Structure-Property Relationship of Amyloidogenic Prion Nanofibrils

The structure and its property for the prion nanofibrils, which exhibit self-assembled steric zipper, amyloid fibrils, are described in this chapter. There is the belief of origin for the infectiousness of the prion can be its molecular structure. It is due to the amyloid toxicity, which is related to its beta sheet rich molecular structure and self-aggregated long fibrils. There is evidence that the difference between PrPc and PrPsc is transitioned beta sheet from alpha helix to self-assemble and then to the amyloidogenic fibrils. Therefore, the scope of this chapter is the amyloidogenic structural characteristics of prion fibrils and its relationship to the property. The molecular structural characteristics can be changed by properties such as affinity, toxicity, infectivity, and so on, so this is a key factor to understand the origin of prion disease and develop the therapeutic strategy. One of the main properties of amyloid fibrils that we want to describe here is mechanical property such as dynamic property and material property for prion nanofibrils. This chapter can shed light on understanding the infectious characteristics of prion and the relationship of its molecular structures.


Introduction
The molecular structure and properties of prion nanofibrils, which exhibit self-assembled steric zipper and amyloid fibrils, result in fatal prion diseases such as transmissible spongiform encephalopathies and neurodegenerative diseases such as Alzheimer's disease. Various origins for the infectious nature of prions have been suggested, including the molecular structure; amyloid diseases exert their toxicity by forming self-aggregated β-sheets and self-assembled long fibrils. For example, hIAPP fibrils induce apoptosis of insulin-secreting β-cells in the pancreas for its hardness and self-propagation characteristics. For the prion, PrP C and PrP Sc differ because of the transition from an α-helix to a β-sheet, respectively, to self-assemble into amyloidogenic fibrils. This chapter describes the amyloidogenic structural characteristics of prion fibrils and their relationship with their functions. The molecular structural characteristics can be quantified based on affinity, toxicity, and infectivity, among others, which are key factors for understanding the origin of prion diseases and developing therapeutic strategies. We focus on the mechanical properties of amyloid fibrils such as the dynamic and material properties of the HET-s prion.
Prion proteins exist in forms such as fibrils, oligomers, and lattice-like plate structures under different physiological conditions. A common structural feature of prion and amyloid proteins is that prions disrupt normal cell function and exhibit toxic behavior; thus, it is necessary to understand the different conformations of prion proteins under various physiological conditions. Different conformations of prion proteins have been reported under various pH conditions determined using various experimental techniques. Furthermore, some computational groups investigated the development of secondary prion structures as well as protonation status of specific prion residues, which enable secondary structures of prions to form oligomer conformation and grow into fibrillar or plaque structures. Similarly, toxic and nontoxic characteristics of prion proteins for β-helices in the presence of physiological agents were determined through the structural stability and mechanical property analyses.
Various experimental and computational studies have provided insight into the amyloid fibril-forming mechanism. Recently, computational studies were performed to overcome the limitation of experimental methods, which are unable to reveal the detailed molecular structures. For several decades, many studies evaluated the mechanical properties (such as bending and torsional rigidities) and mechanical behaviors of amyloid fibrils. These studies increased the understanding of the mechanism of fibril formation. Most studies evaluated homogeneous amyloid fibrils. However, other experiments revealed that heterogenetic interactions are possible for different amyloid monomers. Alpha-synuclein Aβ, Aβ-amylin, and Aβ-tau are well-known heterogenetic interactions.
Previous experimental and computational studies reported that depending on the conformation of amyloids or prion proteins, 2D material-based amyloids including fibrillar and plaque were deposited, which disrupted normal cell functions. Additionally, 1D materials, based on amyloids such as monomers and oligomers, showed toxic characteristics. These various forms of amyloid and prion proteins are affected by physiological conditions such as thermal fluctuation, internal flow, pH, and ionic strength. For instance, Aβ amyloid proteins exhibit various conformations such as cross-β zipper structures and β-turn-β motif structures. Based on their structural conformation features, the generation and development of oligomeric and fibrillar Aβ amyloids are different. Specifically, the existence of metal ions including copper, zinc, and aluminum affects the development of oligomeric or fibrillar Aβ amyloids. Therefore, understanding the various conformations of Aβ amyloid and their characteristics under different physiological conditions is necessary for revealing their toxic behaviors.
In this chapter, we introduce the mechanism of formation of amyloid fibrils and diverse molecular structures of prion fibrils. Moreover, the structure-property relationships and mechanical characterization in silico are described using HET-s amyloidogenic prion fibrils as an example.

