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Size-dependent Conformational Features of A# Protofilaments From Molecular Simulation Studies Prabir Khatua, Sudipta Kumar Sinha, and Sanjoy Bandyopadhyay J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.7b00407 • Publication Date (Web): 30 Aug 2017 Downloaded from http://pubs.acs.org on September 1, 2017

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Journal of Chemical Information and Modeling

Size-dependent Conformational Features of Aβ 17−42 Protofilaments From Molecular Simulation Studies Prabir Khatua,† Sudipta Kumar Sinha,‡ and Sanjoy Bandyopadhyay∗,† †Molecular Modeling Laboratory, Department of Chemistry, Indian Institute of Technology, Kharagpur - 721302, India ‡Department of Chemistry, Indian Institute of Technology Ropar, Ropar - 140001 ,India E-mail: [email protected]

Abstract Alzheimer’s disease is caused due to aggregation of amyloid beta (Aβ) peptide into soluble oligomers and insoluble fibrils in the brain. In this study, we have performed room temperature molecular dynamics simulations to probe the size-dependent conformational features and thermodynamic stabilities of five Aβ 17−42 protofilaments, namely, O5 (pentamer), O8 (octamer), O10 (decamer), O12 (dodecamer), and O14 (tetradecamer). Analysis of the free energy profiles of the aggregates showed that the higher order protofilaments (O10 , O12 and O14 ) undergo conformational transitions between two minimum energy states separated by small energy barriers, while the smaller aggregates (O5 and O8 ) remain in single deep minima surrounded by high barriers. Importantly, it is demonstrated that O10 is the crossover point for which the twisting of

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the protofilament is maximum, beyond which the monomers tend to rearrange them1 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

selves in an intermediate state and eventually transform into more stable conformations. Our results suggest that the addition of monomers along the axis of an existing protofilament with a critical size (O10 according to the present study) proceeds via an intermediate step with relatively less stable twisted structure that allows the additional monomers to bind and form stable larger protofilaments with minor rearrangements among themselves. More importantly, it is demonstrated that a combination of twist angle and end-to-end distance can be used as a suitable reaction coordinate to describe the growth mechanism of Aβ protofilaments in simulation studies.

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INTRODUCTION

Protein aggregation is closely associated with various neurodegenerative diseases, such as Alzheimer’s disease, Parkinson’s disease, Type II diabetes, Huntington’s disease, etc. 1,2 In general, such diseases are believed to be caused by the accumulation of β-sheet-rich structures termed as amyloid fibrils in the brain. Alzheimer’s disease (AD) noticed first by Alois Alzheimer in 1907 3 is the most common form of dementia affecting millions of people worldwide. The characteristic symptoms of AD include loss of memory and thinking power, change of behavioral pattern, etc. 4 Although there is no cure for this disease, but it is known that the extracellular accumulation of amyloid β or Aβ peptide into toxic soluble oligomers and insoluble fibrils in the brain is responsible for its pathology. 5–7 Aβ peptides with 39 to 43 residues are derived from proteolytic cleavage of the transmembrane amyloid precursor protein (APP) by β-and γ-secretases. 8,9 Aβ peptides produced by such cleavage are of different residue lengths since the protease γ-secretase can cleave APP at multiple sites (at the Cterminus of Aβ). However, the predominant components of fibrillar deposits in the brain of AD patients include Aβ peptides containing 40 and 42 amino acid residues (Aβ 40 and Aβ 42 ). It is known that Aβ 42 with two additional C-terminal residues exhibits greater propensity to form amyloid fibrils as compared to Aβ 40 , 9,10 though the later has significantly higher population in healthy individuals. 11 Understanding the driving forces and the mechanistic pathways of Aβ aggregation leading to the formation of insoluble fibrils have been an intense focus of research over the years. 12–15 Experimental data suggest that the formation of fibrils follows a nucleation-dependent polymerization mechanism that involves two distinct stages. 16–18 In the first stage, namely, the nucleation phase, completely unstructured or partially structured soluble monomers selfassociate to form fluid-like oligomers. This is the rate limiting step of amyloid formation, as it needs to overcome a high energy barrier and thus occurs slowly. Such fluid-like oligomers

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then transform into organized globular oligomers with β-sheet rich structures after attaining 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

a critical size. These are often termed as pre-fibrillar aggregates. 19,20 They are also known as protofilaments, as they remain in single-stranded filament conformations. The nucleation stage is followed by thermodynamically favorable elongation/growth phase, where the intermediate protofilaments with β-sheet structures are elongated by the addition of monomers at the filament end via dock and lock mechanism 21 to form elongated protofilaments and finally protofibrils. Such protofibrils constitute the precursor state and eventually assemble together to form mature fibrils that are insoluble. 19,20 It is known that the aggregation of Aβ peptides results in neuronal death and dementia. 22–25 However, how the aggregation of Aβ peptides leads to cell death is still a matter of debate. Soluble oligomers and mature fibrils have been characterized to be primarily responsible for neurotoxicity. Interestingly, a number of recent studies suggest the soluble oligomers to be more neurotoxic than the insoluble fibrils. 6,26–28 Hence, it is worthwhile to study the soluble Aβ oligomers that are considered as the potential targets for therapeutics, in addition to characterizing the insoluble mature fibrils. The characterization of Aβ oligomers is challenging as they often show fluid-like behavior. 29 However, several structures of Aβ oligomers in their β-sheet rich pre-fibrillar forms have been reported using nuclear magnetic resonance (NMR) spectroscopy. 30–34 In general, such pre-fibrillar aggregates consist of U-shaped (hairpin-like) monomer units. For example, L¨ uhrs et al 34 demonstrated the presence of β-strand-turn-β-strand motif in Aβ protofilaments using quenched hydrogen/deuterium exchange NMR spectroscopy. As the experimental characterizations of Aβ oligomers are often non-trivial, simulations have become increasingly important alternative tools to probe different aspects of Aβ assembly. A number of molecular dynamics (MD) simulation studies based on experimentally observed pre-fibrillar aggregates are reported in the literature. 35–38 In an important work, Bevan and co-workers 35 carried out regular MD simulations, as well as center-of-mass pulling and umbrella sampling studies 4


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to probe the stability of Aβ 17−42 protofilaments. They showed that the hydration around 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

Asp-23· · ·Lys-28 salt-bridge plays a vital role in stabilizing the protofilament. It was further demonstrated that the packing between Ile-32 and the aliphatic portion of Lys-28 side chain regulates the hydration level in the pre-fibrillar core and makes the salt-bridge rigid. On the other hand, a recent MD study showed that the Aβ 17−42 protofilament is primarily stabilized by non-polar interactions originating from the peptide backbone and the hydrophobic residues with long side chains, such as Phe, Val, Leu, Ile and Met. 38 In another study, Masman et al 39 probed the contributions of different structural elements of full-length Aβ peptide on the stability of trimeric and pentameric aggregates. Their results revealed that β-strand twist is a characteristic feature of Aβ aggregates which allows compact interdigitated packing of the side-chains of neighboring β-sheets. Most of the studies reported in the literature are based on characterizing the aggregation process of Aβ peptides. 40–42 Only limited attempts have been made to investigate the microscopic properties of aggregated globular Aβ oligomers or on-pathway protofilaments as a function of their size or aggregation number. In an important recent work, Miller et al 43 carried out MD simulations to study the polymorphism of Aβ 17−42 oligomers. They demonstrated that the parallel orientations of the oligomers are more stable than the antiparallel ones. It is suggested that the U-turn plays an important role in determining the stability and conformational polymorphism of such aggregates. In contrast, antiparallel organizations of Aβ aggregates formed by shorter peptides, such as Aβ 16−22 , Aβ 34−42 are known to be more stable. 44 In an important work, Stich and Horn 45 investigated conformational stabilities of Aβ monomer to pentamer from MD simulations. They initiated the simulations of these oligomers in fibril-bound conformations and observed that from trimer onward the aggregates tend to preserve the mature fibril-like conformation. Based on the observation, they proposed that the fibril-like conformation of trimer to pentamer can act as a good nucleation site for further elongation. This study was further extended by Kahler et al, 46 5



