Open Collections

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The nanomechanical properties of amyloid fibrils using molecular dynamics simulations Nassar, Roy 2016

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
24-ubc_2016_may_nassar_roy.pdf [ 1.98MB ]
Metadata
JSON: 24-1.0229564.json
JSON-LD: 24-1.0229564-ld.json
RDF/XML (Pretty): 24-1.0229564-rdf.xml
RDF/JSON: 24-1.0229564-rdf.json
Turtle: 24-1.0229564-turtle.txt
N-Triples: 24-1.0229564-rdf-ntriples.txt
Original Record: 24-1.0229564-source.json
Full Text
24-1.0229564-fulltext.txt
Citation
24-1.0229564.ris

Full Text

The Nanomechanical Properties of Amyloid Fibrils Using Molecular Dynamics Simulations  by  Roy Nassar  B.Sc., The University of British Columbia, 2013  A THESIS SUBMITTED IN PARTIAL FULFILLMENT  OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in The Faculty of Graduate and Postdoctoral Studies (Genome Science and Technology)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2016 © Roy Nassar, 2016 ii  Abstract  Amyloid fibril formation, believed to be a generic property of polypeptides, plays major roles in neurodegenerative pathologies such as Alzheimer’s, Parkinson’s and prion diseases, as well as in functional biological processes in many organisms including humans. Revealing specifics of their molecular architecture, conformational stability, mechanisms of formation and physical properties holds clues to devising effective methods to fight their associated pathologies. An increasing requirement has been the development of a detailed understanding of the nanomechanics of amyloid core structures due to their relevance in biomedicine and nanotechnology. Of special significance is the mechanism of fibril fracture and infectivity in disease as well as the mechanical stability for novel biomaterial design. Here, we use a series of steered molecular dynamics simulations on different amyloid fibrils to report a broad spectrum of mechanical properties ranging from a strong and stiff β-helical fibril to weak and soft amyloid such as those formed by the mammalian prion protein. We relate the strength and elastic modulus with hydrogen bond densities and van der Waals energies in the core of the fibrils and show that weakened side-chain interactions lead to fibrils with reduced tensile strengths as a result of modified molecular packing in the fibril core. This modulation might lead to a combination of exceptional mechanical attributes such as those of the human functional amyloids.        iii   Preface  The bulk of the work presented here focuses on computational and simulation methods and results of which the author of this thesis is fully responsible for. The results from mechanical properties calculations are compared to experiments performed by Dr. Guillaume Lamour as this was a joint experimental and computational project. The work presented here comprises part of a manuscript that is in the process of submission to a peer reviewed journal:   Lamour G., Nassar R., Chan P., Gunes B., Li J., Bui J.M., Yip C., Mayor T., Li H., Wu H., Gsponer J. Quantitative nanomechanics of amyloids provide molecular insight into what makes amyloid functional, pathological or infectious.         This thesis was conducted under the supervision of Dr. Jӧrg Gsponer who provided essential concepts and ideas to guide this work. The author would also like to thank Dr. Guillaume Lamour for the helpful discussions during this collaborative work, as well as for his permission to reproduce figure 5.             iv  Table of Contents  Abstract ............................................................................................................................ii Preface ............................................................................................................................ iii Table of Contents ............................................................................................................iv List of Tables ...................................................................................................................vi List of Figures ................................................................................................................. vii Glossary ........................................................................................................................ viii Acknowledgements .........................................................................................................ix Dedication ....................................................................................................................... x Chapter 1 ........................................................................................................................ 1 Introduction ..................................................................................................................... 1 1.1 Protein folding and energy landscapes .................................................................. 1 1.2 Molecular modeling and simulation ........................................................................ 5 1.3 Misfolding, aggregation and the amyloid state ....................................................... 7 1.3.1 Amyloid formation as a generic property ......................................................... 7 1.3.2 Amyloid structure ............................................................................................. 8 1.4 Prions ................................................................................................................... 10 1.5 Functional amyloids ............................................................................................. 11 Chapter 2 ...................................................................................................................... 13 Motivation ...................................................................................................................... 13 2.1 Amyloid nanomechanics ...................................................................................... 13 2.1.1 Fibril stability .................................................................................................. 14 2.1.2 AFM studies ................................................................................................... 15  v  2.1.3 MD studies ..................................................................................................... 16 2.2 Computational and simulation goals .................................................................... 17 Chapter 3 ...................................................................................................................... 19 Computational methods ................................................................................................ 19 3.1 Fibril models ......................................................................................................... 19 3.2 Molecular dynamics simulations .......................................................................... 22 3.2.1 Heating, equilibration and production runs .................................................... 22 3.2.2 Steered molecular dynamics .......................................................................... 23 3.3 Calculation of molecular interactions ................................................................... 26 3.4 Fibrils of the hexapeptide NNQQN[Y/A/G] ........................................................... 27 Chapter 4 ...................................................................................................................... 29 Results and Discussion ................................................................................................. 29 4.1 Mechanical properties of amyloid fibrils ............................................................... 29 4.2 Molecular interactions in the fibril core ................................................................. 34 4.3 Nanomechanics of NNQQNX (X=Y/A/G) ............................................................. 36 4.4 Comparison of PrP models using SMD ................................................................ 43 Chapter 5 ...................................................................................................................... 45 Conclusions ................................................................................................................... 45 Bibliography .................................................................................................................. 47 Appendix ....................................................................................................................... 52     vi  List of Tables   Table 1. Mechanical properties of amyloid fibrils from SMD simulations ....................... 32 Table 2. Mechanical properties of NNQQNX ................................................................. 39    vii  List of Figures   Figure 1. The energy landscape of protein folding and aggregation ................................... 4 Figure 2. The cross-β structure of amyloid fibrils .................................................................. 10 Figure 3. Fibril models for MD simulations ............................................................................. 21 Figure 4. Summary of the simulation experiments ............................................................... 26 Figure 5. Experimental values of the mechanical properties of amyloid fibrils ................ 30 Figure 6. A representative stress-strain curve from an SMD simulation on IS2 .............. 32 Figure 7. Mechanical properties of amyloid fibrils from SMD simulations ........................ 33 Figure 8. Intermolecular interaction densities in fibril models ............................................. 35 Figure 9. Correlation between molecular forces ................................................................... 36 Figure 10. Fibril model of NNQQNY ........................................................................................ 37 Figure 11. Mechanical properties of NNQQNY, NNQQNA and NNQQNG ...................... 40 Figure 12. Molecular forces and structural fluctuations of NNQQNX fibrils ...................... 41 Figure 13. Backbone and side-chain contributions to the hydrogen bond density and van der Waals energies .................................................................................................................... 42 Figure 14. Strength and Modulus of PrP fibril models .......................................................... 44 Figure 15. BH4 and IS PrP amyloid fibril models .................................................................. 52     viii  Glossary  MD   Molecular dynamics SMD   Steered molecular dynamics Aβ42   Amyloid-beta peptide (1-42) PrP  Prion protein IS2  In-register stacked 2 BH2  β-helical 2 RMSD Root mean square deviation vdW  Van der Waals                ix  Acknowledgements  I would like to thank my supervisor Dr. Jӧrg Gsponer for his input and guidance starting from my undergraduate practicum and continuing throughout my master’s degree. His ideas and mentorship are highly appreciated and have led me to be grateful for my research experiences in this intriguing field of understanding and modeling molecular dynamics and its importance in medicine and technology. His leadership has been unwavering throughout my stay in his group and he has been my role model who inspired my career goals throughout the years.  