Seeding and aggregation mechanisms of prion nanofibrils
In this section, the seeding mechanism and characteristics of prions are introduced with homogeneous/heterogenetic amyloidogenic prion fibrils.

Prion, amyloid folding, and amyloid fibrils
Prion proteins, known as proteinaceous infectious agents, constitute a subclass of amyloids. Prion infection involves the conversion of proteins from their normal functional conformations, via an unfolded intermediate state, into amyloids. The conversion of the α-helical, isoform of the prion protein (PrP c ) into the insoluble, β-sheet-rich, and infectious form (PrP sc ) induces the accumulation of β-sheets and formation of fibrils and bundle structures [1]. After seeding, self-propagation is induced by providing templates for further assemblies [2][3][4]. This is known as the initial event in prion-inducing disease [5][6][7][8][9]. It is important to understand the propagation and amyloid fibril-forming mechanism for the development of therapeutic agents [10][11][12]. To understand amyloid fibril formation, numerous experimental and computational studies have been conducted. The molecular and atomic structure of mammalian and fungal prion fibrils should be determined to understand the propensity for polypeptides to form amyloid fibrils. In many cases, mammalian amyloid fibrils, which are known to induce amyloid disease, such as Aβ, α-synuclein, and amylin, do not form structures determined by their amino acid sequences. It is known that for self-propagation, molecular polymorphisms lead to different structures, and various polymorphic structures have been observed under diverse laboratory conditions, as depicted in Figure 1. For example, Tycko et al. showed that Aβ 1-40 has two main polymorphic structures that form fibrils [13]. One is a twofold, and the other is a threefold β-sheet array. According to the interaction directions of the β-sheet layers, templates for fibril structures were determined. Furthermore, self-propagation of HET-s fungal amyloid fibril was studied previously using high-resolution techniques, offering insight into structural changes induced by pH variations [4].
Advanced experimental techniques such as X-ray crystallography, transmission electron microscopy, scanning electron microscopy, and cryo-electron microscopy have revealed high-resolution amyloid conformations and the self-propagation and fibril formation mechanisms [14][15][16][17][18][19][20]. Amyloid fibrils were suggested to aggregate via a dense inherent hydrogenbond-network and steric-zipper-like interactions between β-sheet layers, resulting in fiber formation along the fibril axis. Amyloid fibrils showed good structural complementarity and highly ordered conformations. However, although the physiochemical characteristics of amyloid proteins have been revealed, the structures and seeding processes remain unclear, and determining the molecular motion of amyloid proteins is challenging.

Self-seeding and cross-seeding of amyloids
Diseases related to the toxicity of amyloid proteins are induced by the accumulation of amyloids, which consists of fibrillar forms and tangles. Experimental studies revealed that amyloid fibrils extracted from patients with amyloid disease brain had a fibrillar form and residual nonfibrillar materials [3]. The extracted fibrils showed widths and morphologies similar to those of synthetic amyloid fibrils in vitro, but the precise morphologies of the extracted amyloid fibrils are difficult to assess because of the self-association of fibrils and adhesive particles. Aβ amyloid fibrils from amyloid disease brains presumably contained chain length variations and chemical modifications. Previously, experimental and computational studies evaluated the kinetics of amyloid fibril formation. For both extracted and synthetic amyloid fibrils, the growth rate of amyloid fibrils was accelerated and amplified by seeding. However, nonfibrillar particles were not accelerated, and they did not show seeding behavior. Typically, amyloid fibrils are constructed by adding amyloid protein blocks composed of 4 or 5 parallel-or anti-parallel-layered β-sheets. These structures may also be 'tetramers' or 'pentamers', depending on the number of layers present. Monomers referred to as seeds act as "Lego blocks," and single amyloid fibrils are constructed in a specific elongation direction when seed monomers are added. Particularly, single monomers can be regarded as templates for fibril formation. Previous studies evaluated the elongation processes of uniformly composed monomers to understand the self-propagation process [2,3,21]. The process is referred to as "self-seeding" and homogeneous amyloid block monomers form fibrillar conformations. Previous studies also provided insight into the structural and physiochemical characteristics of diverse amyloid fibrils. However, accumulated amyloid agents, which are present in neurodegenerative disease, are not uniform. Thus, better models are needed to understand the polymorphic features of the fibril formation mechanism. Recent studies have evaluated the different types of amyloid block monomers that can bind to each other to form fibrils and tangles through a specific mechanism known as "cross-seeding". The key point of this mechanism is that one block monomer of amyloid proteins can be regarded as a template for other block monomers, even if the blocks have different physiochemical characteristics and are constructed with different conformations and compositions [22][23][24][25]. The cross-seeding mechanism can explain the formation of heterogeneous-composed amyloid fibrils and polymorphic fibrils, and these models offered better insight into amyloid accumulation processes. Experimental studies showed that seeding with amyloid-like fibrils made from short synthetic peptides from other amyloid proteins or fibrils of a completely different nature; for example, bacterial curli or Sup35 from Saccharomyces may function through other interactions [26]. It appears likely that the β-sheet structure of the seed has a general effect on the seeded material, inducing misfolding, and production of a new seed that can proceed to an amyloid fibril. In addition, Yan et al. examined the effect of coinjection of murine senile apolipoprotein A-II amyloid and reactive protein A amyloid amyloidosis to determine the heterologous transmissible seeding mechanism [22] shown in Figure 2.