who carried out MD simulations of fibril-like Aβ protofilaments and their laterally associated 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

pairs of different sizes, ranging from tetramer to 48-mer. It was demonstrated that small oligomers favor the protofilament topology, while large oligomers exhibit preference to form protofilament pair topology. Since, no experimental evidence is available till date on sizedependent behavior of on-pathway Aβ pre-fibrillar aggregates, we have verified our findings with the simulation studies of Kahler et al. 45,46 In this work, we have carried out MD simulations in an attempt to probe the size dependent intermolecular interactions and correlated conformational features of on-pathway Aβ 17−42 pre-fibrillar aggregates or protofilaments. Thermodynamic stabilities of different conformational states of the protofilaments are compared. We have considered the protofilaments with Aβ 17−42 fragment of the peptide in the simulations, as the first 16 resideus at the N-terminal end of the full-length Aβ 42 peptide are in general disordered in nature and are believed not to play any significant role in amyloid formation. 34 The amino acid sequence of the peptide Aβ 17−42 (in one letter code) is L(17)VFFAEDVGSNKGAIIGLMVGGVVIA(42), with Leu(17) and Ala(42) being the N- and C-terminal residues, respectively. The peptide secondary structures in the aggregated form consist of the N-terminal segment or NTS (Leu17 to Asn-27) and the C-terminal segment or CTS (Ile-31 to Ala-42) linked by the central turn region (Lys-28 to Ala-30). The rest of the article has been organized as follows. In Section 2, we describe the theoretical methods and the procedure followed to set up the systems, and the simulation protocols employed. The results obtained from the calculations are presented and discussed in Section 3. Finally, the important findings from our study and conclusions reached therefrom are highlighted in Section 4.

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2.1

METHODOLOGY SYSTEM SETUP AND SIMULATION DETAILS

We have used the NAMD code 47 to carry out the MD simulations of aggregated Aβ 17−42 (henceforth will be denoted only as Aβ) protofilaments of different sizes, namely, pentamer (O5 ), octamer (O8 ), decamer (O10 ), dodecamer (O12 ), and tetradecamer (O14 ), in aqueous solutions at room temperature (300K). The initial structures for all the systems were obtained from the NMR spectroscopic data on pentameric Aβ protofilament (model 10 of PDB entry 2BEG). 34 The coordinates of the first 16 N-terminal residues in this model were missing as those are disordered without a unique stable conformation. Therefore, instead of the full-length Aβ 42 peptide, most of the simulation studies consider the truncated Aβ protofilament, mainly, Aβ17−42 . 35,37,38 Furthermore, many experimental and theoretical studies have corroborated that Aβ17−42 protofilament is primarily responsible for the stability of the mature fibril, and thus it serves as a suitable model for Aβ protofilament. 35,48–50 One recent MD simulation study showed that the N-terminal residues marginally affect the structure and dynamics of the remaining residues. 51 Following an earlier report, 52 the higher order pre-fibrillar aggregates were generated from the pentameric structure by placing required number of new hairpins along the z-axis with an inter-monomeric distance of 4.8 ˚ A where the central chain in model 10 of PDB 2BEG was considered as the base unit of the hairpin. The two terminal residues Leu-17 and Ala-42 of each of the peptide monomers were taken as standard ammonium and carboxylate forms, respectively. Similar approach has been followed in earlier simulation studies. 53 After adding the hydrogen atoms, the individual protofilaments were immersed in orthorhombic cells of appropriate dimensions containing equilibrated water molecules. The minimum distance of the solvated protofilaments to the edges of the water boxes was at least 18 ˚ A. Unfavorable protein-water contacts were avoided in all cases by carefully removing the water molecules that were found close to the peptides 7



(within a distance of 2 ˚ A). To avoid any ambiguity, the water molecules found within the 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

protofilament cores were also removed. 5, 8, 10, 12, and 14 Na+ ions were then added to neutralize the overall charges of the systems (O5 to O14 ). The initial cell dimensions and the numbers of water molecules present in different systems are listed in Table 1. The simulation systems containing the Aβ protofilaments were first minimized using the conjugate-gradient energy minimization method as implemented in NAMD. 47 The temperature of each system was then gradually increased to 300 K within a short MD run of 100 picoseconds (ps) under isothermal-isobaric ensemble (NPT) conditions at a constant pressure of 1 atm. The systems were then equilibrated for 5 nanoseconds (ns) each at 300 K under NPT ensemble conditions with positional constraints on the Aβ aggregates. This was followed by another 5 ns of NPT simulation for O5 without constraining the protofilament. To obtain more stable equilibrated configurations of the higher order protofilaments (O8 onward), this step of unconstrained NPT simulation was extended upto ∼50 ns for each case. During this period, the system temperatures were controlled by using the Langevin dynamics method with friction constant 1 ps−1 , and the pressures were controlled by the Nosé-Hoover Langevin piston method, 54 with isotropic fluctuations of the cell volumes to attain appropriate densities. At this stage, the simulation cell volumes attained steady values with dimensions as listed in Table 1. The volume of each cell was then kept fixed and the simulation conditions were changed from constant pressure and tempreature (NPT) to that of constant volume and temperature (NVT). For each system, the NVT equilibration run was continued further at 300 K for another 5 ns, followed by a long NVT production run of 110 ns duration. All the simulations were carried out with an integration time step of 1 femtosecond (fs), and the trajectories were stored with a time resolution of 400 fs for subsequent analyses. All bonds involving the hydrogen atoms were constrained by the SHAKE algorithm. 55 The minimum image convention 56 was employed to calculate the short-range Lennard-Jones inter8


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actions with a spherical cutoff distance of 12 ˚ A and a switch distance of 10 ˚ A. The long-range 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

electrostatic interactions were calculated by using the particle-mesh Ewald (PME) method. 57 We have employed the all-atom CHARMM22 force field with CMAP corrections for the peptides, 58,59 while the mTIP3P 60 model (modified version of TIP3P 61 ) that is consistent with the chosen protein force field was used for water. It may be noted that the average values of the properties of the protofilaments are calculated over last 100 ns of the equilibrated trajectories.

2.2

Property Based Free Energy Calculation

Free energy contour profile has been constructed by calculating the population based free energy as a function of two reaction coordinates, λ1 and λ2 , defined as

∆G(λ1 , λ2 ) = −kB T [ln ρ(λ1 , λ2 ) − ln ρmax ]

(1)

where, kB and T are the Boltzmann’s constant and temperature, respectively. ρ is an estimate of the probability density function obtained from a histogram of the data, while ρmax represents the maximum of the density. This term is subtracted to ensure that ∆G = 0 for the lowest free energy minimum.

