Understanding the Twisted Structure of Amyloid Fibrils via Molecular

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Understanding the Twisted Structure of Amyloid Fibrils via Molecular Simulations Lu Lu, Yixiang Deng, Xuejin Li, He Li, and George Em Karniadakis J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b07255 • Publication Date (Web): 14 Aug 2018 Downloaded from http://pubs.acs.org on August 15, 2018

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The Journal of Physical Chemistry

Understanding the Twisted Structure of Amyloid Fibrils via Molecular Simulations Lu Lu,†,¶ Yixiang Deng,‡,¶ Xuejin Li,† He Li,† and George Em Karniadakis∗,† †Division of Applied Mathematics, Brown University, Providence, RI 02912, USA ‡School of Engineering, Brown University, Providence, RI 02912, USA ¶Contributed equally to this work E-mail: george [email protected]

Abstract

1 Introduction

Accumulation and aggregation of amyloid are associated with the pathogenesis of many human diseases, such as Alzheimer’s disease (AD) and Type 2 Diabetes Mellitus (T2DM). Therefore, a quantitative understanding of the molecular mechanisms causing different aggregated structures and biomechanical properties of amyloid fibrils could shed some light into the progression of these diseases. In this work, we develop coarse-grained molecular dynamics (CGMD) models to simulate the dynamic selfassembly of two types of amyloids (amylin and amyloid β (Aβ)). We investigate the structural and mechanical properties of different types of aggregated amyloid fibrils. Our simulations demonstrate that amyloid fibrils could result from longitudinal growth of protofilament bundles, confirming one of the hypotheses on the fibril formation. In addition, we find that the persistence length of amylin fibrils increases concurrently with their pitch length, suggesting that the bending stiffness of amylin fibrils becomes larger when the amylin fibrils are less twisted. Similar results are observed for Aβ fibrils. These findings quantify the connection between the structural and the biomechanical properties of the fibrils. The CGMD models developed in this work can be potentially used to examine efficacy of anti-aggregation drugs, which could help in developing new treatments.

Amyloid accumulation and aggregation have drawn increased attention in the past few decades as they are associated with many human diseases (see recent review 1 ), such as Alzheimer’s disease (AD), one of the most prevalent neurological disorders, 2 and Type 2 Diabetes Mellitus (T2DM), a metabolic disease that affects about 29 million Americans and more than 422 million adults around the world. 3 Amyloid β (Aβ), the main component of amyloid plaques, is generated from the amyloid precursor protein (APP). 4–7 Under normal conditions, APP is cleaved by α and γ secretases and breaks down to soluble products during the proteolytic processes. However, under pathological conditions, APP is cleaved by β and γ secretases, generating insoluble Aβ. 8–11 Aβ can self-assemble to aggregates and form plague outside neuron cells or near in the peri-vascular between blood vessels and interacting neurons. These amyloid plaques block the inter-neuron signaling, hence impairing the brain function, which is considered to be a possible cause of AD. 12–17 Amylin (or human islet amyloid polypeptide, hIAPP), another type of amyloid, is a neuroendocrine hormone secreted from pancreatic β-cells along with insulin. 18 Amylin complements the function of insulin in controlling the glucose level in blood. 19,20 In T2DM, amylin exhibits great propensity to aggregate and form amylin fibrils.

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ular, we consider the amylin fibrils of “twisted sheets” and Aβ fibrils of “striated ribbon”. We investigate the connections between the structural and mechanical properties of the Aβ and amylin fibrils. The rest of the article is organized as follows. In Section 2, we introduce the CGMD models and simulation methods. In Section 3, we present simulation results of selfassembly of Aβ and amylin and discuss the relationship between the fibril structures and their mechanical properties. The main results and findings are summarized in Section 4.