I’m also grateful to many of my peers for the valuable discussions during this thesis work, especially Dr. Guillaume Lamour for his insights and contributions to this collaborative project. I would also like to thank Dr. Jennifer Bui and Alexander Cumberworth for helpful comments on the simulation methods, and Dr. Ashwani Jha for his assistance in the statistical analysis of the data. I am also thankful to my supervisory committee members Dr. Steve Plotkin and Dr. Christian Kastrup, the chair for my defense session Dr. Harry Brumer, the program coordinator Sharon Ruschkowski and the current and former systems administrators Kevin Griffin, Stephen MacDonald, Vince Tingey and Hugh Brown.  I would also like to thank my family and friends for their continuing support during my studies.         x  Dedication  I dedicate my thesis to my parents and brothers without whom it was impossible for me to complete this degree.  1  Chapter 1 Introduction 1.1 Protein folding and energy landscapes Ever since the early experiments by the Nobel laureate Christian Anfinsen and colleagues on ribonuclease, the protein folding process has intrigued biologists, chemists and physicists alike from all over the world. Over the decades, tremendous scientific efforts and research resources have been dedicated towards the goal of understanding protein structure, function and dynamics, owing to the importance of these macromolecules in biological systems. As cellular machinery, proteins are essential for the survival and growth in all organisms and are responsible for accomplishing a multitude of functions that include structural scaffolds in the cytoskeleton, enzymes that catalyze complex chemical processes, interaction hubs in signaling cascades, regulatory elements of DNA replication and transcription and molecular motors in energy production. It is clear that by enhancing our knowledge of the folding process and structure-function relationship of proteins, we may become able to devise intelligible approaches to tackle diseases caused by their malfunction and aberration.           The observations that a small protein can spontaneously fold and unfold under certain temperature and solution conditions without the external aid of biomolecules had very significant implications [1]. Firstly, the structure of a protein is somehow entirely encoded in its sequence of the amino acid building blocks. In other words, the structure of a polypeptide chain in a solution is dictated by the atomic-scale interactions of its backbone and amino acid side-chains. It was also inferred at the time that the native  2  state of a protein, i.e the functional state, is the most thermodynamically stable form under physiological conditions.        In his insightful review, Ken Dill discussed in details the dominant molecular forces in protein folding [2]. Those include the hydrophobic effect, which causes the collapse of a polypeptide chain, hydrogen bonds stabilizing secondary structures (α-helices and β-sheets) and van der Waals interactions caused by the close packing of atomic groups. Even though the hydrophobic effect—which is entropic and enthalpic in nature [3]—is considered to be the major driving component by forcing nonpolar residues towards the protein core, it is the complex interplay between the various molecular interactions which configures the structural details of a protein and gives rise to a particular native conformation. Consequently, equilibrium between the extended and native forms of a protein is usually a delicate balance between these forces, with the loss of conformational entropy acting as the major opposing force to folding and resulting in typical native state stability on the order of ~10kcal/mol (marginally stable) compared to unfolded forms [2].         In 1969, Cyrus Levinthal postulated a question that has eventually led to the emergence of a new view of the folding process. The famous Levinthal paradox considers a polypeptide chain’s achievement of the native state through random searches of conformational space [4, 5]. A simplified calculation demonstrates that a 100 residue chain with 3 degrees of freedom per amino acid (bond angles) would have ~3100 possible conformations which would require a cosmological number of years (~1027) to sample all of them. Yet, proteins fold on the millisecond to second timescale! Finding a solution to this apparent paradox quickly led to the realization that this search must be guided somehow. This guidance is now thought to occur through local interactions in the protein chain resulting in a rapid energy bias towards more stable states. This ultimately led to a new formalism relying on statistical mechanics and polymer physics to model the folding problem: the energy landscape theory of protein folding [6-13]. In brief, starting with Anfinsen’s thermodynamic hypothesis [1], the folding  3  of a protein corresponds to its navigation of the free energy function as it goes from the unfolded to the folded native state. The energy landscape of the folding process is “funnel-like”, with many high-energy states at the top of the funnel describing ensembles of unfolded states, and a narrower bottom channeling to the free energy minimum native state (fig 1). Quantitatively, the energy function describes the intra-molecular and solvation energies as a function of the polypeptide degrees of freedom and constitutes the vertical axis on the landscape. At any energy level, the funnel width describes the conformational entropy and is related to the density of states defined as the number of conformations having a certain value of the macroscopic variable describing the system. This variable is calculated in order to simplify the high-dimensionality of the energy landscape and is chosen such that it encompasses the important dynamics of the system, which might be, for instance, the number of hydrophobic associations, radius of gyration, or similarity of contacts to the native state. The higher the number of conformations ascribed to a certain state (defined by the chosen variable), the larger is its entropy and the higher that state is in the folding funnel.         Hence, the folding process does not amount to a random search on a flat landscape until the chains come across the native fold, but is rather described as a collection of chains taking paths that gradually lead to lower energies. Starting from an ensemble of unfolded states, early molecular interactions push the polypeptide chains downhill on the landscape, and the micro-pathway taken thereafter is dependent on the starting state of each chain, as well as on stochastic effects from thermal fluctuations and Brownian motions of atoms. For any individual chain, the uphill and downhill paths and the kinetic traps that it faces are not necessarily the same for all other chains, i.e. multiple parallel pathways can be taken by an ensemble of structures, and these pathways converge towards the global energy minimum at the bottom of the landscape [9].         What do folding energy landscapes look like in reality? Evolutionary pressure has likely resulted in relatively smooth (optimized) downhill landscapes allowing nature to  4  fold proteins in biologically relevant timescales [14]. Nonetheless, energy landscapes of proteins are generally rugged to some extent with many kinetic barriers that a chain has to overcome (e.g. by breaking favourable contacts) before continuing on the folding pathway to the native state. At a given temperature, thermal fluctuations allow for the crossing of barriers on the order of     in energy, where    is the Boltzmann constant and   is the temperature. Thus, the size of local energy barriers relative to thermal fluctuations influences the kinetics and transition rates between states on the landscape. Consequently, the barriers cannot be too large if the protein is to successfully fold to its stable functional state. This ‘principal of minimal frustration’ can be quantitatively described by the tendency to maximize the ratio      , where    is the energy gap between the unfolded and native-like ensembles, and    is the energetic roughness scale (~1-5    ) [14-17].    Figure 1. The energy landscape of protein folding and aggregation. (A) The unfolded ensemble is resembled by a large number of high-energy conformations leading to high entropy at the top of the funnel. Formation of favourable interactions guides the chain downhill towards a more compact native state at the energy minimum. (B) The amyloid pathway as an alternative route to folding is made accessible through intermolecular interactions between multiple monomers resulting in ordered arrangements of cross-β fibrils. A B  5  1.2 Molecular modeling and simulation The stability and dynamics of proteins have become of great importance to biomolecular researchers and have led to major endeavors and joint efforts from groups around the world to model protein dynamics using computer systems. This interest stems from the potential that is provided by computer simulations to tackle problems and provide predictions on length and timescales that are not accessible by experiments, especially when it comes to structure prediction and folding mechanisms and pathways. In such systems, a protein molecule is described as a collection of linked atoms having bonds, angles and partial or full charges. In these physics-based methods, the level of details for description of atomic groups of the protein and solvent depends on the length and timescale of the specific process being modeled, as well as, on the computer power available to the modeller. This has spurred the development of a whole array of computational tools and methodologies to combine the diverse reduced representations of proteins and solvents and have become essential to protein research with applications to the modeling of membrane proteins [18, 19], protein aggregation [20-22], and protein-protein interactions [23].         In fact, the Nobel Prize in Chemistry in 2013 was awarded to a team of researchers that have developed a combined classical and quantum mechanical description of biomolecules [24]. Such “multi-scale” representation is of immense significance to the computational modeling of enzymatic reactions, as it allows for detailed quantum mechanical description of the active site, while the rest of the system is described by the classical mechanical force field allowing efficient sampling and simulation of the bulk protein and solvent molecules.         For typical biomolecular simulation purposes the classical molecular mechanics is sufficient to model the relevant dynamics in the system. The atomic positions and momenta of atoms are obtained by solving the Newtonian equations of motion:                                6  The force   is calculated from the potential energy function using        at small discrete time intervals to update the atomic positions. One of the most widely used potential energy functions is the Chemistry at Harvard Molecular Mechanics (CHARMM) force field [25] having the following general form for the bonded and non-bonded atoms:                                                                                                                                                                                                                                 The first five terms in the above potential energy function correspond to covalently bonded atoms. The  ’s are constants of the harmonic terms. The first term accounts for bond vibrations where    is the equilibrium bond length. The second term corresponds to the angles between three atoms and the dihedral term is that of torsion angles (angles between 4 atoms of the backbone) with   the phase shift and   the periodicity. The Urey-Bradley term describes the distance   between an atoms and its third neighbour. The improper term corresponds to the out-of-plane angle. CMAP is a term added for correction of errors in backbone torsional properties. In the non-bonded expression, the first term is the Lennard-Jones potential accounting for van der Waals interactions between the atoms where     is the distance between the interacting atoms,        is the energy well depth and        is the separation distance corresponding to       . The second term describes the electrostatics interactions with scaling factor   which is set to 1 in explicit solvent simulations. The parameters are obtained from  7  experimental and theoretical calculations making this potential function a ‘semi-empirical’ force field.        