2.3

Binding Free Energy Calculation

Binding free energy in this study has been calculated using the Molecular Mechanics Generalised Born Surface Area (MMGBSA) method. 62–65 According to this method, 63 the binding free energy (∆Gbind ) between a ligand and a receptor to form a complex can be written as

∆Gbind = h∆GM M i + h∆Gsol i − T h∆Si

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(2)


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where, ∆GM M is the molecular mechanics contribution that involves the interaction between 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

the ligand and the receptor, ∆Gsol is the solvation free energy, and T ∆S corresponds to the entropic contribution. ∆GM M is the sum of the contributions originating from the intermolecular electrostatic term (∆Gelec ), the van der Waals term (∆Gvdw ), and the internal energy term (∆Gint ). Due to the use of ‘same trajectory method’ in the calculation, the contribution of ∆Gint is zero. 66 Therefore, ∆GM M can be written as

∆GM M = ∆Gelec + ∆Gvdw

(3)

Similarly, the solvation free energy (∆Gsol ) has been divided into the electrostatic and nonpolar solvation energy components (∆GGB and ∆Gnps ) as

∆Gsol = ∆GGB + ∆Gnps

(4)

The electrostatic solvation free energy, ∆GGB , has been calculated using the generalised Born (GB) method. 67 On the other hand, the nonpolar solvation free energy (∆Gnps ) is calculated as a function of the solvent accessible surface area (SASA), given by 68,69

∆Gnps = γ × SASA + b

(5)

˚−2 and 0.0, respectively. 70 We have Here, the constants γ and b are set to 0.005 kcal mol−1 A calculated entropies due to translational, rotational, and vibrational modes by our in house developed codes. Entropy contribution of the binding free energy (T ∆S) can be written as

T ∆S = T ∆Strans + T ∆Srot + T ∆Svib

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(6)

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where, Strans , Srot , and Svib are the contributions from translational, rotational, and vibra1 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

tional motions of the tagged molecule, respectively. Translational and rotational entropies are estimated using Gaussian probability distribution as S trans = R ln

S rot

"

(2πe)3/2 = R ln σs

"µ

µ

4π 2 e2 M kB T h2

2πekB T h2

¶3/2

¶3/2

σx σy σz

#

(7)

# (Ia Ib Ic )1/2 σφ σψ σθ sin θ¯

(8)

where, σx , σy and σz are calculated by diagonalizing the covariance matrix of the center-ofmass motion. M and h denote the mass of the molecule and Planck’s constant, respectively. Ia , Ib , and Ic are the principal components of moment of inertia which are obtained by diagonalizing the moment of inertia tensor. σφ , σψ , and σθ are calculated by diagonalizing the covariance matrix of Euler’s angles, where φ, ψ, and θ are the three Euler’s angles. σs represents the rotational symmetry of the molecule. We have used Schlitter’s method 71 to compute the vibrational entropy. According to this method, vibrational entropy can be written as S

vib

kB T e2 1/2 1 M σM1/2 ] < S = kB ln det[1 + 2 2 ~

(9)

where, e is the Euler’s number, M is the 3N dimensional diagonal matrix containing N atomic masses of the solute, σ is the covariance matrix of atom positional fluctuations, and ~ is the Planck’s constant divided by 2π. The inequality in the equation arises as the entropy (S) obtained by Schlitter’s approach is an upper bound to the true absolute entropy (S vib ) of the molecule. 71 Further details of the entropy calculation are reported in earlier work. 72,73 Following the above discussion, we can rewrite eq. 2 for the total binding free energy as

∆Gbind = h∆Gnonpolar i + h∆GGB,elec i − T h∆Si

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(10)


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Here ∆Gnonpolar and ∆GGB,elec correspond to the contributions originating from nonpolar 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

and electrostatic interactions, respectively, which are given by

∆Gnonpolar = ∆Gvdw + ∆Gnps

(11)

∆GGB,elec = ∆GGB + ∆Gelec

(12)

and

3 3.1

RESULTS AND DISCUSSION Conformational Features

Several configurations of the Aβ aggregates in their pre-fibrillar forms as obtained from our simulations at different time intervals are shown in Figure 1. For comparison, the corresponding initial structures are also displayed. It is apparent from the figure that though the individual monomers exhibit significant flexibility in the aggregated forms, but their hairpin-like conformations are largely retained within the simulation time scale in most cases. Interestingly, the figure reveals that the CTS of the monomers in the protofilaments is more flexible and disordered than the NTS. This is found to be true with a varying degree for all the protofilaments studied. It may be noted that such distorted CTS region in Aβ protofilaments has been reported earlier. 35,39,48 Here, we observe that the NTS of the monomers except for those that are present at the two ends of the protofilaments largely retain their β-strand conformation. Such stable β-strands at the NTS as observed in our study is in accordance with experimental results. 29,74,75 On the other hand, greater disorder at the CTS of the individual peptides has been found to be associated with partial breaking of the β-strands into loops. Such transition leads to the formation of a flexible bent conformation centered around Gly-37 and Gly-38 residues in the CTS. The fact that the formation of such 12


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bent loop in the CTS occurs even for the central monomers in different aggregates as evident 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

from the figure is an important observation. We believe that formation of such bent conformation is likely to enhance side-chain contacts among the CTS of the adjacent monomers, thereby stabilizing the monomeric associations in the on-pathway pre-fibrillar aggregates. It may be noted that the aggregation mechanism of amyloidogenic proteins, such as Aβ is believed to proceed either via elongation or via lateral association. 15 It is suggested that the elongated protofilaments are formed by stacking of monomers one upon another on a preformed aggregate following the dock and lock mechanism. 21 On increased concentration, such protofilaments exhibit propensity to associate laterally to form protofilament pair. Lateral association of aggregated protofilaments requires sufficient flexibility at the association sites. Greater flexibility of the CTS of the Aβ peptide in different pre-fibrillar structures as observed in our study indicates that the lateral association of preformed protofilaments to form protofilament pair is likely to be favored at the C-terminal ends of the aggregates. On the other hand, the relatively rigid NTS is believed to act as the recognition site for the incoming Aβ monomers during the elongation process. 29,74,75 We will analyse the differential flexibility of the CTS and the NTS of the Aβ peptides in the pre-fibrillar aggregates in a more quantitative manner again later. To explore further the conformational flexibility of the Aβ monomers and their deviations from the initial bent hairpin-like structures in different protofilaments, we have computed the root mean square deviations (RMSD) of the simulated configurations with respect to the corresponding initial structures. RMSD data can provide valuable information on local conformational motions of the monomers, which in turn can help to identify possible transitions among different conformational substates. For each protofilament, the calculations are carried out by averaging over all the non-hydrogen atoms of the individual peptide monomers along the entire simulated trajectory. The time evolutions of the data for different aggregates are shown in Figure 2. Here, it may be noted that the high RMSD values 13



do not originate simply from structural unfolding of the peptides, rather from a systematic 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

distortion of the protofilaments. Such distortion is found to be enhanced with increase of the size of the aggregates. This agrees well with an earlier study by Kahler et al. 46 We have also calculated separately the RMSDs of the NTS, CTS and the central turn region of the peptides in different protofilaments, as shown in the figure. The calculated average RMSD values (hRM SDi) are listed in Table 2. Compared to the NTS and the turn segment, significantly greater conformational deviations of the CTS of the Aβ monomers in different protofilaments are evident from the data. In general, the CTS hRM SDi values are found to be 1.3 to 2.3 times more than that of the NTS and the turn segments. We notice that among the five Aβ pre-fibrillar aggregates studied, the monomer units present in O10 exhibit maximum deviations from their initial bent conformations. Importantly, two small but noticeable jumps in the RMSDs, first for the CTS followed by that for the turn region within 40 to 60 ns of the simulation have been noticed for O10 . This suggests that the greater structural disorder of O10 as compared to the other aggregates as observed in the present study originates from cooperative conformational transitions of the CTS and the turn region of the individual monomers. The terminal Aβ peptide monomers in a particular Aβ protofilament are expected to behave differently as compared to the central monomer, as they are bound with only one adjacent peptide unlike the central one which is bound with two adjacent peptides. To examine such differential behavior, if any, we have calculated RMSDs for two terminal Aβ peptide monomers (TREM-1 and TERM-2) in the Aβ protofilaments. We have also computed RMSD for the central monomer (CENTER) for comparison. The time evolutions of RMSD are depicted in Figure S1 in the Supporting Information, while the corresponding average RMSD values over the last 100 ns equilibrated trajectories are listed in Table S1. It is clear from the results that in general, TERM-1 exhibits greater RMSD as compared to TERM-2. Such nonuniform conformational fluctuations of the two terminal peptides with TERM-2 14


