Conformation-Dependent Influences of Hydrophobic Amino Acids in Two In-Register Parallel β-Sheet Amyloids, an α-Synuclein Amyloid and a Local Structural Model of PrPSc

Prions are unconventional pathogens that encode the pathogenic information in conformations of the constituent abnormal isoform of prion protein (PrPSc), independently of the nucleotide genome. Therefore, conformational diversity of PrPSc underlies the existence of many prion strains and species barriers of prions, although the conformational information is extremely limited. Interestingly, differences between polymorphic or species-specific residues responsible for the species/strain barriers are often caused by conservative replacements between hydrophobic amino acids. This implies that subtle differences among hydrophobic amino acids are significant for PrPSc structures. Here we analyzed the influence of different hydrophobic residues on the structures of an in-register parallel β-sheet amyloid of α-synuclein (αSyn) using molecular dynamics (MD) simulation and applied the knowledge from the αSyn amyloid to modeling a local structure of human PrPSc encompassing residues 107–143. We found that mutations equivalent to polymorphisms that cause transmission barriers substantially affect the stabilities of the local structures; for example, the G127V mutation, which makes the host resistant to various human prion diseases, greatly destabilized the local structure of the model amyloid. Our study indicates that subtle differences among hydrophobic side chains can considerably affect the interaction network, including hydrogen bonds, and demonstrates specifically how and in what structures hydrophobic residues can exert unique effects on in-register parallel β-sheet amyloids.


INTRODUCTION
Prion diseases are a group of neurodegenerative disorders that are characterized by the accumulation of the abnormal isoform (PrP Sc ) of prion protein (PrP) in the central nervous system. 1 Prion diseases have three etiologies, sporadic, inherited, and acquired, depending on how the causative PrP Sc propagation is initiated in the body. In sporadic and inherited prion diseases, for example, sporadic Creutzfeldt−Jakob disease (CJD) and fatal familial insomnia (FFI), respectively, the causative PrP Sc are generated by the spontaneous conformational conversion of the endogenous normal isoform PrP (PrP C ) into PrP Sc , with or without the aid of pathogenic mutations in the PRNP gene. Acquired prion diseases are caused by the intake of exogenous PrP Sc as infectious prion agents, such as epidemic bovine spongiform encephalopathy (BSE) in cattle 2 and chronic wasting disease (CWD) in cervids. 3 Prions behave similarly to viruses, with high infectivity, the existence of many strains, species/strain barriers, and adaptation to new hosts, despite the lack of conventional genetic material. These virus-like pathogenic properties of prions are hypothesized to be enciphered in the conformations of PrP Sc , a theory known as the protein-only hypothesis. 1,4 Indeed, the pathogenic properties of prions and the consequent clinical phenotypes are greatly affected by the primary structure of the constituent PrP Sc , which is consistent with the fundamental fact that the conformations of proteins are determined by their primary structures. For example, in sporadic CJD, PrP deposition patterns, lesion profiles in the brain, clinical presentations, and the apparent molecular sizes of protease-resistant cores of PrP Sc vary depending on whether the polymorphic codon 129 is methionine (M129) or valine (V129). 5 A pathogenic mutation D178N of human PrP causes either FFI or familial CJD in association with M129 or V129, respectively. 6 The vast majority of the new-variant CJD cases that resulted from the trans-species transmission of BSE to humans have been homozygous for M129. 7,8 Moreover, the methionine/leucine polymorphism at codon 132 of elk PrP, which is equivalent to the codon 129 polymorphism of human PrP, also affects the susceptibility to CWD. 9,10 From the viewpoint of the protein-only hypothesis, polymorphisms could affect the stability of PrP C /PrP Sc , consequently affecting disease susceptibility. However, the specific manner in which the subtle differences between these hydrophobic amino acids affect the structures of PrP Sc has not been identified. Detailed structures of PrP Sc are needed for such investigation, but even whether PrP Sc is an in-register parallel β-sheet amyloid or a βsolenoid has been controversial due to the incompatibility of PrP Sc with conventional high-resolution structural analyses. 11 −19 In 2021, while our study was under revision, a high-resolution structure of a fully infectious, brain-derived prion was solved by Kraus et al. using cryoelectron microscopy (cryo-EM). 20 This PrP Sc (263K strain) has an in-register parallel β-sheet architecture without paired protofibrils. Then, cryo-EM structures of the glycosylphosphatidylinositol (GPI)anchored and anchorless mouse-adapted RML scrapie strains proved that the conformations of PrP Sc differ depending on the strains. 21,22 In 2022, Hallinan et al. reported cryo-EM structures of human PrP Sc isolated from the brains of patients with Gerstmann−Straüssler−Scheinker syndrome (GSS) associated with F198S mutation. 23 In addition to the well-known example of methionine/valine polymorphic codon 129, strain/species barriers of prions can also be caused by conservative replacements between different hydrophobic amino acids at other residues. In experiments with a C-terminally truncated Y145Stop mutant of human PrP and the counterparts of mouse and Syrian hamster PrPs, whether residue 138 or 139 (in human numbering throughout, unless otherwise noted) was isoleucine or methionine was critical for efficient amyloid formation and cross-seeding among the PrPs. 24,25 In the transmission of the prions of sporadic CJD homozygous for M129 to transgenic mice expressing human-mouse chimeric PrP, I138M substitution substantially extended the incubation periods. 26 Different hydrophobic amino acids at codons 109 and 112 influenced the transmission efficiencies of prions among different hamster species. 27,28 In in vitro cross-seeding between ovine PrP and cervine CWD, an I208M (in ovine numbering) mutation showed a profound influence on the seeding efficiencies. 29 Given these documented facts, we reasoned that the subtle differences among hydrophobic side chains are influential because, in general, amyloids need hydrophobic cores for stabilization. Accordingly, we considered that it would be informative to study the replacement of hydrophobic amino acids with different amino acids, and the effects of such replacement on the structures of amyloids; the question of whether methionine has unique properties compared with other hydrophobic amino acids seems particularly relevant. Currently available structures of pathogenic in-register parallel β-sheet amyloids share basic structures; they consist of intramolecular pairs of short β-strands and at least one βarch. We reasoned that pairing of the constituent β-strands may be required for stability of an in-register parallel β-sheet amyloid and, if so, stable β-arches which bend the backbone at 180°would be advantageous or even essential for efficient intramolecular coupling of the β-strands and eventually for efficient conversion into the amyloid form of the molecule. For instance, it is conceivable that a peptide molecule with one (or more) region prone to the formation of a stable β-arch with 180°bending in the middle of the molecule may be more susceptible to conformational conversion into an in-register parallel β-sheet amyloid, because of the efficient intramolecular pairing of β-strands. Therefore, we are interested in the determinants of stability of 180°-bending β-arches, particularly U-shaped β-arches. The present study was designed to identify some of the conditions which stabilize or destabilize β-arches.
We used an in-register parallel β-sheet amyloid of αsynuclein (αSyn) as a surrogate local structural model for PrP Sc , as in our previous studies. 30,31 αSyn amyloid is the main component of Lewy bodies, which is a hallmark of Parkinson's disease and dementia with Lewy bodies (DLB) and which have been reported to exhibit prion-like properties, including transmissibility and strain diversity. 32 For instance, αSyn forms various types of amyloids in vitro that differ in appearance, proteolytic fragment patterns, and cytotoxicity. 33 Moreover, αSyn amyloids isolated from patients with DLB and multiple system atrophy had different proteolytic fragment patterns suggestive of distinct conformations. 34 These findings are highly reminiscent of prions and imply that prion-like properties are inherent in in-register parallel β-sheet structures. Detailed structures of αSyn amyloids have been determined using solid-state NMR (ssNMR) 35 or cryo-EM. 36−46 In the present study, we first used a Greek-key αSyn amyloid (PDB ID: 2N0A; 35 Figure 1A) to investigate the effects of different hydrophobic residues on the in-register parallel β-sheet structures. 47 Figure 1B compares structures of the αSyn protofilaments. Although the structures have different backbone conformations, the structure of the protofilament core of PDB 2N0A is similar to some of the reported structures. Our experiments revealed that the lengths and C β -branching of the side chains of hydrophobic residues are important for the stability of local amyloid structures, particularly in a U-shaped β-arch. We then applied the knowledge from the αSyn amyloid to a local structural model of PrP Sc encompassing residues 107 to 143 of human PrP, PrP 107−143 , under the assumption that PrP Sc was also an in-register parallel β-sheet amyloid. Specifically, we assessed how mutations and polymorphisms associated with the strain diversity of prions affected the Note that the β-sheets are induced in loop(57−62) of the αSyn(E61M) amyloid and that the αSyn(G84M) amyloid has β-sheets extended to loop (84−87). In αSyn(G84M) and αSyn(G84L), the directions of the side chains of residue 84 after a 400 ns MD simulation are shown with red sticks in the insets. In the inset of αSyn(G84M), the side chains of V82 and A89 are also shown with green and pink sticks, respectively. They are close to the side chains of M84 and form hydrophobic contacts (see also Figure 3 structures of the model amyloid using molecular dynamics (MD) simulation. The results of these studies demonstrated how different types of hydrophobic amino acids specifically affect the local structures of in-register parallel β-sheet amyloids of αSyn and PrP 107−143 . They also showed that the structural stability of U-shaped β-arches requires hydrophobic cores with well-balanced interactions among the constituent hydrophobic residues.