Cross-seeded fibrils
Recently, computational studies were performed to overcome the limitation of experimental studies, which are unable to determine molecular structures in detail. For several decades, many studies have evaluated the mechanical properties and behaviors of amyloid fibrils [27][28][29][30][31][32], providing insight into the amyloid fibril formation mechanism. Most studies examined homologous amyloid fibrils. Experimentally, it was revealed that heterogeneous interactions enabled different amyloid monomers to aggregate with each other. Alpha synuclein-Aβ, Aβ-amylin, and Aβ-tau, which are well-known heterologous amyloid fibrils, have been used to understand the effect of structural affinity on amyloid fibril formation [33][34][35][36][37][38]. Recent studies revealed the structural and interaction features of cross-seeded amyloid oligomers and proto-fibrils. Oligomeric Aβ-tau heterologous amyloid is one example of a cross-seeded amyloid protein. Aβ and U-shaped tau monomers are structural similar in that both have a common U-shaped β-turn-β structure. In addition, Miller et al. determined the structural stabilities of possible compositions of Aβ-tau heterologous oligomers using experimental and computational methods [38], as shown in Figure 3. They studied the interactions between heterologous monomers. Furthermore, Choi et al. studied the mechanical and physicochemical features of heterologous oligomers with diverse-mutated Tau monomers [37]. They found that different binding directions showed different structural stabilities. It was observed that amyloid beta monomers and other monomers could act as templates for seeding processes.
Many computational studies showed that not only structural similarity but also specific interactions between residues of amyloid proteins play a major role in seeding processes. Elongation of amyloid fibrils along the fibril axis is related to the binding features of the seed amyloids and their structural stabilities. The binding sites on monomers enable the attachment of other monomers [39]. The specific interactions can be classified as intra-layer interactions and interlayer interactions, which confer structural stability, as depicted in Figure 4.  [36] and schematic constraint for simulation of heterogeneous amyloid fibrils (right panel) [37].
It was revealed that the structural stabilities of intra-layers were affected by steric-zipper-like interactions [40][41][42] and salt-bridge interactions [37]. Intra-structural stabilities are dominantly affected by specific interactions. Hydrophobic residues in interior regions of amyloid fibrils form steric-zipper-like structures and help maintain cross-sectional structures. Although heterologous monomers contain different residues, hydrophobic residues commonly construct dry-regions and affect structural stabilities. In addition, charged residues such as lysine (K) and aspartic acid (D) form salt-bridge regions and affect intra-stabilities.
The stabilities of inter-layers are also affected by hydrogen-bonding networks and nonbonding interaction energies, such as Van der Waals and electrostatic energy induced by interactions between residues of layers that face each other. Interactions between single layers are dominantly affected by electrostatic and Van der Waals energies. However, as the number of layers is increased, the effect of electrostatic energies becomes dominant. In the fibril formation processes of heterologous amyloids, binding between monomers is affected by electrostatic energies (Figure 5).