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being relatively less flexible than TERM-1 is an important observation, as it explains the 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

unidirectionality of fibril extension. According to a recent study, 76 a fibril generally extends from that end which is relatively less flexible. Thus, the present study demonstrates that the fibrillar growth is likely to occur at the TERM-2 end. TERM-1 hRM SDi values are found to be 1.5 to 4 times higher than that of the central monomers in different protofilaments. Such differential RMSDs between the terminal and the central Aβ monomers in a particular protofilament is consistent with a recent MD simulation study. 76 Importantly, hRM SDi values for O10 are found to be always higher than that of the other protofilaments. This is particularly noticeable for TERM-2 whose hRM SDi values are two times higher than that of the other protofilaments. This illustrates that relatively greater flexibilities of the individual peptide monomers in O10 result in greater disorder for the whole protofilament (see Figure 2). Another important parameter that can be used to probe the size and shape fluctuations of flexible polymers or biomolecules, such as that of the Aβ peptide is the radius of gyration, RG . The time evolutions of RG averaged over the Aβ monomer units present in different protofilaments are shown in Figure 3(a). In Table 3, we have listed the corresponding simulated average RG (hRG i) values for all the systems. It is apparent from the figure that except for O10 , the individual peptide monomers present in other protofilaments (O5 , O8 , and O14 ) exhibit propensity to attain to some extent more compact conformations with lowering of RG values within the simulation time scale, while those present in O12 maintain more or less similar RG values as that of the initial conformation. On the other hand, noticeable increase in the RG value around 40 ns for the monomers in O10 indicates their transformation from relatively compact to fluctuating expanded forms. Such nonuniform effect of formation of O10 as compared to the other protofilaments on the degree of compactness of the individual peptide monomers is consistent with greater structural distortions of the former as discussed earlier (see Figures 1 and 2). It is clear that the propensity of the Aβ monomers to at15



tain relatively expanded conformations leads to the structural distortion of O10 . We notice 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

that compared to the RG value of 13.21 ˚ A for the initial conformation of an Aβ peptide monomer in a protofilament, the simulated hRG i values vary within ±7 % (see Table 3). The variations of the peptide end-to-end distance (RL ) averaged over the Aβ monomers in different protofilaments are depicted in Figure 3(b). In our calculation, RL is defined as the average distance between the Cα atoms of the two terminal residues of each of the monomers in the aggregate. Significant flexibility of the peptide monomers at the two termini in the protofilaments is evident from the figure. It can be seen that among all the protofilaments, increased structural distortion of O10 leads to relatively more extended monomer conformations with increased end-to-end distance. The time-averaged RL (hRL i) values as obtained from the simulated trajectories of different systems are listed in Table 3. Compared to the A for the initial bent conformation of an individual peptide monomer in a RL value of 12.4 ˚ protofilament, significant changes in simulated hRL i values are evident from the data. To further analyse the structural distortions of the simulated protofilaments in a more quantitative manner, we have monitored their twist angles. Twist angle (θ) of a particular protofilament formed by N number of Aβ monomers is defined as the torsional angle between the second and the (N -1)-th or the penultimate monomers. 46,49 Here, we have separately calculated the twist angles involving the NTS and the CTS in the aggregated forms. The twist angle involving the NTS is calculated by measuring the torsional angles formed by the Cα atoms of Val-18 and Val-24 of the two tagged monomers, while that involving the CTS is obtained from the torsional angles formed by the Cα atoms of Ile-31 and Val-36. Time evolutions of twist angles thus calculated for the protofilaments are shown in Figure 4. Note that the deviation of θ from 0◦ corresponds to distorted protofilament structures. The results obtained from our analysis clearly show twisted arrangements of both the β-strands in the aggregated forms. However, a closer examination of the data reveals nonuniform twists of the pre-fibrillar surfaces formed by the NTS and the CTS of the Aβ monomers. Compared to 16


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the NTS, the CTS exhibits larger twisting and hence form a more disordered interface. This 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

is particularly evident for O10 , which is consistent with our earlier discussion and also agrees well with recent experimental reports. 33,34 Interestingly, a sharp change in the twist angle of the CTS for O10 has been observed around 40 ns. This shows that the structural deviation of O10 as revealed in Figure 2 originates from the twisting of the corresponding CTS. We have calculated the average twist angles of the two strands in each of the protofilaments, which are listed in Table 4. Increased twisting of the protofilaments with the size particularly beyond O10 is clearly evident from the data. It may be noted at this stage that Aβ being an intrinsically disordered protein, simulated properties of its aggregated protofilaments may depend on the starting configurations of the systems. To verify such effect, if any, we have performed a second set of independent MD simulations for each of the systems following the same protocols as described in Section 2.1 with different initial velocity distributions. Structural parameters of the protofilaments as discussed above, such as RMSD, RG , RL , etc, have been calculated with the additional second set of trajectories. The calculations reveal that the results obtained from the new trajectories vary within 3-10% of the data presented earlier. This indicates that the overall structural characteristics of the Aβ protofilaments as observed in the present study are largely independent of their initial configurations.

3.2

Property-Based Free Energy

In this section, we calculate property-based free energy contours of the Aβ protofilaments. For this, we have used the peptide end-to-end distance (RL ) and the twist angle (θ) of the CTS as the two order parameters (see eq. 1). Construction of such free energy contour is expected to help identifying conformations corresponding to the local and the global minima, and thus determining the minimum energy pathways between those and the associated free energy barriers. Figure 5 shows the free energy contours corresponding to the five 17



Aβ protofilaments as obtained from the original set of trajectories. We notice that O10 , 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

O12 and O14 exhibit two different significantly populated states as evident from the two minima in each case. This is particularly true for O10 . On the other hand, only one minimum each has been observed for O5 and O8 . To identify the most preferred pathway for any conformational transition, we have constructed the corresponding minimum free energy profile from the contour plot. The algorithm used for the construction of the minimum free energy profiles is described in the Supporting Information. The results are displayed in Figure 6(a). It is clear that the transitions between two minimum energy states for the three higher order protofilaments (O10 , O12 and O14 ) occur due to rather small barrier heights (within 1 kcal mol−1 ) separating those states. However, no such transition has been observed for the smaller protofilaments (O5 and O8 ) within the time scale of our study. This indicates that the conformations of the relatively smaller pre-fibrillar aggregates are present in rather deep minima separated from other minima by high energy barriers. To probe the authenticity of the results presented above with respect to modified initial configurations of the protofilaments, we have carried out same calculation with the second set of trajectories, and the results are shown in Figure 6(b). Consistent with Figure 6(a), the results obtained from the new trajectories also reveal that the three higher order protofilaments (O10 , O12 , and O14 ) exhibit two minimum energy states separated by low transition barriers (within ∼2 kcal mol−1 ), while the relatively smaller protofilaments (O5 and O8 ) are again trapped within a single deep minimum. This demonstrates that different initial configurations of the Aβ protofilaments have minimum influence on their free energy profiles. As a reference, we have marked the conformational states corresponding to the different extremum points along the free energy profiles of the protofilaments in both cases by I to V. In Section 3.3, we will explore the origin behind such non-uniform barrier heights among the Aβ protofilaments of different sizes. We note that it is necessary to probe whether the two states observed in the free energy 18