Investigation of the Mechanism by Which G84M
Mutation Stabilizes the αSyn Amyloid. In a previous study, we compared the effects of isoleucine substitutions at residues 61 (E61I) in a flat loop (loop(57−62)) and 84 (G84I) in a U-shaped loop (loop (84−87)) in the αSyn amyloids. 30 We showed that the G84I mutant substantially destabilized the U-shaped loop, whereas the E61I mutant had little influence on the stability of the αSyn amyloids. Here we investigated the influences of hydrophobic amino acids on the local structures of αSyn amyloids by introducing methionine substitutions at the same positions (E61M and G84M). For all the model fibrils, the radius of gyration fluctuated around 24.5 Å during the simulation ( Figure S1), which indicated that the simulation time was too short to discuss (de)stabilization of the whole structure of the αSyn fibrils. However, our simulation highlighted the (de)stabilization in the local structure of the fibrils as shown below. Figure 2A shows the final snapshots of MD simulations of αSyn amyloids, and Figure 2B shows the heatmaps of the βsheet propensity. The MD simulations of homo-oligomer amyloids of αSyn(E61M) and αSyn(G84M) revealed that both the mutations tended to stabilize the local structures, particularly when these amyloids induced new β-sheets in the flat loop for the E61M mutant or U-shaped loop for the G84M mutant ( Figure 2A). This stabilization in αSyn(E61M) could be interpreted as an effect of the charge difference in the E61M mutation: the side chains of M61 formed hydrophobic contacts with those of the neighboring chains along the stacking direction in the E61M mutant, whereas the negative charge of glutamate hampered the stabilization between the neighboring chains in the wild type (WT). Overall, the influence of the methionine substitution (E61M) was similar to that of the isoleucine substitution (E61I) in the flat loop.
The effects of the G84M substitution were more impressive: almost the entire region C-terminal to residue 80, including loop (84−87), was converted to stable β-sheets, unlike in the case of the G84I substitution. 30 We thus further compared the substitution effects of G84M, G84L, G84V, and G84I. In the G84L mutant (αSyn(G84L)), the loop region around L84 was substantially destabilized like that of αSyn(G84I). 30 A G84V mutant (αSyn(G84V)) also showed a β-sheet propensity similar to that of αSyn(G84L). Because we were interested in the opposite effects of G84M and G84L/V/I, we focused on residue 84 to identify the underlying mechanisms.
The directions of the side chains of αSyn(G84M) and αSyn(G84L) are compared in the insets of Figure 2A. The final status of 400 ns simulations was different between the αSyn(G84M) and αSyn(G84L) amyloids. All the side chains of methionine at residue 84 (M84) pointed inward of loop (84−87) and were close to those of V82 and A89, whereas some side chains of leucine at residue 84 (L84) flipped and pointed outward.
The hydrophobic contact diagrams are shown in Figure 3. The diagrams of the αSyn(G84M), αSyn(G84L), αSyn-(G84V), and αSyn(G84I) amyloids clearly exhibit differences. M84 of the αSyn(G84M) amyloid had strong intrachain interactions with residues 82 and 89 in all the layers, and the interactions were reproducible. In contrast, the αSyn(G84L) and αSyn(G84V) amyloids only infrequently showed that pattern or a pattern similar to the amyloids of another destabilizing mutation, G84I. 30 This result was reflected in the distance between residues 84 and 89. The C α −C α distances (dC α ) between the residues 84 and 89 were about 8.3 Å in all the chains during the simulations of αSyn(G84M), whereas the distances varied among chains and fluctuated during the simulations of αSyn(G84L), αSyn(G84V), and αSyn(G84I) ( Figure S2).
The unique stabilizing effects of M84 would be attributable to the long side chain, which can extend across the β-arch like a crossbeam. During the simulation, the ends of the side chains were fixed in the proximity of A89 (movie S1). The intimate interactions with A89 reinforced the hydrophobic core and stabilized the β-arch. Leucine could not replace methionine despite their similar hydrophobicities and nonbranching C β atoms, because its side chain was not long enough for stable interactions with A89. Other groups have confirmed that the subtle difference between methionine and leucine is significant in at least one case of prion propagation, namely, the methionine/leucine polymorphism of elk PrP affects the susceptibility to CWD infection. 9,10 This might be related to our viewpoint, that is, the length of the side chain of the hydrophobic amino acids.