Aggregates of amylin hormone can destruct the pancreatic β-cells, resulting in decreased insulin production with consequent clinical manifestations such as polydipsia and polyphagia . 21–25 As the aggregation of Aβ and amylin are associated with the pathogenesis of AD and T2DM, respectively, an quantitative insight into the kinetic details of the aggregation processes and the underlying molecular mechanisms inducing different structures and biomechanical properties of amyloid fibrils is essential to address the fundamental questions regarding these two diseases. In the past decades, the amyloid fibrils attracted considerable attention in both experimental and computational studies, leading to discoveries of various monomers, dimmer, oligomer and fibril structures. 26–34 Experimental approaches can detect the detailed structures of Aβ/amylin fibrils at molecular level; however, they cannot be used to explain the molecular basis of formation of various amyloid structures nor to capture the detailed dynamics of aggregation process because of the limitations on the accessible length and time scale. On the other hand, computational modeling based on molecular dynamics (MD) methods, such as traditional MD, 33,35–38 discrete MD, 39 Hamiltonian and temperature replica exchange MD, 40–46 have been implemented to investigate the molecular underpinnings for various structures of Aβ/amylin 47 as well as the dependence of the fibril stability on the sequence and symmetry of their structures. 48 However, there have been very few studies on the dynamic selfassembling of Aβ/amylin into fibrils due to the high computational cost. Bieler et al. 49 performed Monte Carlo simulations with a coarsegrained model of an amyloidogenic peptide to model the amyloid self-assembling following the formation of a critical nucleus, hence connecting nucleation and dynamic aggregation of amyloid. However, only one particular structure of amyloid fibrils was studied in this work and the mechanical properties of the formed fibrils were not considered. In this study, we develop coarse-grained molecular dynamics (CGMD) models to simulate the aggregation of amyloid into fibrils based on two popular amyloid structures. In partic-

2 Computational methods 2.1 Amylin model 2.1.1 Amylin molecule model Amylin, a 37-residue hormone peptide synthesized and co-secreted with insulin, has a U-bend conformation consisting of two antiparallel βstrands connected by one loop 29,50 (Fig. 1A). Amylin can self-assemble to fibrils with various structures. 26,28–30 Each layer of an amylin fibril mainly consists of 2 to 5 monomers. Amylin fibrils with more than two monomers per layer tend to form a structure of “twisted sheets”. Among different possible structures of amylin with three monomers per layer, the C-WT triangular structure (Fig. 1C) has the lowest packing energy and is structurally stable. 31,50,51 In this work, we will simulate self-assembly of amylin into fibrils with the C-WT triangle structure. We propose a coarse-grained patchy particle model 52–54 to simulate the amylin molecules. In this model, an amylin molecule is represented by three rigid spheres (red) with four patches (brown and yellow) on its surface (Fig. 1B). In our simulations, we use the diameter d of each spherical particle to represent the length scale of the simulation system. For the amylin model, we choose d ∼ 17.9 ˚ A, as the amylin in the C-WT structure has an average length of ∼ 53.7 ˚ A. 50 Different patch sites are employed to represent different types of intermolecular interactions, i.e., the coarse-grained model has two axial patches (brown) and two lateral patches


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A

D

C

B

E

F

pi pj

qi qj

Figure 1: CGMD particle model of amylin fibrils. (A) U-bend structure of an amylin monomer. 50 (B) An amylin monomer is represented as a patchy particle with three spheres (red) and four patches (brown and yellow) on the surface. (C) C-WT structure of an amylin oligomer. 50 (D) Top view (left) and side view (right) of the preexisting one-layer nucleus in the simulations. (E) Interstrand lateral bond interactions between yellow patches in the fibril. (F) Intra-strand interactions involving axial bond interactions between brown patches and angle bending potentials between vectors pi -pj and qi -qj . A and C are adopted with permission from Zhao et al. 50 (yellow), which are involved in the amylinamylin interactions (Figs. 1B and D). The positions of the lateral patches on the CG particles such that the fibrils follow the left-handed twist structure. In addition, we introduce two perpendicular vectors p and q into each CG particle to describe its orientations (see the vectors in Fig. 1F). In this study we focus on the growth dynamics, structure and mechanical properties of amylin fibrils and we assume that one layer of the amylin fibril preexists, acting like a nucleus to initiate the growth of fibrils, following the strategies employed in Refs. 54 and 55. The structure of this one-layer nucleus (Fig. 1D), including the relative position and orientation of each amylin molecule, is designed to match the C-WT triangular structure. 50

the patch sites are within the range of interaction. Specifically, the attractive interaction between two axial or lateral patches is described by −A exp (−Br2 ) r < rc , (1) Vpatch = 0 r ≥ rc

amylin

where r is the distance between two patch sites of interacting amylin molecules, A and B are used to determine the strength of the interaction, and rc sets the distance cutoff. The values of all parameters will be given in the following section. If two patch sites come into a close contact, i.e., less than a constant distance δ, a bond is generated between these two patch sites (see the bonds in Figs. 1E and 1F). We choose δ as d/5. The elasticity of the bonds is modeled as Vbond = kbond (r − r0 )2 , (2)