The continuous improvements in design and parameterization of force fields and the recent advancements in distributed computing clusters are increasingly permitting more and more accurate simulations using full-atom descriptions of proteins in explicit solvents reaching up to the microsecond and longer timescales via specialized supercomputers [26-28].  1.3 Misfolding, aggregation and the amyloid state Protein misfolding refers to the phenomenon in which peptides or proteins fully or partially abandon their native conformations rendering the protein inactive due to the loss of the required functional structure. Common causes can be mutational effects in sensitive regions of the protein or changes in solution conditions resulting in the reduction of native state stability. In many unfortunate cases, ensembles of misfolded proteins aggregate into a highly-ordered insoluble fibrillar structures known as ‘amyloids’. These aggregates can then accumulate as extracellular deposits or as inclusion bodies within cells. It is now known that amyloid fibrils play major roles in more than 20 debilitating human pathologies including neurodegenerative and systemic amyloidoses such as Alzheimer’s, Parkinson’s, Huntington’s, Creutzfeldt-Jakob disease, Amyotrophic Lateral Sclerosis and type-II diabetes [29-31].   1.3.1 Amyloid formation as a generic property  Interestingly, most polypeptides can be induced to form amyloid aggregates under specific solution conditions that often destabilize the native state. This ability implies that amyloid formation is a generic property of polypeptide chains [32]. What protects them, then, from aggregating in cells under physiological conditions? Many mechanisms of control are currently under investigation. It turns out that cells, especially in eukaryotes, have evolved complex proteostasis machineries to help proteins fold, remove misfolded  8  ones or even disaggregate proteins [30, 33]. For instance, different classes of molecular chaperones assist in folding proteins to their native states, especially under stress conditions, as exemplified by the upregulated expression of ‘heat shock’ proteins under elevetated temperature environments. Alternative cellular mechanisms are also implemented, such as the ubiquitin-proteasome system that targets aberrantly-behaving proteins for elimination by degradation. However, such quality control systems can in many cases be compromised, due to ageing for example, where the efficiency of such networks to target misfolded and aggregated proteins is believed to diminish over the years resulting in an increased risk for devastating amyloid-related diseases. Due to this inescapable reality of protein aggregation being a generic phenomenon, evolutionary pressure to reduce the likelihood of aggregation also seems to have influenced protein sequences such as the occurrence of charged residues or prolines in certain sequence regions [30, 34]. More generally, it has been shown that the physicochemical properties encoded in the side-chains influence the aggregation propensity of polypeptide chains; those include hyrdrophobicity, charge and secondary-structure propensities of residues [35].  1.3.2 Amyloid structure Strikingly, the proteins causing the various neurodegenerative diseases are very dissimilar in sequence and length, yet they seem to result in similar ordered arrangements in the fibril core structure: they all correspond to fibrils enriched in β-sheets. Amyloids are known to exhibit a ‘cross- β’ structure where the β-strands formed by the individual (misfolded) proteins are aligned perpendicular to the fibril axis forming an elongated β-sheet. Two or more of these β-sheets can associate facing each other in a stacked manner. Amyloid structures are often detected by X-ray diffraction patterns showing intense reflections at ~4.8 Å and ~10 Å corresponding to the inter-strand and inter-sheet distances, respectively (fig 2). Fibrils are typically ~5-10nm in diameter formed from multiple protofilaments that combine and twist into fibers that can go up to hundreds and thousands of nanometers in length [29]. Amyloid assembly is likely to occur through a nucleation-elongation mechanism, which starts by the formation of early  9  small oligomers from multiple monomers that serve as nuclei for further incorporation of additional monomers into the growing fibril. This nucleation stage is the rate-limiting step and is linked to an early lag phase, which is then followed by a relatively fast elongation and maturation stages with dependence on monomer concentration in the solution [36].        From a structural perspective, the molecular architecture of amyloid have proven to be extremely difficult to resolve; this is due to the lack of ordered crystal formation by the fibers as well as their insoluble character, rendering techniques like X-ray crystallography and solution NMR practically ineffective [37]. Nonetheless, researchers in the group of David Eisenberg were able to form microcrystals at high concentrations of short 6-7 residue peptides, and used X-ray diffraction to reveal vital atomic details that offered great insight into the packing of atomic groups in amyloid-like structures [38, 39]. According to their work, the β-spine in the fibril core is created by in-register parallel or antiparallel β-strands aligned perpendicular to the fibril axis. Two such strand arrangements stack to form a double β-sheet structure, where the side-chains from the two sheets at the interface are locked together in a tight complementary construct, termed the “steric-zipper”.  This architecture of β-sheets and their interlocking side-chains are stabilized by hydrogen bonds between each individual β-strand and the ones above and below it in the fibril core with the interface complementarity sustained by van der Waals forces [38, 39].   10   Figure 2. The cross-β structure of amyloid fibrils.The individual monomers form β-strands and align perpendicular to the fibril axis. The cartoon model represented by VMD is that of the Alzheimer’s disease peptide Aβ(1-42) (PDB ID: 2BEG [40]).  1.4 Prions Prions are proteins that can exist in two states: a normal functional form and an infectious form that can catalyze the conversion of the functional form to become infectious. The infectious form often contains amyloid or amyloid-like protein structures. The Nobel Prize laureate Stanely Prusiner discovered that the mammalian prion protein can cause central nervous system disorders when ingested, thereby, reporting on the first non-nucleic acid infectious agent to be discovered [41].  The mammalian prion protein is a 209 residues membrane-bound protein whose normal biological function is yet to be determined. The cellular form PrPC can undergo conformational conversion into an infectious scrapie state PrPSc, a process that can be further stimulated by  11  addition of seeds of PrPSc [42]. In mammals, this conversion of PrPC to PrPsc is associated with significant structural changes in the prion protein: a mostly α-helical, soluble protein transforms into β-rich, insoluble amyloid. The amyloid form of the protein is believed to be responsible for a set of prion diseases known as Transmissible Spongiform Encephalopathies (TSE) that affect the brain and nervous system [43, 44]. Examples are Creutzfeldt-Jakob disease (CJD) and Gerstmann–Sträussler–Scheinker syndrome in (GSSS) in humans, Bovine-Spongiform Encephalopathies (mad-cow disease) in cattle and scrapie in sheep. Most cases of prion conversion seem to be sporadic, yet some are due to mutations in the gene encoding the protein. The atomic-resolution structure of the mammalian prion fibril is not yet known. Instead, sparse experimental data has been used to generate computational models of the amyloid fibrils formed by the mammalian prion protein. Such model generation was guided by limited experimental data from electron-microscopy images, mutational analysis and biochemical studies [45-48].  1.5 Functional amyloids Even though protein aggregation into amyloid fibrils is often associated with pathologies, recent studies have revealed that cells can exploit the intrinsic aggregation ability of certain proteins to their advantage in diverse biological processes [29, 49]. That the same type of macromolecular assemblies that form in disease is also present in functional processes is a very interesting observation in itself, and puts forward yet more evidence of why cells are the master engineers of the living universe. Maji and coworkers reported on more than 30 peptide hormones of the endocrine system that are stored as amyloid-like fibrils in secretory granules, from which the active state of the hormones get released upon pH changes [50]. Another important discovery of functional amyloid in humans is that formed by Pmel17; a protein involved in melanin biosynthesis where Pmel 17 amyloid acts as a structural matrix that templates melanin polymerization and deposition [51]. Interaction between the two kinases RIP1 and RIP3 has been shown to mediate programmed cell necrosis. This signaling complex forms via  12  association of interaction motifs on both RIP1 and RIP3, resulting in a fibrillar complex composed of β-sheets and coils, and is thought to be regulated via activation of the kinases by phosphorylation and the exposure of otherwise hidden interaction domains [52].         In yeast and fungi, several prions were observed to act as molecular agents of protein-based heritable phenotypes. The functions of these prions are currently under investigation and are suspected to play roles in nitrogen source uptake, long-term memory formation and induction of programmed cell death [53]. The latter is associated with the protein HET-s in a process known as the ‘heterokaryon incompatibility’ in fungus cells. In brief, cells may possess one of two different versions of the het-s gene: one encoding a soluble HET-S protein form and the other an aggregation-prone HET-s form that can convert to a fibrillar prion state, which results in the purposeful death of the fused cells if they display different versions of het-s [54]; this process might protect cells from viral transmission. Another widely studied system for investigating the “protein-only” mode of inheritance of prions is that of the Sup35 protein in yeast. Aggregation of this translation termination factor into an insoluble amyloid form results in a read-through of stop codons and leads to an altered proteome [53]. Whether this process confers phenotypic diversity that might be advantageous or detrimental is still a topic of controversy in the field.        While the discovery of functional amyloids was surprising at first, further thought might realize that it is not that bizarre. After all, it follows from the generic aptitude of polypeptides for self-assembly. It seems then that the existence of functional amyloids is nothing but a matter of the cell’s evolved ability to regulate, fine-tune and employ the aggregation processes of certain proteins to its advantage. This, however, implies tight control of the formation mechanism and reversal capability of these double-edged molecular swords. Possible policing mechanisms are currently under investigation by researchers and are likely to provide valuable insights into new approaches for fighting or reversing the amyloid state in disease situations.  