Molecular structure of prions in various physiological environments
In the previous section, we described the general aggregation and seeding mechanism of amyloid-like prion fibrils based on homogeneous and heterogeneous structures. During the aggregation of prion fibrils in the seeding mechanism, the external environment affects growth of prion-like amyloid fibrils. Here, the effect of the external environment is referred to as the physiological conditions, which have been shown to affect molecular conformational variation in the fibrillary growth of PrP C , HET-s, and Sup35, in detail.
First, the development of prion proteins is caused by the conversion of native prion protein monomeric PrP C as misfolded and denatured PrP Sc because of external conditions such as partial mutation, internal flow, pH, ionic strength, and temperature variations. This PrP C protein is glycosylated and functions similar to components of the extracellular surface of neurons, which play a significant role in signal transduction. This native PrP C is converted to monomeric PrP Sc , which gradually aggregates to form oligomeric, fibrillar, and plaque structures. These converted monomeric PrP Sc act as seeds at specific concentrations with a lag phase, which induce the aggregation of fibrillar and plaque prions. This conversion is frequently observed in amyloidosis including Alzheimer's disease by Aβ from amyloid precursor protein and cardiovascular diseases by transthyretin (105-115) from native functional transthyretin monomers [6,43,44]. As shown in Figure 6, aggregation of converted PrP Sc from PrP C monomer deposited near the brains of human and mouse represents the hallmark of neuropathological features [45].
The other type of prion proteins is the HET-s prion protein. According to Govaerts et al., the left-handed β-rich helical structures containing α-helices are located outside of the β-helical structures of prion fibers and are responsible for their toxicity (refer Figure 6(a)) [46]. In contrast, righthanded prion proteins are not toxic based on combined experimental and computational studies.
HET-s prion amyloid proteins were also reported to have β-solenoid conformations and triangular hydrophobic cores [47].  A third type of prion proteins is known as the Sup35 prion proteins, which exhibit cross-β characteristics with steric zipper structures as shown in Figure 3 [48,49] and are similar to other proteins that cause several degenerative diseases such as Alzheimer's diseases, type II diabetes, and dialysis-related amyloidosis by Aβ, human islet polypeptide, and β 2 -microglobulin [41]. Specifically, partial prion proteins fragment from the Sup35 prion protein and show polymorphic features including lateral thickness increases (Figures 8 and 9) with changes in physiological conditions such as pH, thermal variation, internal flow, and ionic strength [50].
Fibrillar and plaque forms of PrP Sc prion proteins are frequently observed because of their considerable infectivity ability. These fibrillar and plaque types of prion proteins can be generated through repetitive fragmentation and elongation mechanisms. The prion proteins grow by adding monomers or attracting other fragmented prion segments. A previous study showed that fragmented and denatured prion proteins add PrP C to grow PrP Sc based on protein-misfolding cycling amplification techniques [45] (refer to Figure 10).   Colby et al. investigated the prion propagation mechanism via repetitive fragmentation and elongation by adding additional prion monomers and evaluated the kinetics study and conducted imaging analysis [15]. Through the repetitive process of fragmentation and elongation mechanism, neuro-toxic prion oligomers could be generated. In this aggregation, after conversion from PrP C to PrP Sc , prion proteins showed toxic characteristics and affected intercellular processes. Similarly, for the fragmentation and elongation mechanisms of HET-s prion proteins, Mizuno et al. investigated similar fibrillar and plaque proteins such as prion, particularly HET-s, under various pH conditions [4]. Fragmentation and addition of prion seeds generated different types of fibrillar HET-s near pH 2 and 3, while lattice-like HET-s was observed under neutral physiological conditions. Between pH 2 and 3, a tight fibrillar HET-s structure was observed, while fibrillar HET-s exhibited a cavity at pH 3 [4, 37] To discuss the structural characteristics of plaque and fibrillar prions from converted PrP Sc , in this section, we described the conversion mechanism of PrP C from PrP Sc prion proteins at the atomic scale based on computational results. As described previously, native PrP C proteins varied from misfolded PrP C to PrP Sc based on the physiological conditions [52][53][54][55][56]. In 2001, Daggett et al. reported computational results for the conversion of PrP C when pH conditions were varied from neutral to low pH conditions [56]. They observed that the core region of PrP C was stabilized, while the N-terminus exhibited considerable structural fluctuations compared to the core and C-terminal regions. In addition, they reported the conversion process from PrP C to PrP Sc over time.
As shown in Figure 11, additional β-strands were generated at the N-terminal regions with lengthening of the β-strands after 2 ns. Furthermore, they found that Met-129 at the N-terminal region triggered the conversion of the turn-rich N-terminal region into β-strands. Therefore, external physiological factors such as ionic strength and pH altered the native PrP C resulting in misfolding into PrP Sc structures with the additional generation of β-strands, which may be related to the aggregation of PrP Sc structures.   Another study observed protofibril formation of scrapie prion protein, which contained numerous β-strand conformation variations [55]. They computationally found that the conversion from monomeric syrian PrP C segments to PrP Sc occurred because of a point asparagine mutation at the 147th aspartate residue (D147N) under neutral and low pH conditions. Subsequently, they observed that the prion protofibril was stabilized and compared their computational results to the experimental results of DeMarco et al. [55]. The monomeric conversion from D147N PrP C to PrP Sc occurred near β-strands at the 1st and 2nd β-sheet regions of the original structures. In this procedure, they determined the critical role of additionally generated β-strands in the conversion of PrP C structures through computational analysis. The salt bridge region between the 147th aspartate and 151st arginine residue was disrupted; this event did not critically alter the structural stability of D147N PrP C structures, but the D147 mutation affected expansion of the N-terminal region, generating additional β-strands regions. These results support their previous computational results for the role of the Met-129 residue.
Based on the converted PrP Sc unit monomers, they constructed the basic protofibril unit of the converted PrP Sc monomer by connecting adjacent β-strand regions of the monomer. As shown in Figure 12  Additionally, they observed conformational variation in the full-length bovine PrP prion at low pH using molecular dynamics [53]. The conformational variation of native full-length bovine PrP prion structures was found to be PrP Sc with additional generation of β-strands; the role of the Met-129 residue was determined by conformational and secondary structure analysis, as shown in Figure 13.
Based on computational studies of prion proteins, physiological conditions such as pH, ionic strength, point mutation, and temperature variation have a considerable effect on structural variations in HET-s and native PrP C structures as PrP Sc structures; some conditions enlarge the N-terminal region and cause formation of additional β-strands, which are similar to reported experimental results. Converted PrP Sc with additional β-strands can connect to protofibril structures. Therefore, understanding prion proteins under external physiological conditions may be useful for preventing the generation of fibril structures and their toxic behaviors.

