-mortar A
Extrinsic toughening
E
30-p
**1.
zone
Grain bridging
vage fracture
L6
ijrovoidcoalescence
I
C
10
Nacr e
Ahead of crack tip
Behind crack tip
A
Lamellar
00
03
1.2
Fibre bridging
20-
K3 =0.012
A1203
0.2
0.8
0.6
0.4
Crack extension, Aa (mm)
1
Figure 24 | Intrinsic (plasticity) versus extrinsic (shielding) toughening mechanisms associated with crack
extension and R-curve. (a) The illustration shows mutual competition between intrinsic damage
mechanisms, which act ahead of the crack tip to promote crack advance and extrinsic crack-tip-shielding
mechanisms, which act primarily behind the tip to impede crack advance [24]. Intrinsic toughening results
essentially from plasticity and enhances a material's inherent damage resistance; as such it increases both
the crack-initiation and crack-growth toughnesses. (b) Toughness behavior of various materials. In many
natural materials, it is an order of magnitude tougher than its constituent phases. Figure adapted from [24],
copyright @ 2011, with permission from the Nature Publishing Group.
In their fundamental studies on the fracture strength of nanocomposites, Gao et
al. [219] derived a fracture mechanics argument to determine the optimum
platelet aspect ratio and platelet size. Their analysis is based on the concept of
89
nanoconfinement and flaw tolerance (scaling of fracture strength). It is often
argued, at least for crystalline materials, that the increasing strength of confined
materials is related to the decreasing occurrence of defects on smaller scales (see,
e.g., Reference [220]). In contrast, Mishra et al. [221] discovered that the defect
density actually dramatically increases with decreasing film size. Their analysis
is valid for block-copolymer nanofilms with low Flory-Higgins parameter. If a
dimension (in the case of a composite, the height of the platelet size h; in the case
of a fiber, its diameter D) becomes confined to the size of the zone of large
deformation around the crack tip, the stress concentration vanishes and the
composite/fiber is homogeneously deformed. This defines the flaw-tolerant
state, as none of the material strength is lost [215, 219, 222]. The flaw tolerance
mechanism, Figure 25, has been experimentally confirmed for thin, steel sheets
and for notched, nanoscale thin films [223] and recently also via molecular
dynamics simulation for graphene [224] and hydroxyapatite [225]. In each case,
no stress concentration could be observed and failure initiated far away from the
crack tip. For many materials including nanotubes, the critical size tends to be
close to the size of the unit cell of a crystal [226], but depends on the boundary
conditions and other material properties [47, 219, 227]. Gao et al. [219] argue that
during the biomineralization process, crack-like flaws in the form of soft protein
inclusions are trapped within the mineral crystals (Figure 26). They derive a
scaling law for the optimum flaw-tolerant platelet size h*
h =
F2 ysEm
4.5
U2
Below h* the fracture strength of a perfect crystal is reached despite the presence
of a crack. Therein, F is a geometry-dependent parameter of order unity (see
chapter 2.2.1), y, is the surface energy, Em the elastic modulus of the mineral
phase, and Ut the strength of the perfect crystal. The results from molecular
dynamics simulation of the coarse-grained (CG) model of bone are shown in
90
Figure 26. Coarse graining is a molecular dynamics technique that reduces
degrees of freedom and is often used for protein materials simulation.
a
1.73pm
0.17pm 0.05pm b
I
10 nm
Flaw tolerant state
1
d
C
Strength scaling of a
flawed crystal
(classical)
1
W 1h
,
D
Figure 25 1 Confinement and flaw tolerance. The graph shows the concept of flaw tolerance. According to
the classical prediction, the strength of a material scales with Jiili or, Ji73 respectively. In the case where
the strength of the perfect crystal is reached at h = h* (D = D*), the flawed system exhibits no loss of
strength. This concept has been experimentally and computationally verified, e.g., for (a) spider dragline silk
[47], (b) hydroxyapatite nanocrystals [225], (c) thin metal strips [223], and (d) nanocrystalline graphene
[224]. Images in panel (a) reprinted from Reference [47]; images in panel (b) from Reference [225]. Images in
panel (c) adapted with permission from Reference [223]. Copyright @ 2009, American Institute of Physics.
Image in panel (d) adapted with permission from Reference [224]. Copyright @ 2012 American Chemical
Society. Figure adapted with permission from Reference [121].
91
Y
1
b
a
I
OA
0
0.8
Ih!I
0.6.
0.40.2-
At
1
-
Hydroxyapatite
Surface Adhesion
Spider Silk
-
A
2
Wh,
IIColagnma
aCG Bone Model
*
3
C
Flaw due to
surface
'ouC1""
4
rD/D*
Figure 26 1 Critical size of a composite and an adhesion system. Bone-like materials typically consist of
fragile, brittle mineral platelets (hydroxyapatite) embedded in protein matrix materials (collagen). (a) The
mineral platelets carry a tensile load and the protein transfers carry loads between the platelets via shear. (b)
These platelets are confined and optimally arranged to maximize the strength and toughness of the material.
(c) Similarly, the adhesion of a spatula on a rigid surface is optimized for a critical diameter D*, e.g., for
gecko adhesion [211]. The critical sizes h* and D* determine the point at which the system becomes flawtolerant. The solid line on the left corresponds to the classical fracture mechanics prediction, which breaks
down at the length scales at approximately the critical size (on the order of a few nanometers). Figure
adapted with permission from Reference [121].
Wei et al. [2281 derived a closed-form solution for two critical overlap lengths L*
and L** to which the polymer/mineral interface is confined. They found that
L*
=
2.318
Ehb
4.6
-
in the elastic limit using the shear-lag model to maximize the elastic strain energy
density and the shear transfer efficiency. The respective parameters are shown in
Figure 27a. For the plastic, limit they found that
4.7
L** = U b,
Tf
at which the strong and the weak phase fail simultaneously. Here,
Tf
is the shear
strength of the interface (Figure 27b). Wei et al. also showed that in the case
where L* ~ L**, the toughness and the strength of the composite are both
92
optimized. Comparing their model predictions with abalone shell, collagen, and
spider silk nanocomposites, they find a remarkable agreement with the overlap
length scales (Figure 27b). De Gennes & Okumura [229] developed a scaling
argument for the strength of biocomposites with stratified structure based on a
CG elasticity field that neglects plastic flow and viscoelasticity where
0f
th
lEs(hs +
a
og
8
h4.8
Ehds
with the subscript h for the stiff mineral phase and subscript s for the weak
polymer phase, h as the respective layer thicknesses, a as the crack size, and 6 as
a cutoff length scale in the continuum (-h). In the thin layer limit and by
neglecting bending of the platelets, they approximate the energy functional for a
notched, stratified structure where the organic layers are much thinner than the
platelet size. Based on their analysis, De Gennes & Okumura find that nacre
enhances its fracture toughness by a factor of 1,000 and the fracture strength by a
factor of 30 in comparison with pure aragonite. Notably, this behavior could be
controlled by the stiffness ratio Es/Eh. This idea can be used for the design of
composite materials, to increase the fracture toughness [230, 231].
93
b
25
---
Fracture Toughness
Elastic Energy Density
L
1600
1400
23
21
_
-1200
~21
-
*1:2
10005
8000
LM
1600
1400
100.
U2
1
200
0
C
'-
15
0.5
0
2b
0
1
LA
1.5
2
107
103
0
Experimeental Data
17
10rs aModel
Prediction
10
5
LU
100
10'
10,
101
Size (nm)
composite (e.g., nacre). (a) Hierarchical structure
scales
length
Figure 27 Optimized
2012
merian
Soie0y
Cemiclin a ineral-polymer
of nacre and a schematic of a 2-dimensional continuum model for the composite architecture to predict the
critical sizes that maximize the strength of the whole material. (b) Elastic and fracture toughness varying
with overlap length normalized byL. Total elastic strain energy density (squares) maximizes at L = V, and
fracture toughness (circles) exhibits a sudden drop when L > L*. (c) Comparison of overlap lengths for basic
building blocks of three natural materials (nacre, tendon, and spider silk) from experimental observation
(circles) and model prediction (squares). Figure adapted with permission from Reference [228]. Copyright@
2012 American Chemical Society.
4.1.5 Nanoconfinement in Silk
Silk heterogeneous nanostructure features aspects of composites materials
(namely, the composite of 1-sheet crystal and semi-amorphous phase) and
fibrous materials (fibrillation). As explained in the previous chapter, many
fibrous biomnaterials achieve their strength by confining their basic building
blocks at critical length scales. This can occur at several hierarchical levels,
spanning from nanometers to micrometers, i.e., confined nanocrystals and
confined fibrils.
94
The breaking of H-bonds represents a fundamental unit mechanism of failure in
protein materials, see chapter 4.1.3.1 [157, 197, 232]. The studies of simultaneous
failure of H-bond clusters (chapter 4.1.3.2) reveal critical dimensions for
structural constituents such as helices and nanocrystals. For example, it has been
shown that networks of a-helices are flaw-tolerant [233]. In a recent study, Keten
et al. [49] determined the critical size for the most stable P-sheet nanocystal to be
H = 2 - 4 nm. Figure 28 shows the robustness, a measure of its stability against
failure, of a single P-sheet crystal as a function of its height H. Larger crystals do
not fail in a shear deformation (with optimized cooperativity of the H-bond
clusters with Ncr = 4, see chapter 4.1.3.2) but rather in a bending deformation.
In this unfavorable deformation mode, water molecules enter in the crystal
regions under tension and split up the crystal, leading to an early and
catastrophic (brittle) failure. In accordance with the simulation, the crystal
dimensions were experimentally determined to be 2-4 nm [234]. The P-sheet
nanocrystal size may be tuned through genetic modification and control of the
self-assembly process. For example, by controlling the poly-Alanine length in
MaSpi protein aggregation in dragline silk, the resulting stability of the
nanostructure can be tuned through the p-sheet crystal size [130]. Computational
atomistic structure predictions with REMD (see chapter 2.1.5) predicted a critical
poly-Alanine length of four to six residues for the amyloidization of a defined
and stable p-sheet nanocrystal. This result has been experimentally verified
through the observation that MaSp dragline silk typically has poly-Alanine
repeats of six to eight residues in length, whereas the minor ampullate spidroin
protein of viscoelastic capture silk (less strong) has poly-Alanine repeats of only
two to four residues [235]. This study revealed an in-depth understanding of
how nature controls material self-asssembly processes and creates its highperformance materials. Furthermore, it is an important engineering opportunity
for tailored polymer materials.
95
35
-,
30
H
25
E 20
15-
0
0
Crystal size
2
4
H [nm]
6
8
Figure 28 | Robustness of f-sheet nanocrystals as a function of their height. P-Sheet nanocrystals are
especially strong and robust if their height is confined to 2-4 nm. This critical dimension is in agreement
with experimental results. Figure adapted from Reference [49].
Similar to the elastic modulus, the dependence of the fiber strength on the fiber
diameter is ambiguous in the literature. Almost no effect of diameter has been
reported in silk-elastin-like protein polymer fibers [149], whereas a dramatic
increase is seen, e.g., in native and regenerated Bombyx Mori silk [152], natural
plant fibers [150, 236], and polycaprolactone nanofibers [154, 237]. In fibrillar
nanoscale adhesion systems, nanoconfinement has been shown to be the
dominant strategy to ensure a robust design, thus giving an explanation for the
widespread occurrence of hairy attachments in nature (gecko, fly, beetle, spider)
[238]. Most biopolymer materials are flawed, meaning that preexisting cracks,
inclusions, and tears compromise the mechanical integrity under load through
the existence of stress concentrations. The mechanical strength and robustness of
flawed fibers can also be maintained by use of a confinement strategy [219].
96
Nanoconfinement of P-sheet crystals has been determined to be the driving
mechanism in squid sucker ring teeth [239].
Recent work has quantified a flaw tolerance mechanism for spider silk fibers [47].
The result for the critical silk fibril size D*(MaSpi) = 20 - 80 nm, determined in
Reference
[47] via simulation, agrees remarkably well with experimental
observations in the range of 20-150 nm [42]. This critical size can be similarly
determined by Equation 4.5 using the specific geometric boundary conditions of
a fiber. The results from MD simulation with different loading conditions are
shown in Figure 29. Silk fibers consist of nanoconfined fibrils of 20-150 nm that
are capable of maintaining their full strength and robustness despite possible
flaws in the fiber material. The robustness can be for example measured by the
toughness modulus, the area under the stress-strain curve of a material after
fracture. The relation to the fracture toughness is discussed elsewhere [230]. A
similar mechanism to increase the structural robustness could be at play in many
biological fibers that feature a fibrillar nanostructure. This idea will be explored
in the following chapters.
97
* Loading Condition (1)
I
0.8 F
=*
a Loading Condition (2)
- Loading Condition (3)
A Loading Condition (4)
N. Pilipes (exp.)
C. Darwini (exp.)
A. Argentata (exp.)
Atomistic Simulation
2 0O- 80~
f/l
11
(1)
(2)
(3)
(4)
0.9
0.8
E3
0.7
0.6
0.5
0.4
20.4
D> 1000nm
0
*
0.2F
*
A
DA1
-0.2
OI
0.4
Relative Strain
0.8
I
10
Figure 29 1 Critical size of spider dragline silk major ampullate spidroin 1 (MaSpi). The graph shows the
dependence of the failure strain and failure stress on the fibril size D under various loading conditions (1-4)
as well as a direct comparison with experimental results (under the tensile loading condition 1 and the
mechanical behavior of a defect-free silk fiber. For decreasing fibril sizes, the perfect material behavior (i.e.,
= 1,400 MPa failure stress and 68% failure strain) is approached and reached at D = D* = 50 30 nm. D*
is denoted the critical flaw-tolerant size of the fiber. The results show that the high strength and extensibility
observed in experimental studies can only be reached by nanoconfinement of fibrils close to D*. Figure
adapted from Reference [471 with permission.
4.2 Fracture Mechanics Analysis
In this chapter, the characteristic length scales in hierarchical biological fibrous
materials are related to their fracture strength. The fracture strength of natural
fibers like silk remains a topic of intense debate, as it has not yet been possible to
predict their fracture strength directly from an atomistic point of view [240, 2411.
The impact of such stress concentrators on a material's performance was first
quantified by Griffith and Weibull, see chapter 2.2. They developed strong
theoretical arguments to explain the experimentally observed scaling of strength
with specimen size, where smaller tends to be stronger, suggesting that the
probability of having a critical flaw decreases with diameter.
98
4.2.1 Importance of the Process Zone
A polymer fiber of diameter D with no intrinsic flaws is considered (Figure 30a).
Under applied tension uO, such a fiber's failure strength af would reach the
theoretical limit of the interatomic bonds it consists of, denoted by ath. Similarly,
one could consider a fiber with a distribution of intrinsic flaws. Such a fiber
would fail at a finite 'macroscopic' strength. In contrast, a fiber made of the same
bonds but containing a large flaw will significantly decrease its strength
according to Griffith's size scaling [219, 222], where the crack size scales with the
diameter, such that af ~ 1/T.
The process zone, also depicted schematically in Figure 30b, characterizes the
amount of material that contributes to resisting fracture, and is also referred to as
the 'cavitation box' [240]. It can be understood as the region surrounding a crack
that is damaged during crack propagation. In the limit of a very small process
zone (Figure 30b), on the order of atomic bonds, the material is very brittle like
glass and bonds simply snap to create new surfaces. In the limit of a very large
process zone (Figure 30c), driving a crack through the material leads to
widespread damage that is not limited to the crack surface. An important aspect
of a large process zone is that stress concentrations at the crack tip are
diminished,
further reducing the threat imposed
catastrophic damage to a material.
99
by cracks of causing
C
b
a
oo
D
af=oa
at r
D
D
0
unflawed
no nanostructure
with nanostructure
Figure 30 I (a) A fiber of diameter D that has no intrinsic flaws. Under tension ao, such a fiber's failure
strength af would reach the theoretical strength of the interatomic bonds it consists of, ot. (b) A fiber made
of the same bonds without internal structure but containing a flaw of length a would decrease its strength
according to Griffith's size scaling as the ratio 1 0/D and the strength of the fiber become smaller. (c) A
possible strategy to maintain the strength of the fiber at the macroscale is to increase the size of the process
zone, such that 1o = D. Then, the strength of the fiber will approach the theoretical strength of the internal
structure, af Cath. Figure adapted from Reference [100].
4.2.2 Derivation of the Process Zone Size
The process zone size, characterized by the length-scale to, is indicative of the
fracture toughness K of the fiber [242, 243], since K-,fl0 [244]. This makes
intuitive sense because dissipative processes that increase the size of the process
zone will thereby lead to a larger fracture resistance of polymeric fibers.