13  Chapter 2  Motivation  2.1 Amyloid nanomechanics Amyloids are emerging as remarkable nanoscale structures with great potential for application in the technological and medical fields. Their protein nature renders them compatible for applications in biological systems in addition to their spontaneous self-assembly capability requiring little to no input for the polymerization process and fibril formation. Furthermore, what is remarkable about the amyloid structure is that weak non-covalent intermolecular interactions produce notably robust mechanical properties and give rise to stable biomaterials [55]. If this inherent ability to form hierarchical structures can be artificially controlled, a wide range of applications in diverse fields is of great promise as such self-assembling biocompatible material can be exploited for the design of nanostructures in biotechnology. Indeed, the amyloid form is being employed as templates for the fabrication of electrically conducting nanowires by coating with silver and gold particles [56, 57], for climate change research where fibers were used for capturing carbon dioxide that binds to a lysine amino group [58], for biomedicine by forming nano-scaffolds for regeneration of brain neurons after injury [59], as light-sensing devices by attachment of fluorophores [60] and as long-acting drugs for the controlled release of active hormone monomers [61].        From an engineering viewpoint, nonetheless, designing materials for nanoscale applications requires profound understanding of their stabilities and nanomechanical properties. How stable are amyloids? And what are their mechanical properties?  14  Answers to these questions are just starting to emerge from key experimental and theoretical efforts.  2.1.1 Fibril stability The growth of an amyloid fibril can be initiated by chain conversion from the soluble to the aggregated state or by seeding using aggregated nuclei that act as templates for incorporation of soluble monomers. The latter can occur due to fragmentation of existing fibrils, which in turn exponentially increases the number of fibril ends that are able to react with free monomers in solution [62]. As amyloid fibrils get longer and approach the micrometer scale, their tendency to fragment increases, for instance due to thermal fluctuations or disruptive interactions with other cellular macromolecules [63]. This ability to fragment and speed up the fibril proliferation process clearly depends on the stability and mechanical properties of the existing fibrils.          Experiments by Baldwin and coworkers provided an indication of the thermodynamic stability of the amyloid species [64]. Their findings suggest that the amyloid form of a polypeptide might represent the global energy minimum structure under physiological conditions; it is even at a lower energy state than the soluble native form for polypeptides of length ~100 amino acids or less. However, abandoning the soluble state in vivo and transitioning to the amyloid pathway is likely prohibited by a large kinetic energy barrier, despite the existence of many proteins at concentrations that favor the aggregated state [64]. In other words, at a critical concentration, the thermodynamic stability of the native state equals that of the amyloid state                    , and at higher concentrations the native state becomes kinetically metastable, where the only obstacle for a soluble chain to switch to the amyloid form is the crossing of that energy barrier [62]. In energy landscape terminology, the amyloid pathway is dynamically disconnected on the energy surface due to high barriers that prevent accessibility to it, even though it constitutes the global thermodynamic minimum (fig 1B).  15   2.1.2 AFM studies Atomic force microscopy (AFM) is a high-resolution scanning technique that is able to probe the surfaces at the nanometer scale [65]. In its simplest form, AFM consists of a micro-cantilever with a sharp silicon tip that is held a few nanometers above the sample of interest which is situated onto a stage. In the widely used AFM tapping mode, a feedback loop gauges and maintains the oscillation amplitude of the tip, which is affected by force interactions with the material (piconewton scale). The displacement of the tip as it scans the landscape of the surface is measured via reflections of a laser beam hitting the cantilever and is recorded and converted into a high-resolution image. Advanced AFM techniques have proven extremely valuable in nanoscale biotechnology where they were employed in probing microscale mechanics in single molecule experiments [66] as well as in revealing topologies of cellular, protein and DNA nanostructures [65].         Knowles et al. used shape-fluctuation analysis on AFM images of amyloid fibrils formed from different proteins to calculate the bending rigidities    of these ordered structures [67]. They calculated the cross-sectional moments of interia   of the fibrils from the heights in the AFM images, which allowed estimation of the fibrils’ resistance to bending as given by the Young’s (elastic) modulus       . They reported stiffness values for fibrils formed by different proteins, where the majority had elastic moduli between 2 -14 GPa, which are about two orders of magnitude higher than those of other biofilaments such as the ones formed by actin or tubulin. Moreover, their theoretical calculations suggested that the high stiffness of amyloid fibrils stems from the common network of backbone hydrogen bonds that stabilizes the cross-β structure, but can also be modulated by side-chain hydrogen bonds. Lamour et al. were the first to measure the mechanical properties of fibrils formed by the mammalian prion proteins. Their AFM techniques reported less stiff PrP fibrils with elastic moduli between 0.1-1.4 GPa [68]. Measurements of low modulus (soft) PrP fibrils tie well with previous observations that  16  prion amyloids may possess a high breakage rate providing them with the ability to propagate and seed new fibrils by fragmentation, which in turn might explain their infectivity [69].  2.1.3 MD studies Despite the essential insights into the remarkable mechanical properties of amyloids provided by experiments so far, the details of the structural dynamics that give rise to these properties cannot be observed by experiments as it warrants high-resolution probing of the atomic features in the core of the fibril. Moreover, elucidating the nanomechanics of a fibril's response to deformation is a crucial step in understanding the source of stability, strength, elasticity and resistance of amyloid structures. Towards realizing this goal, recent studies are increasingly focusing on computationally modeling fibril systems at atomic resolution. Even though such studies initially relied on implicit solvent models and simplified molecular representations due to the sheer size of such molecular systems, recent improvements in computer power have increasingly allowed much more accurate representation of both the fibril and the solvent atoms. Markus Buehler and his group investigated the mechanics of amyloid fibrils using molecular dynamics simulations by inducing mechanical deformation due to an applied external force [70]. In their approach, compressive and tensile loading on fibrils of the Alzheimer's causing peptide Aβ40 resulted in measurement of high stiffness given by a modulus in the range of 12-18 GPa under compression and tension, confirming the stiffness of amyloid fibrils observed from experiments [67].        Solar and Buehler used steered molecular dynamics simulations (SMD) to investigate the mechanical performance of fibrils having different core architectures. During SMD, an external force is applied to one or more atoms of the protein to reveal its response to perturbation (see methods for more details). Their findings pointed to higher strengths and moduli for fibrils with β-helix cores as compared to those with stacked β-sheets [71]. The observation that β-helix-based structures with triangular cross sections led to the highest mechanical performance is explained by the  17  considerable enrichment in hydrogen bonds per area of such structures; the rupturing of these bonds between the β-strands is necessary for fibril deformation and failure [71]. Due to their ability to mimic single-molecule experiments—such as the stretching of molecules by optical tweezers or AFM—these in silico (by computer modeling) techniques have been successfully used to reveal detailed molecular mechanisms of protein unfolding and fibril mechanics [71-73].   2.2 Computational and simulation goals In an effort to gain further insight into these illusive macromolecules of nature with seemingly wide array of behaviours, and in light of the studies mentioned above, we hypothesize that amyloids formed by different proteins can have diverse mechanical properties, and that amyloid that can confer prion behaviour such as amyloid fibrils formed by the mammalian prion protein (PrP) are less mechanically robust compared to other amyloids.  To test our hypothesis, we propose to investigate the following: 1- Compare the mechanical properties of amyloid fibrils formed by different proteins by calculating their tensile strength and Young’s elastic modulus using steered molecular dynamics simulations.  2- Examine the differences in molecular interactions in the fibril structure that give rise to the mechanical properties.  3- Investigate the effects of alterations in side-chain interactions on the mechanical properties in order to describe the high modulus and low strength of the human functional amyloids as observed in AFM experiments.   18   To explore the first two goals, we conduct a series of steered molecular dynamics simulations on five fibril models selected to represent the different classes of amyloids, i.e. amyloid formed by disease-related non-prions (Aβ42 and insulin), a pathological prion (BH2 and IS2) and a functional prion (HET-s), and determine their tensile strength and Young’s elastic modulus. Then, we compute the hydrogen bond densities and van der Waals energies between the layers in the fibrils and correlate them to the strength and modulus values for each model. To investigate the third goal, we rely on a simple fibril model of the hexapeptide NNQQNY and its mutants (NNQQNA and NNQQNG) in a proof-of-principle study by showing the effects of weakened side-chain interactions on the strength and modulus and show how reduced packing densities in the fibril may lead to lower tensile strength.  Throughout the thesis, comparison of MD simulation results to the relevant findings from recent AFM experiments conducted in our lab will be done; however, emphasis will be placed on the computational and simulation parts of the project.           