Modeling a Local Structure of PrP Sc Based on
Knowledge from the αSyn Amyloids. As in our previous studies on αSyn amyloids, 30,31 we hypothesized that PrP Sc has an in-register parallel β-sheet structure and attempted to model a local structure of PrP Sc with a U-shaped loop. (Note that the present study was conducted before the publication of the paper by Kraus et al. 20 ) A region comprising a glycine-rich motif encompassing residues 123−127 of human PrP (-GGL 125 GG-) seemed to be suitable for a U-shaped loop. In addition, the antiprion effect of the valine at residue 127 against various sporadic CJD 48 was reminiscent of the destabilizing effects of V84 in the αSyn amyloid, which suggested the presence of a U-shaped loop in the region. Moreover, the structures of amyloid cores of Y145Stop mutant PrP investigated with ssNMR were available, although not in atomic resolution. 16,49 Amyloids of the Y145Stop mutant induced infectious PrP Sc , which caused bona fide prion disease when inoculated into mice, 50 and could therefore share similar local structures with full-length PrP Sc . We thus tentatively modeled the local structures of human CJD PrP Sc in the region 107−143, PrP 107−143 , utilizing the structural model of the Y145Stop mutant propounded by Theint et al. 49 and the knowledge from the αSyn amyloid for stable β-arches discussed in section 2.1. That is, the side chains of hydrophobic residues in the U-shaped loop (A120, V122, L125, and M129) were modeled to point inward for investigation of their hydrophobic contact. The structure of the modeled PrP 107−143 amyloid is represented in Figure 4A.
The detailed procedure used for the modeling is described in section 4.4. Although a β-solenoid structural model based on cryo-EM was recently reported, 51 this model was not compatible with the observed results of our previous works with cultured cells and disulfide-scanning mutants of PrP. 52,53 Additionally, Terry et al. suggested that the 10 nm fiber might represent a noninfectious component of the inoculum. 54 We thus did not adopt the β-solenoid model.
A comparison of our model and cryo-EM structures is given in section 2.8. Although the cryo-EM structures 20−23 have hydrophobic cores in the relevant region, their backbone conformations are different from our model. However, as the main purpose of our study is to investigate factors that contribute to the stability of U-shaped β-arches, the To sample the conformational space of PrP 107−143 more broadly, we conducted five independent 400 ns MD simulations for the WT. Although the stack ends of the WT model amyloid (chains A and J) were not very stable as expected, as a whole our model was sufficiently stable during the MD simulations ( Figures 4B, S3A, and S4A for the last snapshots; Figure S5 for the radius of gyration; see also movie S2). We then modeled mutants of PrP 107−143 (G127V, M129V, The values were calculated from five independent 400 ns MD runs: gray boxes, a disordered loop(120−134); yellow boxes, a more demarcated loop(116−119) than in the WT; black boxes, a more stable β-sheet(110−115) with higher βsheet propensity and lower RMSF values than in the WT; red boxes, a more stable β-sheet(128−133) with lower RMSF and higher β-sheet propensity around L130 than in the WT, the higher SD-β values at A133 are induced by an "upward shift" (see Figure 9E,F); purple boxes, a more demarcated β-sheet(121−122) with lower RMSF values than in the WT; green boxes, a more demarcated β-sheet propensity at M129 and V133 with lower RMSF and SD-β values than in the WT. I138M, M129V&I138M, and A133V) and performed MD simulations. The results are discussed in the following sections.