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contours (Figure 5) of the higher order protofilaments (O10 , O12 , and O14 ) represent true 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

states uniformly distributed along the simulated trajectories. For that, we have monitored the time evolutions of the two-dimensional free energy contours of O10 , O12 , and O14 , which are shown in Figure S2 of the Supporting Information. In particular, this is done by plotting the peptide end-to-end distance (RL ) along the x-axis, the CTS twist angle (θ) along the y-axis, and the simulation step number along the z-axis. Here, it may be noted that such time evolution of the contour can be used to show the distribution of configurations of a protofilament along the simulated trajectory that constitutes a particular state. It can be seen that the two states corresponding to the minima (II and IV) for O10 appear in two distinct time domains. This suggests that once state II transforms into state IV, it does not revert back to the former. On the other hand, it is apparent that the configuration distributions of the two minimum free energy states (II and IV) for O12 and O14 are rather uniform over the corresponding trajectories. This is particularly true for the most stable states (state II for O12 and state IV for O14 ). Therefore, the results presented in this study clearly demonstrate that the two minimum free energy states observed in the contour plots of higher order protofilaments are indeed true states comprising of configurations from all over the trajectories, this is being particularly true for O12 and O14 .

3.3

Binding Free Energy

In this section, we attempt to probe the origin behind the non-uniform free energy barriers between different conformational states of the Aβ protofilaments, as discussed in the previous section. For that, we have calculated the binding free energy (∆Gbind ) of the aggregate formation using the MMGBSA method (see Section 2.3), 62–65 as implemented in AMBER14. 70,77 As the protofilaments studied here contain different numbers of peptide monomers, we consider a trimeric aggregate as the unit complex structure with the central monomer defined as the receptor and the two adjacent monomers as ligands. In other words, our calculation 19



provides the free energy associated with the binding of two adjacent monomers to the central 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

one. Thus, the binding free energies have been calculated by averaging over 3, 6, 8, 10, and 12 such trimeric units present in O5 , O8 , O10 , O12 , and O14 , respectively. The calculations are carried out for the selected conformational states around the extremum points along the free energy profiles of different protofilaments (marked I to V in Figure 6(a)). As a reference, the total number of trimeric units considered for the calculation of the binding free energy along the free energy profiles of different protofilaments in each of the states is listed in Table S2 of the Supporting Information. In particular, conformations corresponding to three states (I, II and III) have been considered for O5 and O8 . Here, II corresponds to the most stable state, whereas I and III represent the least stable ones. On the other hand, conformations corresponding to the five different states (I to V) have been considered for the larger protofilaments (O10 , O12 , and O14 ). Out of these five states, II and IV represent the most stable conformations, while I and V correspond to the conformations that are least stable, and III represents the intermediate that populates the transition state along the minimum energy pathway between the states II and IV. One representative configuration for each of these states for a lower order protofilament (O5 ) and a higher order one (O10 ) is shown in Figure 7. We have calculated the ∆Gbind values for the conformations corresponding to these states as marked in Figure 6(a) for different protofilaments. The results are depicted in Figure 8(a). Additionally, in Table 5 we have listed the ∆Gbind values and their different contributing components for the selected states. It is apparent from Figure 8(a) that the states representing the minima in the free energy profiles (states II for O5 and O8 , and states II and IV for O10 , O12 , and O14 ) have negative ∆Gbind values, whereas positive binding free energies have been obtained for the conformations corresponding to the maxima (states I and III for O5 and O8 , and states I and V for O10 , O12 , and O14 ). It may be noted that the entropy contribution due to solvent is not explicitly calculated in MMGBSA method. Thus, we believe that the positive binding free energies as obtained for some of the selected states of 20


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the protofilaments originate from non-inclusion of the entropy gained by the solvent around 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

the peptides on aggregation in the MMGBSA method. However, the primary objective of the present study has been to compare the relative free energies of binding of Aβ peptides to protofilaments of different sizes to predict the amyloid growth mechanism, rather than to calculate the absolute free energy values. Therefore, the error involved in the calculation based on the MMGBSA method is expected to be comparable for all such states and thus cancel out in the final outcome. Importantly, Figure 8(a) reveals that the ∆Gbind values for the most populated states in different pre-fibrillar aggregates, such as state II in O5 , O8 and O12 , and state IV in O10 and O14 in general decrease with the size of the protofilament, thereby increasing their stability. However, interestingly, significant anomaly in ∆Gbind values has been observed for different conformational states of O10 . In a recent study, Kahler et al 46 demonstrated that elongated large protofilaments become energetically unstable after reaching a critical size and tend to break into shorter protofilaments. Such shorter protofilaments exhibit propensity to associate laterally to form protofilament pairs, which eventually grow into mature fibrils. Dodecamer has been identified as the limiting size beyond which protofilament pair topology becomes energetically favorable over elongated protofilament. In fact, it is shown that a protofilament consisting of 10 Aβ monomers (O10 ) has nearly similar binding energy as that of a pair of Aβ pentamers (O5 ). Thus, consistent with the earlier study, 46 our result indicates O10 as the crossover point at which the protofilament tends to attain a more twisted structure. Importantly, it is evident from Figure 8(a) that for relatively larger protofilaments (O10 , O12 and O14 ), conformational states with relatively higher binding free energies (state IV for O12 , and state II for O10 and O14 ) can transform to more stable states with lower free energies (state II for O12 , and state IV for O10 and O14 ) by crossing the respective transition states III. Note that the ∆Gbind for the intermediate transition state III gradually decreases with increase in the size of the protofilament, and it attains a negative value of around -58 kcal mol−1 for O14 (see Table 5). This indicates no21



ticeable contribution of the twisted conformations comprising state III in the conformational 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

distribution of relatively larger protofilaments. Once again, to verify the dependence of the results presented above on the initial configurations of the protofilaments, if any, we have computed the binding free energies (∆Gbind ) for the selected conformational states around the extremum points (as marked in Figure 6(b)) along the free energy profiles of the protofilaments, as obtained from the second set of trajectories. The results are shown in Figure 8(b). The relative ∆Gbind values for the selected states are congruous with that shown in Figure 8(a). In particular, consistent with Figure 8(a), the ∆Gbind values for the most populated states have been found to decrease with the increase of the size of the protofilaments, except for O10 , which again serves as the cross-over point. The ∆Gbind values and their different components for the selected states for the second set of trajectories are tabulated in Table S3 in the Supporting Information. It can be seen that though the individual components of ∆Gbind (in particular, ∆Gelec and ∆GGB ) for the second set of trajectories often vary significantly with respect to the corresponding values obtained from the first set (see Table 5), but the overall ∆Gbind values between the two sets of trajectories vary within ±10% of each other. Thus, the present results illustrate that individual electrostatic components of ∆Gbind are noticeably sensitive to the subtle conformational changes of the protofilaments, however, their summations virtually remain independent of their initial configurations. Such differential influence of protofilament configurations on the overall ∆Gbind values and that of the corresponding electrostatic components as observed in the present study is consistent with a recent MD simulation study by Hansmann and co-workers, 78 where three sets of independent simulations were carried out to probe the stability of the Osaka mutant and the wild-type Aβ fibril. As discussed earlier, the individual peptide monomers in a relatively larger protofilament (O10 onward) tend to rearrange themselves by optimum twisting in the intermediate state III, which eventually leads to further stable conformation (either state II or state IV). On 22