For
example, a self-healing processes (via H-bond stick-slip or hidden length in
molecular domains) can increase the toughness during fracture. In addition to
molecular processes, distributed failure processes can encompass micro-cracking,
crack bridging, crack-deflection, as well as interfacial sliding (e.g., shearing of
interfaces and unfolding of organic matrices) [1, 20, 24, 159, 241].
How can the process zone size 10 be identified? In most cases, it can be measured
by experimental analysis only. Some progress has been made from a continuum
mechanical point of view [93, 96, 245]. One can estimate the process zone size 10
100
from the ratio between a materials fracture strength ug and its yield strength -y
(defined as the stress where the material undergoes irreversible, plastic
deformation),
10
= fl
UY
4.9
,
where fl is proportional to the crack size, depends (for example) on the specimen
geometry, and can include nonlinear geometric effects [92].
Equation 4.9 is
related to Equation 2.19, chapter 2.2.1. The scaling law in Equation 4.9 reflects the
importance of the nonlinear nature of the stress-strain relationship as a means to
decouple the failure stress from the yield stress. However, this does not provide
an immediate route to predict 10, because the ratio of failure to yield stress is not
generally known.
4.2.2.1 Experimental observations
For many biomaterials, the process zone size 10 has been experimentally
determined to be on the order of several micrometers, e.g. for bone [20, 246],
polymers [247-249], and quasibrittle materials [250, 251]. The process zone has
also been directly measured in concrete, graphite, and wood via acoustic
emission, digital imaging, and SEM [252-255]. In these studies, the damage zone
surrounding the crack tip was visually identified as process zone. In a recent
paper, empirical relations were used to estimate the process zone size 10 in spider
silk and other polymeric fibers, and found to be on the order of one micrometer
[240, 256]. To obtain this result, the authors invoked an empirical scaling relation
that relates the yield stress to the elastic properties via -y = 0.028 E. As other
analyses, Reference [240] did not describe the fracture properties of fibers from a
fundamental, interatomic potential point of view but rather lumped a variety of
mechanisms into an empirical equation that ultimately relates the yield strength
to the fracture strength.
101
4.2.2.2 Atomistic Derivation
The process zone size can be directly estimated from an interatomic potential.
This fundamental approach accounts for the fact that fracture involves the
rupture of atomic bonds. The generalized Lennard-Jones-n, m-potential (J)
is
often used as an approximation for the behavior of interatomic interactions in
polymers and crystalline materials (e.g., Reference [257]), and therefore provides
a good basis for the study of the fracture mechanisms in natural fibers [258, 259].
The generalized LJ-(n, m)-potential formulation is given by
n
m
n
-L)
L(rnm)=-)
r-
4.10
,
n-mr
Here, ro is the equilibrium bond distance, r the current bond distance, and W, n, m
potential parameters. Similar to the derivation in Reference [258], one finds for
this potential the strain energy density
W =4.11
the stress-displacement function with a = dW/&E, where E = (r - ro)/ro is the
bond strain,
n+1
nmw
a(r, n, m) = (n -
)
+
m+1
0
4.12
-
,
and the elastic modulus E = d2 W/gE 2
nmw
E(r, n, m) =
nm-
(ro n+2 _ (+1)rom+2]
[(n + 1)
-
(m + 1)
-
],
4.13
with fi as the bond volume.
The theoretical attainable bond stress is given by setting E = 0,
_Uth "nt, Mi) =
,
nmw
(m
m+1
+ _1n-m
414
102
Furthermore, the cohesive energy, which equals the fracture surface energy of
the bond, is given by
4.15
dr = -
Ys = fu(r)
These definitions have been reported in Reference [258].
The process zone 10 is given by the Dugdale-Barenblatt yield-strip model (see
chapter 2.2.2),
1 =
8
E
4.16
2'
where GC is the critical energy release rate, a material parameter that quantifies
the amount of energy needed to drive a crack through a surface.
Usually, derivations for nonlinear constitutive behavior entail a linearization of
the elastic modulus around E = 0 (i.e., r = r0 ) [258],
nmw
EO(n, m) =
4.17
,2'
The modulus as it appears in Equation 4.16 is the modulus of the stress far field,
to account for the change in strain energy in the specimen upon crack
propagation. In a very large specimen, it is reasonable to set E = E0 . However, if
the specimen size is small (in the order of the plastic zone), then E # E0 . This is
the case for nanoconfined constituents in many biological materials, e.g., the
fibrils in spider dragline silk or cellulose fibrils in wood, as discussed in chapter
4.1.
In most nonlinear elastic material models, the stress behind the crack tip
degrades with 1/VT, similar to the linear elastic case. This implies that the
material within a zone of 3-5 times the crack size (which can be estimated from
fracture mechanics, here without proof), has a much lower modulus than the far
field. In a nano-sized material, this zone can contain the entire specimen. To
103
account for the highly nonlinear behavior in the cohesive zone, it seems more
appropriate to calculate an average elastic modulus that averages from the crack
.
tip, E = 0, to the linearized modulus E = E0
nmwo
nm+
=
oth(n, m)
m+1
.
E(n,m)
((
m
f2(n + 1) n ++1-1 4.18
Most materials have a modulus that is higher than the theoretical strength, so the
estimate E = P will serve as a lower bound for the process zone size 10 in
Equation 4.16.
Due to the elastic nature of the potential, G, as given by Equation 2.21, chapter
2.2.2, can be simplified to
G= Ys +
dy
0 (fuijdEi
ys.
4.19
Now, an expression for the plastic zone size only in terms of the bond potential
parameters using Equation 4.16 can be written. The lower bound for 10 is given
by the averaged modulus in Equation 4.18,
M+1
n(n + 1) (n+1) n10'0,
=
4.20
r.
8nm
Alternatively, using the linearized expression of the elastic modulus, Equation
4.17, an upper bound for 10 is given by,
2
+ 1)
8nm
w(n + 1)2 (n
10,E=
m+1
n-
4.21
r
The values for 10 are only a function of (n, m) and the bond distance ro. This
assumes a 1D arrangement of bonds, for example present in P-sheets. For a
lattice-like arrangement one would need to sum over the contributions from
several bonds, which would lead to an increase in 10.
104
Equation 4.20 and 4.21 give the ratio of process zone size to the characteristic
length scale ro, with 10/ro = f(n, m). Here, f(n, m) is a function of the parameters
of a generalized Lennard-Jones-potential. Table 4 summarizes the results for
typical combinations of (n, m) and it can be seen l0 /ro is relatively insensitive to
the parameters (n, m). Estimating an upper and lower bound for this ratio yields
an interval of l 0 /ro ~ [0.5,16], or [0.25 nm, 8 nm] for most real materials. An
important observation from this derivation is the existence of a relation between
characteristic length scale ro and process zone size 10, which is in turn directly
connected to the fracture toughness of the material. On the level of chemical
bonds, one can think of ro as the 'lattice' spacing in the strong and often ordered
polymer domains. In strong and tough protein or polymer fibers this refers to the
inter-chain distance in highly aligned P-sheets (e.g., nylon, amyloids, spider
dragline MaSpi and silkworm silks, strained collagen, titin rich myofibrils, and
some synthetic polymers) [260, 261], a-helices (e.g., intermediate filaments, actin
fibers), and P-turns (e.g. silk MaSp2, elastin and some synthesized polymer
fibers) [118]. The ratio ro/1o depends on the actual lattice structure present in the
material and on the specific make-up of its substructure, as well as other effects
such as orientation and temperature. In view of the generality of this analysis
and the purpose of obtaining an order of magnitude estimate, this is considered
negligible.
Table 4
I Process zone (cohesive zone) for the generalized
LJ potential.
n
m
I r
12
8
0.4-9.2
105
The predictions are in agreement with several earlier reports. For soft elastic
materials, Hui et al. estimated the size of the process zone to be approximately 1
nm [262]. Similarly, Porter et al. derived the process zone size 10 for silk materials
to be around 4 nm [263]. Keten et al. investigated the fracture behavior of
hydrogen bond clusters, found in many secondary structural elements of (semi)crystalline polymer fibers, leading to a process zone size of approximately 1 nm
[197]. Generally, this analysis holds not only for polymeric fibers but also for
metals or ceramics. In sum, the calculation based on the LJ potential results in
exceedingly small sizes on the order of a few nanometers. Consequently, this
suggests a low fracture toughness (as K-1fi), in contrast to the experimental
results, which will be addressed in the next section.
4.2.3
Fracture Length Scales in Silk Fibers
How is it possible that polymer materials, like spider silk, show dramatically
higher fracture toughnesses than predicted by the preceding atomistic analysis,
with a remarkable mismatch by a factor of 1,000? This contradiction can be
explained by Equation 4.9. Considering the purely elastic nature of the potential
up to failure, the ratio between yield strength ay and fracture strength af
=
oU
of
a LJ material is approximately one, i.e. af ~ ay (or close to it) [264].
In order to achieve a very large process zone size the yield stress and fracture
strength must be decoupled. As shown in chapter 4.2.2.2, this cannot be achieved
in a homogeneous material and therefore the existence of a heterogeneous
material microstructure is critical. Spider silk's heterogeneity is caused by a
composite arrangement of Alanine-rich nanocrystals within a Glycine-rich semiamorphous phase, see chapter 3. Other well-known examples that incorporate
such comnlec microstructural architectures are wood, bone, glassy sponges,
nacre, and tendons, to name a few [1].
106
In such structures, the characteristic length scale ro is not a material constant, but
depends on the length scale of observation [265]. Figure 31 depicts this concept in
the context of spider dragline silk. On the lowest hierarchical level, the scale of
the atomic bonds, ro and l are small. Locally, the maximum stress is then the
theoretical stress of the perfect crystal ot. Therefore, a strong and tough fiber
requires a nanoscale substructure that has dimensions of the process zone size in
order to be robust at larger scales. In spider silk, nanocrystals constitute this
nanoconfined substructure with dimensions of 2-4 nanometers, see chapter 4.1.5.
On the next hierarchical level, the P-sheet crystals form a structure that can be
understood as a lattice with spacing of ro ~ 10 nm, the distance between the
crystals (ro changes with the length scale of observation). This composite is also
confined to the size of the fibril, such that ro and 10 are again of the same order of
magnitude.
107
Process Zone Size 10
50nm
1nm
M
ET
c
ro
1pm
ro
Stress transfer through
lattice of confined size
Purely
elastic
r
Fibril sliding and delocalization
(soft and hard phases)
Nanoconfined
Fibril
Hydrogen
Bonds
Fiber
Semi-amorphous Phase and
Nanoconfined Crystals
0.2 nm
10 nm
Characteristic Length Scale ro
150 nm
Figure 31 1 Length scales and toughening mechanisms in spider dragline silk. At the lowest hierarchical
level (the scale of the atomic bonds) the maximum stress is the theoretical bond stress O-th, and ro as well as
1o are small (in the order of nanometers). The nanocrystal is extremely robust because it is geometrically
confined to the size of the plastic zone. At the next hierarchical level, the beta-sheet crystals form a structure
that can be understood as a lattice with spacing of ro ~ 10 nm (the distance between the crystals). The
intrinsic strength of the lower scale feature - here the crystal and amorphous phase - is scaled up to the next
scale. Paired with the unfolding of the semi-amorphous protein domains, the process zone size is then on
the order of 20 -150 nm, the size of the fibrils. Through hierarchical assembly, i.e., the weak binding of many
layers of flaw-tolerant fibrils to fibers, the material induces further toughening mechanisms (fibril sliding
and delocalization, inducing a process zone of 1 pm) and maintains its toughness at micrometer dimensions.
Figure adapted from Reference [1001.
The intrinsic strength of the lower scale feature - here the crystal and amorphous
phase - is scaled up to the next larger scale. Paired with the unfolding of the
semi-amorphous protein domains, the process zone size is then of the order of
20-150 nm, the size of the fibrils [56]. This is in agreement with the estimate of the
process zone size 10 /ro ~ [0.5,16].
4.2.4 Continuum Fracture Mechanics Analysis
In order to estimate the length scales of the process zone size in a continuum
sense, appropriate boundary conditions to the crack problem in a fiber must be
selected [85]. Notably, the Griffith crack condition is not an appropriate model
for a flawed fiber, because of the confined boundary. Figure 32 shows three
108
boundary conditions that reflect the influence of intrinsic defects such as cavities
and surface cracks, e.g. on a polymer fiber.
(ii)(i)
(i)
D
D
a
2a
Figure 32 | Three typical boundary conditions for a fiber under tension. (i) Cylinder with circumferential
crack. (ii) Cylinder with inclusion. (iii) 2D tensile specimen with surface crack. Figure adapted from
Reference [100].
cracks with a/D = 0.05 are given by K,(i) = 1.144 aTV, K,(ji) = 0.6368 aV
,
For the three cases the stress intensity factors for a typical value of macroscale
and KJ,(ii) = 1.1473 cirV. Generally, case (i) and case (ii) display a very similar
stress intensification behavior (for a/D < 0.3).
To find the process zone size for this continuum analysis, Equation 2.19 from
chapter 2.2.1, which is a particular form of Equation 4.9 in chapter 4.2.2, is used.
Here, it is important to know that Equation 2.19 and Equation 4.9 differ only by a
factor for a linear elastic material. Equation 2.19 can be rewritten in a more
general form that does not entail the crack length as a specific parameter. Rather,
it is written in terms of the material parameter K, (the stress intensification
factor). The size of the plastic zone for a linear elastic material under mode I
loading is then more generally given by
10
2mI~r \Uy)
=4.22
'
*0
109
where m is a parameter between 1 (plain stress) and 3 (plane strain).
From experimental data for spider silk fibrils, the relation between the 'yield
stress', i.e. the stress at which the unfolding of the protein domains begins (a sort
of plasticity mechanism), and the maximum tensile strength is acf/Cy ~ 4 [37]. At
the failure point of a fiber this yields for plane strain conditions and lo,a,c =
0.22 (uf/cy) 2 a ~ 0.17 D
-
700 nm and lo, = 0.068 (f /y)
2
a
0.04 D ~ 200 nm.
It is well known that most polymer fibers cannot be considered linear elastic.
Either they feature a non-linear 'post-yield' behavior (e.g., spider dragline silk
with a stiffening behavior [50] or silkworm silk with a softening behavior [29]) or
they are generally nonlinear elastic (e.g., elastin with a pronounced stiffening
behavior [266]). Furthermore, fibrous materials often are anisotropic, deform
hyperelastically and/or plastically and are subjected to geometric confinement.
Accounting for these nonlinearities is possible, but does not influence this orderof-magnitude estimate significantly. Therefore, an estimate using linear elastic
fracture mechanics is sufficient.
Finally, the process zone size expected for biomaterials is in the order of
10
300 - 1000 nm,
4.23
in agreement with experimental estimates of the process zone sizes for many
polymeric materials.
4.3
The Importance of Heterogeneity in Silk Fibers
The importance of spider silks heterogeneity in connection with these length
scales has been intensively studied using SEM, X-Ray and neutron scattering
techniques [41, 55, 267-269]. Through hierarchical assembly (chapter 3), i.e. the
weak binding of many layers of flaw-tolerant fibrils to fibers, the material
induces further toughening mechanisms (fibril sliding and delocalization,
110
chapter 4.1.2) and maintains its toughness at micrometer dimensions. This shows
that the resilience of materials is greatly enhanced through hierarchical structure
originating at the nanoscale, as deformation and damage processes become
translated to larger scales [230, 231]. A similar setup can be found in the cellulose
fibers in wood, where an arrangement of nanocrystals forms nanometer-sized
microfibrils that are densely packed into a lattice like structure [270]. Also
collagen (e.g., in bone and mussel threads), keratin based materials, chitinprotein fibers and their derivatives contain highly repetitive patterns on several
length scales that can be interpreted as a lattice with spacing ro [271-273]. The
concept is schematically shown in Figure 33 for a general case. The fiber becomes
robust to flaws at all length scales and does not fail in a brittle manner, when
part of a larger-scale hierarchical structure. This is achieved through the
confinement of each microstructure to the length scale of the process zone size
(called r* in Figure 33), governed by
10/ro ~ [0.5,16],
where ro is the
characteristic size of the length scale under observation.
Hierarchy
Level 0
Level 1
Leve1 2
Building Block
Assembly
M
(m
MWe
ri= rono:r*
seeen
son 0
r2 =rlnlr2*
0
000
..
r3 =r 2 n 2 <r3*
Figure 33 1 Schematic picture of the hierarchical build-up of materials, where at each level the building
blocks are repeated n times such that the total length is confined to r*. At each hierarchical scale, the stress
concentrations become delocalized. This is achieved through the confinement of each microstructure to the
length scale of the process zone size lo/ro = [0.5,16], where ro is the characteristic size of the building block.