Influence of G127V Mutation on the PrP 107−143 Amyloid.
A final snapshot of MD simulation for the G127V mutant, PrP 107−143 (G127V), is presented in Figure 4C, from which we confirmed the destabilizing effects of the mutation on the region including the U-shaped loop (residues 120−134; see also Figures S3B and S4B, and movie S3). These effects are reflected in the root-mean-square fluctuation (RMSF) of C α atoms and β-sheet propensity values shown in Figure 5: the heatmaps of PrP 107−143 (G127V) indicate the disorder around the U-shaped loop. To validate the (in)stability of the modeled amyloids, we used a parameter defined by the sum total of the persistence of the hydrophobic contacts between two hydrophobic residues over the eight chains, B−I (hereafter called the proximity score; see Figure S6A). This score counts hydrophobic contacts between the two residues of interest irrespective of intra-or interchain interactions and presumably indicates the total contribution of these residues to the stability of the amyloid. Unlike when using contact maps, we can set a threshold for the contact so that the score reflects the stability of the system. Here the threshold for the hydrophobic contact was set at 5 Å, 55 because the typical distance between neighboring β-strands within a β-sheet was 4.8 Å. The scores correlated with distances between the two corresponding residues in certain cases ( Figure S6B) and reflected the stability of the hydrophobic cores. Figures 6 and 7 summarize the proximity scores in the U-shaped loop and the N-/Cterminal-side regions, respectively. The proximity scores for V122-V122, L125-L125, and L130-L130 of PrP 107−143 (G127V) decreased significantly compared with those of the WT. The score for V122-M129 also decreased, although not to a statistically significant degree. These results indicated that those residues were frequently wide apart, consistent with disordered U-shaped loops. In the other regions, the proximity scores for A115-V121 and A118-P137 decreased, although this result was also not statistically significant. Figure 8A shows the result of the hydrogen bond (H-bond) analysis. We compared the H-bond score defined in the same manner as the proximity score, that is, the sum total of the Figure 6. Bar plots of proximity scores between two residues in the U-shaped loop (residues 120−130). The proximity score was evaluated with chains B−I, because chains of the stack ends (i.e., chains A and J) were not stable during the MD simulations (see Figure S3). The error bar represents the standard error (SE) of the mean of values from five independent MD runs. Bars sharing the same letter are not significantly different according to Tukey's test with α = 0.05. In the figure of the PrP 107−143 amyloid, plotted interactions are represented with light-blue boxed residues (for hydrophobic contacts along the stacking direction) or lines (for the others). In the other regions, the scores of G119(BB)-A117(BB), S132(SC)-L130(BB), S132(BB)-S132(SC), and A/V133(BB)-S132(BB) were lower than those of the WT, although this result was not statistically significant. These results are also consistent with the disorder of the region including the U-shaped loop.
The V127 polymorphism of human PrP is known to confer the protective effects against CJD transmission. 48 Further research (e.g., a longer MD simulation) will be needed to ascertain the relationship between the protective effect and the destabilization of the local amyloid structure caused by the G127V mutation.
2.4. Influence of M129V Mutation on the PrP 107−143 Amyloid. Next, we analyzed the influence of M129V substitution, which is equivalent to V129 polymorphism of human PrP, on the stability of the hydrophobic cores. The mutant amyloid, PrP 107−143 (M129V), appeared more stable during the 400 ns simulation than the WT ( Figure 4D). Comparison of the RMSF and β-sheet propensity values between the WT and M129V validated the stability, with more 133) and the β-sheet(139−141) appeared to be near-square to acute in many runs of the M129V mutant. The increase of the proximity score for A133-P137 supported this bending ( Figure  7). Proximity scores of the WT and the mutant revealed more detailed differences. Most notable was the alteration in the balance of interactions between A120, V122, L125, and V129 in the hydrophobic cores of the U-shaped loops ( Figure 6). The WT showed outstandingly high intrachain proximity scores for V122-M129 (∼400) in the U-shaped loop, whereas the M129V mutation reduced the score (to about 250) and, instead, increased the scores for A120-V129 (to about 650) and V122-L125 (to about 400). The markedly enhanced hydrophobic interaction for A120-V129 may have yielded the higher β-sheet propensity of A120 ( Figure 5B). The higher score for V129-V129 reflected the greater structural stability of the mutant amyloid. The mutation also affected interactions in remote regions, as demonstrated by the decrease of the proximity score for A118-P137 (Figure 7), although this decrease was not statistically significant. Some increases of the proximity scores were also seen, such as those for A113-V121, A116-I139, A116-F141, A117-A133, A118-A133, and A133-P137, although these increases were also not statistically significant. The altered interactions in the N-terminal-side region (A113-V121 and A115-V121) were particularly interesting, because they were located on the opposite side from V129 across β-strands 120−122 and did not directly contact V129. Presumably, the dynamics of the β-sheet(120− Figure 9. (A) Scatter plot showing correlations of the final C α −C α distances for A118-A/V133 (dC α (A118-A/V133)) and A118-S132 (dC α (A118-S132)) in the WT and mutant PrP 107−143 amyloids. The dashed line is merely a guide for the eye. (B) Bar plot of the difference between the final C α −C α distances, δC α , for dC α (A118-S132) and dC α (A118-A/V133) in the WT and mutant PrP 107−143 amyloids. The bars and error bars represent the mean ± standard error (SE) of values obtained from five independent MD runs. Bars sharing the same letter are not significantly different according to Tukey's test with α = 0.05. (C) Identical to panel A, except for dC α (A120-M/V129) and dC α (A118-S132). Note that the dC α (A120-M/V129) values of PrP 107−143 with M129V mutations (green and blue squares) are shorter than 9 Å in most of the MD runs; their dC α (A120-M/ V129) and dC α (A118-S132) values also tend to be shorter than those of the other mutants. 122) were initially affected by the mutation and subsequently altered the interaction patterns of V121; this mechanism could explain the increase in β-sheet propensity for residues 110− 115. Notably, the above description almost applied to the M129V&I138M mutant, and some interactions were enhanced by the I138M mutation (see section 2.5).
As shown in Figure 4D, the distance between the βsheet(120−122) and β-sheet(128−133) seemed to be narrower in the M129V mutant. Indeed, the M129V mutation increased the proximity scores for A118-A133 (Figure 7), and the distances between the C α atoms of A118 and S132, dC α (A118-S132), tended to be shorter in mutants with M129V mutations (Figure 9A, green and blue squares) than in the WT (red dots). Interestingly, the WT and mutants with M129 mostly had shorter dC α (A118-A/V133) than dC α (A118-S132), whereas dC α (A118-S132) was slightly shorter than dC α (A118-A/V133) in the V129 mutants (M129V and M129V&I138M) ( Figure 9B). Figure 9C shows the correlation between dC α (A120-M/V129) and dC α (A118-S132). The mutants with V129 showed obviously shorter dC α (A120-M/ V129) compared with the mutants with M129. Additionally, in the mutants with V129, the distances between C α atoms of A120 and V129, dC α (A120-V129), were shorter than dC α (V122-V129), while the other mutants showed the opposite tendency ( Figure 9D). All these findings could be explained by assuming an "upward" positional shift of the βsheet(128−133) in the mutants with V129 ( Figure 9E,F) that is attributed to the side chain of V129 being shorter than that of M129. This shortness enabled V129 to further approach toward A120 and consequently caused well-balanced interactions of the hydrophobic residues and closer positioning of the two β-sheets. In addition to the local effects, the positional shift also expanded the range of motion of the C-terminal-side region, leading to a loss of interaction for A118-P137 and facilitating the interactions of A116-I139 and A116-F141 ( Figure 7). Notably, this "upward shift" was compatible with the bending at the loop(134−137) mentioned above. In contrast, in the case of the long side chain of M129, the biased interactions with V122 seemed to hamper the approach of residue 129 toward A120 ( Figure 6, A120-M/V129 and V122-M/V129).