To model the interactions between amylin molecules, we hypothesize that two amylin molecules interact through their patches when

where kbond is the bond strength, and r0 is the equilibrium bond distance. To model the helical twist, we employ angle bending potentials between axial vectors pi and

2.1.2 Interactions molecules

between


3


A

pj , and lateral vectors qi and qj of two adjacent amylin molecules in the same strand. These potentials are given by Vaxial = kangle (θ − θ0 )2 ,

(3)

Vlateral = kangle (β − β0 )2 ,

(4)

B

p1 d

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r0,axial p2

where kangle is the angle bending strength, θ = ˆ j ) and β = cos−1 (ˆ ˆ j ) are angles cos−1 (ˆ pi · p qi · q between each pair of vectors, and θ0 and β0 are the corresponding equilibrium values of these two angles. To avoid particle overlapping, an excluded volume, which is equal to the volume of the CG particles, is defined for each amylin CG particles. The effect of excluded volume is represented by the repulsive term of the standard Lennard-Jones potential.

r0

,lat

era

l

Figure 2: Fibril geometry used to calculate the potential parameters. (A) The centers of amylin molecules in one strand form a circular helix. The distance along the axial direction between two adjacent centers is d. (B) Three amylin molecules of the same cross-section are in a triple helix (dash lines), and the long axis of each amylin molecule is perpendicular to its corresponding helix curve.

2.1.3 Simulation method and model parameters

lowing equations

We simulate the growth dynamics of amylin molecules using the CGMD method, where the position and orientation of a particle are updated at discrete time steps. 56 All simulations are performed in a N V T ensemble using the Langevin thermostat. 57 For numerical integration of the translational and rotational equations of motion, we use velocity Verlet algorithm with a time step of 0.001τ , where τ is the time scale of CGMD simulation. In our simulation, it takes about 100τ to form one triangular layer in the fibrils. To precisely map this time unit to physical unit, we need compare the dynamic growth of fibrils with experimental results, following the strategy in Refs. 54 and 55. Initially, amylin particles are placed randomly in the cuboid simulation box employing periodic boundary conditions. The equilibrium distances r0 of axial and lateral bonds in Eq. 2 and the equilibrium angles θ0 and β0 in Eqs. 3 and 4 are correlated with the pitch length of the simulated fibrils. We derive this correlation as follows. The centers of amylin molecules in each strand form a circular helix structure (Fig. 2A), which can be described in Cartesian coordinates by the fol-

x(t) = a cos(t), y(t) = a sin(t), z(t) = bt, (5) √

where a = 2 3 3 d is the radius, b = s/(2π), and s is the pitch length. The distance along the axial direction between two adjacent centers is ∼d, because amylin molecules are close packed in the fibrils. In this way, the equilibrium axial bond distance r0,axial can be calculated (see Table I), and the equilibrium angle between the axial vectors of two adjacent particles θ0 is calculated as cos−1 (p1 ·p2 ). The crosssection of the amylin fibril consists of three amylin molecules in a triple helix arrangement (dash lines in Fig. 2B), and the long axis of each amylin molecule is perpendicular to its corresponding helix curve. Then, the equilibrium lateral bond distance r0,lateral can also be calculated (see Table I). However, no analytical solution is available for the equilibrium angle β0 between two lateral vectors. Thus, we perform a parametric study of β0 to identify the value that can match the targeted pitch length. Since the typical pitch length for C-WT structure is 610.7 ˚ A ≈ 34.1d, 50 we examine the structural and mechanical properties of amylin fibrils under pitch length ranging from 30d to 50d. As a reference, the geometrical parameters used for these pitch lengths are listed in Table 1.


