Comparing atomistic molecular mechanics force fields

This article was downloaded by: [CEA Saclay] On: 18 September 2013, At: 13:47 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Journal of Biomolecular Structure and Dynamics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tbsd20

Comparing atomistic molecular mechanics force fields for a difficult target: a case study on the Alzheimer’s amyloid β-peptide a

a

a

Stacey R. Gerben , Justin A. Lemkul , Anne M. Brown & David R. Bevan

a

a

Department of Biochemistry , Virginia Tech , 111 Engel Hall, Blacksburg , VA , 24061 , USA Published online: 13 Sep 2013.

To cite this article: Stacey R. Gerben , Justin A. Lemkul , Anne M. Brown & David R. Bevan , Journal of Biomolecular Structure and Dynamics (2013): Comparing atomistic molecular mechanics force fields for a difficult target: a case study on the Alzheimer’s amyloid β-peptide, Journal of Biomolecular Structure and Dynamics, DOI: 10.1080/07391102.2013.838518 To link to this article: http://dx.doi.org/10.1080/07391102.2013.838518

PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

Journal of Biomolecular Structure and Dynamics, 2013 http://dx.doi.org/10.1080/07391102.2013.838518

Comparing atomistic molecular mechanics force fields for a difficult target: a case study on the Alzheimer’s amyloid β-peptide Stacey R. Gerben, Justin A. Lemkul, Anne M. Brown and David R. Bevan* Department of Biochemistry, Virginia Tech, 111 Engel Hall, Blacksburg, VA 24061, USA Communicated by Ramaswamy H. Sarma

Downloaded by [CEA Saclay] at 13:47 18 September 2013

(Received 6 June 2013; accepted 23 August 2013) Macromolecular function arises from structure, and many diseases are associated with misfolding of proteins. Molecular simulation methods can augment experimental techniques to understand misfolding and aggregation pathways with atomistic resolution, but the reliability of these predictions is a function of the parameters used for the simulation. There are many biomolecular force fields available, but most are validated using stably folded structures. Here, we present the results of molecular dynamics simulations on the intrinsically disordered amyloid β-peptide (Aβ), whose misfolding and aggregation give rise to the symptoms of Alzheimer’s disease. Because of the link between secondary structure changes and pathology, being able to accurately model the structure of Aβ would greatly improve our understanding of this disease, and it may facilitate application of modeling approaches to other protein misfolding disorders. To this end, we compared five popular atomistic force fields (AMBER03, CHARMM22 + CMAP, GROMOS96 53A6, GROMOS96 54A7, and OPLS-AA) to determine which could best model the structure of Aβ. By comparing secondary structure content, NMR shifts, and radius of gyration to available experimental data, we conclude that AMBER03 and CHARMM22 + CMAP over-stabilize helical structure within Aβ, with CHARMM22 + CMAP also producing elongated Aβ structures, in conflict with experimental findings. OPLS-AA, GROMOS96 53A6, and GROMOS96 54A7 produce very similar results in terms of helical and β-strand content, calculated NMR shifts, and radii of gyration that agree well with experimental data. Keywords: molecular dynamics; protein folding; molecular mechanics; force field; simulation

Introduction The function of a biomolecule, such as a protein or nucleic acid, arises from its structure. The overall fold of a protein dictates its ability to bind other molecules or carry out mechanical functions. The misfolding of proteins is associated with numerous disease states, and the formation of amyloid fibrils is a common pathological consequence in diseases like Alzheimer’s, Parkinson’s, Huntington’s, among others (Chiti & Dobson, 2006). Given the difficulty of studying the aggregation pathway of the proteins associated with these diseases, theoretical techniques can provide insight into conformational changes that give rise to aggregate formation. The quality of these theoretical methods derives from the ability of the underlying parameters and energy functions (known as “force fields”) to reproduce known behavior. Molecular mechanics (MM) force fields are derived in a number of different ways, often involving quantum mechanics (QM) calculations that seek to reproduce gasor condensed-phase geometries or free energy calcula*Corresponding author. Email: [email protected] Ó 2013 Taylor & Francis