Characterization of amyloid molecular structure by mechanical testing
Above, we introduced the generation of amyloid-like prion fibrils via self-aggregation and seeding mechanisms based on previously reported experimental and computational studies. Specifically, we described the aggregation mechanism from native PrP C segments to denatured PrP Sc segments under physiological conditions, where pH variation caused partially disordered N-terminal regions of PrP C to convert to β-strands at the N-terminal region of PrP Sc . These denatured PrP Sc segments aggregated as fibrillar prion amyloids, which are toxic to cell function and delete the lipid bilayer of membranes. In this section, we explain the role of the β-sheet-rich prion fibrils and their toxic characteristics from a mechanical perspective determined through experimental and computational studies.

Disease-breakage and infections
Amyloid fibrils are disease-related proteins found in various types of neurodegenerative and degenerative diseases. Aggregated fibrils were detected in diseased cells. Understanding the mechanical behavior of amyloid fibrils is important because it is related to fibril breakage. Misfolded amyloids do not initially form long fibrils. Single amyloid monomers inside the body begin to aggregate. They stack into small oligomers, forming aggregates, which grow into the fibrillar form. These fibers may be up to 100-nm long [5]. In humans, amyloid fibrils eventually break. In our surroundings, breakage of an item is not a good thing. For example, if a ruler is broken into two pieces, we do not use it anymore. Because we cannot measure the length which it was made to measure. However, Long amyloid fibrils breakage creates small oligomers, which become seeds for new fibrils. Additionally, in environments containing both fibrils and oligomers, aggregation occurs more rapidly than in environments containing only oligomers [5]. Thus, breakage of amyloid fibrils generates additional fibrils. Understanding when the fibril will break may be determined by measuring mechanical properties of amyloid fibrils.