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Table 1: Pitch-length dependent parameters in the amylin model. s/d

r0,axial /d

r0,lateral /d

θ0

β0

30 35 40 45 50

0.029 0.021 0.016 0.013 0.011

0.149 0.109 0.083 0.066 0.054

0.049 0.036 0.028 0.022 0.018

0.34 0.25 0.18 0.15 0.13

2.2 Aβ model A B

kB T L3 , 3 Δu(L)2 κ , lp = kB T

pi

pj

qi

qj

C

The potential strength parameters kbond and kangle are related to the bending rigidity κ and persistence length lp of amylin fibrils. The bending rigidity of an amylin fibril can be computed by measuring the thermal fluctuations of fibrils. 54,58–60 In this method, κ and lp can be calculated as κ=

D

Figure 3: CGMD particle model of Aβ fibrils. (A) The structure of triplet fibril cross-section of Aβ fibrils. (B) Front view (top) and top view (bottom) of our model. Aβ molecules in the same layer of the fibril are represented by three spheres (red and blue) and six patches (brown and yellow). (C) Bond interactions and angle bending interactions between Aβ particles.

(6)

Aβ fibrils exhibit a variety of structures, which depend on the precise details of environmental conditions. 63 However, Aβ fibrils with “striated ribbon” structure are predominately observed in prior experimental and computational studies. 31,51,62–67 The cross-section of the “striated ribbon” fibril could accommodate pairs of two, three, or four interconnected protofilaments. 32,62 Here, we develop a CGMD model to simulate self-assembly of Aβ into “striated ribbon” structures with triplet cross-section as reported by Fitzpatrick et al. 32 (Fig. 3A). As shown in Fig. 3B, the coarsegrained model has three hard spheres (red and blue), two axial patches (brown) on the surface of the middle sphere (red), and four patches (yellow) on the surface of the boundary spheres (blue). We adopt the same type of interactions between Aβ molecules as the aforementioned amylin model, see Fig. 3C. These interactions include patch-patch attractions (Eq. 1), bond interactions (Eq. 2), angle bending potentials (Eqs. 3 and 4), and excluded volume effect. The same CGMD simulation method is used as described in the amylin model. All the parameters are the same as those in the amylin model, except the geometry-related parameters

(7)

where L is the fibril length, and Δu(L) = u(L) − u(L) is the normal deviation of the fibril-end from its average position. We find that when kbond = kangle = 50, the bending rigidity measured from the simulated fibrils is close to the experimentally measured persistence length, which is of the order of microns. 58,61,62 Therefore, we select the values kbond = kangle = 50 in our simulations. We also perform parametric studies for parameters in the attractive interaction potentials between patches in Eq. 1. Our simulation results show that larger attractive forces between patches lead to faster growth rates of the fibrils, but the final fibril structure is insensitive to these parameters. In the following simulations, we choose rc = 3d, which is the length of amylin monomers. The parameters that control the strength of the attractive forces are selected to be A = 5 and B = 0.5 such that the potential represented by Eq. 1 provides attractive forces that are comparable to the Lennard-Jones potential.


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r0,axial , r0,lateral , θ0 and β0 . Since the middle red particles tend to be arranged in a straightline manner, we set r0,axial = 0 and θ0 = 0. In addition, because the blue lateral particles are in a double helix structure, we set β0 = 2π/N where N = s/d is the number of layers in one pitch. r0,lateral is determined based on fibril pitch length, analogous to the analysis performed for amylin fibrils (see Fig. 2A). The values of the model parameters r0,lateral and β0 resulting in fibril pitch lengths that are comparable to those observed in Ref. 32 are summarized in Table 2.

First, we simulate the aggregation of amylin molecules into a fibril with pitch length 35d ≈ 63 nm, a typical pitch length for C-WT structure, 50 using the parameters in the second row of Table 1. Initially (t = 0), a preexisting nucleus is placed in the center of the simulation box. Once simulation starts, free molecules commence aggregating at the two ends of the fibril (see Movie S1 in Supporting Information). Fig. 4 illustrates sequential snapshots during the growth of an amylin fibril, showing that the “twisted sheets” fibril structure is well maintained throughout the simulation without fibril splitting or branching.