The fiber becomes robust to flaws at all these length scales and does not fail in a brittle manner, when part of
a larger-scale hierarchical structure. The resilience of materials is greatly enhanced through hierarchical
structuring from the nanoscale upwards, as deformation and damage processes are translated to larger
scales. Figure adapted from Reference [100].
111
In spider silk, the onset of failure in the early deformation stages of the weakly
bonded semi-amorphous phase controls the nonlinear softening after the elastic
regime (chapter 1.2.2). This constitutes a yield mechanism where c-y ~ (1/4)uf
[37, 50]. A general observation of great importance is that spider silk features a
very small yield stress and at the same time, a very large fracture stress. This
leads to a very large process zone size on the order of 300 nm to 1,000 nm (see
chapter 4.2.4).
The key to these considerations is that the particular nonlinear
stress-strain relationship in silk fibers originates from a hierarchical arrangement
of distinct components, starting at the nanoscale. An overview of various
mechanisms at different hierarchical levels of silk fibers is shown in Table 5.
112
larger
Table 5 1 Summary of key structures and associated mechanisms of upscaling from the atomistic to
scales. Table adapted from Reference [47].
1p-sheet
I Sci
nanocrystals
I
I
Critical P-sheet crystal size
between 2-4 nm allows for
robust and shear-dominated
deformation, enabled by
cooperative action of clusters of
nm
1-Lhnndc
Fibers
Bundling of several fibrils into
fibers where each fibril is in
homogeneous deformation
state; akin to concept of
structure splitting mechanism
where bundles of fibrils are
assembled into fibers to enhance
the overall mechanical
pm
4.4 Conclusion
In this chapter, the existence of an intrinsic mismatch between the length-scales
involved in the fracture mechanics of biological materials is shown and a simple
model to connect the interatomic potential to the fracture toughness of
113
hierarchical materials is derived. Without considering heterogeneous structures,
the size of the process zone derived from the atomistic scale is only a few
nanometers, constituting a mismatch by up to factor 1,000. By incorporating a
hierarchy of structures, each confined to a certain critical length-scale, one can
explain the process zone size observed in experimental observations and link it
directly to an interatomic potential. Beyond the specific case of silk, the strategy
to achieve large process zones is ubiquitous in many natural materials, where
strong nanoconfined constituents (in fibers: crystallized fibrils, in composites:
platelets) are bound by a weak matrix (in fibers: weak chain interactions, in
composites: a weak polymer phase).
The scaling law (Equation 4.9) for the strength of a material and also the related
experimental and theoretical analysis are universal throughout all length scales.
What matters is the interpretation of the parameters, which differs between the
nano- and the macroscale. The nanostructure is fundamental to the mechanisms
that transfer the strength from atomic bonds to the macroscopic fiber. This
paradigm could provide an answer to the longstanding question how natural
fibers scale up the nanoscale strength to the experimentally observed high
strength, extensibility, and robustness. By controlling parameters such as the
stiffness at the scale of molecular bonds, it is possible to map nanoscale features
to the macroscale, enabling a synergistic interplay of effects at different length
scales. Through the regulation of deformation mechanisms of biopolymer fibers
at the nanoscale by chemical engineering it will become possible to tune the
mechanical
performance,
and
specifically
the
failure
characteristics,
to
engineering requirements [274-277]. This insight provides a path towards new
material designs by embracing heterogeneous structures.
114
5 Supercontraction - Silk's Interaction with
Water
The research and review presented in this chapter will be published in:
*
T. Giesa, R. Schuetz, A. Masic, P. Fratzl, M.
J.
Buehler, Molecular Origin of
Supercontraction in Spider Dragline Silk Revealed by
Simulation and
Experiment. In submission, 2015.
All experiments presented in this chapter were performed by Roman Schuetz
and Dr. Admir Masic at the Max Planck Institute for Colloids and Interfaces in
Potsdam, Germany.
In this chapter, the following questions regarding silk supercontraction are
answered:
" What is silk supercontraction?
*
Which parts of silk's heterogeneous nanostructure is responsible for the
supercontraction mechanism?
" Are there specific residues in the silk sequence that can be identified as
key players?
" How can the supercontraction mechanism be suppressed or modified?
Research strategy:
Supercontraction is the phenomenon where dragline silk shrinks by up to 50%
when immersed in water, and if the fiber is constrained this will generate a
tensile stress called supercontraction stress. The molecular origin of dragline silk
supercontraction is explored using a full-atomistic model and molecular
115
dynamics combined with in situ Raman spectroscopy and mechanical testing in a
humidity controlled chamber. The experimental platform can monitor the extent
of supercontraction
and
molecular
interactions
simultaneously,
whereas
molecular dynamics simulations provide a detailed view on the thermodynamics
of the material and the behavior of individual residues. A genetic engineering
strategy to alter silk's behavior to industrial requirements is proposed. The most
important parts of the silk amorphous structure that control supercontraction are
identified using a hydrogen bond analysis and a rotamer analysis. Informed
mutations to the core sequence of N. Clavipes dragline silk are tested that reduce
or even reverse the supercontraction mechanism. This study demonstrates the
importance of a combined experimental and computational approach for genetic
engineering and innovative materials design, not only for silk.
5.1 Background
Spider dragline silk has evolved over millions of years to develop finely tuned
mechanical properties to serve specific functions, including the ability to change
its material properties upon external signals [28, 278, 279]. The structure of
Nephila Clavipes MaSpi dragline silk is described in detail in chapter 3.1.2. Water
has the ability to fundamentally reorganize silk's molecular structure and can
cause dramatic changes in mechanical properties and physical characteristics
[280-284]. Immersion in water typically results in the reduction of the fiber's
stiffness by up to an order of magnitude, and noticeable improvement in
breaking elongation [282, 285-289]. At high humidity, some spider dragline silks
will shrink by up to 50%, a phenomenon known as supercontraction [290, 291].
N. Clavipes dragline silk reversibly shrinks 15-20%, and if the fiber is constrained
it will generate a tensile stress [41, 282, 292-296]. There is an ongoing discussion
on whether supercontraction is an evolutionary advantage [296, 297], or a
116
constraint [298]. It is an essential feature of the spinning process, since the wet
elastomeric silk can be processed easier [291].
5.1.1 Mechanism of Supercontraction
While there are numerous studies on supercontraction, the exact mechanism
behind it has not yet been revealed [299]. It has been suggested that since the Psheet crystals are hydrophobic, they do not undergo significant structural
changes when hydrated, so the origin of the supercontraction phenomenon is
likely to be located in the semi-amorphous phase only [288, 300]. Above a critical
hydration level (-70%), water molecules intrude the H-bond network between
strands in the amorphous structure and allow them to reorganize into a less
ordered, more coiled, lower energy state [294, 296, 298]. Also, their orientation
relative to the bulk fiber decreases [296]. Concurrently, the orientation of the
disordered and Glycine-rich linker regions (GGX motif) decreases [298]. The
response of silk to water indicates that the dry fiber is frozen into a glassy state
that is partially extended. Exposed to water releases the glassy state and the
wetted silk turns into an elastomer [300-303]. Using nuclear magnetic resonance
Yang et al. linked the supercontraction process to the highly conserved
YGGLGSQGAGR block in the silk sequence [284]. They identified Leucine (Leu,
L) as potential key residue of the supercontraction effect, while noting the
proximity of Tyrosine (Tyr, Y) and Arginine (Arg, R).
5.1.2 Combined Simulation and Experimental Approach
Figure 34 shows the heterogeneous hierarchical structure of dragline silk
(chapter 3.1.2) together with the experimental setup (Figure 34e) used to measure
the in situ supercontraction process of N. Clavipes silk. After increasing the
humidity, the strain in the fiber decreases under isostatic conditions. The
molecular dynamics study consists of two experiments, in both silk is
117
represented by 15 repeats of the main silk sequence, Figure 34a. This constitutes
the representative unit of silk, with a stable P-sheet crystal and two independent
amorphous phases. The first experiment considers a model of spider dragline
silk protein MaSpi, equilibrated in a water box by Replica Exchange Molecular
dynamics and explicit water simulation [304]. To measure supercontraction, the
effect of removing the solvent on the molecular structure and shape, hydrogen
bonding, and entropy of the P-sheet crystal and semi-amorphous phase of MaSpl
is evaluated. By comparison to Raman spectroscopic results of wet and dry silk,
the residues most active in the supercontraction process are identified. In the
second experiment, point mutations on the core sequence shown in Figure 34 are
performed, where the identified residues are replaced by residues with shorter
side chains. The effect on the level of supercontraction and stability of the
structure is investigated (Figure 34f).
118
0
a
I
CO
.0
's-
0r
ynm
0
2
'0
Wildypedr 9gIne silk sequence
GGAGQGGYGGLGSQGAGRGGLGGQGAG
GGAGQGGYGGLGSQGAGRGGLGGQ
Sequence modification to suppress supercontraction
4
GGAGQGGFGGLGAQGAGLGGLGGQGAG
GGAGQGGFGGLGAQGAGLGGLGGQ
Figure 34 1 Nephila Clavipes dragline silk nanostructure and supercontraction mechanism- Bridging from
experiments to modeling. Supercontraction is the shrinking of silk in water in comparison to its dry state (by
up to 50% depending on the silk, around 15% in Nephila Clavipes silk). (a) In the full-atomistic molecular
dynamics simulation silk is represented by a unit of silk, with a stable 1-sheet crystal and two amorphous
phases. The amorphous phase is believed to be responsible for the supercontraction mechanism. (b)-(d) Silk
assembles in nanofibrils of size 20-150 nanometers. Hundreds of fibrils form dragline fibers of micrometer
size. The spider spins the strong dragline silk as structural support for its webs and as lifeline for escape. (e)
Measurement of the supercontraction process on dragline silk fibers in a humidity chamber using tensile
testing and in situ Raman spectroscopy. (f) In this multiscale approach the macroscale supercontraction
effect is linked to nanoscale changes in the structure. Mutations to the core sequence can be proposed to
suppress the supercontraction effect. (d) courtesy of Charles J. Sharp. Figure composition, courtesy of Dr.
James Weaver, Harvard University.
5.1.3
Molecular Dynamics Setup
MD simulations are performed using a model of N. clavipes MaSpi dragline silk,
predicted from REMD and equilibration in explicit solvent [279, 304, 305]. The
15-strand sample of MaSpi including a crystal and two amorphous phases is
further equilibrated in an explicit water box for 30 ns without holonomic
constraints and a 0.5 fs timestep. The GROMACS software package with
CHARMM27 force field and the Tip3P water model is used for the explicit water
simulations of this complex biological molecule. This force field is able to capture
electrostatic interactions without chemical reactions [306]. Isobaric-isothermal
119
conditions (1 bar, 300 K) are modeled with charge-neutralizing solvent and 15
mmol sodium chloride. Equilibration is performed with Particle Mesh Ewald
(PME) electrostatics, velocity-rescale thermostat and Nose-Hoover barostat.
The vacuum model is also simulated for 30 ns in a canonical ensemble. To
prevent image interactions, the periodic box wraps the protein by at least 10 A
distance. VMD including the STRIDE secondary structure algorithm is used for
visualization
trajectories
and analysis
[307].
Hydrogen
of protein molecules
bonding
and
and their equilibration
hydrogen bond
energies
are
determined by geometric proximity of hydrogen donor and acceptor, using DSSP
[133]. For the H-bonds, a 3.0 A cutoff distance and a 300 cutoff angle is used.
5.2 Supercontraction of the silk wildtype
5.2.1 Silk Supercontraction in Simulation and Experiment
The graph in Figure 35 shows the typical (macroscopic) in vitro supercontraction
process of N. Clavipes dragline silk using the experimental setup schematically
shown (also in Figure 34e). After increasing the humidity from 10% to 90% (blue
line), the strain in the fiber decreases under isostatic conditions (red line).
120
Humidity Generator
To spectrograph
Motor
|Laser
Silk fiber
Load cel
0
--
-
90
75
-T560
C
45
~30
-15
15
20
60
40
Time (min)
80
the humidity (blue
Figure 35 I In vitro supercontraction process and experimental setup. After increasing
A. Masic. Data
credit:
Image
line).
(red
line), the strain in the fiber decreases under isostatic conditions
Masic.
A.
courtesy
collected by R. Schuetz and A. Masic. Figure
Dry silk, at a humidity around 10%, is very stiff and not extensible, and wet silk,
at 100% humidity, is much more compliant and extensible [282, 286-289]. Figure
36 shows a tensile experiment sequence of a single N. Clavipes fiber in the elastic
region at three different humidity conditions: at 25%RH (black line), 50%RH
(blue line) and after the supercontraction at 90%RH (red line).
121
3,0 --
2,5
-
25% rh
50% rh
90% rh
2,0-
E
0
LL
,1,51,0
0,5
0,0
I
10500
----
-------------
11000
11500
-----------
12000
I
12500
I
13000
Length (pm)
Figure 36 I Tensile experiment sequence of a single fiber in the elastic region at three different humidity
conditions: at 25%RH (black line), 50%RH (blue line) and after the supercontraction at 90%RH (red line).
Data collected by R. Schuetz and A. Masic. Figure courtesy A. Masic.
In the simulation, supercontraction is measured by the change in the average
end-to-end length of the molecule chains as well as the radius of gyration from
the molecular dynamics equilibrium trajectory of the silk vacuum and hydrated
model, shown schematically in Figure 37. The radius of gyration (weight
averaged ellipsoid) reflects the shape of a 3D molecule and is indicated in Figure
37 together with an overlay of snapshots of the hydrated and the vacuum
structure. For details, see chapter 2.1.4. In the wildtype, a contraction from dry to
wet state of 13.2 + 5% (radius of gyration) and a contraction of 8.6 + 1.7%
(average end-to-end length) is determined. For the contraction in the axial
direction of N. Clavipes dragline silk fibers, agreement between simulation and
experiment (13.2
0.2%) is found. The values also reflect other literature results
for dragline silk fibers [282]. The contraction does not lead to a significant change
in volume, as determined from the radius of gyration in the three axis directions
of the fiber, Figure 37.
122
f
Simulation Radius
Simulation Length
Experiment
20
15
0-
10
-
-5
Sz
LO
-20
AL 2
DRY
15-
z (axis)
-y
is
Figure 37 | Supercontraction measured from Simulation and Experiment. The strand silk model
well
as
length
end-to-end
average
by
measured
is
supercontraction
equilibrated in water and vacuum and
as radius of gyration of vacuum versus hydrated model. Results of the simulation in three axis directions are
compared with experimental results and good agreement is found for the contraction in the axial direction.
5.2.2 Secondary Structure Change during Supercontraction
Figure 38 shows the secondary structure of the N. Clavipes MaSpi silk wildtype
sequence determined from Molecular Dynamics Simulation in dry and wet
conditions. The -sheet content increases from wet to dry conditions, while there
is more disordered (coiled) structure in wet conditions, in agreement with
experimental results reported elsewhere [116]. The secondary structure is
averaged over 30 ns of the simulation time and determined using the STRIDE
algorithm. Raman spectroscopy
performed on supercontracted
silk fibers
suggested a change in secondary structure, specifically the loss of ordered
structures including turns, helices, and to a lesser extent, r-sheets, and the gain of
disordered random coils [308].
123
80-
iWater
iVacuum
70.
60
50S403020'
10
0
Betasheet
I
Coil
Helix
Turn
Figure 38 1 Secondary Structure of the MaSpl dragline silk wildtype determined from molecular dynamics
simulation using the STRIDE algorithm.
5.3 Molecular Origin of Supercontraction
5.3.1 Raman Spectroscopy and Hydrogen Bonding
In Figure 39 the Raman spectra of N. Clavipes dragline silk in wet (85% RH) and
dry (15% RH) conditions are reported. While slight differences can be easily
detected in the analyzed spectral range, the most striking change is observed in
the 830 - 860 cm' region associated with vibrations in the Tyrosine (Tyr) side
chain (Fermi resonance between the in-plane breathing mode of the phenol ring
and an overtone of the out-of-plane deformation mode). The relative intensity of
the two bands depends sensitively on the extent of mixing of the two modes, and
thus on the hydrogen bonding condition of Tyr's phenol side-chain. The relative
intensity ratio of two peaks 1860/1830 is up to 2.5 when the OH-group of
Tyrosine serves as an acceptor (A) of a strong hydrogen bond (A/D >> 1) and is
down to 0.3 when the OH-group serves as a donor (D) of a strong hydrogen
bond (A/D << 1) [3091. Figure 39 (left) shows values for 1860/1830 peak ratios
124
determined from the deconvoluted Raman spectra. The line at peak ratio 1.5 is
not established and serves only to illustrate a comparison to the simulation. On
average, the Tyr residues tend to be both donor and acceptor of hydrogen bonds
in dry conditions and turn into strong acceptors in supercontracted wet state.