Bio-materials
Several studies have compared the mechanical properties (e.g., Young's modulus) of amyloid fibrils with those of other bio-materials. Amyloid fibrils exhibit a Young's modulus comparable to those of wood and silk, and its strength is comparable to those of metals such as aluminum or steel (Figure 14) [57]. Comparable mechanical properties of amyloid fibrils with these materials indicate that amyloid fibril is a potentially useful bio-material. Compared to proteinaceous biomaterials such as actin filaments, amyloid fibrils exhibit longer persistence length [19]. Persistence length is a basic mechanical property quantifying the stiffness of a polymer. Materials with shorter lengths than its persistence length behave as elastic materials and form longer polymers. The mechanical properties and behaviors of elastic materials and polymers are very different. Polymers are materials that act as soft chains, making them unsuitable for use as support materials. Proteins are composed of poly-peptide chains and are polymers. The poly-peptide chain folds as a globular protein (or misfolds as an amyloid), and the structure is maintained by noncovalent interactions between amino-acids. Amyloid fibrils or actin filaments are large structures constructed by large numbers of proteins composed of polypeptide chains.

Experiments
Studies have focused on the relationship between amyloid fibril mechanical properties and behaviors in biology. One of the pioneer studies of mechanical property measurement of amyloid fibril was conducted by Smith et al. in 2006 [58]. In their study, the mechanical properties of insulin fibrils (not prions) were measured using atomic fore microscopy to determine ultimate strength, Young's modulus, persistence length, bending rigidity, shear modulus, and torsional rigidity (Figure 15). Young's modulus and persistence length were measured to be 3.3 ± 0.4 GPa and 22 ± 3 μm, respectively. Several studies revealed that amyloid fibril's mechanical properties are comparable to those of silk, a well-known and broadly used biomaterial [57][58][59]. Interestingly, amyloid fibrils share some structural characteristics with silk: (1) frequently repetitive primary sequences; (2) stable and irreversible β-sheet-enriched state; (3) structural similarity with β-sheet rich structure; (4) self-assembling behavior to fibrillary structures in solution; and (5) hydrogen bonding between β-sheets. Comparable mechanical properties and structural features indicate that amyloid fibrils can also be used in various applications [59]. The Young's modulus of various amyloid fibrils ranged from 10 9 to 10 10 Pa, which is similar to that of silk [57]. The mechanical properties of amyloid fibrils are not affected by covalent bonds constructing the β-sheets, but rather by noncovalent bonds between β-sheets. Hydrogen bonds are important for maintaining amyloid fibrils and their mechanical properties; other non-covalent bonds (e.g., electrostatic interactions, π-π interactions, etc.) can also affect strength depending on the amyloid fibril structures.

Simulations
Experimental studies have revealed that various types of amyloid fibrils exist. Not only disease-related fibril types such as Alzheimer's disease, Jakob-Cruetzfeld disease, type 2 diabetes, and Parkinson's disease, among others but also those that form amyloid fibrils in same phenotypes of amyloids are important. For example, human islet amyloid polypeptide (hIAPP), which is found in cells of type 2 diabetes patients, forms eight different fibril types by stacking in different directions [17,41]. Differences in the composition of amyloid fibrils lead to different mechanical behaviors and fractions in the body. Small fraction structures are more difficult to form than large fraction structures. Simulation methods constitute an easier approach for evaluating these variations in amyloid fibrils. A common structural characteristic of the amyloid fibril is its repetitive structure of β-sheets. Structural information determined experimentally may differ from that determined computationally. Detailed structural information (distance between β-sheets, twist angle between layers, etc.) of amyloid fibrils is clearly needed to rapidly and effectively build the fibrils [17]. An important simulation study evaluated the size-dependent mechanical properties of Aβ 1-40 [60]. In this study, two different types of Aβ amyloid fibrils were constructed: a twofold symmetric structure and threefold symmetric structure. A computational model was prepared using an elastic network model (ENM), and normal mode analysis (NMA) was applied to calculate eigenvalue eigenvectors of the structure. Torsional modulus, bending rigidity, and Young's modulus were calculated for different types of amyloid fibrils, with the twofold symmetric structure showing better mechanical properties. Yoon et al. analyzed four configurations of hIAPP amyloid fibrils. They also applied ENM to calculate the mechanical properties of hIAPP amyloid fibrils. Despite this detailed chemical interaction information, each structure exhibited different mechanical properties related to differences in H-bond interactions [61]. Additionally, the effects of mutations on the mechanical properties of amyloid fibrils [62] or multi-strand effects can be calculated [63].