19  Chapter 3 Computational methods  3.1 Fibril models  Atomic resolution models of fibrils belonging to different structural classes of amyloid were chosen for the simulations (fig 3). The amyloid classes represented here consist of disease-related fibrils and fibrils of the prion protein PrP, as well as a functional amyloid. Specifically, the fibrils are of the functional prion HET-s (residues 218-289 and PDB code 2KJ3 [74]), the Alzheimer’s peptide Aβ42 (residues 1-42 and PDB code 2BEG [40]), insulin (chain A residues 1-21 and chain B 1-19 [75]) and two mouse prion protein amyloid models. The first PrP model (residues 90-231), which is referred to as “IS2” in this work, consists of an in-register architecture formed by parallel β-strands stacked into multiple β-sheets as recently built by Caughey and coworkers from solid-state NMR data [46]. The second PrP model “BH2”, originally built by Langedijk and colleagues [47] and later re-constructed by Shirai et al [48], is known as the “two rung” model due to the incorporation of triangular loops in a β-helix formed by residues 104-142 of core PrP with the helix-bundle α2- α3 (residues 143-231) kept intact as in the native cellular form PrPC. These two models were selected for simulations since most prion protein fibrils built so far fall under these two structural categories, that is, based on either a β-helix core or a stacked β-sheet architecture.        We define a layer to be one or more monomers, depending on the model, that fall in the same plane perpendicular to the fibril axis. For the purpose of the simulation, ten layers of each structure were prepared by elongating the fibrils, originally composed of only a few layers, through the addition of monomers along the fibril axis direction. The  20  fibril elongation was accomplished through copying existing monomers followed by translation and twisting using transformation matrices in the Visual Molecular Dynamics package (VMD) [76]. For each fibril model, these translation and rotation matrices were first learned from the backbone of existing layers and then applied to the newly created layers to complete the fibril extension. Fig. 3 below shows the detailed structures of each model in the yz (side-view) and xy (top-view) planes. The fibrils were initially centered and oriented along the vertical axis in VMD by aligning to the fibril’s molecular vector (long axis) calculated using centers of mass of the top and bottom layers.    21   Figure 3. Fibril models for MD simulations. Equilibrated fibril models for HET-s, Aβ42, Insulin, IS2 and BH2 as displayed in side and top views using VMD. Secondary structures are shown in color: β-strands in yellow, α-helices in purple and random coils in white.   22  3.2 Molecular dynamics simulations In order to calculate the mechanical properties of the fibril models: we first minimized the structures to remove clashes between the atoms and then heated the systems to the physiological temperature (300 K); the fibrils were then allowed to equilibrate in the solvent before the steered molecular dynamics (stretching) simulations were carried out.  3.2.1 Heating, equilibration and production runs All simulations were carried out in NAMD version 2.10 [77] using the CHARMM22 all-hydrogen force field with CMAP correction [78] and a cutoff distance of 12 Å for non-bonded interactions. Particle Mesh Ewald (PME) was used for calculating long-range electrostatics [79, 80]. The simulations were  carried out on a 2.00GHz Genuine Intel(R) Xeon(R) CPU using CUDA extension running on a NVIDIA GeForce GTX 780 graphics card. Each protein was solvated in a periodic box of TIP3P water molecules with at least 15Å buffer distance between protein atoms and the side of the box. Na+/Cl- ions were added to neutralize the system. Each system was minimized until convergence and heated to 300 K in 30 ps. A similar but modified procedure to Solar and Buehler [71] was followed for equilibration and pulling simulations. The systems were equilibrated under constant volume and temperature (NVT) conditions for 100 ps with the protein backbone atoms restrained, followed by a constant pressure and temperature (NPT) equilibration for 120 ps with gradual release of the positional restraints. The widely used Langevin dynamics were used to keep the temperature at 300 K and a modified Nosé-Hoover barostat in NAMD was used to maintain the pressure at 1 bar [81, 82]. The SHAKE algorithm [83] was implemented to fix the length of covalent bonds involving hydrogen atoms, allowing for a 2 fs integration time step. The production run was performed under isothermal-isobaric (NPT) conditions at 300 K and 1 bar for 20 ns and without positional restraints on any atoms.    23        The structural evolution of the models was monitored using root mean square deviation (RMSD) to confirm convergence of the simulation. This variable is widely used for comparison of two conformations and for checking structural changes over time.                           where      is the position of atom   in the first conformation,      is the position of that atom in the second conformation and   is the total number of protein atoms. Here, the RMSD was calculated using backbone Cα atoms with the reference structure taken to be the conformation in the middle of the simulation trajectory.        The insulin model underwent considerable deformation when the restraints were released and, thus, did not lead to a stable structure during the production run. For this reason, the steered molecular dynamics (SMD) simulation described below was carried out on the insulin fibril directly after 30,000 minimization steps.  3.2.2 Steered molecular dynamics Protein structures were extracted from multiple time points during the production simulation for the SMD experiments. The proteins were re-centered and re-solvated in a bigger box to allow for the pulling experiments. The new water molecules were relaxed via a minimization and a 100 ps NPT equilibration steps.        During SMD experiments, one or more atoms are fixed in space while an external force in a specified direction is applied to another group of atoms (SMD atoms). Pulling on the SMD atoms stretches the molecule and allows to simulate the unfolding of a protein or to probe the elastic response as a result of an external perturbation. In SMD experiments, pulling can be in one of two modes; either via a constant force or via a constant velocity. In our simulations, we apply constant velocity since we intend to  24  measure the force it takes to break the fibrils. This mode measures the force in a virtual spring attached to the SMD atoms as a function of time and position of the atoms [77]:                                Where   and    are the current and initial SMD atom positions, respectively,    the direction of pulling,   the time,   the spring constant and   the velocity.        Constant velocity SMD simulations have been used effectively to calculate the rupture force in tensile deformation simulations, allowing for estimation of ultimate tensile strength and elastic modulus of amyloid-like fibrils [71]. Here, similar in silico experiments were conducted by fixing the bottom layer of each protein and pulling on the center of mass of the top three layers upwards along the fibril axis with a spring of constant                  and a velocity of         .  The recorded force values from the SMD run were divided by the cross sectional area of each fibril to obtain the stress:       The relative fibril extension, known as the engineering strain, was calculated as          where   is the instantaneous fibril length and    is its original length before stretching. The peak in the stress-strain curve gives the ultimate tensile strength, defined as the maximum amount of stress the fibril can withstand before braking. The stiffness of a  25  solid material is described by the Young’s (elastic) modulus and calculated from the stress and corresponding strain:         Here, the slope in the elastic (linear) regime in the stress-strain curve provides an estimate of the Young’s modulus. For each fibril model, we report the values averaged from three or more pulling runs on the structures extracted at different time points (e.g at 5, 10 and 20ns) in the 20ns production simulation.       Since the mechanical properties (stress and modulus) calculated are sensitive to the cross sectional area, we devised a method for the accurate determination of the area of a fibril. The van der Waals surface of a layer was projected onto a 2D plane perpendicular to the fibril axis; the surface corresponding to disordered segments were removed to avoid overestimation of the core cross section. The 2D layer was then imported as a binary image into MATLAB and its area calculated using the “bwarea” function with the appropriate pixel calibration. Values for three layers were averaged to provide the cross sectional area estimate of each fibril model.         A good measure of the resistance of a fibril to deformation is the resilience; defined as the amount of energy a fibril can absorb before it begins to break. The resilience was calculated from the area under the elastic regime of the stress-strain curves using MATLAB’s trapezoidal integration function.      26   Figure 4. Summary of the simulation experiments. The fibril structure is solvated in water and ions (left) and simulated under constant pressure and temperature conditions for 20 ns. The structure is then extracted (middle) and re-solvated in a bigger box (not shown) to allow for stretching. An SMD simulation using constant-velocity pulling eventually leads to fibril fracture (right). The VMD representation shown here is that of the stacked-sheet fibril model of Aβ42.   3.3 Calculation of molecular interactions  The last 10 ns of the production simulation were used to calculate the inter-layer interactions, under the assumption that forces within a layer are of negligible contribution towards tensile deformation. Van der Waals energies and the number of hydrogen bonds between the layers were computed using VMD scripting by looping over the layers of the fibril. The top and bottom layers at the fibril extremities were not included in the analysis since they only interact with one other layer. For hydrogen bond calculations, a donor-hydrogen-acceptor angle of 30° and a donor-acceptor distance of 3.5Å were used. The calculation of van der Waals energies were performed in VMD using the CHARMM22 force field. The van der Waals term in the force field is given by the Lennard-Jones 6-12 potential.   27        The number of H-bonds and vdW energies were normalized by the cross sections and the resulting densities correlated with strength and modulus measurements to investigate the effects of the inter-layer interactions onto the mechanical properties.         The R package [84] was used for statistical comparison of the results between the models. Specifically, we compared values of strength, modulus, H-bonds, vdW energies and layer separation distances between the models using p-values computed according to the unpaired t-test. In addition, Cohen’s  , defined as the standardized difference of the means is calculated as           where    is the mean of sample 1,    is that of sample 2 and    is the average of the standard deviations. The reason for using this measure is that, for datasets of large sizes, the p-value between the sets might be small, hence, indicating statistically significant differences; however, this value might be due to the large size of the sets and does not describe how large this difference is. Cohen’s   estimates the Effect Size, which provides a measure of the magnitude of the mean difference of two data sets and, hence, is a useful complement to statistical tests [85]. Here, statistical significance was achieved if   < 0.05 and   > 0.8.  