Influence of I138M Mutation on the PrP 107−143 Amyloid with or without M129V Mutation.
Residue 138 is one of the residues that is often varied between species. For example, this residue is isoleucine in humans, methionine in many rodents, and leucine in many ruminants. Moreover, residue 138 is the most influential on the mouse−human species barrier in the transmission of sporadic CJD 26 and also in the cross-seeding of Y145Stop peptides of human and mouse PrP. 25 We assessed how the I138M mutation affected the local structural model of PrP Sc .
In a comparison between the I138M mutants and the WT, the RMSF, the β-sheet propensity, and the proximity scores were similar, but interestingly, the proximity scores for A133-P137 were higher in the I138M mutants, although not significantly so (Figures 5, 6, and 7). As mentioned in section 2.4, the score for A133-P137 is related to the bending at the loop(134−137), which was also observed in I138M mutants, particularly in PrP 107−143 (M129V&I138M) (Figure 4E,F; see also Figures S3D,E and S4D,E). The angle between the βsheet(128−133) and the β-sheet(139−141) also seemed to be near-square to acute in the I138M and M129V mutants, whereas the WT or the other mutants tended to have obtuse angles (Figures 4, S3, and S4). Figure 10 shows the proximity scores for A/V133-P137 of each MD run. The scores of five independent MD runs showed dispersed values in each mutant. However, the scores for A133-P137 of five MD runs were higher than 200 in PrP 107−143 (M129V&I138M), whereas in the other mutants, the scores for A/V133-P137 of zero to three runs were higher than 200. In the runs with relatively high proximity scores for A133-P137, the amyloids tended to form small loops like an Ω-shape ( Figure 4F). Each of these loops encompassed A133 and P137 and had near-square to acute angles between the β-sheet(128−133) and the βsheet(139−141), irrespective of the primary structures (see the boxed snapshots in Figures S3 and S4). For example, the final snapshot of run 1 of PrP 107−143 (M129V) ( Figures S3C  and S4C), which had an Ω-shaped loop(134−137), also had a high proximity score (541.2; Figure 10).
The deeper bending of the loop, even to acute angles, caused by the I138M mutation was attributable to the high intrinsic αhelix propensity of methionine, 56,57 which increased the freedom of motion of the loop and the thermodynamically favorable contact between A133 and P137. In this particular conformation, V129 seemed to be compatible with M138; that is, the "upward shift" of the β-sheet(128−133) brought A133 into sufficient proximity with P137 for their efficient hydrophobic contact and allowed loop(134−137) to bend deeper, without the C-terminal-side region colliding against loop(116−118) ( Figure 9F). As a result, the interaction of A118-P137 was considerably weakened in the M129V mutants ( Figure 7). In contrast, in the mutants with M129, the full degree of deeper bending was not allowed due to a steric clash. This may explain why the effects of the I138M mutation were more accentuated in