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the other hand, it is observed that within the time scale of the simulations, Aβ monomers 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

present in smaller protofilaments (O5 and O8 ) do not undergo any twisting to search for more stable conformational states. In other words, due to smaller size, O5 and O8 restrict the movement of the end residues of the monomers to prevent twisting. Based on this finding, we propose a probable growth mechanism of elongated Aβ protofilaments: addition of the monomers along the filament axis of an existing aggregate with a critical size (O10 according to the present study) proceeds via an intermediate step with relatively less stable twisted structure. Such twisting allows the additional monomers to bind and eventually form stable larger protofilaments with minor rearrangements among themselves. In Figure 9 we show the contributions of different components of ∆Gbind (see eq. 2) for the selected states I to V (as marked in Figure 6(a)). To probe the effect of initial configurations of the protofilaments on the ∆Gbind components, the calculations are repeated with the second set of trajectories, as depicted in Figure S3 of the Supporting Information. It is apparent from Figure 9 that while the inter-molecular interaction energy (∆GM M ) makes favorable contribution to ∆Gbind , the corresponding entropy contribution (T ∆S) becomes unfavorable. Besides, we find that in addition to the peptide entropy component, the solvation free energy (∆Gsol ) also makes sufficiently unfavorable contribution (except for O12 ) to the overall ∆Gbind for a protofilament. Interestingly, comparison of the results shown in Figure 9 with that of Figure 8(a) reveals strong influence of the entropic term (T ∆S) on the overall binding free energy (∆Gbind ) of the selected conformational states of the Aβ pre-fibrillar aggregates, as evident from the clear anticorrelation that exists between them. Comparison of the results presented in Figure S3 of the Supporting Information with that of Figure 8(b) clearly demonstrates that the influence of entropy on ∆Gbind is largely independent of the starting configurations of the protofilaments. Note that unlike entropy, such systematic correlation has not been observed between ∆GM M and ∆Gbind . It is clear that the relatively lower entropic costs for the conformational states II and IV as evident 23



from the figures have largely been compensated by the corresponding favorable enthalpic 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

contributions, thereby leading to their reduced ∆Gbind values, and hence greater stability. Reverse is the case for the less stable states of the protofilaments (I, III and V), for which the enthalpy contributions are not sufficient enough to overcome the corresponding large entropic penalties. The results presented here show that irrespective of the starting configurations, entropy plays a very crucial role in determining the thermodynamic stability of different conformational states of the Aβ pre-fibrillar aggregates. A closer look at the contributions originating from different components of ∆Gbind (see Table 5 and Table S3 in the Supporting Information) further reveals interesting behavior. It is found that both the nonpolar van der Waals interaction (∆Gvdw ) and the electrostatic interaction (∆Gelec ) involving the Aβ peptide monomers in the pre-fibrillar aggregates make favorable contributions to ∆GM M , the effect of ∆Gvdw being more significant in most cases. Surprisingly, the contributions originating from the polar and nonpolar components of solvation free energy (∆GGB and ∆Gnps ) provide a contrasting picture. We notice that the favorable contributions of the nonpolar term ∆Gnps are more than compensated by the unfavorable polar solvation component ∆GGB in most cases, thereby leading to a definite weakening effect of solvation toward the overall binding free energy (∆Gbind ) of the aggregated protofilaments. Additionally, as already discussed, favorable inter-peptide interactions (∆GM M ) are found to be sufficient to overcome the relatively lower entropic costs (i.e., T ∆S varying within -80 to -130 kcal mol−1 ) of a few particular conformational states (II and IV) of the protofilaments, thereby making them thermodynamically stable. However, large entropic penalties (T ∆S varying within -200 to -350 kcal mol−1 ) associated with the formation of states I, III and V of different protofilaments dominate over the gain in the corresponding ∆GM M values, thereby rendering them unstable with large positive ∆Gbind values. So far, we have discussed that the higher order protofilaments exhibit two minimum energy conformations which can transform between each other due to low free energy barrier 24


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between them, while the lower order protofilaments are trapped within single minima sepa1 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

rated from the rest of the conformational space by high free energy barrier. Such inference has been made based on the property-based free energy contour constructed as a function of peptide end-to-end distance (RL ) and CTS twist angle (θ). To examine the sensitivity of this observation to the selection of reaction coordinates, we have calculated the distribution of binding free energies without the T ∆S term (denoted as ∆G′bind ), as shown in Figure 10. Note that we have not included T ∆S term in this calculation, as entropy being a correlated property cannot be computed independently for a single snapshot. It is evident from the figure that the lower order protofilaments (O5 and O8 ) exhibit one peak suggesting the presence of a single minimum. On the other hand, we observe three peaks for O10 and O12 . The peak with highest intensity corresponds to the most populated minimum energy structure, while the other two peaks with relatively lower intensities represent the intermediate and another minimum energy conformation (see Figure 6). In contrast to O10 and O12 , O14 exhibits only two peaks. It is apparent from the figure that the peak with higher intensity represents the most stable structure (state IV). The absence of third peak can be explained by the fact that ∆Gbind for the intermediate transition state III gradually decreases with the increase in the size of the protofilament, and it attains a negative value for O14 (see Figure 8). The single broad peak that is observed for this protofilament is in fact a superposition of the states II and III. Therefore, the present result ascertains that the presence of two minima for the higher order protofilaments (beyond O10 ) and only one minimum for the lower order ones is a general fact and is not biased to the selection of the reaction coordinates. It may be further noted that in this work we have presented results obtained from simulations of the protofilaments comprising of truncated Aβ peptides, where the two ends were kept in zwitterionic form. It is important to probe whether the charged state of the residue at the point of truncation (Leu-17) has any influence on the proposed growth mechanism. For that, we have further carried out two additional simulations by capping the N-terminal 25



residues, one with the lower order protofilament (O5 ) and the other with the higher order 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

protofilament (O12 ), following the same protocols as described in Section 2.1. Results obtained from preliminary analysis of these two trajectories are summarized in the Supporting Information. It is apparent from the results that the data presented in this article and the proposed amyloid growth mechanism are independent of whether the individual N-terminal residues of the peptides are present in the ionic form or in the capped form. In other words, the growth mechanism proposed here is expected to hold good for the full-length Aβ 42 aggregates.