3.4 Fibrils of the hexapeptide NNQQN[Y/A/G] To assess the effects of weakened side-chain interactions onto the mechanical properties of amyloid fibrils, we use a model system composed of short peptides arranged in a parallel in-register fashion forming two anti-parallel β-sheets as show in fig 10 below. This system was chosen due to both its sequence simplicity (NNQQNY) and the existence of a high-resolution structural model showing the “steric zipper” interface between the sheets as well as the atomic arrangements in the side-chains [39]. The TYR residues in the original microcrystal structure of the amyloid-like NNQQNY system were mutated to ALA and GLY to serve as potential models for assessing the effects of weakened interlayer interactions on the fibril nanomechanics, due to the replacement of the aromatic ring in the TYR model with smaller less reactive side-chains CH3 and H in  28  the fibrils of the ALA and GLY mutants, respectively. The simulation procedures described in the section above were applied to all three systems; however, a 10 ns simulation run (instead of 20 ns) was enough for these smaller systems since they reached conformational stability very early on in the production run. The structures for SMD experiments were taken at 5, 7.5 and 10 ns and the interactions calculated using the last 5ns of the simulation.                                29  Chapter 4 Results and Discussion  4.1 Mechanical properties of amyloid fibrils  Recent experiments by Guillaume Lamour in our group considered the mechanical properties of diverse amyloid fibrils. These experiments relied on analysis of fibril shape fluctuations in AFM images to obtain bending rigidities   , in addition to calculations of cross-sectional areas from TEM images to obtain Young’s elastic modulus (      ). A sonication-based fragmentation technique [86] was performed on the fibrils to calculate their tensile strengths using:                   where   is the tensile strength,   and   are the height and width acquired from AFM and TEM images, respectively, and      is the shortest fragment length that can still break, also obtained from AFM image analysis. The values of strength and modulus on fibrils considered in AFM experiments are shown in fig 5 below.   30    Figure 5. Experimental values of the mechanical properties of amyloid fibrils. Unpublished results of measurements of tensile strength and Young’s (elastic) modulus on different amyloid fibrils. The lower left corner of the plot corresponds to fibrils formed by a fragment of the Sup35 yeast prion, the wild-type mouse prion protein PrP (W) and its mutants (FV) showing weak and soft properties compared to the disease-related amyloids of insulin and lysozyme and the functional prion protein HET-s. The human functional amyloids of RIP1/3 and TRIF show relatively high modulus (stiff) but low strength (weak). Figure reproduced with permission from Guillaume Lamour.         The simulation procedures described in methods were performed with the dynamics package NAMD using the CHARMM22 force field. The SMD simulations were conducted using the same velocity and spring constant for all fibril models until the fibril was clearly fragmented, usually requiring 1-2 ns depending on the model. The pulling force was recorded during the SMD run and divided by the cross sectional area to obtain the stress. A representative plot of the stress as a function of the engineering  31  strain is shown in fig 6 below for stretching of the PrP fibril model IS2. We obtain the ultimate tensile strength and the Young’s modulus from the peak and slope in the stress-strain curve, respectively. Averaged strength and modulus values for the fibril models BH2 and IS2 of the mouse prion protein (PrP) indicate that they are weaker and softer when compared with other fibrils as shown in fig 7A. Specifically, the BH2 and IS2 fibrils displayed half the strength as that of insulin and Aβ42 amyloids, implying much weaker structures of the PrP models. The PrP fibrils are also less stiff as given by lower elastic moduli, which interestingly, were somewhat similar for both PrP models despite a very different molecular architecture of the fibril core. The HET-s fibril, supporting the triangular β-helix design, showed extremely robust mechanical properties with few hundred mega-pascals higher strength, and a modulus that is more than two times larger than the values of insulin and Aβ42 amyloids. Besides the strength and modulus, the ability of fibrils to resist breaking can also be quantified by the resilience. This energy quantity is calculated from the area under the stress-strain curve in the elastic regime and has revealed considerably lower values for the PrP models (fig. 7B) confirming the ability of such fibrils to fragment due to a much lower disruptive energy input.        Altogether, the strength calculations from our simulations showed values between 100-800 MPa, a range that is in excellent resemblance to the ones obtained from very recent experiments by our group (fig 5), as well as to ones reported previously for insulin fibrils [63]. Even though the modulus calculated here for HET-s, insulin and Aβ42 fibrils are similar to the ones reported experimentally, the in silico modulus values for the PrP models (~1 Gpa) were higher than the experimental measurements on the mouse PrP fibrils (~0.1 GPa). It is difficult to point at the source of this discrepancy here, however, it is worth noting that the structures of the amyloid fibrils of PrP have not yet been determined experimentally and the models used here are not but mere designs of proposed structures created computationally using limited experimental data [46, 48]. Nonetheless, our simulation results showed a similar trend in the mechanical properties (fig 7A & Table 1) as the one obtained by experiments (fig 5); the PrP fibrils are clearly  32  the weakest, softest and least resilient in comparison to non-prion disease-related amyloid, as in the case of insulin and Aβ42, and the functional prion HET-s (fig 7). These findings are in agreement with suggestions of high fragmentation rates and increased infectivity of the mammalian prion protein fibrils [69, 87], which are believed to be the source of an enhanced expansion ability of the scrapie amyloid form PrPSc.     Figure 6. A representative stress-strain curve from an SMD simulation on IS2. The peak of 183 MPa is the ultimate tensile strength of the fibril and the slope corresponds to the Young’s elastic modulus.    Table 1. Mechanical properties of amyloid fibrils from SMD simulations Fibril Model Cross-section (nm2) Tensile Strength (Mpa) Young’s Modulus (GPa) Resilience (MJ/m3) HET-s 4.4 ± 0.1 642 ± 63 14.2 ± 4.9 7.8 ± 4.1 Aβ42 5.6 ± 0.3 345 ± 46 4.4 ± 0.7 6.3 ± 1.8 Insulin 15.6 ± 1.5 402 ± 25 3.93 ± 0.6 7.0 ± 1.7 IS2 (PrP) 41.3 ± 1.4 187 ± 13 3.25 ± 0.36 1.4 ± 0.7 BH2 (PrP) 52.2 ± 3.1 132 ± 22 2.81 ± 0.26 1.8 ± 1.2  33          Figure 7. Mechanical properties of amyloid fibrils from SMD simulations. Asterisks indicate statistically significant differences between the mechanical properties of the prion model compared to the other fibrils.     A B * *  34  4.2 Molecular interactions in the fibril core We investigate the molecular forces in the fibril core that give rise to such varying nanomechanics for the different amyloid models. Atomic resolution simulations are ideal for such endeavors which are nearly impossible to resolve by experiments. Intuitively, these forces are the same players that give rise to conformational stability in protein folding, namely, hydrogen bonding and van der Waals repulsive/attractive interactions. To account for the size difference of the fibrils, we calculate the hydrogen bond density by normalizing the number of H-bonds per layer by the cross sectional area of each fibril. We calculate the van der Waals energies using the force field as described in methods; that is, for each layer only the interactions of its atoms with the ones belonging to the layers above or below are considered, and not within the layer itself. This is necessary to avoid overestimation of the van der Waals energies that contribute to the tensile stability; for instance, a considerable part the BH2 PrP model consists of α-helices stabilized by internal interactions (H-bonds), but most of those are not interactions with other layers and, thus, do not contribute to the resistance of that layer to tensile deformation. The average interaction densities are clearly correlated with the mechanical properties of the fibrils as shown in fig 8. Perhaps not surprising, both the strength and modulus correlate well with the H-bond density and van der Waals energies, suggesting that these two mechanical properties result from an interplay between both types of intermolecular forces in the fibril core. Even so, it seems that the elastic modulus correlates slightly better with the H-bond density and, conversely, the strength correlates slightly better with the van der Waals interactions. Furthermore, we found an excellent correlation between the H-bond density and the van der Waals energies as shown in fig 9. This finding led us to the conclusion of a strong dependence of the mechanical properties on the aptitude of the molecular groups to pack tightly in the fibril core. In other words, the better the arrangement in the interior of the fibril, the higher the densities of H-bond and van der Waals interactions due to closer proximities between the atomic groups. Despite the weakness of each of those non-covalent forces on an individual scale, they can collectively form very dense networks of interactions in  35  amyloid structures that result in one of the most robust natural biomaterial known, as exemplified by the HET-s fibril in this work which has stiffness comparable to that of bone and strength similar to that of steel [55].        It is interesting to note that the cross sectional area seems to be inversely proportional to the mechanical properties (Table 1); the larger the area the less robust the resulting fibril is. This seems to be in-tune with previous suggestions that smaller peptides likely face less structural constraints when it comes to packing the side-chains in the fibril core, which in turn leads to higher density of the molecular forces stabilizing fibrils with smaller cross-sections as compared to larger ones with less optimal arrangements [67].      Figure 8. Intermolecular interaction densities in fibrils models. Correlation of each of the strength and modulus with the hydrogen bond density and van der Waals energy in the fibril models.  36    Figure 9. Correlation between molecular forces. The hydrogen bond density is correlated with the dispersion interactions indicating a better packing of the molecular groups in fibrils with more robust mechanical properties.    4.3 Nanomechanics of NNQQNX (X=Y/A/G) Recent experiments revealed unique mechanical properties of the human functional amyloids formed by RIP1/RIP3, a kinase complex that plays a major role in programmed necrosis [52], as well as by a segment of the adaptor protein TRIF, which is involved in the Toll-like receptor pathway. Amyloid fibrils corresponding to these proteins displayed Young’s moduli similar to those obtained by the disease-related insulin and lysozyme amyloids indicating relatively high stiffness in the structures (fig 5). Strikingly, the measured strengths of RIP1/RIP3 and TRIF scored in the range of 80-200 MPa, values that are similar to the weak fibrils formed by mouse PrP. These findings are very remarkable given the neighboring disease-related amyloid classes in the mechanical properties plot (fig 5). This requires new insight into the molecular features of the fibrils in order to explain such exceptional mechanical properties and to relate them to their cellular behavior. High resolution structures of fibrils formed by these functional amyloids would certainly be precious; but unfortunately, no such models exist  37  yet. For this reason, we refer to a simplified model system to assist in probing the effects of modified molecular interactions on the nanomechanics of amyloid structures. We hypothesize that, given a similar H-bond density, weakened side-chain interactions might lead to reduced strengths in cross-β fibrils. We use the amyloid-like microcrystal structure of NNQQNY [39] composed of two stacked β-sheets with parallel in-register strands as shown in fig 10 below. The TYR residue at the end of each strand was mutated to the smaller ALA and GLY to reduce the side-chain contacts along the fibril.      