Influence of A133V Mutation on the PrP 107−143
Amyloid. V136 (in ovine numbering) is one of the scrapieprone polymorphisms of ovine PrP. 58 In the present model shown in Figure 4A, the corresponding residue of human PrP, A133, faced the same direction as M129; we were therefore interested in whether an A133V mutation would somehow affect the PrP 107−143 amyloid structures. The mutant PrP 107−143 (A133V) appeared to have a β-sheet(120−122) and β-sheet(128−133) that were slightly more stable than those of the WT overall ( Figures 4G, S3F, and S4F). In the heatmap patterns, these regions were characterized by more demarcated β-sheet propensities and lower RMSF values ( Figure 5). Consistent with this appearance, the distances between the C α atoms of residues 118 and 133 were very stably maintained at ∼7 Å ( Figure 11), with the proximity score for A118-V133 being significantly higher than that for the WT (Figure 7). The interaction of A118-V133 may cause a significant increase in the proximity scores for L130-L130 and M134-M134. In the U-shaped loop, the score for V122-M129 was significantly higher and, reciprocally, those for A120-M129 and V122-L125 were slightly lower in the A133V mutant than in the WT, although these decreases were not statistically significant ( Figure 6). The hydrophobic interaction in the N-/ C-terminal-side regions was also affected: the score for A117-I139 was increased, although not significantly so. This increase could be explained from the viewpoint of the positional relationship between the β-sheet(120−122) and the βsheet(128−133), as discussed above ( Figure 9E,F). In the A133V mutant, the stable A118-V133 relationship and the stacking interactions of L130 and M134 would fix the positional relationship of the two β-sheets as in the left panel of Figure 9F. This positional relationship would facilitate interactions of V122-M129 and A117-P139, because of the restricted motion range of the C-terminal-side region.
The A133V mutation also affected the H-bond network. One notable finding was a ladder-like H-bond network observed at S132, which we term a "serine ladder". In the serine ladder, the OH group of S132 formed an intrachain Hbond with the carbonyl oxygen atom of L130, and the NH group of S132 formed an interchain H-bond with an oxygen atom of the OH group of S132 ( Figure 8B, see also S132(SC)-L130(BB) and S132(BB)-S132(SC) in Figure 8A). In contrast, the H-bond score of G131(BB)-L130(BB), which corresponds to the interchain H-bond from the NH group of G131 to the CO group of L130, significantly decreased. This is because the CO group of L130 is used as the acceptor of the H-bond with the OH group of S132 mentioned above. The serine ladder explains the low β-sheet propensity with low RMSF values in the region of 130−132 ( Figure 5). A similar motif was reported by Garnham et al. 59 The enhancement of the stacking interaction around S132 affected the stability of the neighboring region. For example, the H-bond score of L130(BB)-M/V129(BB), V133(BB)-S132(BB), M134(BB)-V133(BB), and R136(BB)-S135(BB) largely increased. The decrease of G119(BB)-A116(BB) and L125(BB)-G124(BB) and the increase of G119(BB)-A117(BB) could be also explained from the viewpoint of the positional relationship between the β-sheet(120−122) and the β-sheet (128−133), which was fixed by the hydrophobic contacts A118-V133 and V122-M129 (see above).

2.7.
Conclusions about the PrP 107−143 Amyloid Model. Collectively, the above results suggested that the present local structural model of PrP Sc was more compatible with V129 than with M129. This is an example of an amyloid conformation in which differences between methionine and valine affect the structural stability. Development of another model that is more compatible with M129 than with V129 is underway.
Reinforcement of a single hydrophobic interaction between the β-sheets induced by mutations, for example, the interaction of A120-V129 in PrP 107−143 (M129V&I138M), did not facilitate stabilization of the local structures. To the contrary, the significantly lowered L125-L125 proximity score of PrP 107−143 (M129V&I138M) suggested that this alteration caused a certain degree of destabilization of the β-arch ( Figures S3E and S4E). The results of αSyn(G84M) and PrP 107−143 (M129V) implied that well-balanced interactions of constituent residues in the hydrophobic core might be essential for the maximal stability of a β-arch.
Incidentally, the spontaneous approach of the N-and Ctermini of the PrP 107−143 amyloid, which occurred with high A/ V133-P137 proximity scores, was notable because the N-and C-termini lead to positive-and negative-charge clusters, respectively, in a full-length human PrP. Those charged clusters were able to electrostatically interact and contribute to the stabilization of the amyloid structures. Interestingly, the positive-charge cluster was previously suggested to be essential for the structural conversion of the N-terminal region. 60 Knowledge from the present study may help in the design of useful amyloids or the prediction of potentially amyloidogenic proteins.