Table 2: Pitch-length dependent parameters in the Aβ model. s/d

r0,lateral /d

β0

18.5 23.5 33.9

0.057 0.036 0.017

0.34 0.27 0.19

t=0

t = 5000τ

t = 10000τ

Cross section

t = 2500τ

3 Results and discussion

∼174 nm

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In this study, we first investigate the dynamic aggregation of amylin fibrils and calculate their mechanical properties. Then, we analyze the relation between the fibril structure and mechanical properties. In the following subsection, we discuss the dynamics of Aβ fibrils in a similar manner and compare the simulation results between the two amyloid fibrils.

3.1 Amylin fibrils 3.1.1 Formation dynamics of amylin fibrils

Figure 4: Sequential snapshots of the aggregation of an amylin fibril (left), and the fibril cross-section (right). Initially, i.e., t = 0, an amylin nucleus is placed in the center of the simulation box filled with amylin particles (for clarity, free amylin particles are not shown in the figure). Once the simulation starts, the amylin particles in the vicinity of the nucleus quickly aggregate towards the amylin nucleus in both directions to form a long fibril. τ is simulation time unit.

Extensive studies have been devoted to understand the underlying mechanisms of formation of amyloid fibrils and two hypotheses have been proposed: 1) amyloid protofilaments coil into fibrils; 68,69 2) amyloid fibrils are assembled from longitudinal growth, rather than lateral association of existing protofilaments. 70,71 Here, we simulate the formation of amylin fibrils to investigate the potential underlying mechanism.


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These simulation results demonstrate that the aggregation of amylin fibrils could result from the attachment of amylin monomers, confirming the hypothesis of longitudinal growth. We notice that the homogeneity of the protofilament growth rate is an important determinant of the stability of the three-protofilament fibril structure: when the growth of one protofilament overwhelms the other two, the resulting fibril tends to split into branches. This finding implies that protofilaments with various lengths are less likely to coil into a fibril, thereby eliminating the possibility of fibril formation through lateral association of existing protofilament. 68,69 It is worth noting that the aggregation mechanism discussed above is consistent with the molecular mechanism of sickle hemoglobin polymerization, 54,55 which plays an essential role in sickle cell disease.

A

0.25 n = 50

Probability

0.2 0.15 0.1 0.05 0 55

B

60

65 Pitch length (nm)

70

75

0.3

Probability

n = 50 0.2

0.1

0 0

3.1.2 Structural and mechanical properties of amylin fibrils

3

6 9 12 Persistence length (μm)

15

Figure 5: Structural and mechanical properties of amylin fibrils. (A) Distribution of pitch lengths from 50 different amylin fibrils obtained from CGMD simulations with the same set of simulation parameters. (B) Distribution of 50 different persistence length measurements performed on the grown amylin fibrils.

Next, we investigate the structural and mechanical properties of amyloid fibrils, which are increasingly recognized to be essential for understanding pathological behaviors of fibrils in a variety of debilitating diseases. 58,60 In this section, we first focus on the amylin fibrils we simulated previously. To account for the randomness in the aggregation process, we perform 50 independent simulations of self-assembling of the amylin into fibrils with the same model parameters. The initial amylin molecules’ positions are randomly selected in the simulation box. We compute the pitch length of simulated fibrils, see Fig. 5A. We see that under the same model parameters, most simulated fibrils exhibit a pitch length close to mean value of 62 nm, which is very close to the presumed 63 nm. Fibrils with pitch lengths deviated from 63 nm are also observed in a few cases due to the aggregation randomness, consistent with the previous finding that even for the amyloid fibrils with the same structure, their pitch lengths and persistence lengths are not unique. 62 Amyloid fibrils are highly ordered structures, with bending rigidity ranging from 10−26 N m2 to 10−25 N m2 , corresponding to a persistence

Persistence length (μm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


14 n = 25 11

8

5

50

60

70

80

90

Pitch length (nm)

Figure 6: Dependence of amylin persistence length on its pitch length. Error bars represent one standard deviation, and each distribution is calculated from 25 samples.