This suggests a specific involvement of Tyr and specifically of the OH-group in
the folding and supercontraction of silk. While this phenomenon has been
observed [310], the precise implications for the supercontraction process have not
yet been investigated.
3
DRY
wet
D
2.5
-WET
Tyr
U)
0.5
800
900 1000 1100
Raman shift (1/cm)
0
Raman Spectroscopy
Figure 39
I Polarized
Raman scattering of N. Clavipes dragline silk in wet (85% RH) and dry (15% RH)
1
conditions. Significant changes are observed in the 830 - 860 cm- region which can be associated with
vibrations in the Tyrosine OH-group. The relative intensity ratio of two peaks 1860/1833 suggests a role of
Tyrosine and specifically of the OH-group in protein folding and the supercontraction of silk. Experimental
data collected by R. Schuetz and A. Masic. Figure (left) courtesy A. Masic.
125
The hydrogen bonding in the 20 nanoseconds molecular dynamics trajectory in
fully solvated and vacuum conditions is analyzed. The change in
Acceptor/Donor (A/D) ratio,
Figure 40, follows the same trend as in Figure 39. In agreement with the Raman
experimental results, Tyr changes its donor/acceptor nature of hydrogen bonds
when passing form dry to wet conditions. This change is mainly associated with
the OH-group, as seen in the subplot of
Figure 40. Interestingly, a similar change is prominent in other polar and/or
charged side chains such as Arginine (Arg) and Serine (Ser), suggesting a
possible contribution to the macroscopic contraction of silk also from these
residues. Note, that all these residues are located in the amorphous part of the
silk sequence.
1.5
15
0.5
Molecular Dynamics
Figure 40 1 The acceptor/Donor (A/D) ratio determined from the hydrogen bonding analysis of the
molecular dynamics trajectory is in agreement with the Raman experimental results. Tyrosine tends to be a
donor in dry conditions and a donor/acceptor in wet conditions. In the simulation, other polar and/or
charged residues in the amorphous part of silk such as Arginine and Serine display a similar behavior.
126
5.3.2 Simulated Infrared Spectrum and Vibrational Density of States
When shined on with monochromatic light, silk features characteristic peaks in
its spectrum. Using the infrared (IR) and Raman spectrum, the composition,
crystallinity and bonding state can be determined. Both spectra are established
experimental tools, see chapter 2.1.8. Although quantities like crystallinity and
H-bonding can be determined from molecular dynamics trajectories, a direct
comparison to the experimental spectra is useful. Figure 41 and Figure 42 show
the simulated IR spectrum for the MaSP1 silk nanostructure. The characteristic
peaks around 1650 cm-' indicate the amount of P-sheet present. Silk in wet
conditions cannot be analyzed using IR spectroscopy.
However, Raman
spectroscopy can be applied in dry and wet conditions, but is not easily
simulated. Figure 43 shows the vibrational density of states of dry and wet silk
versus the Raman spectrum (dry silk). While many similarities, especially in the
high frequency regime, can be observed, the spectra do not match perfectly. This
is due to the light-to-excitation coupling factor C(o>) that has to be determined.
More fundamental studies are necessary to connect the Raman spectrum and the
VDOS for biomolecules, as to date no literature is available. Especially in the low
frequency spectrum, e.g. in the 850 cm-' regime of Tyr's breathing mode, the
spectrum is not detailed enough. Longer simulations are necessary to capture
those low frequency vibrations.
127
0.0140.012[
Z.
0.01
0.008
h
C
0.0060.004
0.002
0
2000
1 uuU
Shift [cm~ 1]
Figure 41 1 Simulated infrared (IR) spectrum for silk in vacuum (no filter).
LI I~
0. r~4'~.
6..
I--Water
0.01[
I
0.00W1
C
0.006F
a
I
0.0040.002-
100
I
1.
RmR
.I
1000
Shift [cm- 1
1500
Figure 42 1 Simulated infrared (IR) spectrum for silk in water (no filter).
128
2000
45
-VDOS
-VDOS
DRY
WET
-Raman
DRY
40
35
30
20
15
10
5
800
1000
1200
1400
1600
Shift [cm 1]
Figure 43 | Simulated VDOS spectrum for silk in water and vacuum versus Raman spectrum.
5.3.3 Energy Balance and Supercontraction Stress
To gain a more fundamental understanding of the supercontraction process, the
energetics of supercontraction and how a stress can be generated from it is
discussed in this chapter. The supercontraction strain esc = AL/LO is the strain
generated in an unconstrained fiber when immersed in a humid environment.
The supercontraction stress -scis the stress needed to retain a contracting fiber at
its original uncontracted length. It can be determined from tensile tests
(experiment and simulation) or a free energy balance (simulation). In the
following, the energy balance of supercontraction is derived from the Helmholtz
Free Energy.
To estimate the supercontraction stress, the change in free energy of the system
during supercontraction has to be determined. The thermodynamic ensemble
during the simulation is NVT, since the vacuum simulation requires a constant
volume (otherwise the box collapses). The simulation in full solvation is first
equilibrated in NPT, to set the pressure at ibar.
129
For clarity, all described changes are from dry to wet state. For the protein, the
change in entropy AS is expected to be positive (since the wet system is more
'disordered'). The change in enthalpy (or in this case internal energy AU) is
related to the free energy of solvation, and changes due to the formation of new
hydrogen bonds. It consists of an endothermic part (breaking protein-protein
and solvent-solvent H-bonds) and a competing exothermic part (forming new
solvent-protein H-bonds). Hence, the change in free energy can be decomposed
as
AA = Awet - Ady ~ AAH- TAS.
5.1
It is assumed that the change in free energy is directly converted into the 1D
supercontraction stress. The change in free energy is then related to the
supercontraction force by
F ~
AA
A
Al'
5.2
where Al is the change in length due to supercontraction.
The stress needed to pull a supercontracted silk fiber into its original (dry) state
is given by
4AA
irD2 Al
-
4(AAH - TAS)
D 2A
5.3
'
sc
4F
D2
with D as the molecule diameter.
5.3.3.1
Entropic Contribution
The entropic term TAS is determined using the methodology described in
chapter 2.1.6. In order to reduce the memory required to compute the
eigenvalues of the covariance matrix, the system is divided in three parts, the left
and right amorphous parts and the crystalline part separating them. This is
possible due to the stability of the crystal, since the number of representations of
130
the total system can be computed as the product of the number
representations of the subsystems, M
=
of
M 1M 2 M3 . This holds true as long as the
particles in the three systems remain distinguishable (which they are in a
molecular dynamics simulation). Therefore, the entropy S = k ln(M) can be
calculated as the sum of the entropies of the subsystems, S
= S1
+ S2 + S3. By
splitting the calculation into three parts using the different subsets of atoms of
the same trajectory, the computation becomes feasible.
The entropy is determined from a 5 ns unconstrained simulation in a canonical
ensemble (NVT) with 0.5 fs timestep. In the vacuum simulation the entropy is
calculated from the trajectory of the aligned molecule. In the solvated simulation
the entropy is calculated by removing the solvent from the final trajectory and
determining the entropy of the silk molecule. While this neglects the entropic
contribution of the water in the structure, the silk molecule before and after
desolvation in a canonical ensemble can be compared (since N, V, and T are equal
in both systems). The thermostat in the solvated simulation separated water and
solute, such that the temperature in the protein was indeed constant at 300 K.
Table 6 summarizes the entropies for the silk molecule. The change in entropy,
from dry to wet, is AS ~ 2.1 MJ/mol at T = 300 K, a 12.3% increase of absolute
entropy.
.
Table 6 1 Entropy in J/molK for vacuum and solvated structure split in three independent parts S 1 , S 2 , S 3
The change in entropy is calculated for the amorphous phase only and the value in brackets gives the
change for the entire structure.
Entropy [J/molK]
S,
Vacuum
S2
S3
S,
Water
S2
S3
Difference
Quasiharmonic
Schlitter
28,272
7,060
30,696
7,920
29,931
30,739
8,361
34,299
7,035 (7,476)
27,477
31,041
7,495
32,008
7,300 (7,735)
131
5.3.3.2 Enthalpic Contribution
The enthalpic term AAH is approximately the change in internal energy, in this
case the solvation energy. This can be shown by the following approximation. In
-
the present isothermal system the change in Helmholtz Free Energy dA = dU
TdS
and
the
Gibbs
Energy dG = dH - TdS = dU + d(pV) - TdS
Free
are
approximately identical:
0(d(pV))
dp dV : 10 N/mm
2
(150 nm 45 nm 45 nm)
3 - 10-30 kJ
1.83 10-6 kj/mol «TdS.
Here, dp is approximated with the change in pressure from vacuum to
atmospheric conditions (i.e., 1 bar). The change in volume is approximated as the
system volume of the silk unit cell. This yields an upper bound and shows that
the term d(pV) is several orders of magnitude smaller than the other terms.
Therefore, in this case, dG ; dA holds.
AAH is determined with the methodology described in chapter 2.1.7. The silk
molecule in this study contains 15 chains and approximately 10,000 atoms. With
the water molecules this amounts to approximately 150,000 atoms. Therefore, it
is not possible to decouple the degrees of freedom, which is needed for the Amethod. The solvent accessible surface area has AAH = 1.25 + 0.05 MJ/mol free
energy of solvation associated with it (GROMACS). The core sequence of silk is a
slightly hydrophobic material [311], therefore the enthalpic term is endothermic
(of opposite sign as the entropic term, but smaller) and reduces the stress needed
to reverse supercontraction. The internal energy part that actively contributes to
the supercontraction effect is the change in H-bonding within the silk molecule,
which then alters the shape of the molecule. For comparison, the number of Hbonds within the protein (solute-solute) in dry and wet state is calculated. On
average, 90 to 100 additional H-bonds are formed in the dry structure (with a
132
typical bonding energy between 4-20 kJ/mol). This strongly contributes to the
free energy of solvation.
5.3.3.3
Supercontraction Stress
The entropic part of the supercontraction stress cent needed to transition from
the supercontracted to the un-contracted state is then determined by cent ~
4 TAS/(wr Ar D 2 ), where Ar is the change in length (-13%), and D is the diameter
of the molecule (- 4 nm). This yields an entropic supercontraction stress of
Uent = 64.5 + 10.9 MPa.
With TAS ~ 2.1 MI/mol and AAH ~ 1.25 MJ/mol follows
usc = 37.4 + 12.4 MPa,
5.4
where Al ~ 3 nm and D ~ 4 nm.
Figure 44 shows the supercontraction strain versus stress of silk dragline silk
fibers from simulation and experiment. Specifically, the simulation data points in
Figure 44 are determined in two different ways. The data point at zero stress is
obtained directly from the change of shape, as equilibrium simulations are used
to determine the size of the silk molecule. The zero-strain stress is the
supercontraction stress usc (computed by decomposing the free energy as
described above). The change in entropy and enthalpy is calculated, not absolute
values. This change in internal energy generates the supercontraction stress.
Alternatively, the supercontraction stress is directly estimated from simulation
with a tensile test, using the stress at supercontraction strain, the blue dots in
Figure 44. This stress is determined as asim ~ 70 MPa (blue line in Figure 44),
very close to the entropic stress of cent = 64.5 + 10.9 MPa (red shaded area in
Figure 44). This is intuitive, since the tensile test is performed in solvent and the
energy related to the desolvation has not yet been considered.
133
-
0.2-
o
o
v
0.15
Experiment (this study)
Experiment (Literature)
Pulling Simulation
Entropic
9 Entropic + U.
Z9
C
0
0.1
0.05
0
60
40
20
Supercontraction Stress [MPa
80
Figure 44 I Supercontraction strain versus stress for dragline silk fibers determined from experiment and
in
simulation. The simulation data points are found by determining the entropy of spider silk protein
in
similarity
The
supercontraction.
reverse
to
needed
stress
the
deriving
and
hydrated and dry conditions,
a
provides
difference
size
in
magnitude
of
orders
the
despite
simulation
and
shape of the experimental
amorphous
the
in
strong indication that the supercontraction process is mainly driven by entropic effects
structure as well as changes in H-bonding. Experimental data collected by R. Schuetz and A. Masic.
The shaded area in between the zero-stress and zero-strain value connects the
lower and upper values of the standard deviation and hence indicates only a
possible pathway between those two states. This pathway is not necessarily
linear. Figure 44 also presents experimental data for silk fibers that were
generated from tensile tests of dragline silk fibers. The experimental
supercontraction stress and strain of N. Clavipes (orb-weaving) is osc ~ 30 MPa
and Esc ~ 13 %.
This is in agreement with literature results for N. Clavipes
dragline silk (a = 38 + 5 MPa) and A. Aurantial A. Diadematus (same family as
Nephilae, a = 40 + 4 MPa) [312]. It is notable that these stresses are well below the
yield point of spider dragline silk (ca. 150 MPa).
The results presented in Figure 44 have a range of important implications.
Agreement is found between the experimental results and the theoretical
134
predictions, when including the enthalpic contribution in the free energy
balance.
5.3.3.4 Ratio of Enthalpicand EntropicContribution
Among the different types of silks of orbweaving spiders, the ratio between
supercontraction stress and supercontraction strain is of similar magnitude,
2 - 3 MPa/%. This suggests that the free energy scales directly with the
supercontracted length. Therfore, the mechanism behind supercontraction is
similar for different types of dragline silk. This claim is supported with
supercontraction experiments of C. Salei (non-orbweaving, asc ~ 150 MPa, esc =
0.23), shown in Figure 45 (in similar style as Figure 44). Literature results for a
range of orbiculariae(Lsc = 66 + 10 MPa, esc = 0.32 + 0.06) are also plotted [313].
0 .4 rT'
O1
-
T
0
N. Clavipes (this study)
v N. Edulis (this study)
0.35
a N Edulis (Literature)
0j
0 C. Salei (this study)
0 Orbiculariae (Literature)
N. Clavipes (Simulation)
1
S0.25
.0
- --
0.21
W0.15j
.
o
0.054
0
0
100
50
Supercontraction Stress [MPaj
150
-
.n
among species.
Figure 45 I The ratio between supercontraction strain and supercontraction stress is similar
the mechanism
Therefore,
This suggests that the free energy scales directly with the supercontracted length.
collected by R.
data
Experimental
behind supercontraction is similar for different types of dragline silk.
Schuetz and A. Masic.
135
In conclusion, the supercontraction process is predominantly driven by entropic
effects
in
the
rearrangements),
amorphous
part of
whereas the
the structure
(and H-bond
related
P-sheet crystals remain mainly unaffected.
Therefore, it should be possible to control the supercontraction effect by
performing a targeted mutation on the key residues that mostly contribute to the
change in entropy and internal energy.
5.3.4 Conformational Changes
From the hydrogen bonding analysis and the Raman spectrum it can be inferred
that polar and/or charged amino acid residues with large side chains such as Tyr
and Arg are potential key players in the supercontraction process. This is
reasonable considering the polar nature of water interacting with the protein.
However, it remains unclear through which type of mechanisms these residues
are able to affect the protein structure. Conformational changes in proteins are
often linked to changes in dihedral angles, the torsion angles in the residue
backbone and the side-chain. Probability distribution for the backbone dihedrals
(P and 'T in form of a Ramachandran plot are plotted [314]. They are calculated
from the trajectory of the molecular dynamics simulation in wet and dry state.
Figure 54 shows the Ramachandran for the entire silk molecule (excluding
Glycine) in dry (left) and wet (middle) state as well as the change in dihedral
angle distribution from dry to wet state (right). The distributions are normalized
as probabilities. The P-sheets present in the dry state turn into mostly random
and helical structures in the wet state.
136
ALL No GLY
0.015
150
150
100
100
IOGLY
5050
-L
0
-.
0.05
150
0045
0-04
.035
100
0
0
000
-50
-150O
-10
005
so
P0
0
-.
-50
0
001-.0
o[oz
-150
-
0.01
-100
-100-100
-100
n0LY
0
0
100
150
-150
-100
-50
100
0
150
0
-15o-00
-1
-100
-so0
50
100
ISO
-0.015
wet (middle)
Figure 46 I Ramachandran plot of the entire silk molecule (excluding Glycine) in dry (left) and
are
distributions
The
(right).
state
wet
state as well as the change in dihedral angle distribution from dry to
helical
and
random
mostly
into
turn
state
dry
the
in
normalized as probabilities. The P-sheets present
structures in the wet state.