Figure 10. Fibril model of NNQQNY. Left: side view of the fibril showing the β-strands (cartoon) and their side chains (lines) in blue. The tyrosine ring stacks are highlighted in orange. Right: top-down view of the fibril axis showing the side-chains in the steric zipper (complementary interface) between the β-sheets.            The three fibril models were equilibrated and simulated in a water box and stretched using SMD simulations as described in methods to determine the mechanical properties. As seen in fig 11A and table 2, all three fibril models displayed similar modulus values; this is perhaps an expected result given structures with the same initial  38  backbone hydrogen bond density since only the side-chain groups are modified. However, the tensile strength for the NNQQNA and NNQQNG fibrils showed statistically lower values compared to NNQQNY. Additionally, the NNQQNY fibril exhibits significantly higher resilience than the two mutant fibrils (fig 11B); which seems to tie more with the differences in strength than modulus.         The difference of ~200 MPa in tensile strength is an effect of reduced side-chain interactions and the resultant looser packing along the fibril. Indeed, the interlayer van der Waals energies indicate much stronger interactions in the NNQQNY fibril (fig 12B). Since the difference in H-bond density is small and the moduli are not statistically different between the three fibrils, the increased TYR side-chain contacts in NNQQNY is clearly the source of extra stability in this model. This in turn results in denser molecular packing and lower structural fluctuations during the simulation. This is made apparent in fig 12C, where the combination of lower root mean square deviation (RMSD) as well as lower separation distances between the layers in the NNQQNY fibril suggests smaller conformational dynamics in solution compared to the other two fibrils.        To further pinpoint the source of variation in the calculated molecular forces, we dissected the composition of each of the H-bond density and vdW energy between backbone and side-chains contributions (fig 13) during the last 5 ns of the production simulation. Comparing the backbone H-bond density between the three fibril models, one can see a slightly higher density in the backbone of the NNQQNY model compared to the mutant fibrils, while the side-chain hydrogen bonding network seems unaffected. The situation is reversed for the vdW energy density where the difference in contribution originates from the side-chain and not the backbone. The small increase in backbone H-bond (~0.5 H-bond/nm2) is likely a result of the increased packing and reduced distances between the layers in the NNQQNY fibril that originate from the TYR ring stacking. Altogether, our results show how varied molecular interactions and hence different packing density in the fibril core may result in mechanical properties of amyloids that are stiff but weak even when starting with the same stacked β-sheet  39  architecture. This may explain the general concept behind the variation in nanomechanical properties between the functional amyloids, RIP1/3 and TRIF, and the pathological stacked-sheet amyloids like those of lysozyme and insulin.    Table 2. Mechanical properties of NNQQNX Fibril Model Cross-section (nm2) Tensile Strength (Mpa) Young’s Modulus (GPa) Resilience (MJ/m3) NNQQNY 3.32 ± 0.1 793 ± 29 20.2 ± 5.6 15.2 ± 2.1 NNQQNA 3.15 ± 0.05 609 ± 84 21 ± 6.4 9.8 ± 3.5 NNQQNG 3.03 ± 0.07 562 ± 39 16.3 ± 1.4 9.1 ± 2.5                            40        Figure 11. Mechanical properties of NNQQNY, NNQQNA and NNQQNG. Asterisks indicate statistically significance values compared to NNQQNY.   A B * * * *  41      Figure 12. Molecular forces and structural fluctuations of NNQQNX fibrils. (A,B) Strength as a function of H-bonds and vdW energies. (C) The root mean square deviation and layer separation distances in the last 5 ns of the simulations. B C A * * * *  42     Figure 13. Backbone and side-chain contributions to the hydrogen bond density and van der Waals energies. Asterisks indicate statistical significance of backbone (top panel) and sidechain (bottom panel) interactions of the mutants compared to NNQQNY.       43  4.4 Comparison of PrP models using SMD We next use the SMD simulation method to provide additional data for the comparison of the PrP amyloid fibril models designed computationally. The generation of in silico models were motivated by the importance of creating working models for the PrP amyloids, but seemingly, none of the ones designed so far have been able to successfully describe all the experimental clues, limited as they are, that were obtained on PrP fibrils [88]. Here, we propose using the calculations of mechanical properties to provide extra clues for the evaluation of the various PrP models. Specifically, we compare strength and modulus values by simulation of two additional PrP models: the in-register stacked model (IS) and the β-helical model (BH4) using initial fibril coordinates provided by Shirai et al [48]. Figure 15 in Appendix shows the architecture of these two additional models where the IS fibril is mostly composed of β-sheets and the BH4 is a mixed fibril of β-core and α-helices (an improved model of BH2). The models were simulated to 20 ns and pulled on using the same SMD parameters as described in methods. Figure 14 below shows the measurements of the mechanical properties on the four PrP fibrils simulated in this work. There seems to be a trend in the properties where the stacked β-sheet models (IS and IS2) result in fibrils of higher strengths and moduli than the models based on β-helix cores (BH2 and BH4). This might be due to the stacked-sheet models having more ordered β-strands and hence a higher proportion of residues that contribute to interlayer interactions as compared with the β-helix based models which have the intact α-helices with mostly intramolecular interactions that contribute very little resistance to tensile deformation. Given the results, more description of the physical properties of these models is required to support one of the models as a starting point for the development of a newer more accurate structure. One approach, for instance, is to computationally simulate x-ray diffraction patterns using the coordinates of existing fibril models and comparing them to experimental x-ray diffraction results to check for similar patterns. It is worth noting, however, that such an approach warrants careful analysis as PrP fibrils obtained experimentally are often characterized by a high level of morphological heterogeneity [89].  44     Figure 14. Strength and Modulus of PrP fibril models.                     45  Chapter 5 Conclusions We perform a series of steered molecular dynamics simulations to measure the nanomechanical properties of amyloid fibrils. Our simulations reveal tendencies that are consistent with experiments from sonication and AFM image analysis. Specifically, we show that fibrils formed by distinct proteins can have diverse values of tensile strength and elasticity and demonstrate that those formed by the mammalian prion protein PrP are weaker, less stiff and much less resilient than fibrils of non-infectious disease amyloids (insulin and Aβ42) and functional prion amyloid (HET-s). Furthermore, we elucidate that hydrogen bond density and van der Waals forces are at the origin of such mechanical traits and that the side-chain packing density in the fibril core can lead to unique mechanical attributes that may influence fibril behaviour in biological systems.         Our results may provide further basis for the design of amyloid-based biomaterials with the desired nanomechanical characteristics. This can be done in principle by optimizing sequences in the fibril core to yield the desired structure and stability. Suggestions for the design of strong filaments, for instance, include the addition of aromatic residues or hydrophobic amino acids that sequester away from the solvent. It is clear by now that there are tremendous potential applications of these unique biostructures in various technologies. Admittedly, even though our findings provide solid insight into the nanomechanics of amyloid fibrils, we have likely just scratched the surface and further efforts are required to improve our understanding of the formation and stability of amyloids. Perhaps the most pressing issue for experimentalists at the moment is to obtain new high-resolution structures of amyloids formed by various proteins, and in light of the results presented here, special interest should be given to functional amyloids and those of the mammalian prion protein. In this regard, the  46  techniques of solid-state NMR [37, 90] and cryo-EM [91] are proving of great significance in revealing amyloid structures. If the mechanical classes described in this work can be generalized using other functional and non-functional amyloids, then researchers can delve deeper into the molecular architectures of the assemblies as done here and directly relate them to their behavior in cells. Investigating mechanisms of formation, stabilization and possible reversibility of the distinct systems will undoubtedly shed new light on novel ways to not only fight their polymerization and proliferation in disease, but also to harness their wide-ranging stabilities in new nanoscale technologies such as biotemplates and scaffolds in biological systems or as long-lasting drug vehicles in the therapeutic industry.                     47  Bibliography  1. Anfinsen, C.B., Principles that govern the folding of protein chains. Science, 1973. 181(4096): p. 223-30. 2. Dill, K.A., Dominant forces in protein folding. Biochemistry, 1990. 29(31): p. 7133-55. 3. Chandler, D., Interfaces and the driving force of hydrophobic assembly. Nature, 2005. 437(7059): p. 640-7. 4. Levinthal, C., How to fold graciously. Mossbauer Spectroscopy in Biological Systems: Proceedings of a Meeting held at Allerton House, Monticello, Illinois, 1969. 67(41): p. 22-24. 5. Zwanzig, R., A. Szabo, and B. Bagchi, Levinthal's paradox. Proc Natl Acad Sci U S A, 1992. 89(1): p. 20-2. 6. Bryngelson, J.D., et al., Funnels, pathways, and the energy landscape of protein folding: a synthesis. Proteins, 1995. 21(3): p. 167-95. 7. Bryngelson, J.D. and P.G. Wolynes, Spin glasses and the statistical mechanics of protein folding. Proc Natl Acad Sci U S A, 1987. 84(21): p. 7524-8. 8. Dill, K.A., Polymer principles and protein folding. Protein Sci, 1999. 8(6): p. 1166-80. 9. Dill, K.A. and H.S. Chan, From Levinthal to pathways to funnels. Nat Struct Biol, 1997. 4(1): p. 10-9. 10. Dill, K.A., et al., The protein folding problem. Annu Rev Biophys, 2008. 37: p. 289-316. 11. Leopold, P.E., M. Montal, and J.N. Onuchic, Protein folding funnels: a kinetic approach to the sequence-structure relationship. Proc Natl Acad Sci U S A, 1992. 89(18): p. 8721-5. 12. Brooks, C.L., 3rd, J.N. Onuchic, and D.J. Wales, Statistical thermodynamics. Taking a walk on a landscape. Science, 2001. 293(5530): p. 612-3. 