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Since there is only one sheet in this Aβ fibril model, there is no fibril splitting or branching. In comparison with the amylin fibrils, the growth rate of Aβ fibril is calculated to be ∼0.05 nm/τ , which is faster than that of amylin fibrils (∼0.02 nm/τ ). This discrepancy is likely to result from the simple structure of Aβ fibrils with just one left-handed coiling sheet.

length of the order of micrometers, see Ref. 61 for a comprehensive comparison of ∼10 types of biological fibrils. Using Eq. 7, we compute the persistence lengths of amylin fibrils modeled in our simulation. The measured persistent lengths are presented in Fig. 5B, which resembles to a distribution with a mean value of ∼7.5 μm and range from 3 μm to 12 μm. These results are consistent with prior experimental measurements. 58,60,61 To probe the effect of fibril pitch length on its mechanical property, we employ five sets of parameters listed in Table 1. We perform 25 independent simulations with random initial conditions for each parameter set, to probe the relation between pitch length and persistence length. Our simulation results in Fig. 6 illustrate that as the fibril pitch length increases, the mean persistence length increases as well, which is characterized by the trend of the square markers in Fig. 6. This finding demonstrates that the structure of the fibril determines its mechanical properties, in agreement with a prior study using all-atom MD simulations. 72 Furthermore, our results quantify the connection between the mechanical properties of amyloid fibrils and their structures. A similar pitch–bending correlation is also observed in studies of sickle hemoglobin fibers in sickle cell disease. 54

t=0

t = 2100τ

Cross section

t = 700τ

∼100 nm

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Figure 7: Sequential snapshots of the aggregation of an Aβ fibril (left), and the fibril crosssection (right). Initially, i.e., t = 0, an Aβ nucleus is placed in the center of the simulation box filled with Aβ particles (for clarity, free Aβ particles are not shown in the figure). Once the simulation starts, the Aβ particles in the vicinity of the nucleus quickly aggregate towards the Aβ nucleus in both directions to form a long fibril. τ is the simulation time unit.

3.2 Aβ fibrils 3.2.1 Formation dynamics of Aβ fibrils Here we study the dynamic formation of Aβ fibrils in a similar manner as amylin fibrils. As for the fibril structure, we follow the triplet fibril cross-section reported by Fitzpatrick et al. 32 (Fig. 3A) with pitch length of ∼47 nm, i.e., using the parameters in the second row of Table 2. Fig. 7 presents sequential snapshots of the fibril growing process from t = 0 to t = 2100τ . Movie S2 in Supporting Information illustrates the dynamic aggregation process of Aβ fibrils. Aβ molecules near the two ends of the fibril are drawn close to the ends by the attractive potential described by Eq. 1. Then, these particles bond with the molecules already in the fibril.

3.2.2 Structural and mechanical properties of Aβ fibrils We examine the distributions of pitch length and persistence length of Aβ fibrils under the same set of parameters as in the simulations above. We perform 50 simulations with different initial conditions, and obtain the distribu-


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tion of fibril pitch length, as shown in Fig. 8A. The distribution resembles a normal distribution with a mean value of 47.5 nm, close to the pitch length of 47 nm reported in previous study. 32 We then compute the persistence length of the fibrils. Fig. 8B shows the distribution of persistence length with mean value around 7 nm, close to the persistence length 6 nm measured in Ref. 62. To investigate the relation between the mechanical property of Aβ fibrils and their pitch lengths, we perform 25 simulations for each set of model parameters listed in Table 2, and compute the corresponding pitch length and persistence length distributions. As shown in Fig. 9, the persistence length of Aβ fibril increases with the growing pitch length, but the growth rate is lower than that of amylin fibrils. We also note that the variances of the pitch length and persistence length of Aβ fibrils are much larger than those of amylin fibrils. This increased heterogeneity is probably caused by the fact that amylin fibrils simulated in this work possess a stable triangular nucleus, whereas the simulated Aβ fibrils has only one strand. These findings suggest that the basic structures of amyloid fibrils play an essential role in determining their morphologies and mechanical properties.

A

0.12 n = 50

Probability

0.09 0.06 0.03 0 35

B

40

45 50 Pitch length (nm)

55

60

0.15

Probability

n = 50 0.1

0.05

0 0

5

10 15 20 Persistence length (μm)

25

Figure 8: Structural and mechanical properties of Aβ fibrils. (A) Distribution of pitch length from 50 different Aβ fibrils obtained from CGMD simulations with the same set of simulation parameters. (B) Distribution of 50 different persistence length measurements performed on the simulated Aβ fibrils.