A more detailed analysis is possible when the side-chain dihedrals Xi of all
residues are analyzed individually. The following graphs and tables show the
change in backbone and side-chain dihedrals of the amino acids in the semiamorphous phase of silk. The distribution of the side-chain dihedrals Xi is also
plotted. The allowed configurations of an amino acid are called rotamers. They
are tabulated in libraries [315, 316] and are associated with specific secondary
structures. Therefore, one can infer conformational changes and associated
secondary structure changes from the dihedral shifts of individual amino acids.
Secondary structures (letter symbols, see
Table 7) are assigned to the rotamers present in the silk structure and the
configurational shifts are identified. In the tables, the rotamer type for each
-
combination of dihedrals is shown: + stands for gauche-positive rotamer type,
stands for gauche-negativerotamer type, t stands for trans rotamer type.
137
Table 7 | Nomenclature for Secondary Structure Assignments
Letter
o, g, n
e,m
Associated Secondary Structure
Right-handed helix, 3 10-helix
I P-sheet
5.3.4.1 Alanine
Figure 47 shows the structure, dihedrals and associated structure shift for
Alanine (Ala, A). Agreement with the experimental dihedral value (-135,150) is
found [123]. Small changes are observed from dry to wet.
ALA
0.015
15'
).09
10(
0.01
D.07
0.005
D.06
54
.05
0
D.04
-5'
D.03
D.02
-101
-0.01
D.01
-15
-0.015
Figure 47 1 Changes in backbone dihedrals of Alanine.
138
5.3.4.2 Glycine
Figure 48 shows the structure, dihedrals and associated structure shift for
Glycine (Gly, G). Agreement with the experimental dihedral value is found [123].
Glycine is extremely flexible, hence the presence of additional dihedral
conformations is not unexpected. Changes are observed from dry to wet, but no
clear assignment is possible.
GLY
0015
0.03
r
iso5 GY
1et
ISO4LY
0.01
0.026
100
100
so
50
0-O
D
IDO
0.0150-
0
0,01
-Wo
-50
-
000.O5
0.02
0
0
-so-000
-a0
_01
00010.006
-150015
015
-10-100- 5
0
so
100
-
-100
-so
0
so
100
So 0
-iso -1
-so
0
so
I i NO 0so
Figure 48 1 Changes in backbone dihedrals of Glycine.
5.3.4.3 Serine
Figure 49 and Table 8 show the structure, dihedrals and associated structure shift
for Serine (Ser, S). Serine has a rather small but polar and hydrophilic side-chain
that is not very flexible. While Serine features a shift from rotamer 3 to rotamer 1
(from dry to wet), there is no clear association with the changes in secondary
structure. Serine is not expected to be important for supercontraction.
139
SER
,-weI
a
2
X1
3
-150
-100
-50
0
X,
50
100
150
1
0.1
0.09
0.00
19
D.05
Is
D.04
UC
0.03
0,07
0.02
0.06
0.01
0.05
-0.01
-002
0.04
0.03
-10
-15
0.02
-10(
0.01
-15(
0
4p
Figure 49 | Changes in backbone and side-chain dihedrals of Serine.
140
-0.03
-0.04
-.005
Table 8 | Rotamers and associated secondary structures of Serine.
Rotamer
Xi
2
-67' (t)
0, gn
x
x
e,m
p
e
x
5.3.4.4 Tyrosine
Figure 50 and
Table 9 show the structure, dihedrals and associated structure shift for Tyrosine
(Tyr,Y). Tyrosine has a larger polar and hydrophobic side-chain with two
degrees of freedom. xjis rather unflexible and does not shift from dry to wet
state. X2 (movement of the phenol ring) is associated with shifts from rotamer 3
and rotamer 4 to rotamer 2 (from dry to wet). In the dry state Tyrosine is
involved in structures (sheets and helices), whereas in the wet state it tends to
form random structures. Due to its hydrophobicity, Tyrosine tends to interact
with the solute itself. Here, a clear shift can be observed. Tyrosine could be
important for supercontraction.
141
TYR
+
2
2,4
1,3
C1
3
3
X2
4
1
Xii
A
4)
-50
-100
-150
--
0
X, M*)
[
50
150
100
-100
-150
-50
0
z 2 I'
50
100
[003
I
0.03
005
W.yi
150
0.02
0.045
10.04
-001
0.035
50
0.025
0.02
so
-50
-001
.015
-IC
-i
150
-100
0.005
A
-
!
-1500
10
50.0
0
4.
4,
Figure 50 1 Changes in backbone and side-chain dihedrals of Tyrosine.
Table 9 1 Rotamers and associated secondary structures of Tyrosine.
Rotamer
Xi
2
65 (+)
98* (-)
4
740 (+)
167'(t)
I
i
X2
Io,g,nI e,m I
X
x
x
I
I
e
p
Ix
I
5.3.4.5 Leucine
Figure 51 and Table 10 show the structure, dihedrals and associated structure
shift for Leucine (Leu,L). Leucine, like Tyrosine, has a hydrophobic side-chain
with two degrees of freedom, but is non-polar. xjis rather unflexible and does
not shift from dry to wet state. X2 is associated with a small shift from rotamer 4
142
to rotamer 1 and more importantly from rotamer 6 to rotamer 2,3,4 (from dry to
wet). In the dry state Leucine is involved in structures (sheets and helices),
whereas in the wet state it tends to form random structures. Since most of these
rotamers are involved in the formation of various structures, there is no clear
assignment possible.
-wet
LEU
-
1,3,6
2
2,3,4,5
46
5.'V XX
a.
6
4
5
10
-50
-100
150
0
x, [M
50
100
150
-150
LEU ciy
-100
0
-50
x 2[1
so
150
100
0.03
15
005
50
002
10
0.04
0,01
60
003
0
9.
0
0.025
005
0.026
-0
-5
-. 01
0.0
-10
-0.02
0.006
-is
M
-100
-150
-0.03
10
00
Figure 51 1Changes in backbone and side-chain dihedrals of Leucine.
143
Table 10 | Rotamers and associated secondary structures of Leucine.
o,g, n e, m
Rotamer
X1
X2
2
-177" (t)
65" (+)
4
-143* (t)
-148"/-1720 (t
6
-770(-
5.3.4.6
x
X
e
X
xx
x
-54"(-)
P
x
Glutamine
Figure 52 and Table 11 show the structure, dihedrals and associated structure
shift for Glutamine (Gln, Q). Glutamine is polar and hydrophilic and has a large
side-chain with three degrees of freedom. Xjis rather unflexible and does not
shift from dry to wet state. X2 is associated with a small shift from rotamer 1,2,5
to rotamer 4,6 (from dry to wet). X3 is associated with a small shift from rotamer
1,2,3,4,5 to rotamer 1,5,7 (from dry to wet). Due to the flexibility of Glutamine,
especially in X4, no clear assignments are possible.
144
GLN
2
q
X
5
5
-2,4,7
1,2,3,4
-1,2,-+
--
0
50
1,5,7
1,2,5,6
3,7
ISO -100 -50
ll
1,2,3,4,5
+-1,5
1,3,6
100
150
-150
X, M1
-100
-50
4,6
0
Z211
50
-150
150
100
-100-50
0
50
100
10
Y31
0.015
0.05
151
0.045
0,04
15
0.0t
101
0.035
51
0.03
S
0.005
0
0025
0,02
-5
-0m
0.015
-1CH
-10
001
005
-0.01
0
-0015
Figure 52 1 Changes in backbone and side-chain dihedrals of Glutamine.
145
Table 11 1 Rotamers and associated secondary structures of Glutamine.
Rotamer
X1
X2
2
-1740 (t)
177*0t
o, , n
X3
-110* (Ng9)
e,m P
xX
65' (Og -)
O*(Nt), 62*(0g+)
4
-176* (t)
69- (+)
-76- (0g-) 110 (Nt)
6
-73' (-)
81*-(+)
760 (Ng +)
x
x
x
X
5.3.4.7 Arginine
Figure 53 and Table 12 show the structure, dihedrals and associated structure
shift for Arginine (Arg, R). Arginine is polar and the only (positively) charged
residue in the core sequence of MaSpi and has a large side-chain with four
degrees of freedom. X1 is rather unflexible and does not shift from dry to wet
state.
X2
is associated with a significant shift from rotamer 1,2,4 to rotamer 5,6
(from dry to wet). X3 is associated with a small shift from rotamer 2,3,4 to
rotamer 5 (from dry to wet). X4 is associated with a significant shift from rotamer
1,2,3 to rotamer 6 (from dry to wet). Similar to Tyrosine, Arginine tends to shift
towards more random structures. This is important for the supercontraction
mechanism since the random structures increase the entropy which in turn leads
to the fiber contraction.
146
ARG
/
2,5
X3
-I
w,3
4,6
X1
1
X2
-150
50
-100
0
50
100
150
xM
-
-- Wet
DT
34
2,3,4,5
+
6
1,5,6
5,6
3
3,4
1,2,3,5
,
1,2,4
3,4,5
5
53,4
53,4
50 -100
-50
0
50
X,f1*1X,
100
150
150 -100
-0
0
50
100
-150
150
-100
-50
0
7. ll
50
100
150
0.05
0.05
0.04
0.045
0.03
004
002
0.035
0.03
I.
0025
0.02
0.01
9.
0.015
0.01
0005
-1
0
Figure 53 | Changes in backbone and side-chain dihedrals of Arginine.
147
0
-am2
.,ot
-003
-is(
-0.04
-0.05
Table 12 | Rotamers and associated secondary structures of Arginine.
Rotamer
Xi
X3
X2
X4
IiIo,g,n e,ml p e
x
68' (+)
4
-1770 (t)
6
1
460 (+)
j
80 (+)
1760 (t), -820(-),
1800 (t),
-
x
68-(-)
700 (+)
lxI
850(+)
-150 0 (t)
x
I
x x
5.3.5 Hydrogen Bonding of Tyrosine and Arginine
Prominent changes are found in the X 2 -angle of Tyr, shown in Figure 54. The X2angle describes the torsion angle of the aromatic ring that is coplanar with the
hydroxyl group of Tyr. From wet to dry conditions, a peak shift from -90* to
-10' as well as a symmetric shift from 90* to 1700 is observed. As seen in the
previous chapter, Arg's and Tyr's shift in the side-chain dihedral angles is
specifically associated with a secondary structure transition from sheet-like in the
dry state to coiled or helical structure in the wet state leading to a contraction in
the wet state.
148
-- Wet
Dry
--
2
*X21
-150
-100
-50
0
50
100
150
X2 ["
Figure 54 I Dihedral side chain angle distribution of Tyr determined from simulation. The X2 -angle
describes the torsion angle of the aromatic ring that is coplanar with the hydroxyl group of Tyr. From dry to
wet conditions, a peak shift from -90* to -10* as well as a shift from 90 to 170* is observed.
Figure 55 illustrates these transitions with two detailed snapshots from the
molecular dynamics simulation showing the local environment of Tyr associated
with the peaks (1) at -10' and the peaks (2) at ~170* peaks in Figure 54. The
identical residues at a similar simulation time in both dry and wet conditions are
shown. Three of the 15 polypeptide chains are visible (blue, red and green), while
Tyr and its hydrogen bond partners are highlighted. Peak (1) in dry conditions is
associated with the intermolecular hydrogen bonding of Tyr's OH-group with
the Gly residue of an adjacent chain. The H-bond is formed between hydrogen of
Tyr and the C=O oxygen of Gly that also forms the protein backbone. In this
case, Tyr acts as a hydrogen bond donor. In the wet state, Tyr both accepts
hydrogen bonds from mobile water within the structure as well as donates Hbonds through intramolecular interactions with the hydrophobic Gly, associated
with peaks (2).
149
H-bond
with water
1: Intermolecular
H-bond
2:
TYR
TYR
H2
SGLY
GLY
DRY
WET
IntramolecularR
H-bond
Figure 55 1 Two detailed snapshots from the molecular dynamics simulation showing the Tyr local
environment. The same residues at a similar simulation time are shown in dry and wet conditions. Three
(out of 15) polypeptide chains are visible (blue, red and green), while Tyr and its hydrogen bond partner are
highlighted. The peak at -10* and 170* (1) in the dry state is associated with the intermolecular hydrogen
bonding of Tyrosine's OH group with the Gly of the adjacent chain. The hydrogen bond is formed through
hydrogen of the Tyr and oxygen of the Gly involved also in forming protein backbone. In this case, Tyr acts
as a hydrogen bonds donor. In the wet state, Tyr both accepts hydrogen bond from mobile water within the
structure as well as donates H-bonds through intramolecular interactions with the hydrophobic Glycine (2).
Similar results are found for the peaks in the X 4 -angle of Arg, Figure 56, where
intra-molecular interaction is replaced by interaction with water. In the dry state,
Arginine is a strong H-bond donor, mainly donating through its NH 2 groups to
Glycines that are part of adjacent chains, peak (1) at -130*. In water, Arginine
becomes both donor and acceptor, where H-bonds are formed with mobile
water, peak (2) at 180*. This is illustrated in Figure 57.
150
Wet
--Dry
2
2
1
-150
-100
0
-50
X
50
100
150
[01
Figure 56 1 Dihedral side chain angle distribution of Arg determined from simulation. The X4 -angle is the
last torsion angle in the long side chain of Arginine where three possible H-bonding sites are present. From
dry to wet state, a peak shift from -130* to 180* is observed.
1: Intermolecular
H-bond
2: H-bond
with water
H2 0
ARG
ARG
GDLY
WET
DRY
-
Figure 57 | Two detailed snapshots from the molecular dynamics simulation showing the Arg local
environment. The same residues at a similar simulation time are shown in dry and wet state. Two (out of 15)
polypeptide chains are visible (blue and red), while Arg and its hydrogen bond partner are highlighted. The
peak at -130* (1) in the dry state is associated with the intermolecular hydrogen bonding of Arginine's NH 2
group with Glycine of an adjacent chain. In the wet state, Arg donates hydrogen bonds to mobile water
within the structure (2).
151
5.3.6 Key Residues for Supercontraction
The findings presented in the previous chapter take the understanding of
supercontraction to a new stage. On one hand, the large mobile side chains of
Arg and Tyr lead to a significant increase in entropy during the supercontraction
process, thus shrinking the molecule. On the other hand, the changes in Hbonding (and associated rotamer configuration indicated by the side-chain
dihedrals) relate to the finding that the supercontraction process is additionally
controlled by enthalpic effects. The entropic term is so dominant that even at the
freezing point of water, MaSp 1 silk still uptakes water, although it contains
many hydrophobic components. In dry conditions, the chains are stabilized
through intra-molecular interactions and the fiber compacts in radial direction,
while the chains elongate in axial direction. The formation of short P-sheets in the
non-crystalline part, especially in the GGX motifs (X = Arg, Ala, and Leu)
increases this effect. Interestingly, many of the newly formed P-sheets start or
end with a Tyr residue. In the wet state, mobile water disturbs these interactions
and the chains, especially the long side-chains of Tyr and Arg fold onto
themselves. The abundance of hydrophobic Gly in the amorphous silk phase
drives the large side-chains of Tyr and Arg to form H-bonds. This marks the
fundamental trigger for supercontraction in silk and highlights the importance of
the sequence of specific amino acid residues in the amorphous phase.
In summary, the potential key players for supercontraction are: Tyrosine (polar,
hydrophobic, uncharged),
Glutamine (polar, hydrophilic, uncharged), and
Arginine (polar, hydrophilic, charged). As a polar and charged amino acid, it can
be assumed that Arginine is most active in the supercontraction mechanism. As a
polar and hydrophobic (structure building) amino acid, it can be assumed that
Tyrosine is also active in the supercontraction mechanism. Furthermore, there is
evidence
from the Raman spectrum
supercontraction mechanism.
152
that Tyrosine is
involved
in the
The following structure mutations are proposed: Tyrosine is substituted with its
counterpart without hydroxyl group, PhenylAlanine (Phe, F). Arginine is
substituted with an uncharged smaller amino acid, e.g. Leucine (Leu, L). As
control experiment, Serine is substituted with Alanine (Ala, A) and no change in
supercontraction is expected.
5.4
Controlling Supercontraction
Control of the dynamics in the presence or absence of solvent is crucial for the
design of polymer materials [284]. In this context, genetic engineering and
synthetic chemistry are offering pathways to design materials on demand if
appropriate modifications to the sequence can be proposed [317]. In the previous
chapters, the crucial role of polar/charged
amino acid residues in the
supercontraction mechanism was demonstrated. Through simulations, the effect
of the substitution of these key residues with their apolar equivalents can now be
evaluated. The sequence of N. Clavipes dragline silk is altered and residue
mutations on Tyr, Arg, and Ser are performed, as illustrated in Figure 34f. This is
especially of interest in view of the technical application of spider silk, where
contraction may not be a desirable effect.