Generally Applicable Findings of the Present Study.
The unique effects of each group of hydrophobic amino acids in the in-register parallel β-sheet amyloids were conformation-dependent and attributable to C β -branching and/or the length of the side chains. Methionine and isoleucine showed similar influences in the flat loop of the αSyn amyloid (E61M and E61I), whereas isoleucine and valine in the U-shaped loops destabilized the local structures when they were not stably incorporated in hydrophobic cores (G84I and G84V). As the latter effects were observed in two different protein models, αSyn(G84I) and PrP 107−143 (G127V), this notion may be generally applicable to other in-register parallel amyloids. In certain situations, methionine can behave distinctly from other hydrophobic amino acids, as in αSyn(G84M) amyloid, where its long side chain functions as This viewpoint may be helpful to understand strain-specific influences of M/V polymorphisms of amyloids including PrP. As mentioned in section 1, while our study was under revision, the cryo-EM structures of brain-derived prion proteins (263K and GPI-anchored/anchorless RML strains) were reported. 20−22 Figure 12 shows the cryo-EM structure of the 263K prion protein (PDB: 7LNA 20 ), which has an inregister parallel β-sheet structure with a Greek-key motif at its hydrophobic core, residues 112−134. This feature fits nicely with our model, but some differences are also apparent between the two models. In our model, for example, the side chain of M129 points inward for the U-shaped loop ( Figure  4A), whereas it points outward in the cryo-EM structure. Moreover, these structures have different hydrophobic interaction networks in the Greek-key domain. In contrast, the structures of amyloids of human PrP isolated from patients with GSS associated with F198S mutation, which were identified using cryo-EM, also have Greek-key motifs and similar hydrophobic interactions to our model. Although the side chain of L125 points outward and stabilizes through interaction with the N-terminal-side region, those of A120, V122, and V129 point inward to form a hydrophobic core as in our model. The authors reasoned that the delay of age at onset seen in heterozygous GSS(F198S) patients might be due to the inefficient aggregation of the endogenous M129 PrP because the bulky side chain of M129 does not fit the narrow space of the core. 23 It is intriguing that every PrP Sc whose structure was identified thus far has a Greek-key motif in the same region. This could imply the significance of a U-shaped loop in this region for PrP C −PrP Sc conversion. Our findings of the present study might assist in the analysis of these hydrophobic interactions and their influences on (de)stabilization of the local structures of the PrP amyloids and might be applicable to other amyloids.

Limitations to the Present Method.
A caveat to our hypothesis is that the MD simulation is an artificial setting, which starts with the same initial conformations irrespective of mutant types. In reality, distinct conformations are implied for some mutants. For example, the spontaneous amyloid formation caused by the Y145Stop mutant of Syrian-hamster PrP, which has more methionine than the mouse or human PrP counterparts, is inefficient. 28 We consider that the higher freedom of motion of the backbone and potential steric effects of the long side chain of methionine hamper its settling into amyloid conformations. Such inefficiency in folding into a conformation may divert a certain fraction of molecules to aberrant refolding pathways in in vitro or in vivo experiments. Regardless of these limitations, MD simulation provides direct insight into the structures and dynamics of in-register parallel β-sheet amyloids, and this approach would shed light on the mechanisms of the strain diversity of amyloids, including PrP Sc . One approach to overcome these limitations would be to generate initial structures for all-atom MD simulations with coarse-grained (CG) MD simulations and backmapping. 63 The CG models allow us to simulate the dynamics of biomolecular systems on a longer time scale; thus, the effect of a mutation might be reflected after a longer-term CG MD simulation.
Another caveat concerns the force field for the MD simulations. Many studies have assessed the quality of the force fields for amyloidogenic proteins using a segment or the full length of Aβ peptides. 64−71 In this study, we used the AMBER ff99SB-ILDN force field, 72 which provides fairly good performance and is one of the safest choices for this purpose. 65,66,68 However, Watts et al. reported that several force fields including AMBER ff99SB-ILDN yield a positive value of binding energy in the Aβ(1−40) dimer, resulting in instability of the quaternary structures. 67 In contrast, CHARMM36 shows favorable protein−protein interactions. 67 The CHARMM36 force field was refined for the simulation of intrinsically disordered proteins (CHARMM36m). 73 Samantray et al. demonstrated that CHARMM36m is suitable for simulating peptide aggregation. 64 From these points, we expect that the MD simulation with CHARMM36(m) can stabilize our systems (i.e., αSyn and PrP 107−143 ) and highlight the instability caused by the mutation.
In addition to these technical considerations, there is a gap between the results of the simulations and the biological/ clinical relevance of the point mutants. Our model amyloid is different from the cryo-EM structures, and the discussions from our results were limited to the (de)stabilization of (or around) the U-shaped β-arches. However, the main purpose of our study was to investigate how hydrophobic interactions affected the stability of the local structure of amyloids. Thus, these limitations do not compromise the results of our analysis.

CONCLUSION
We have demonstrated how different hydrophobic amino acids uniquely affect the stability of the local structures in two different in-register parallel β-sheet amyloids. Our studies have also revealed how the manifestations of one mutation are affected by another mutation. This concept would be applicable to various in-register parallel β-sheet amyloids and other β-arches of PrP Sc . We expect that the knowledge from the present study will contribute to the prediction of potentially amyloidogenic proteins or proteins which might interact with a given pathogenic amyloid in the future, in addition to advancing our understanding of the strain diversity of amyloids.