4 Conclusions We have developed coarse-grained patchy particle models to simulate the self-assembling of two types of amyloids, amylin and Aβ. The aggregation of the amyloids is considered by assigning interacting patch sites on protein surface, following the strategies of prior studies. 52,54,55 The locations of the patch sites are designed to construct the molecular arrangement in a twisting fiber. In our simulations, amylin and Aβ fibrils are distinguished by their particular structures. We also vary the geometrical parameters to produce fibrils with different pitch lengths and measure the corresponding persistence lengths, hence quantifying the connections between the fibril structure and their mechanical properties. Our simulation results show that the employed model parameters are

Persistence length (μm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


20

n = 25

15 10 5 0

30

40

50

60

70

Pitch length (nm)

Figure 9: Dependence of Aβ persistence length on its pitch length. Error bars represent one standard deviation, and each distribution is calculated from 25 samples.


9


sufficient to construct fibril models with pitch lengths and persistence lengths that are consistent with prior experimental measurements. We find that the persistence length of amylin fibrils increases as the pitch length increases, implying that the bending stiffness of amylin fibril becomes larger when the twisted structure of fibrils is less pronounced. Similar tendency is also observed for Aβ fibrils. These findings improve our understanding of the aggregation process and quantify the pitch length and persistence length of amyloid fibrils. Our results also provide quantitative correlations between the fibril structures and their bending stiffness. This proposed CGMD amyloid model can be potentially combined with existing microscopicscale all-atom models 31,50,72 using the adaptive resolution scheme, 55 to simulate multiscale phenomena in amyloid fibrils, from nucleation to fibril growth. In this context, we can explore the dynamic aggregation of amyloid over a wide range of length and time scales, as suggested by a recent review paper by Nasica-Labouze et al. 47 More importantly, this proposed model can be used to examine the efficacy of existing and potential anti-aggregation drugs 73–75 to accelerate the development of clinical treatments and therapeutic interventions for diseases induced by amyloid aggregation.

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Acknowledgement The work was supported by National Institutes of Health grants No. U01HL114476 and No. U01HL116323. This research used resources of the Argonne Leadership Computing Facility under contract No. DE-AC02-06CH11357 and resources of the Oak Ridge Leadership Computing Facility under contract No. DE-AC05-00OR22725.

(8) Vassar, R.; Bennett, B. D.; BabuKhan, S.; Kahn, S.; Mendiaz, E. A.; Denis, P.; Teplow, D. B.; Ross, S.; Amarante, P.; Loeloff, R. et al. β-Secretase Cleavage of Alzheimer’s Amyloid Precursor Protein by the Transmembrane Aspartic Protease BACE. Science 1999, 286, 735–741.

Supporting Information Available: Movie S1: aggregation of an amylin fibril; Movie S2: aggregation of an Aβ fibril. This material is available free of charge via the Internet at http://pubs.acs.org/.

(9) Seubert, P.; Oltersdorf, T.; Lee, M. G.; Barbour, R.; Blomquist, C.; Davis, D. L.; Bryant, K.; Fritz, L. C.; Galasko, D.; Thal, L. J. et al. Secretion of β-Amyloid Precursor Protein Cleaved at the Amino

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Rao, K.; Durant-Archibold, A. A. AntiAmyloid Aggregation Activity of Novel Carotenoids: Implications for Alzheimer’s Drug Discovery. Clin. Interv. Aging 2017, 12, 815. (75) Doig, A. J.; del Castillo-Frias, M. P.; Berthoumieu, O.; Tarus, B.; NasicaLabouze, J.; Sterpone, F.; Nguyen, P. H.; Hooper, N. M.; Faller, P.; Derreumaux, P. Why Is Research on Amyloid-β Failing to Give New Drugs for Alzheimer’s Disease? ACS Chem. Neurosci. 2017, 8, 1435–1437.


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TOC Graphic Amylin Model Fibril aggregation

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Understanding the Twisted Structure of Amyloid Fibrils via Molecular

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