Three
additional
sequences
are equilibrated
using molecular
dynamics
simulations in solvent and in vacuum. In the first mutation experiment, Tyr is
replaced by Phe (similar molecular structure, but no hydroxyl group on the
aromatic ring). In the second mutation experiment, Arg (positively charged
amino acid with long side chain) is substituted with Leu and in a third mutation
experiment, Tyr is replaced by Phe, Arg by Leu and Ser by Ala. As before, the
contraction/expansion (by radius of gyration and average end-to-end length) is
measured. Furthermore, the P-sheet content of the mutated sequences is
evaluated (using equilibrium simulations) and compared to the wildtype silk.
153
While the wildtype silk shows a strong contraction (-15%), a mutation of Tyr
indeed leads almost to the suppression of the contraction, Figure 58. The effect of
the Arg mutation is even more significant, leading to an expansion in the wet
state. Similarly, mutation of all three residues yields a strong expansion in the
wet state (and hence a predicted axial expansion of the fiber). The effect of the
Serine mutation is small, which can be explained with its comparatively small
side-chain and small changes in side-chain dihedral angles. These results provide
further evidence for the fundamental role of Tyr and Arg in the supercontraction
mechanism through polar and charged side-chain group that can be related to
entropic effects (large side chains), but also to internal energy contributions (less
hydrogen bonding in the wet state). In all of the mutated sequences, the P-sheet
crystals remain intact (and the P-sheet content approximately constant, Figure
59) suggesting that the mechanical properties of the entire structure is unaffected
by the point mutations. A computational tensile experiment, shown in the
supplemental material, confirms this hypothesis.
Figure 60 shows the stress-strain plots determined from MD simulation using
steered molecular dynamics in full solvation, with boundary conditions as
described in Reference [48]. In the mutated sequence Tyr has been replaced by
Phe, Arg by Leu and Ser by Ala. While the stress strain behavior changes
slightly, the characteristics are very similar. Thus, it can be concluded, that
changing the molecular structure of the amorphous phase, at least concerning the
residues investigated, does not alter the high strength and toughness behavior of
silk.
154
0
0
Expansion
----------
--------
-------
-
-- --
.
0)
10
1
1
1
0 z-Radius
V End-to-End Length
-
20
.:
CD)
-10
Contraction
-20
Wildtype
Tyr
-+
Phe
Arg
-
Leu
Tyr/Arg/Ser -uPhe/Leu/A4
Figure 58 1 Molecular dynamics simulations of point-mutations of the spider dragline sequence and its
effect on supercontraction. Three additional sequences are equilibrated, where polar and/or charged amino
acids are substituted by their apolar/uncharged counterparts. The contraction/expansion of the structure is
measured by radius of gyration and average end-to-end length. In the first mutation experiment, Tyrosine is
replaced by PhenylAlanine (similar molecular structure, but no hydroxyl group on the aromatic ring). In the
second mutation experiment, Arginine (positively charged long side chain) is replaced by Leucine. In a third
mutation experiment Tyrosine and Arginine are substituted with additional replacement of Serine with
Alanine. While the wildtype shows significant contraction (-15%) in the wet state in comparison to the dry
state, a replacement of Tyr leads to suppression of the contraction. Mutation with Arginine even leads to an
expansion in the wet state. The effect of the Serine replacement is quite small, which can be explained with
its comparatively small side-chain. From these results it becomes clear that Tyrosine and Arginine play a
crucial role in the supercontraction mechanism through polar and charged side-chain group that can be
related to mostly entropic effects.
155
4(
3X
Dry
* Wet
*
5C
CL
Cn
1OF
Cii
Tyr
Wildtype
-+
Arg
Phe
-
Leu
T.yr/Arg/Ser *Phe/Leu/Ald
P-sheet content
Figure 59 1 In all of the mutated structures the P-sheet crystal remains intact (and the
unaffected by
is
structure
entire
the
of
properties
approximately constant). This suggests that the mechanical
the point mutations.
I
-
160C
-
140( -
-
Wildtype Dry
Wildtype Wet
Mutated Wet
T
1200
1000
,.-
CO 800
600
400
200
0
0
20
40
Strain [%]
60
80
Figure 60 1 Stress-strain curve of wildtype and mutated silk determined with SMD.
156
100
5.5 Conclusion
Full-atomistic simulation combined with in situ spectroscopic and tensile
experiments provides an excellent experimental platform to monitor the extent of
supercontraction and molecular interactions simultaneously. It is a powerful
approach to study supercontraction in N. Clavipes dragline silk fibers. Molecular
dynamics simulations allow a detailed view on the thermodynamics of the
material and the behavior of specific residues or regions within the molecule.
Parallelization has enabled computation to investigate environmental changes
and mutations with high precision, and has made molecular dynamics a feasible
tool for materials engineering. For the first time, these strategies are applied in a
synergetic effort to understand the supercontraction mechanism at the molecular
level, followed by targeted adjustment of the sequence to tailor properties of the
biomaterial. To this end, simulations offer the possibility to explore many
options in the material's design space effectively and in a relatively short time.
Tyrosine and
Arginine are identified
as key residues involved
in the
supercontraction process. They are then mutated with their apolar/uncharged
equivalents (PhenylAlanine and Leucine). This results not only in suppression of
the supercontraction effect, but even its reversion. By tuning the protein
sequence of the amorphous silk phase, a silk material lacking supercontraction
while maintaining its extraordinary mechanical properties could be engineered.
157
158
6 Summary and Outlook
Silk is a hierarchically structured protein fiber with a high tensile strength and
great extensibility, making it one of the toughest materials known. Nephila
Clavipes MaSpi, the protein in dragline silk studied in this thesis, contains a
sequence of Alanine- and Glycine-rich repeats leading to distinct higher-level
structures. Its heterogeneous structure comprises P-sheet crystals embedded in
an amorphous matrix. The Alanine-rich region makes up the hydrophobic Psheet crystals, while the semi-amorphous phase associated with the Glycine rich
region features a significantly poorer orientation of the strands. The crystals
provide strength to the material while the amorphous phase is responsible for
elasticity and dissipative mechanisms. Dragline silk has a hierarchical structure
where the silk unit cell assembles into nanofibrils of size 20-150 nanometers.
Hundreds of fibrils are spun through the spider's spinneret and form a dragline
fiber of micrometer size.
In chapter 3, the origin of the nanoscale heterogeneity during the Nephila Clavipes
dragline silk assembly is investigated. Using molecular dynamics simulations, a
shear flow at natural pulling speeds is modelled and the secondary structure
transitions as well as the shear stresses in the silk protein chains are determined.
Robust results are found where a shear stress of the order of 20-50% of the failure
stress induced an c - P-transition in the poly-Alanine region. The results are in
agreement with the experimentally determined secondary structure and pulling
forces of spider dragline silk. While the transition stress is independent of the
chain length, the crystal is stable only in larger configurations. The stability of the
assembled p-sheet structure seems to arise from a close proximity of the a-helices
in the silk solution. The smallest molecule size that might give rise to a silk-like
structure is determined to comprise four to six repeats of the silk sequence. The
159
results emphasize the role of shear in the assembly process of silk and other
biopolymers. The determined critical shear values can inform the design of
microfluidic devices that attempt to mimic the natural spinning process.
Establishing the molecular details of the assembly process can guide the
synthesis of bioinspired protein materials.
In chapter 4, the heterogeneity of silk fibers on the nanoscale is related to the
fracture mechanical properties of the entire fiber. Analytical fracture mechanical
arguments are presented to illustrate the relation between fracture strength and
toughness
and
heterogeneity
in
silk
as
well
as
other
biopolymers.
Nanoconfinement and flaw tolerance are presented as natural strategies to
increase the mechanical performance of the entire material system. Confinement
refers
to
the splitting of a macrostructure
into small-scale
micro- or
nanostructures, as observed in brick-and-mortar structures (e.g., bone, nacre) and
fibrillation (e.g., silk, collagen). In natural composites and fibers, the hierarchical
architecture of the structural components together with a confinement strategy
leads to improved load transfer and robustness against failure. Fibrils that are
confined to only a few nanometers and then bundled to form fibers maintain
their mechanical performance despite the presence of stress concentrations such
as cracks, tears, and other flaws. It is shown that the considerations of
interatomic interactions alone cannot explain the fracture strength observed in
biological fibers. Instead, structures at multiple length-scales must be considered
to explain the remarkable mechanical performance and resilience of silk.
In chapter 5, the interaction of water with silk's heterogeneous nanostructure is
investigated. At high humidity, some spider dragline silks will shrink up to 50%,
a phenomenon known as supercontraction. The molecular origin of dragline silk
supercontraction
is explored using a full-atomistic model and molecular
dynamics simulation supported by in situ Raman spectroscopy and mechanical
testing performed at the Max Planck Institute in Potsdam, Germany. Tyrosine
160
and Arginine are identified as the key residues in the Nephila Clavipes silk
sequence that control supercontraction. They are then substituted with their
apolar/uncharged equivalents (PhenylAlanine and Leucine). This results not
-
only in suppression of the supercontraction effect, but even in the reverse effect
expansion in the wet state. By tuning the protein sequence of the amorphous silk
phase,
a
silk
material
lacking
supercontraction
while
maintaining
its
extraordinary mechanical properties could be engineered.
From the H-bond clustering at the lowest scale to the self-assembly of
nanocomposites and subsequent fibrillation, there are still many lessons to be
learned before manmade fibers will be able to compete with nature's versatile
architectures. Despite the attention and research efforts dedicated to polymers
and biocomposites in the past years, there is no consistent explanation for the
mechanisms that govern the confined constituents or even for the reason why the
microstructures confine during the material's assembly process. Dissection of the
constituents of the highly complex natural systems and the determination of the
single phase contribution to the overall performance remain major challenges.
There is significant evidence showing that the interplay of mechanisms in fibrous
biomaterials at all length scales is responsible for their remarkable mechanical
properties. It is in the control of this interplay that recent manufacturing
techniques cannot compete with natural biopolymers and biocomposites.
Interesting novel pathways to manufacture composites have been revealed, e.g.,
by mixing polymer matrices with highly functional materials such as singlewalled carbon nanotubes. In these materials, the confinement effect due to
alignment increases modulus and strength significantly. Furthermore, recent
studies have led to the discovery of P-sheet crystals as an important structural
component not only in silk, but also in less studied biomaterials such as squid
sucker ring teeth.
161
Computational studies (through statistical thermodynamics and mechanics, e.g.,
molecular dynamics simulations) have made important contributions to the
understanding of natural assembly and deformation processes. With increasing
computing power, it will be possible to model and analyze larger systems at
atomic or quantum resolution to link biology, chemistry, and mechanics. One of
the future research
opportunities
relates
to
the connection
of Raman
spectroscopy and the simulation of vibrational properties, briefly addressed in
chapter 2.1.8 and 5.3.2. Further research is necessary to identify the isolated
(confinement, deformation, supercontraction)
mechanisms in a real-world
material environment. Experimentally validated modeling and simulation will
enable the control of material properties from a bottom-up perspective. The
combination of synthesis, controlled processing, and modeling of biopolymer
fibers within a unified framework will result in tailored materials with prespecified properties. The research in this thesis presents a step towards the
industrial manufacturing of low-cost and environmentally benign functional
fibrous materials processed from abundantly available resources.
162
7 Appendix
7.1 Secondary Structure and Shear Stress Trajectories
Figure Al-A4 show the secondary structure transition and shear stress during
the 10 ns pulling simulation for a = 1 (Figure Al), a = 3 (Figure A2), a = 5
(Figure A3), inter-chain (Figure A4). The upper panel (a) refers to shear
boundary condition (i), as seen in Figure 11, chapter 0, and the lower panel (b)
refers to shear boundary condition (ii).
a
14
n
2500
90 -Heix
Betasheet
80 -Coil
Turn
80
70
2000
60
1500
1000
40
500
6
8
10
0?
0
2
4
2
4
6
8
6
8
10
Time Ins)
Time [ns)
b
100
90 -Betnsheet
-coil
Tur
80
2000
70
1500
60
1000
40
500
2010
''
2
4
Timne (ns]
6
8
10
0
0
Time [ns]
(b)
Figure S1 I Secondary Structure Transition and Shear Stress for a = 1 in (a) shear boundary condition (i)
shear boundary condition (ii).
163
10
a
2500
100
go.
..
80.
-Helixci
-- Tum
Betasheet
2000
70
1500
60
1000
30
500
2010
00
A
et-
2
-
S
6
4
Time [ns]
10
2
4
2
4
6
8
10
6
8
10
Time [ns]
b
100
2500
--
-90 -
Helix
Betasheet
80 --
Tr
Tum
2000
70
60
100
0~
40
30
500
20
10
n
4[n
Tm2
Timne [ns]
8
10
0
Time [ns]
Figure S2 I Secondary Structure Transition and Shear Stress for a = 3 in (a) shear boundary condition (i) (b)
shear boundary condition (ii).
164
a
2500
1uu
-Helix
90 Betasheet
-- Coil
Tum
70-
2000
a 1500
60
50
~1000 I
40
30
500
20
10
o0
2
4
Time (ns]
6
8
10
0
2
4
2
4
Time [ns
6
8
10
6
8
10
b
100
90. -Beteet
-Helix
coil
o -Tum
2000
70
a1500
60
d
50
1000
40
500
30
20
10
00
n
2
6
4
8
10
Time ins)
0
Time [ns]
Figure S3 I Secondary Structure Transition and Shear Stress for a = 5 in (a) shear boundary condition (i) (b)
shear boundary condition (ii).
165
a
2500
irvi
-Helix
90 -Betsheet
-Coil
80
-Tum
70
t
2000
1500
LI
60
50
1000
500
6
4
8
10
0
6L
2
4
2
4
Time [ns]
Time (ns]
6
8
10
6
8
10
b
krivi
100
90
---
Helix
- Betashe
so-coil
2000
20
~1500~
50
40
1000
30
500
10
00
-
2-
4
6
8
10
Time [ns)
0
0
Time [ns]
Figure S4 I Secondary Structure Transition and Shear Stress for inter-chain in (a) shear boundary condition
(i) (b) shear boundary condition (ii).
166
7.2 Probability for the a-0-Transition
Figure B1-B5 show the probabilities associated with the secondary structure
transitions for a = 1 (Figure Bi), a = 3 (Figure B2), a = 5 (Figure B3), 2 layers
antiparallel (Figure B4), 2 layers parallel (Figure B5). The left part (a) refers to
transition from a-helix to
-sheet and the right part (b) refers to the transition
from 3 1 0-helix/turn to P-sheet. See methods section in main manuscript for
details. Tables B1 -B6 show the residues that have a joint probability higher than
10% (for a = 5, 2 layers anti-parallel and 2 layers parallel)
167
a
1.5 a
bb
1.5
-REMD 1loop
-SMD I loop
Equilibration 1loop
-Joint Probability I oop
-REMID I oop 310
SMD Ioop 310
Equilibration 1 loop 310
-Joint Probability Iloop 310
1
1
e
0.5
JA
20
'0
60
40
MAA#
0.5
"0
80
Figure B1 I Transition probability for a = 1 from (a) a-helix to
a 1. 5
-
-
20
40
AA[#
i
60
A
'
0.
80
P-sheet (b) 3 10 -helix/tum to P-sheet.
b 1.51
,--~-
3loops 310
-REMD
SMD 3loops 310
Equilibration 3loops 310
REMID 311oops
__SMD 3loops
--
-
Equilibration 3loops
-Joint
-Joint
Probability 3s
Probability 3loops 310
1
Z
.
0-
0. 5
I.
0
Figure B2
50
100
150
AA [#]
0.5
_'0
100
50
AA [#]
I Transition probability for a = 3 from (a) a-helix to P-sheet (b) 3 10 -helix/tum to P-sheet.
168
150
a
1.5
b
-_____
1.5
-REMD 5loops
SMD 5loops
Equilibration Sloops
-Joint Probeblt 5op
Equilibration Sloops 310
-Joint Probability Sloops 310
1-
.1
0.
0.5
0
50
100
AA [#1
150
Figure B3
I Transition probability for a =
Table B1
I Residues with joint probability
I Residue Number
161-162
Table B2 I Residues with joint probability
REMD 5loops 310
SMD 5loops 310
-Post
0.5
i
200
5 from (a) a-helix to
I
50
100
AA [#]
150
200
P-sheet (b) 3 10 -helix/turn to P-sheet.
10% for a = 5 from a-helix to P-sheet.
I Residue Name
I
I L. OGAGAAAA
I
I AA
I
10% for a = 5 from 3 10 -helix/turn to 1-sheet.