4

CONCLUSIONS

In this article, we have presented results obtained from atomistic MD simulations of onpathway Aβ pre-fibrillar aggregates of different sizes in aqueous solutions. Efforts have been made to obtain a microscopic understanding of the conformational flexibility of the Aβ peptides and the interactions between them in the aggregated forms. In particular, structural distortions of the protofilaments and their thermodynamic stabilities have been investigated in order to predict their growth mechanism. Analysis of the free energy profiles revealed that the higher order Aβ protofilaments (O10 , O12 and O14 ) exist in two minimum energy conformational states with significant populations. Transitions between such minimum energy states occur due to small barrier heights (within 1 kcal mol−1 ) separating those. On the other hand, the smaller aggregates (O5 and O8 ) did not undergo any conformational transition within the simulation time scale, as they exist in single deep minima surrounded by high energy barriers. This has been found to be true irrespective of the initial configurations of the protofilaments. In general, it is found that the binding free energy of Aβ monomers to the most populated conformational state of an aggregated pre-fibril decreases with its size, thereby increasing its thermodynamic

26


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stability. This is true for all the protofilaments studied, except O10 . It is indicated from our 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

calculation that O10 is the crossover point at which the protofilament tends to attain a more twisted structure. Beyond O10 , the monomers tend to rearrange themselves by optimum twisting in an intermediate state, which eventually leads to transformation into more stable conformations. Based on the findings, we have proposed a possible growth mechanism of large Aβ protofilaments. According to this, addition of the monomers along the filament axis of an existing aggregate with a critical size (O10 according to the present study) proceeds via an intermediate step with relatively less stable twisted structure, that allows the additional monomers to bind and eventually form stable larger protofilaments with minor rearrangement among themselves. Importantly, the calculations revealed that a combination of the twist angle of CTS and the end-to-end distance of the peptide can be used as an appropriate reaction coordinate to describe the growth mechanism of Aβ protofilaments from simulation studies. We believe that the findings from this study have important implications for the development of viable medication for Alzheimer’s disease. Only a single drug may not be sufficient to combat this disease, since it is now known that structurally different small soluble oligomers, protofilaments and mature fibrils, all are responsible for the disease. 5–7 Hence, different set of drugs may be necessary to stop the disease in different individuals. Based on structurestability information, a large number of studies indicate that the C-terminal surface may be the promising target for drug design since it is believed to be primarily responsible for the stability. 35,39 Our results also specifically highlighted the role played by the CTS in governing the stability of the protofilaments. However, further studies are necessary to examine whether the CTS of the Aβ peptide can serve as a target for suitable drugs.

27



Acknowledgement 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

This study was supported by grants from the Department of Science and Technology (DST), Government of India, under the DST-FIST programme (SR/FST/CSII-011/2005). PK thanks University Grants Commission (UGC), Government of India for providing a scholarship (18-12/2011(ii)EU-V, dated 16/08/2012). We thank Dr. Neelanjana Sengupta for many useful discussions.

Supporting Information Available Supporting Texts: (1. Construction of the minimum energy profile; 2. Effect of charged state of N-terminus) Supporting Tables: (Table S1: Average values of RMSD for the two terminal and central peptide monomers of the Aβ protofilaments; Table S2: Total number of trimeric units considered for the calculation of binding free energies for the selected conformational states of the Aβ protofilaments; Table S3: Binding free energies and the corresponding components for the selected conformations of the protofilaments as obtained from the second set of independent simulations) Supporting Figures: (Figure S1: Time evolutions of the RMSDs of two terminal and central Aβ peptide monomers in different protofilaments; Figure S2: Time evolutions of the two-dimensional free energy contour plots based on the end-to-end distance and the CTS twist angle as obtained from the first set of simuated trajectories of three higher order protofilaments (O10 , O12 and O14 ); Figure S3: Contributions of different components of ∆Gbind as obtained from trajectories with modified initial configurations of the Aβ protofilaments; Figure S4: Free energy profiles along the minimum free energy pathways for the protofilaments with capped N-terminus) This material is available free of charge via the Internet at http://pubs.acs.org/. 28


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Table 1: Dimensions of the Simulation Cells at the Beginning and after the Equilibration Runs for Different Aβ Protofilaments. The Number of Water Molecules are also Listed.

protofilament O5 O8 O10 O12 O14

dimension (˚ A3 ) initial after equilibration 90 x 70 x 70 90 x 70 x 85 90 x 70 x 90 90 x 70 x 100 90 x 70 x 105

no. of water molecules 87.36 x 68.37 x 68.37 13178 87.48 x 68.46 x 82.73 15779 87.36 x 68.37 x 87.36 16475 87.49 x 68.47 x 96.99 17874 87.31 x 68.33 x 100.74 18489

Table 2: The Average Values of RMSD (hRM SDi) as Obtained for the Whole Peptide Monomers and Their Segments in Different Aβ Protofilaments. The Values in the Parentheses are the Standard Deviations.

protofilament whole O5 6.85 (0.31) O8 4.93 (0.16) O10 10.14 (1.79) O12 7.49 (0.21) O14 7.54 (0.56)

hRM SDi (˚ A) NTS turn 3.60 (0.20) 4.49 (0.58) 2.92 (0.11) 3.03 (0.18) 6.62 (0.40) 4.93 (0.86) 5.42 (0.14) 4.01 (0.20) 6.18 (0.86) 5.03 (0.56)

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CTS 8.33 (0.41) 6.31 (0.24) 10.32 (0.79) 7.62 (0.25) 7.67 (0.27)

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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


Table 3: The Average Values of Radius of Gyration (hRG i) and End-to-End Distance (hRL i) of the Aβ Peptides in Different Protofilaments. The Values in the Parentheses are the Standard Deviations.a protofilament O5 O8 O10 O12 O14 a

hRG i (˚ A) 12.26 (0.07) 12.52 (0.04) 14.26 (0.20) 13.36 (0.06) 12.72 (0.04)

hRL i (˚ A) 22.78 (0.51) 16.72 (0.55) 22.30 (1.94) 22.34 (0.74) 18.02 (0.32)

RL is defined as the average distance between the Cα atoms of Leu-17 and Ala-42 of each of the Aβ peptide monomers present in the protofilament.

Table 4: The Average Twist Angle (θ) Values for the NTS and the CTS of the Aβ Peptides in Different Protofilaments. The Values in the Parentheses are the Standard Deviations.a θ (◦ ) protofilament O5 O8 O10 O12 O14 a

NTS -21.85 (1.35) -12.51 (1.19) -53.15 (3.13) -83.96 (2.34) -43.04 (6.91)

CTS -40.94 (4.38) -7.97 (2.04) -118.09 (13.33) -62.35 (4.36) -66.56 (4.54)

The twist angle involving the NTS is calculated by measuring the torsional angles formed by the Cα atoms of Val-18 and Val-24 of the two tagged monomers, while that involving the CTS is obtained from the torsional angles formed by the Cα atoms of Ile-31 and Val-36.

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Table 5: Binding Free Energies and the Corresponding Components (in kcal mol−1 ) for the Selected Conformational States (See Figure 6 (a)) of the Aβ Protofilaments. The Values in the Parentheses are the Standard Deviations. protofilament

state I

O5

II III I

O8

II III I II

O10

III IV V I II

O12

III IV V I II

O14

III IV V

∆Gvdw -98.90 (7.74) -109.76 (1.91) -144.32 (3.76) -171.93 (0.61) -172.66 (0.13) -174.17 (0.50) -60.90 (8.51) -95.68 (2.05) -101.21 (2.81) -132.48 (0.63) -130.17 (3.05) -164.80 (0.55) -163.79 (0.13) -164.92 (0.34) -165.33 (0.25) -164.61 (0.64) -175.24 (0.51) -170.12 (0.17) -169.51 (0.25) -169.13 (0.12) -170.08 (0.69)

∆Gelec -7.44 (2.12) -15.22 (0.40) -26.14 (1.88) -51.27 (1.74) -38.98 (0.40) -34.83 (1.61) -75.55 (1.96) -71.70 (0.55) -59.84 (1.04) -41.30 (0.36) -31.79 (2.06) -29.40 (2.22) -27.23 (0.31) -23.58 (0.90) -20.55 (0.71) -18.95 (1.89) -76.57 (3.16) -86.66 (0.80) -92.73 (1.22) -89.41 (0.50) -81.28 (2.60)