Structural variation depending on environment and its properties
Proteins functioning in living bodies interact with various surroundings such as water, ion, proteins, ligands, and DNA. Protein conformation, which is determined by sequence and length of the polypeptide chain, is important in the interactions with the surroundings of a protein.
Some environmental conditions may favor amyloid formation (which may lead to an unhealthy condition). Studies of prions revealed that prions form a certain shape or structure under specific conditions, indicating that amyloid structure depends on the surroundings [4]. In this study, prions were exposed to different pH conditions, including pH 2, 3, 4, and 7. In each state, prions formed triplets, singlets and triplets, an angled-layer aggregate, and bundles at pH 2, 3, 4, and 7, respectively. The stability of each conformation changed when the pH was changed (surroundings). For example, a triplet structure formed at pH 2 and 3 but with different conformations. Additionally, a singlet was detected at pH 3. When the pH was changed to 4, the triplet fibril disappeared while the angled-layer structure remained. These structures may be related to the mechanical properties or interactions between fibrils. Triplet prion fibrils are stable and noninfectious (pH 2). However, when pH is increased, the triplet fibril structure is broken into singlets (pH 3) and become infectious. These singlet fibrils can easily break and form new fibrils from new seeds, forming an angled-layered structure (pH 4) as shown in Figure 16.

Simulation methods
Changes in pH affect the chemical interactions of prion amyloid fibrils. Although simulation researches do not reveal chemical interaction, they provide other useful information.
A study conducted in 2013 compared the mechanical properties of prion amyloid fibrils (lefthanded turn) and nonprion fibrils (right-handed turn) using ENM and NMA [27]. Basic structural units were very similar β-sheets, but mechanical properties such as elastic modulus and bending rigidity differed for both fibrils as shown in Figure 17. In fact, a toxic prion fibril exhibited higher mechanical properties. Additionally, left-handed prion fibrils had more local contacts than nonprion fibrils, which are consistent with the results of a previous study analyzing hydrogen bonds.  Triplet fibrils were also examined by ENM and NMA [64]. In this study, prion triplet fibrils were compared at pH 2 and 3. Mechanical properties such as bending rigidity and torsional modulus were calculated for both models; fibrils for the pH 2 model showed better values for both parameters. This indicates that the pH 2 model was more stable than the pH 3 model, which is known to be noninfectious [4]. However, the pH 3 triplet showed a bending rigidity of 0.6 × 10 −26 Nm 2 , which is much larger than the value of 0.3 × 10 −26 Nm 2 determined for a singlet fibril in a previous study [27]. The structure and mechanical properties of prion fibrils are related, explaining their toxicities. Moreover, in the previous study, the potential for conformational changes between the pH 2 and 3 models was observed. NMA provides results in eigenvalues and eigenvectors, which are connected to natural frequencies and normal modes. A normal mode corresponds to a single natural frequency, and the low frequency normal mode describes large motions of structures (i.e., for amyloid fibril, bending, twisting, and extension). Comparison of the normal mode calculated from the pH 2 model and direction vector between the pH 2 and 3 model showed that low-frequency normal modes up to the 23rd mode described conformational changes in triplet fibril caused by pH change. These results indicate that conformational changes are caused by pH changes, but the conformational change direction can reveal structure information (Figure 18).

Summary
In this chapter, the formation of amyloidogenic prion nanofibrils and the relationship between molecular structure and its properties are presented. In the first section, the seeding mechanisms of prions for the homogenous and heterogeneous fibrils are introduced, and the Figure 18. Cumulative overlap between normal modes calculated from pH 2 model and direction vector between pH 2 and pH 3 model [64]. molecular structure differences in the assembly process of amyloid fibrils under environmental conditions are described in the second section. Finally, the mechanical characterization of amyloid fibrils in vitro and in silico is explained. It remains challenging to determine the infectiousness and toxicity of prions and amyloids. Therefore, additional studies are needed to determine the molecular structure, aggregation kinetics, and properties of prions and amyloids. Increasing the understanding of these molecules will aid in the development of therapeutic strategies for prion diseases.