Residue Number
Residue Name
65
A
103-104
GQ
169
b1.5
a
-
- REMD 2layers 310
SMD 2iayers 310
Equilibration 2layers 310
Probabilit ayers 310
-Joint
REMD 2ayers
SMD 2layers
Equilibration 21ayers
-Joint Probability 2iayers
1
110
0.5
0.5[
0
50
100
150 200
AA [#]
250
00
300
50
100
150
200
250
Figure B4 I Transition probability for 2 layered structure (anti-parallel) from (a) a-helix to -sheet (b) 31ohelix/turn to 1-sheet.
Table B3
I Residues with joint probability
10% for 2 layers anti-parallel from a-helix to 1-sheet.
I Residue Name
I AAAA
213.216-222
I QGAAAAAA
Table B4 I Residues with joint probability > 10% for 2 layers anti-parallel from 3 10 -helix/turn to 1-sheet.
I Residue Name
236
170
300
a
b
1.5
REMD 2layers parallel
SMD 2layers parallel
Equilibration 2layers parallel
-Joint Probability 2layers parallel,
1.5
R
EMD 2layers parallel 310
SMD 2layers parallel 310
Equilibration 2layers parallel 310
-Joint Probability 2layers parallel 310
-
0.
0.5
0.5
00
50
100
150
AA [#J
200
250
00 50
300
100
Figure B5 I Transition probability for 2 layered structure (parallel) from (a) a-helix to
helix/turn to P-sheet.
Table B5 I Residues with joint probability
10% for 2 layers parallel from a-helix to
94-97
I AAAA
216-221
I GAAAAA
283
IA
Table B6
200
150
250
AA [#
P-sheet (b) 310-
P-sheet.
I Residues with joint probability > 10% for 2 layers parallel from 3 10 -helix/ turn to 1-sheet.
Residue Number
I Residue Name
92. 97-98
I A, AA
248
13%
IA
NU
171
300
7.3
Nomenclature
Symbol
Name
Unit
a
Crack length
m
a
Number of silk core sequence
repeats
A
Helmholtz Free Energy
J/mol
AAH
Change in enthalpy
J/mol
b
Platelet width
m
C(&w)
Light-to-excitation
coupling
factor
C
Covariance tensor of atomic
fluctuations
Deq
Equivalent
radius
of
a
m
molecule
D
Diameter
m
e
Electronic charge
C
E
Young's modulus
N/m2
Eb
Bulk modulus
N/m2
Eb
Height of energy barrier
J
Em
Elastic modulus of mineral
N/m 2
phase
E
Elastic tensor
N/M 2
EO
Initial modulus
N/m 2
R
Average modulus
N/m2
E'
Equivalent Young's modulus
N/m2
fconf
Accessible volume fraction
ftahTheoretically
allowed fraction
of configurations
172
g R(O)
Convoluted VDOS intensity
G
Gibbs Free Energy
G
Critical strain energy release
J/m2
rate
h*
Platelet height
m
h*
Critical height
m
h
Planck constant
Js
H
Fibril width
m
H*
Enthalpy
J/mol
H**
Critical
size,
homogeneous
m
complete
m
deformation
H**
Critical
size,
unfolding
IRaman
Raman intensity
kB
Boltzmann constant
J/K
k
Spring stiffness in SMD
kcal/mol/ A
K
Kinetic energy
J
Kc
Stress intensity factor, mode
Viii N/m2
Iji,1II
10
Process zone size
Al
Length
m
during
change
m
supercontraction
L
Length/ fiber length
m
L*, L**
Critical overlap length
m
m
Lennard-Jones
potential
parameter
Mi
Mass of atom i
M
Number of configurations
173
kg
M
Mass tensor
n(w)
Population
kg
of
vibrational
mode ae frequency w
n
potential
Lennard-Jones
parameter
n
Number of fibrils in a fiber
n
Surface normal vector
N
Number of atoms in a system
Ncr
Critical number of bonds
NREMD
Number of replicas in REMD
simulation
N/M 3
p
System pressure
r
Distance from crack tip
ro
Equilibrium bond length
m
ri
Bond length between atom i
m
and j
R
Gas constant
J/molK
S
Entropy
J/molK
t
Surface traction vector
N/m 2
T
Temperature
K
u
Displacement
m
U
Potential energy
J
Vi
Velocity vector of atom i
m/s
V
Volume
M3
W
Strain energy density
J/m 3
Xb
Distance between equilibrated
m
state and transition state
acr
Ratio
between
174
end-to-end
length and persistence length
/
Geometry parameter, related
m
to F(()
Ys
Adhesion energy
S
Cutoff length scale
N/m
in the
m
continuum
E
Strain
Emax
Failure strain
ESC
Supercontraction strain
Ratio of crack size to system
size (a/H)
Coupling
parameter
(BAR
method)
Aj
Eigenvalues of the radius of
m
gyration tensor
x
Off-rate
1/s
Xi
Side-chain dihedral angle
rad
6
Angle
rad
between
reaction
pathway and applied load
4,
Persistence length
v
Poisson's ratio
Ub
Bulk strength
N/m 2
07ent
Entropic stress
N/M 2
af
Failure stress
N/m 2
UsC
Supercontraction stress
N/m 2
Uth
Failure stress of the perfect
N/M 2
m
crystal
UY
N/m 2
Yield stress
175
Far-field stress
N/m 2
Stress tensor
N/m2
Shear stress
N/M 2
Interface shear strength
N/m 2
>
Frequency
1/s
>
Lennard-Jones
CO, U00
Tf
potential
parameter
(AO
Eigenfrequency
1/s
Frquency of hydrogen bond
1/s
vibrations
'
Backbone dihedral angle
rad
Backbone dihedral angle
rad
Bond volume
M3
176
7.4
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
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7.5
List of Figures
Figure 1 1 Complex hierarchical structures found in natural materials. (a)
Scanning electron microscopy (SEM) pictures displaying the intricate hierarchical
porous silica wall structure of diatoms. Figure adapted from [12], with
permission from Elsevier. (b) SEM pictures of the mineralized skeletal system of
Eucleptella. The caged structure consists of struts (bundled spicules) which
themselves are a ceramic composite with laminated silica layers and organic
interlayers. Figure adapted from [8], copyright @ 2005, with permission from the
American Association for the Advancement of Science. ....................................
15
Figure 2 1 Hierarchical structures of biological materials such as spider silk and
bone. Biological materials are designed bottom-up to overcome fundamental
strength limits at the nanoscale. Spider dragline silk, specifically the protein
MaSpi, consists of P-sheet nanocrystals embedded in an amorphous phase.
These are aligned along the fiber axis to form fibrils of size 20-150 nm. Hundreds
of fibrils are spun together in a fiber that eventually forms the frame of an orb
web. Compact bone is composed of osteons that surround and protect blood
vessels. Osteons have a lamellar structure. Each individual lamella is composed
of fibers arranged in geometrical patterns. These fibers are the result of several
collagen fibrils, each linked by an organic phase to form fibril arrays. Each array
makes up a single collagen fiber. The mineralized collagen fibrils are the basic
building blocks of bone. Bone figure adapted from Reference [20], copyright D
2010, Annual Reviews. Web image courtesy of Charles
J.
Sharp. Silk figure
composition courtesy of Dr. James Weaver, Harvard University. .....................
18
Figure 3 1 Density vs. failure strength of synthetic and natural materials as
Ashby plot. Adapted from Reference [34]...............................................................
21
Figure 4 | Silk features a hierarchical structure, where P-sheet crystals play a key
role in defining the mechanical properties by providing stiff and orderly crosslinking
domains
embedded
in a semi-amorphous
197
matrix
that
consists
predominantly of less ordered structures. These (-sheet nanocrystals, bonded by
means of assemblies of H-bonds, have dimensions of a few nanometers and
constitute roughly 15-50% of the silk volume. Adapted from Reference [43]...... 22
Figure 5 1 Stress-strain behavior for a defect-free silk fiber, noting the key
transition points between the four regimes marked by molecular events at the
molecular scale. The transition from Regime I to Regime II marks the onset of
unfolding of the semi-amorphous phase of silk; the transition from Regime II to
Regime III marks the onset of stretching of the P-sheet nanocrystal phase. In
Regime IV P-sheet nanocrystals fail via a stick-slip mechanism, eventually
leading to failure. Figure adapted from Reference [43]........................................
25
Figure 6 1 Microscopic images of Nephila madagascariensis dragline silk fibers
showing the skin-core structure as well as flaws and cavities in the material. The
white arrows point in the axial fiber direction, and the red ellipses highlight
some of the defects found in the structure. Pictures reprinted from [51], 9
copyright 1998, with permission from John Wiley & Sons, Inc. .........................
26
Figure 7 1 Approximate length and time scale regimes of the tools for multiscale
engineering. Computational tools predict and explain phenomena that are
observed experimentally, but are limited to certain regimes due to constraints on
computational
performance.
While mesoscale
and
continuum
modeling
(subpanel a) cannot capture atomistic details, they are trained by atomistic
results from Density Functional Theory (DFT) and Molecular Dynamics (MD)
simulations. They cover the same length scale range as experimental tools (e.g.
atomic force microscopy (AFM, subpanel b), optical/ magnetical tweezers,
microelectromechanical systems (MEMS, subpanel c) and nano-indentation. The
lower part indicates classes or scales of protein materials that can be studied with
the respective techniques. Figure reprinted from [18], copyright @ 2009, with
permission from the Nature Publishing Group. ..................................................
30
Figure 8 1 Stress variation in the cohesive zone according to the DugdaleBarenblatt model. Adapted from Reference [100].................................................
198
44
Figure 9 1 Molecular model of the silk fiber assembly process. Silk is processed
from spidroin to a solid fiber in the spinning duct under ambient conditions. The
dragline silk spidroin consists mainly of MaSpi (studied here) and MaSp2. The
sequence is highly repetitive, a ~ 0(100). Shear stresses at the wall together with
the removal of water from the protein lead to the formation of a nano-composite
having an aligned, fl-sheet rich crystalline phase. A change of ionic conditions
during the spinning process is believed to lead to a conformational change in the
terminal regions of the silk protein. ........................................................................
48
Figure 10 1 (a) Model of the silk spidroin in equilibrium. Using Replica Exchange
Molecular Dynamics for a total of 1 microsecond the equilibrium structure of the
protein is determined for different chain lengths (a = 1,3,5), here denoted as
poly-Alanine regions (blue) and remainder of the intervening sequence (red). (b)
Model of the silk assembly process. Using Steered Molecular Dynamics at
natural pulling speeds a shear flow is modeled and the secondary structure
transitions as well as shear stresses in the silk protein chains are determined.
Intra- as well as inter-chain interactions are investigated. (c) Model of the final
fiber structure. After shearing the assembled structure is simulated in solvent
and vacuum to test the stability of the structure as a single-chain or as layered
structure, i.e. multiple stacked sheets after shear.................................................
53
Figure 11 1 Two different boundary conditions (i) and (ii), both shear, are tested
to investigate the trajectory of secondary structure and shear stress. The part of
the sequence colored in blue is the Alanine rich region and the part of the
sequence colored in red is the Glycine-rich region. The pulling force is
determined with the steered molecular dynamics (SMD) algorithm................. 55
Figure 12 1 Secondary structure transition and shear stress during the assembly
of silk. (a) Secondary structure trajectory during the pulling simulation in explicit
solvent. The graph shown is one out of four tests for a = 3 (with boundary
condition (i)). Starting from the spidroin, a high a-helical and coil content and no
P-sheets can be found. During the shear induced assembly all helices and other
199
structures
transition
into P-sheets or are destroyed
in agreement with
experimental observations of the processes in the spinning duct. The P-sheet
content after pulling for each structure is determined by averaging the P-sheet
content for 1 ns around the maximum content as indicated in the figure.
(b)
Shear stress associated with the secondary structure transition. The transition
shear stress is averaged in the same region as that taken to assess the P-sheet
content. In all cases, the structure transition happens prior to reaching the
strength limit of the material...................................................................................
56
Figure 13 1 P-sheet content versus pulling speed for a set of spring stiffnesses.
The observed P-sheet content after shear is insensitive to the simulation
p aram eters.......................................................................................................................
60
Figure 14 1 (a) The P-sheet content attained after the shear flow experiment is
independent of the chain length and well within the range of experimental
observation. (b) The transition shear stress for the silk assembly is calculated to
be between 300 and 700 MPa, whereas experimental observations put it between
20-60% of the breaking stress (300-850 MPa). This agrees with the observation
that the reorganization of silk requires significant shear stresses. ..................... 62
Figure 15 1 Stability of the silk chains (P-sheet content) after shearing and a
further equilibration in explicit solvent. The shorter chains (a = 1, a = 3) cannot
retain the P-sheet crystal and the structure returns in its spidroin state; the larger
structure a = 5 rem ains relatively stable...............................................................
63
Figure 16 1 Stability in water. Summary of the secondary structure content of the
spidroin and the simulated structures after equilibration in explicit solvent.
While the shorter chains start to form 310-helices and retain only a low
percentage of P-sheets, the larger structure is stable and shows the secondary
structure composition of final assembled dragline silk fibers.............................
64
Figure 17 1 Stability in vacuum. Summary of the secondary structure content of
the spidroin and the simulated structures after equilibration in vacuum. All
chains remain stable independent of the chain length........................................
200
64
Figure 18 1 Transition probabilities for a = 5 from a-helix to P-sheet. The graph
shows the probability for each of the 206 residues of the structure with a = 5 to
be in a-helical state after REMD, in P-sheet state after SMD and in in P-sheet state
after Equilibration. The dark blue line is the joint probability defined as the
product of the three probabilities and indicates the residues that transition from
helical to sheet structure with high probability......................................................
66
Figure 19 1 Transition probabilities for a = 5 from turn/310-helix to P-sheet.
Probability for each of the 206 residues of the structure with a = 5 to be in 310helical/turn
state (after REMD)
and
in
s-sheet
state
(after SMD/after
E q uilib ration )..................................................................................................................67
Figure 20 1 Structure snapshots (a = 5) with highlighted residues identified from
Table 2 of the four transition stages (i - iv), in agreement with ..........................
68
Figure 21 1 P-sheet content of sandwich structures after equilibration in vacuum
and solvent. Layered structures are formed from chains with a = 3. Independent
of the amount of layers or the orientation 10-15% of the structure stabilize as Psheets in solvent, and 20-30% in vacuum ..............................................................
71
Figure 22 1 Relative elastic modulus and strength of polymer materials as a
function of size. (a) In most nanofibers, the relative elastic modulus, as compared
with the bulk modulus Eb, increases dramatically at a critical diameter D *. This
behavior is explained by the role of spatial confinement on entropy and the
dominance of intermolecular interactions in thin nanofibers. Thin polymer films
with free surfaces tend to display a decrease in the relative modulus due to the
formation of highly mobile surface layers. (b) The alignment of crystallites and
the degree of crystallinity in the fiber also improve with smaller diameter,
leading to greater strength and toughness, sometimes even exceeding the bulk
properties. The data for the fracture strength of thin films show a decrease of the
material strength. (The references, critical length scales, and bulk values are
summarized in Table 3.) Figure reprinted from Reference [121]........................
201
77
Figure 23 1 Rupture strength of H-bond clusters and critical sizes of some
protein secondary structures. Top: The intrinsic strength limit of H-bonds can be
overcome by clusters of three to four H-bonds that then interact synergistically to
resist deformation and failure. The H-bond assemblies are loaded in parallel in ahelices, p-sheets, and
p-helices.
Note that the shear strength curve is derived for a
single P-sheet in a pull-out test. The natural load condition for an a-helix is
tension, for which an unzipping effect is easily achieved. Bottom: This result
explains the cluster size found in natural protein secondary structures (a-helix:
N = 3.5; P-helix: N = 5; and P-sheet: N = 2.5 - 8). Figure adapted with
permission from [157] Copyright @ 2008 American Chemical Society..............85
Figure 24
1 Intrinsic
(plasticity) versus extrinsic
(shielding) toughening
mechanisms associated with crack extension and R-curve. (a) The illustration
shows mutual competition between intrinsic damage mechanisms, which act
ahead of the crack tip to promote crack advance and extrinsic crack-tip-shielding
mechanisms, which act primarily behind the tip to impede crack advance [24].
Intrinsic toughening results essentially from plasticity and enhances a material's
inherent damage resistance; as such it increases both the crack-initiation and
crack-growth toughnesses. (b) Toughness behavior of various materials. In many
natural materials, it is an order of magnitude tougher than its constituent phases.
Figure adapted from [24], copyright
2011, with permission from the Nature
Publishing G roup.......................................................................................................