∆GGB 34.10 (1.79) 38.43 (0.31) 45.92 (1.43) 69.21 (1.61) 55.98 (0.37) 49.83 (1.36) 85.49 (1.93) 78.23 (0.58) 64.98 (1.18) 43.22 (0.41) 35.88 (2.51) 31.16 (1.11) 24.24 (0.30) 20.08 (0.81) 18.25 (0.66) 17.25 (1.74) 80.10 (3.22) 84.73 (0.79) 89.17 (1.19) 82.33 (0.51) 76.88 (2.58)

∆Gnps -26.61 (0.09) -25.94 (0.02) -25.59 (0.10) -27.03 (0.07) -26.96 (0.01) -27.09 (0.06) -25.91 (0.11) -24.68 (0.03) -24.26 (0.07) -23.51 (0.03) -23.54 (0.18) -26.34 (0.08) -26.25 (0.02) -26.40 (0.04) -26.58 (0.03) -26.45 (0.07) -27.63 (0.08) -27.00 (0.03) -26.97 (0.04) -26.96 (0.02) -26.99 (0.12)

∆GM M -106.34 (8.64) -124.97 (2.03) -170.46 (4.40) -223.20 (1.77) -211.64 (0.43) -208.99 (1.68) -136.45 (9.48) -167.38 (2.24) -161.05 (3.13) -173.77 (0.73) -161.96 (4.15) -194.20 (1.37) -191.02 (0.33) -188.50 (0.88) -185.88 (0.66) -183.57 (1.82) -251.81 (2.95) -256.78 (0.75) -262.23 (1.14) -258.53 (0.49) -251.35 (2.62)

42


∆Gsol 7.50 (1.79) 12.49 (0.31) 20.33 (1.43) 42.18 (1.62) 29.02 (0.37) 22.74 (1.37) 59.58 (1.99) 53.55 (0.60) 40.72 (1.20) 19.71 (0.42) 12.34 (2.60) 4.82 (1.13) -2.01 (0.31) -6.32 (0.83) -8.33 (0.68) -9.20 (1.77) 52.47 (3.26) 57.73 (0.80) 62.20 (1.21) 55.38 (0.52) 49.88 (2.61)

T ∆S -306.72

∆Gbind 207.88

-102.83

-9.65

-309.10

158.97

-345.13

164.11

-88.96

-93.66

-332.01

145.76

-334.10

257.23

-103.02

-10.81

-198.42

78.09

-87.52

-66.54

-296.43

146.81

-324.55

135.17

-80.38

-112.65

-198.86

4.04

-131.28

-62.93

-320.60

127.83

-325.94

126.60

-104.57

-94.51

-142.50

-57.73

-131.28

-121.32

-366.27

164.80

Page 43 of 52

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


Figure 1: Snapshots of the initial and a few representative configurations of different Aβ protofilaments as obtained from the simulations. For visual clarity, the NTS, CTS and the interconnecting turn-segments of the peptides are drawn in blue, green and red, respectively.

43


RMSD [Å] RMSD [Å] RMSD [Å]

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

RMSD [Å]


15

O5 O8 O10 O12 O14

whole

10 5 0 15

Page 44 of 52

NTS

10 5 0 15

turn

10 5 0 15

CTS

10 5 0

0

20

40

60

80

100

t [ns] Figure 2: Time evolutions of the RMSDs averaged over the individual Aβ peptides and their segments in different protofilaments. The calculations are carried out with respect to the corresponding initial structures.

44


Page 45 of 52

16

O5 O8 O10 O12 O14

RG [Å]

(a)

14 12

30

RL [Å]

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


(b)

20

10

0

20

40

60

80

100

t [ns] Figure 3: Time evolutions of (a) the radius of gyration (RG ) and (b) the end-to-end distance (RL ) averaged over the individual Aβ peptides in different protofilaments.

45



θ [°]

0

(a)

NTS

(b)

CTS

O5 O8 O10 O12 O14

-60 -120 -180 0

θ [°]

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

Page 46 of 52

-60 -120 -180

0

20

40

60

80

100

t [ns] Figure 4: Time evolutions of the twist angles (θ) involving (a) the NTS and (b) the CTS of the tagged Aβ peptides in different protofilaments.

46


Page 47 of 52

0

−30

8

−40 −50

4

8

−20 −30

−60

4

−40 20

22

24

26

0

14

16

RL [˚ A]

18

−50

O12

O10

−125 4

−150 −175

A] RL [˚

25

30

O14

−50

θ [◦ ]

8

20

0

−40

12

−60

8

−80

4

−100 18

0

20

22

24

RL [˚ A]

26

0

12

−60 8 −70 4

∆G [kcal mol−1 ]

−100


12

−75

15

20

RL [˚ A]


−70

θ [◦ ]

12

−10

θ [◦ ]

−20

θ [◦ ]

O8

12


O5


−10

θ [0 ]

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


−80 −90

16

17

18

19

0

RL [˚ A]

Figure 5: The free energy contours of different protofilaments based on the end-to-end distance (RL ) and the twist angle (θ) involving the CTS of the Aβ peptides.

47



4

I

-1

∆G [kcal mol ]

I

3 2

O5 O8 O10 O12 O14

III

I

III I I

V

(a)

V V

III

III

1

IV II

0 4

-1

∆G [kcal mol ]

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

Page 48 of 52

3

II II II II

I I

III IV

IV

I V

III III

(b)

V

I

I

V

III

2

IV III

1 0

II

III

II

II II

II

IV

IV

λ [arbitrary unit] Figure 6: (a) The free energy profiles (∆G) along the minimum energy pathways for different Aβ protofilaments as constructed from the free energy contours. For comparison, the corresponding results as obtained from trajectories with modified initial configurations of the protofilaments are shown in (b). The selected conformational states corresponding to the extremum points are marked (I to V).

48


Page 49 of 52

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


Figure 7: Representative configurations for the selected conformational states (a) I to III for lower order Aβ protofilament (O5 ) (b) I to V for higher order protofilament (O10 ) along the minimum energy pathways (see Figure 6(a)).

49



-1

∆Gbind [kcal mol ]

300

I

200

III

100

O5 O8 O10 O12 O14

(a) V

II

0

IV

-100 300 -1

∆Gbind [kcal mol ]

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

Page 50 of 52

I

(b)

200

V

III

100 0

II IV

-100

λ [arbitrary unit] Figure 8: (a) The binding free energies (∆Gbind ) of Aβ peptides in different protofilaments for the selected conformational states I to V (see Figure 6(a)). For comparison, the corresponding results as obtained from trajectories with modified initial configurations of the protofilaments are shown in (b).

50


-1 -1

∆Gsol [kcal mol ]

-50 -100

I

(a) II III

-150

IV

V

-200

O5 O8 O10 O12 O14

-250 100 80 60 40 20 0

(b) I

II

III

IV

V

0 II

-1

T∆S [kcal mol ]

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


∆GMM [kcal mol ]

Page 51 of 52

-100

(c)

IV III

-200 -300

V

I

-400

λ [arbitrary unit]

Figure 9: Contributions of different components of ∆Gbind (see eq. 2), namely, (a) the intermolecular interaction energy (∆GM M ), (b) solvation free energy (∆Gsol ), and (c) entropy contribution on complexation (T ∆S) for the selected conformational states I to V (see Figure 6(a)) of different Aβ protofilaments.

51



0.03

P(∆G′bind)

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

Page 52 of 52

O5 O8 O10 O12 O14

0.02

0.01

0 -250

-200

-100 -150 -1 ∆G′bind [kcal mol ]

-50

Figure 10: Probability distribution of the binding free energies (P (∆G′bind )) in differerent Aβ protofilaments. Note that the T ∆S term is not included here.

Graphical TOC Entry

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Size-Dependent Conformational Features of AÎ² 17 ... - ACS Publications

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