Modeling Structures of αSyn Amyloids. We used a
Greek-key αSyn amyloid (PDB ID: 2N0A 35 ) as a starting structure, after truncating the disordered N-and C-terminalside regions (residues 1−35 and 100−140, respectively) (see Figure 1). 31 The N-and C-termini were acetylated and Nmethylated using AmberTools16, respectively. 74 For modeling the αSyn mutants, we used SCWRL4. 75 The modeled amyloids were solvated with a rhombic dodecahedron water box with a minimum wall distance of 12 Å using GROMACS (version 5.0.4). Na + and Cl − ions were randomly placed to neutralize the system and yield a net concentration of 150 mM NaCl. The protonation state of the histidine at residue 50 was fixed as the N δ -H tautomer (HID form in the AMBER naming convention) in all simulations. 4.2. MD Simulation of the αSyn Amyloids. GROMACS (versions 5.0.4 and 5.1.2) 76 with the AMBER ff99SB-ILDN force field 72 was used for MD simulations with the TIP3P water model. 77 The system was initially minimized for 5000 steps with the steepest descent method, followed by 2000 steps with the conjugate gradient method. During minimization, heavy atoms of the amyloids were restrained with a harmonic potential with a force constant of 10.0 kcal/mol·Å 2 . After minimization, the system temperature was increased from 0 to 310 K during a 1 ns simulation with the restraints. Next, a 1 ns equilibration run was performed while gradually removing the restraints from 10.0 kcal/mol·Å 2 to zero, and subsequent equilibration was performed in the NPT ensemble for 2 ns at 310 K and 1 bar. The production runs were carried out for 400 ns in the NPT ensemble at 310 K and 1 bar ( Figure S7A). We used the velocity-rescaling scheme 78 and the Berendsen scheme 79 for the thermostat and barostat, respectively. The LINCS algorithm 80 was used to constrain all bonds with hydrogen atoms, allowing the use of a 2 fs time-step. Electrostatic interactions were calculated with the Particlemesh Ewald method. 81 The cutoff length was set to 12 Å for the Coulomb and van der Waals interactions. The Verlet cutoff scheme 82 was used for neighbor-searching. Trajectory snapshots were saved every 10 ps. We conducted five (for WT) and three (for the mutants) independent 400 ns MD simulations.

Analyses.
Backbone root-mean-square deviation (RMSD), RMSF, potential energy, and distance between atoms were calculated using GROMACS. 76 Convergence of the MD simulations was assessed with the root-mean-square inner product (RMSIP) 83 between two halves of the last 300 ns of the trajectories. The essential subspace was extracted by using principal component analysis (PCA) for C α atoms. Table  S1 shows that the first 20 PCs explain 69% or more of the variance for all the simulations of αSyn. From this result, the first 20 eigenvectors of C α atoms were used to calculate RMSIP. The RMSIP values are also summarized in Table S1. In all the simulations of αSyn, the RMSIP values are larger than 0.6, which suggests good convergence of the trajectories. 83 Backbone RMSD ( Figure S8) and potential energy ( Figure S9) support the convergence of this region.
The secondary structure content during the simulations was calculated with DSSP 84,85 using gmx do_dssp in GROMACS. Hydrophobic contacts were analyzed using PyInteraph. 86 A hydrophobic contact was assigned if the distance between the centers of mass of the side chains was less than 5 Å ( Figure  S6A). 55, 86 The results of the hydrophobic contact analyses were visualized using Cytoscape (version 3.5.1). 87 The proximity score was defined by the sum total of the persistence of the hydrophobic contacts between two hydrophobic residues over the chains B−I. Hydrogen bond analysis was carried out using HBonds Plugin in VMD. 88 An H-bond was assigned if the distance between the donor (D) and acceptor (A) atoms was shorter than 3.2 Å and the angle A−D−H was smaller than 30°. 89,90 The H-bond score was defined in the same manner as the proximity score, that is, the sum of the Hbond persistence over the chains B−I. All molecular structures for the amyloids were drawn with UCSF Chimera (version 1.12) 91 or VMD. 88 Movies of the MD simulation trajectories were prepared with UCSF Chimera. 91 4.4. Modeling PrP 107−143 Amyloids and MD Simulations. In designing the local structural models of human PrP Sc , we adopted the region comprising -GGL 125 GG-, as denoted above (see section 2.2), and avoided charged residues in the N-and C-termini of the peptide because they can excessively destabilize in-register parallel β-sheet structures, particularly when they are at the free ends. There were positive-and negative-charge clusters in regions 101−106 and 144−147, respectively; thus, the region between them was used for the modeling. First, we roughly designed conformations of a single layer of amyloid with Swiss PDB viewer 92 based on the structural model proposed by Theint et al. 49 and then piled the layer up at intervals of about 5 Å to make an in-register parallel β-sheet amyloid with UCSF Chimera. 91 The model amyloids with 10 layers were refined using Modeller (version 9.15) 93 with β-sheet restraints for the residues A120−V122, Y128−L130, and I138−F141. Mutants were generated by using SCWRL4, 75 and subsequently the Nand C-termini of the refined models were acetylated and Nmethylated using PyMOL, respectively. 94 We performed five independent 400 ns MD simulations for each model using nearly the same procedure as for the MD simulations of αSyn ( Figure S7B). We checked the convergence of the simulations with RMSIP (Table S2), backbone RMSD (Figure S10), and potential energy ( Figure S11). Table S2 summarizes the RMSIP between two halves of the last 100 ns of the trajectories and cumulative proportion variance evaluated with the first 20 PCs. The RMSIP values are larger than 0.6 in all the simulations, and the first 20 PCs explain over 65% of the variance in most cases. We thus used the last 100 ns for the analyses described in section 4.3.

Statistical Analyses.
Tukey's multiple comparison test (α = 0.05) was applied for the statistical analysis with the aid of the multcomp package in R. 95 The graphs of the statistical analysis were drawn with the ggplot2 R package. 96 ■ ASSOCIATED CONTENT
Radius of gyration as a function of time for the αSyn mutants; C α −C α distance between residues 84 and 89 in the αSyn mutants; final snapshots of MD simulations of PrP 107−143 ; radius of gyration as a function of time for PrP 107−143 ; definition of hydrophobic contact and proximity score; correlations between proximity score and C α −C α distance; procedure of MD simulation;

Notes
The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS
The numerical calculations were performed on the TSU-BAME2. 5