89
Figure 25 1 Confinement and flaw tolerance. The graph shows the concept of
flaw tolerance. According to the classical prediction, the strength of a material
scales with 1/h or, 1/D respectively. In the case where the strength of the perfect
crystal is reached at h = h * (D = D *), the flawed system exhibits no loss of
strength. This concept has been experimentally and computationally verified,
e.g., for (a) spider dragline silk [47], (b) hydroxyapatite nanocrystals [225], (c)
thin metal strips [223], and (d) nanocrystalline graphene [224]. Images in panel
(a) reprinted from Reference [47]; images in panel (b) from Reference [225].
202
Images in panel (c) adapted with permission from Reference [223]. Copyright @
2009, American Institute of Physics. Image in panel (d) adapted with permission
from Reference [224]. Copyright @ 2012 American Chemical Society. Figure
adapted with permission from Reference [121].....................................................
91
Figure 26 1 Critical size of a composite and an adhesion system. Bone-like
materials typically consist of fragile, brittle mineral platelets (hydroxyapatite)
embedded in protein matrix materials (collagen). (a) The mineral platelets carry a
tensile load and the protein transfers carry loads between the platelets via shear.
(b) These platelets are confined and optimally arranged to maximize the strength
and toughness of the material. (c) Similarly, the adhesion of a spatula on a rigid
surface is optimized for a critical diameter D *, e.g., for gecko adhesion [211]. The
critical sizes h * and D * determine the point at which the system becomes flawtolerant. The solid line on the left corresponds to the classical fracture mechanics
prediction, which breaks down at the length scales at approximately the critical
size (on the order of a few nanometers). Figure adapted with permission from
R eferen ce [121]................................................................................................................
92
Figure 27 1 Optimized length scales in a mineral-polymer composite (e.g., nacre).
(a) Hierarchical structure of nacre and a schematic of a 2-dimensional continuum
model for the composite architecture to predict the critical sizes that maximize
the strength of the whole material. (b) Elastic and fracture toughness varying
with overlap length normalized by L *.
Total elastic strain energy density
(squares) maximizes at L = L *, and fracture toughness (circles) exhibits a sudden
drop when L > L **. (c) Comparison of overlap lengths for basic building blocks
of three natural materials (nacre, tendon, and spider silk) from experimental
observation (circles) and model prediction (squares). Figure adapted with
permission from Reference [228]. Copyright @ 2012 American Chemical Society.
...........................................................................................................................................
94
Figure 28 1 Robustness of P-sheet nanocrystals as a function of their height. PSheet nanocrystals are especially strong and robust if their height is confined to
203
2-4 nm. This critical dimension is in agreement with experimental results. Figure
adapted from Reference [49]. ...................................................................................
96
Figure 29 1 Critical size of spider dragline silk major ampullate spidroin 1
(MaSpi). The graph shows the dependence of the failure strain and failure stress
on the fibril size D under various loading conditions (1-4) as well as a direct
comparison with experimental results (under the tensile loading condition 1 and
the mechanical behavior of a defect-free silk fiber. For decreasing fibril sizes, the
perfect material behavior (i.e., ~ 1,400 MPa failure stress and 68% failure strain)
is approached and reached at D = D * = 50 + 30 nm. D* is denoted the critical
flaw-tolerant size of the fiber. The results show that the high strength and
extensibility
observed in experimental
studies can only be reached
by
nanoconfinement of fibrils close to D *. Figure adapted from Reference [47] with
p erm ission .......................................................................................................................
98
Figure 30 1 (a) A fiber of diameter D that has no intrinsic flaws. Under tension
aO, such a fiber's failure strength af would reach the theoretical strength of the
interatomic bonds it consists of, ath. (b) A fiber made of the same bonds without
internal structure but containing a flaw of length a would decrease its strength
according to Griffith's size scaling as the ratio 10/D and the strength of the fiber
become smaller. (c) A possible strategy to maintain the strength of the fiber at the
macroscale is to increase the size of the process zone, such that 10 = D. Then, the
strength of the fiber will approach the theoretical strength of the internal
structure, af =
th. Figure adapted from Reference [100]....................................
100
Figure 31 1 Length scales and toughening mechanisms in spider dragline silk. At
the lowest hierarchical level (the scale of the atomic bonds) the maximum stress
is the theoretical bond stress oth, and rO as well as 10 are small (in the order of
nanometers). The nanocrystal is extremely robust because it is geometrically
confined to the size of the plastic zone. At the next hierarchical level, the betasheet crystals form a structure that can be understood as a lattice with spacing of
rO
10 nm (the distance between the crystals). The intrinsic strength of the
204
lower scale feature - here the crystal and amorphous phase - is scaled up to the
next scale. Paired with the unfolding of the semi-amorphous protein domains,
the process zone size is then on the order of 20 -150 nm, the size of the fibrils.
Through hierarchical assembly, i.e., the weak binding of many layers of flawtolerant fibrils to fibers, the material induces further toughening mechanisms
(fibril sliding and delocalization, inducing a process zone of 1 pm) and maintains
its toughness at micrometer dimensions. Figure adapted from Reference [100].
.........................................................................................................................................
1 08
Figure 32 1 Three typical boundary conditions for a fiber under tension. (i)
Cylinder with circumferential crack. (ii) Cylinder with inclusion. (iii) 2D tensile
specimen with surface crack. Figure adapted from Reference [100]....................109
Figure 33 1 Schematic picture of the hierarchical build-up of materials, where at
each level the building blocks are repeated n times such that the total length is
confined to r *.
At each hierarchical scale, the stress concentrations become
delocalized. This is achieved through the confinement of each microstructure to
the length scale of the process zone size 10/rO = [0.5,16], where rO is the
characteristic size of the building block. The fiber becomes robust to flaws at all
these length scales and does not fail in a brittle manner, when part of a largerscale hierarchical structure. The resilience of materials is greatly enhanced
through hierarchical structuring from the nanoscale upwards, as deformation
and damage processes are translated to larger scales. Figure adapted from
R eferen ce [100]..............................................................................................................
111
Figure 34 1 Nephila Clavipes dragline silk nanostructure and supercontraction
mechanism- Bridging from experiments to modeling. Supercontraction is the
shrinking of silk in water in comparison to its dry state (by up to 50% depending
on the silk, around 15% in Nephila Clavipes silk). (a) In the full-atomistic
molecular dynamics simulation silk is represented by a unit of silk, with a stable
P-sheet crystal and two amorphous phases. The amorphous phase is believed to
be responsible for the supercontraction mechanism. (b)-(d) Silk assembles in
205
nanofibrils of size 20-150 nanometers. Hundreds of fibrils form dragline fibers of
micrometer size. The spider spins the strong dragline silk as structural support
for its webs and as lifeline for escape. (e) Measurement of the supercontraction
process on dragline silk fibers in a humidity chamber using tensile testing and in
situ Raman spectroscopy. (f) In this multiscale approach the macroscale
supercontraction effect is linked to nanoscale changes in the structure. Mutations
to the core sequence can be proposed to suppress the supercontraction effect. (d)
courtesy of Charles
J.
Sharp. Figure composition, courtesy of Dr. James Weaver,
H arvard University......................................................................................................119
Figure 35 1 In vitro supercontraction process and experimental setup. After
increasing the humidity (blue line), the strain in the fiber decreases under
isostatic conditions (red line). Image credit: A. Masic. Data collected by R.
Schuetz and A. Masic. Figure courtesy A. Masic. ...................................................
121
Figure 36 1 Tensile experiment sequence of a single fiber in the elastic region at
three different humidity conditions: at 25%RH (black line), 50%RH (blue line)
and after the supercontraction at 90%RH (red line). Data collected by R. Schuetz
and A. M asic. Figure courtesy A. M asic...................................................................122
Figure 37 1 Supercontraction measured from Simulation and Experiment. The
strand silk model is equilibrated in water and vacuum and supercontraction is
measured by average end-to-end length as well as radius of gyration of vacuum
versus hydrated model. Results of the simulation in three axis directions are
compared with experimental results and good agreement is found for the
contraction in the axial direction. ..............................................................................
123
Figure 38 1 Secondary Structure of the MaSp1 dragline silk wildtype determined
from molecular dynamics simulation using the STRIDE algorithm.........124
Figure 39 1 Polarized Raman scattering of N. Clavipes dragline silk in wet (85%
-
RH) and dry (15% RH) conditions. Significant changes are observed in the 830
860 cm - 1 region which can be associated with vibrations in the Tyrosine OHgroup. The relative intensity ratio of two peaks 1860/1833 suggests a role of
206
Tyrosine and specifically
of the OH-group
in protein folding and the
supercontraction of silk. Experimental data collected by R. Schuetz and A. Masic.
Figure (left) courtesy A . M asic...................................................................................125
Figure 40 1 The acceptor/Donor (A/D) ratio determined from the hydrogen
bonding analysis of the molecular dynamics trajectory is in agreement with the
Raman experimental results. Tyrosine tends to be a donor in dry conditions and
a donor/acceptor in wet conditions. In the simulation, other polar and/or
charged residues in the amorphous part of silk such as Arginine and Serine
126
display a sim ilar behavior. .........................................................................................
Figure 41 | Simulated infrared (IR) spectrum for silk in vacuum (no filter)......128
I Simulated infrared (IR) spectrum for silk in water (no filter). ......... 128
43 I Simulated VDOS spectrum for silk in water and vacuum versus
Figure 42
Figure
129
R am an spectru m . .........................................................................................................
Figure 44
1 Supercontraction strain versus stress for dragline silk fibers
determined from experiment and simulation. The simulation data points are
found by determining the entropy of spider silk protein in hydrated and dry
conditions, and deriving the stress needed to reverse supercontraction. The
similarity in shape of the experimental and simulation - despite the orders of
magnitude
in size difference -
provides
a strong
indication
that the
supercontraction process is mainly driven by entropic effects in the amorphous
structure as well as changes in H-bonding. Experimental data collected by R.
Schuetz and A . M asic. .................................................................................................
134
Figure 45 1 The ratio between supercontraction strain and supercontraction
stress is similar among species. This suggests that the free energy scales directly
with
the
supercontracted
length.
Therefore,
the
mechanism
behind
supercontraction is similar for different types of dragline silk. Experimental data
collected by R. Schuetz and A . M asic........................................................................
135
Figure 46 1 Ramachandran plot of the entire silk molecule (excluding Glycine) in
dry (left) and wet (middle) state as well as the change in dihedral angle
207
distribution from dry to wet state (right). The distributions are normalized as
probabilities. The P-sheets present in the dry state turn into mostly random and
helical structures in the w et state...............................................................................
Figure 47
Figure 48
Figure 49
Figure 50
Figure 51
Figure 52
Figure 53
137
I Changes in backbone dihedrals of Alanine......................................... 138
I Changes in backbone dihedrals of Glycine......................................... 139
I Changes in backbone and side-chain dihedrals of Serine.................140
I Changes in backbone and side-chain dihedrals of Tyrosine............142
I Changes in backbone and side-chain dihedrals of Leucine.............. 143
I Changes in backbone and side-chain dihedrals of Glutamine.........145
I Changes in backbone and side-chain dihedrals of Arginine............147
Figure 54 1 Dihedral side chain angle distribution of Tyr determined from
simulation. The X2-angle describes the torsion angle of the aromatic ring that is
coplanar with the hydroxyl group of Tyr. From dry to wet conditions, a peak
shift from -90* to -10* as well as a shift from 90* to 170* is observed...................149
Figure 55 1 Two detailed snapshots from the molecular dynamics simulation
showing the Tyr local environment. The same residues at a similar simulation
time are shown in dry and wet conditions. Three (out of 15) polypeptide chains
are visible (blue, red and green), while Tyr and its hydrogen bond partner are
highlighted. The peak at -10* and 1700 (1) in the dry state is associated with the
intermolecular hydrogen bonding of Tyrosine's OH group with the Gly of the
adjacent chain. The hydrogen bond is formed through hydrogen of the Tyr and
oxygen of the Gly involved also in forming protein backbone. In this case, Tyr
acts as a hydrogen bonds donor. In the wet state, Tyr both accepts hydrogen
bond from mobile water within the structure as well as donates H-bonds through
intramolecular interactions with the hydrophobic Glycine (2).............................150
Figure 56 1 Dihedral side chain angle distribution of Arg determined from
simulation. The X4-angle is the last torsion angle in the long side chain of
Arginine where three possible H-bonding sites are present. From dry to wet
state, a peak shift from -130* to 1800 is observed. ................................................
208
151
Figure 57 1 Two detailed snapshots from the molecular dynamics simulation
showing the Arg local environment. The same residues at a similar simulation
time are shown in dry and wet state. Two (out of 15) polypeptide chains are
visible (blue and red), while Arg and its hydrogen bond partner are highlighted.
The peak at -130*
(1) in the dry state is associated with the intermolecular
hydrogen bonding of Arginine's NH2-group with Glycine of an adjacent chain. In
the wet state, Arg donates hydrogen bonds to mobile water within the structure
(2 )....................................................................................................................................1
51
Figure 58 1 Molecular dynamics simulations of point-mutations of the spider
dragline sequence and its effect on supercontraction. Three additional sequences
are equilibrated, where polar and/or charged amino acids are substituted by
their apolar/ uncharged counterparts. The contraction/expansion of the structure
is measured by radius of gyration and average end-to-end length. In the first
mutation experiment, Tyrosine is replaced by PhenylAlanine (similar molecular
structure, but no hydroxyl group on the aromatic ring). In the second mutation
experiment, Arginine (positively charged long side chain) is replaced by Leucine.
In a third mutation experiment Tyrosine and Arginine are substituted with
additional replacement of Serine with Alanine. While the wildtype shows
significant contraction (-15%) in the wet state in comparison to the dry state, a
replacement of Tyr leads to suppression of the contraction. Mutation with
Arginine even leads to an expansion in the wet state. The effect of the Serine
replacement is quite small, which can be explained with its comparatively small
side-chain. From these results it becomes clear that Tyrosine and Arginine play a
crucial role in the supercontraction mechanism through polar and charged sidechain group that can be related to mostly entropic effects....................................155
Figure 59 | In all of the mutated structures the P-sheet crystal remains intact (and
the P-sheet content approximately constant). This suggests that the mechanical
properties of the entire structure is unaffected by the point mutations..............156
209
Figure 60 1 Stress-strain curve of wildtype and mutated silk determined with
S MD ................................................................................................................................
210
1 56
7.6 List of Tables
Table 1 1 Model structures of the stages during the assembly process. The spider
silk dope is stored in the abdomen of the spider in globular form. In the
simulation, the general form of the simulated peptide/ protein structure is
largely independent of the size of the molecule (left hand column). It remains
unassembled and predominantly contains helices and turns. During the shearing
process (second column) a large part of the structure transitions into P-sheet
structures. Subsequently, equilibration of the structure in vacuum or explicit
water in the presence of ions, the silk relaxes again (third and fourth column
respectively). In vacuum, irrespective of simulation size, all structures are stable
and retain their ft-sheets. In water, the smaller silk structures (two and four polyAlanine stretches; a = 1, a = 3) return to their original largely disordered
'spidroin-like' state and only the larger structure (six poly-Alanine stretches;
a = 5) remains stable. The natural condition can be assumed to be an
intermediate between fully hydrated and vacuum due to the removal of water
and ions from the silk as it is spun into air. ...........................................................
59
Table 2 1 Residues involved in the structural transition of silk chains with length
a = 5 (206 residues). From the transition probabilities (a-helices - bold, 310helices/turns - italicized) the residue numbers are identified whose joint
probability to transition is higher than 10%. These residue groups are the
potential key players in the silk assembly mechanism of the core structure........ 67
Table 3 | Bulk modulus, bulk strength, and critical length scales for polymer
m aterials. Taken from Reference [121]...................................................................
Table 4
Table 5
78
I Process zone (cohesive zone) for the generalized J potential. ........... 105
I Summary of key structures and associated mechanisms of upscaling
from the atomistic to larger scales. Table adapted from Reference [47].......113
Table 6 1 Entropy in J/molK for vacuum and solvated structure split in three
independent parts S1, S2, S3. The change in entropy is calculated for the
211
amorphous phase only and the value in brackets gives the change for the entire
stru cture .........................................................................................................................
13 1
I Nomenclature for Secondary Structure Assignments........................... 138
Table 8 I Rotamers and associated secondary structures of Serine.....................141
Table 9 I Rotamers and associated secondary structures of Tyrosine.................142
Table 10 I Rotamers and associated secondary structures of Leucine................144
Table 7
Table 11
I Rotamers and associated secondary
structures of Glutamine. .......... 146
Table 12
I Rotamers and associated secondary
structures of Arginine. ............. 148
212