13. Wolynes, P.G., J.N. Onuchic, and D. Thirumalai, Navigating the folding routes. Science, 1995. 267(5204): p. 1619-20. 14. Wolynes, P.G., Evolution, energy landscapes and the paradoxes of protein folding. Biochimie, 2015. 119: p. 218-30. 15. Schafer, N.P., et al., Learning To Fold Proteins Using Energy Landscape Theory. Isr J Chem, 2014. 54(8-9): p. 1311-1337. 16. Whitford, P.C. and J.N. Onuchic, What protein folding teaches us about biological function and molecular machines. Curr Opin Struct Biol, 2015. 30: p. 57-62. 17. Whitford, P.C., K.Y. Sanbonmatsu, and J.N. Onuchic, Biomolecular dynamics: order-disorder transitions and energy landscapes. Rep Prog Phys, 2012. 75(7): p. 076601. 18. Bond, P.J., et al., Coarse-grained molecular dynamics simulations of membrane proteins and peptides. J Struct Biol, 2007. 157(3): p. 593-605. 19. Scott, K.A., et al., Coarse-grained MD simulations of membrane protein-bilayer self-assembly. Structure, 2008. 16(4): p. 621-30. 20. Cecchini, M., et al., Replica exchange molecular dynamics simulations of amyloid peptide aggregation. J Chem Phys, 2004. 121(21): p. 10748-56. 21. Gsponer, J., U. Haberthur, and A. Caflisch, The role of side-chain interactions in the early steps of aggregation: Molecular dynamics simulations of an amyloid-forming peptide from the yeast prion Sup35. Proc Natl Acad Sci U S A, 2003. 100(9): p. 5154-9.  48  22. Wu, C. and J.E. Shea, Coarse-grained models for protein aggregation. Curr Opin Struct Biol, 2011. 21(2): p. 209-20. 23. Baaden, M. and S.J. Marrink, Coarse-grain modelling of protein-protein interactions. Curr Opin Struct Biol, 2013. 23(6): p. 878-86. 24. Jorgensen, W.L., Foundations of biomolecular modeling. Cell, 2013. 155(6): p. 1199-202. 25. Brooks, B.R., et al., CHARMM: the biomolecular simulation program. J Comput Chem, 2009. 30(10): p. 1545-614. 26. Dror, R.O., et al., Biomolecular simulation: a computational microscope for molecular biology. Annu Rev Biophys, 2012. 41: p. 429-52. 27. Pan, A.C., et al., Demonstrating an Order-of-Magnitude Sampling Enhancement in Molecular Dynamics Simulations of Complex Protein Systems. J Chem Theory Comput, 2016. 12(3): p. 1360-7. 28. Piana, S., J.L. Klepeis, and D.E. Shaw, Assessing the accuracy of physical models used in protein-folding simulations: quantitative evidence from long molecular dynamics simulations. Curr Opin Struct Biol, 2014. 24: p. 98-105. 29. Chiti, F. and C.M. Dobson, Protein misfolding, functional amyloid, and human disease. Annu Rev Biochem, 2006. 75: p. 333-66. 30. Dobson, C.M., Protein folding and misfolding. Nature, 2003. 426(6968): p. 884-90. 31. Selkoe, D.J., Folding proteins in fatal ways. Nature, 2003. 426(6968): p. 900-4. 32. Dobson, C.M., The structural basis of protein folding and its links with human disease. Philos Trans R Soc Lond B Biol Sci, 2001. 356(1406): p. 133-45. 33. Hartl, F.U., A. Bracher, and M. Hayer-Hartl, Molecular chaperones in protein folding and proteostasis. Nature, 2011. 475(7356): p. 324-32. 34. Gsponer, J. and M. Vendruscolo, Theoretical approaches to protein aggregation. Protein Pept Lett, 2006. 13(3): p. 287-93. 35. Tartaglia, G.G., et al., Prediction of aggregation-prone regions in structured proteins. J Mol Biol, 2008. 380(2): p. 425-36. 36. Invernizzi, G., et al., Protein aggregation: mechanisms and functional consequences. Int J Biochem Cell Biol, 2012. 44(9): p. 1541-54. 37. Meier, B.H. and A. Bockmann, The structure of fibrils from 'misfolded' proteins. Curr Opin Struct Biol, 2015. 30: p. 43-9. 38. Nelson, R., et al., Structure of the cross-beta spine of amyloid-like fibrils. Nature, 2005. 435(7043): p. 773-8. 39. Sawaya, M.R., et al., Atomic structures of amyloid cross-beta spines reveal varied steric zippers. Nature, 2007. 447(7143): p. 453-7. 40. Luhrs, T., et al., 3D structure of Alzheimer's amyloid-beta(1-42) fibrils. Proc Natl Acad Sci U S A, 2005. 102(48): p. 17342-7. 41. Prusiner, S.B., Novel proteinaceous infectious particles cause scrapie. Science, 1982. 216(4542): p. 136-44. 42. Prusiner, S.B., Prions. Proc Natl Acad Sci U S A, 1998. 95(23): p. 13363-83. 43. Aguzzi, A. and A.M. Calella, Prions: protein aggregation and infectious diseases. Physiol Rev, 2009. 89(4): p. 1105-52. 44. Colby, D.W. and S.B. Prusiner, Prions. Cold Spring Harb Perspect Biol, 2011. 3(1): p. a006833. 45. Govaerts, C., et al., Evidence for assembly of prions with left-handed beta-helices into trimers. Proc Natl Acad Sci U S A, 2004. 101(22): p. 8342-7.  49  46. Groveman, B.R., et al., Parallel in-register intermolecular beta-sheet architectures for prion-seeded prion protein (PrP) amyloids. J Biol Chem, 2014. 289(35): p. 24129-42. 47. Langedijk, J.P., et al., Two-rung model of a left-handed beta-helix for prions explains species barrier and strain variation in transmissible spongiform encephalopathies. J Mol Biol, 2006. 360(4): p. 907-20. 48. Shirai, T., et al., Evaluating prion models based on comprehensive mutation data of mouse PrP. Structure, 2014. 22(4): p. 560-71. 49. Shewmaker, F., R.P. McGlinchey, and R.B. Wickner, Structural insights into functional and pathological amyloid. J Biol Chem, 2011. 286(19): p. 16533-40. 50. Maji, S.K., et al., Functional amyloids as natural storage of peptide hormones in pituitary secretory granules. Science, 2009. 325(5938): p. 328-32. 51. Watt, B., et al., PMEL: a pigment cell-specific model for functional amyloid formation. Pigment Cell Melanoma Res, 2013. 26(3): p. 300-15. 52. Li, J., et al., The RIP1/RIP3 necrosome forms a functional amyloid signaling complex required for programmed necrosis. Cell, 2012. 150(2): p. 339-50. 53. Shorter, J. and S. Lindquist, Prions as adaptive conduits of memory and inheritance. Nat Rev Genet, 2005. 6(6): p. 435-50. 54. Greenwald, J., et al., The mechanism of prion inhibition by HET-S. Mol Cell, 2010. 38(6): p. 889-99. 55. Knowles, T.P. and M.J. Buehler, Nanomechanics of functional and pathological amyloid materials. Nat Nanotechnol, 2011. 6(8): p. 469-79. 56. Reches, M. and E. Gazit, Casting metal nanowires within discrete self-assembled peptide nanotubes. Science, 2003. 300(5619): p. 625-7. 57. Scheibel, T., et al., Conducting nanowires built by controlled self-assembly of amyloid fibers and selective metal deposition. Proc Natl Acad Sci U S A, 2003. 100(8): p. 4527-32. 58. Li, D., et al., Designed amyloid fibers as materials for selective carbon dioxide capture. Proc Natl Acad Sci U S A, 2014. 111(1): p. 191-6. 59. Ellis-Behnke, R.G., et al., Nano neuro knitting: peptide nanofiber scaffold for brain repair and axon regeneration with functional return of vision. Proc Natl Acad Sci U S A, 2006. 103(13): p. 5054-9. 60. Channon, K.J., G.L. Devlin, and C.E. MacPhee, Efficient energy transfer within self-assembling peptide fibers: a route to light-harvesting nanomaterials. J Am Chem Soc, 2009. 131(35): p. 12520-1. 61. Maji, S.K., et al., Amyloid as a depot for the formulation of long-acting drugs. PLoS Biol, 2008. 6(2): p. e17. 62. Knowles, T.P., M. Vendruscolo, and C.M. Dobson, The amyloid state and its association with protein misfolding diseases. Nat Rev Mol Cell Biol, 2014. 15(6): p. 384-96. 63. Smith, J.F., et al., Characterization of the nanoscale properties of individual amyloid fibrils. Proc Natl Acad Sci U S A, 2006. 103(43): p. 15806-11. 64. Baldwin, A.J., et al., Metastability of native proteins and the phenomenon of amyloid formation. J Am Chem Soc, 2011. 133(36): p. 14160-3. 65. Vahabi, S., B. Nazemi Salman, and A. Javanmard, Atomic force microscopy application in biological research: a review study. Iran J Med Sci, 2013. 38(2): p. 76-83. 66. Muller, D.J. and Y.F. Dufrene, Atomic force microscopy as a multifunctional molecular toolbox in nanobiotechnology. Nat Nanotechnol, 2008. 3(5): p. 261-9.  50  67. Knowles, T.P., et al., Role of intermolecular forces in defining material properties of protein nanofibrils. Science, 2007. 318(5858): p. 1900-3. 68. Lamour, G., et al., High intrinsic mechanical flexibility of mouse prion nanofibrils revealed by measurements of axial and radial Young's moduli. ACS Nano, 2014. 8(4): p. 3851-61. 69. Tanaka, M., et al., The physical basis of how prion conformations determine strain phenotypes. Nature, 2006. 442(7102): p. 585-9. 70. Paparcone, R., S. Keten, and M.J. Buehler, Atomistic simulation of nanomechanical properties of Alzheimer's Abeta(1-40) amyloid fibrils under compressive and tensile loading. J Biomech, 2010. 43(6): p. 1196-201. 71. Solar, M. and M.J. Buehler, Tensile deformation and failure of amyloid and amyloid-like protein fibrils. Nanotechnology, 2014. 25(10): p. 105703. 72. Ndlovu, H., et al., Effect of sequence variation on the mechanical response of amyloid fibrils probed by steered molecular dynamics simulation. Biophys J, 2012. 102(3): p. 587-96. 73. Sotomayor, M. and K. Schulten, Single-molecule experiments in vitro and in silico. Science, 2007. 316(5828): p. 1144-8. 74. Van Melckebeke, H., et al., Atomic-resolution three-dimensional structure of HET-s(218-289) amyloid fibrils by solid-state NMR spectroscopy. J Am Chem Soc, 2010. 132(39): p. 13765-75. 75. Ivanova, M.I., et al., Molecular basis for insulin fibril assembly. Proc Natl Acad Sci U S A, 2009. 106(45): p. 18990-5. 76. Humphrey, W., A. Dalke, and K. Schulten, VMD: visual molecular dynamics. J Mol Graph, 1996. 14(1): p. 33-8, 27-8. 77. Phillips, J.C., et al., Scalable molecular dynamics with NAMD. J Comput Chem, 2005. 26(16): p. 1781-802. 78. Mackerell, A.D., Jr., M. Feig, and C.L. Brooks, 3rd, Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. J Comput Chem, 2004. 25(11): p. 1400-15. 79. Darden, T., D. York, and L. Pedersen, Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems. J Chem Phys, 1993. 98(12): p. 10089-92. 80. Essmann, U., et al., A smooth particle mesh Ewald method. J Chem Phys, 1995. 103(19): p. 8557-93. 81. Feller, S.E., et al., Constant pressure molecular dynamics simulation: The Langevin piston method. J Chem Phys, 1995. 103(11): p. 4613-21. 82. Martyna, G.J., D.J. Tobias, and M.L. Klein, Constant pressure molecular dynamics algorithms. J Chem Phys, 1994. 101(5): p. 4177-89. 83. Ryckaert, J.P., G. Ciccotti, and H.J.C. Berendsen, Numerical integration of the cartesian equations of motion of a system with constraints: molecular dynamics of n-alkanes. 23, 1977. 3: p. 327-341. 84. R development core team a language and environment for statistical computing. 2011, R Foundation for Statistical Computing: Vienna, Austria. 85. Sullivan, G.M. and R. Feinn, Using Effect Size-or Why the P Value Is Not Enough. J Grad Med Educ, 2012. 4(3): p. 279-82. 86. Huang, Y., T.P.J. Knowles, and E.M. Terentjev, Strength of Nanotubes, Filaments, and Nanowires From Sonication-Induced Scission. Advanced Materials, 2009. 21: p. 3945-48. 87. Knowles, T.P., et al., An analytical solution to the kinetics of breakable filament assembly. Science, 2009. 326(5959): p. 1533-7.  51  88. Requena, J.R. and H. Wille, The structure of the infectious prion protein: experimental data and molecular models. Prion, 2014. 8(1): p. 60-6. 89. Anderson, M., et al., Polymorphism and ultrastructural organization of prion protein amyloid fibrils: an insight from high resolution atomic force microscopy. J Mol Biol, 2006. 358(2): p. 580-96. 90. Tycko, R., Solid-state NMR studies of amyloid fibril structure. Annu Rev Phys Chem, 2011. 62: p. 279-99. 91. Fitzpatrick, A.W., et al., 4D cryo-electron microscopy of proteins. J Am Chem Soc, 2013. 135(51): p. 19123-6.                  52  Appendix   Figure 15. BH4 and IS PrP amyloid fibril models. Side and top view of the fibrils showing the β-strands (yellow) and α-helices (purple).  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.24.1-0229564/manifest

Comment

Related Items