tions to reproduce thermodynamic observables. These force fields are then often calibrated and validated against proteins and model peptides of known structure. Assessing disordered or highly dynamic proteins is not often part of a standard evaluation of MM force fields because of the difficulty in experimentally validating the structures of these molecules. Intrinsically disordered or misfolded proteins are involved in a wide variety of disease states such as Alzheimer’s disease (AD), which affects approximately 5.2 million people in the USA and is the sixth leading cause of death (Alzheimer’s Association, 2013). According to the “amyloid hypothesis,” the principal neurotoxic entity in AD is the amyloid β-peptide (Aβ), whose aggregation and deposition in neural tissue give rise to the symptoms of AD (Hardy & Higgins, 1992). Due to variable proteolytic processing, the length of Aβ ranges from 38 to 43 residues, with the 40- (Aβ40) and 42-residue (Aβ42) alloforms being the most common. Aβ40 forms a collapsed coil structure in water with any α-helix


2

S.R. Gerben et al.

or β-sheet structures tending to occur near the C-terminus (Zhang et al., 2000). An NMR study has shown that at low temperatures Aβ40 shows PPII-helical structures for residues 1 4 and 11 15 and β-sheets for residues 16 24 and 31 40, however these areas of structure disappear at higher temperatures (Danielsson, Andersson, Jarvet, & Gräslund, 2006). Other studies have sought to quantify secondary structure content in Aβ40 and Aβ42 using circular dichroism (CD) and NMR spectroscopy. An early CD study found that the α-helical content of Aβ40 was very low (1.1%), while β-strand content was the predominant secondary structure feature (60.4%) (Soto, Castaño, Frangione, & Inestrosa, 1995). CD and NMR studies on Aβ42 in water have shown similar results, with low α-helical content (3% or less) and βstrand content between 13 and 20% (Hou et al., 2004; Kirkitadze, Condron, & Teplow, 2001). In Aβ42, the principal secondary structure feature is random coil. Though monomeric Aβ is normally nontoxic, its accumulation causes aggregation into toxic oligomers and plaques in the brain, with Aβ42 aggregating faster than Aβ40 (Harper & Lansbury, 1997; Jarrett & Lansbury, 1993). This aggregation and associated neurotoxicity have been linked to an increase in the adoption of β-sheet structure (Haass & Selkoe, 2007). Since the conformational state of Aβ has implications for neurotoxicity, it is essential to accurately predict its structure to understand the underlying driving forces for these changes. One effective way to study Aβ is to perform molecular dynamics (MD) simulations to gain atomistic insight into conformational ensembles. One challenge in conducting MD simulations relates to the choice of force field, since each has different parameterization strategies and has been calibrated against different biomolecular structures. Since Aβ is not well-ordered in solution, finding a force field that matches experimental data can be difficult. In this study, we compare five common MM force fields available in the GROMACS package (Hess, Kutzner, van der Spoel, & Lindahl, 2008; Pronk et al., 2013) in order to determine which of them best models Aβ40 in water. The AMBER03 (Duan et al., 2003) and CHARMM22 + CMAP (Foloppe & MacKerell, 2000; MacKerell, Banavali, & Foloppe, 2001; MacKerell et al., 1998; MacKerell, Feig, & Brooks, 2004) force fields were originally parameterized using QM, and OPLS-AA (Kaminski, Friesner, Tirado-Rives, & Jorgensen, 2001) was derived from AMBER parameters and optimized for liquid simulations. GROMOS96 53A6 (Oostenbrink, Villa, Mark, & van Gunsteren, 2004) and GROMOS96 54A7 (Schmid et al., 2011) are two recent versions of the GROMOS96 force field lineage. GROMOS96 54A7 was shown to reproduce stable α-helical structures more accurately than GROMOS96 53A6 (Schmid et al., 2011). A previous replica exchange MD study showed

that the GROMOS96 43A1 force field (Scott et al., 1999) and OPLS-AA both modeled the structure of Aβ40 and Aβ42 well in the context of reproducing NMR J-coupling constants, though OPLS-AA agreed more closely with experimental results (Sgourakis, Yan, McCallum, Wang, & Garcia, 2007). A study by Best et al. showed that both AMBER03 and CHARMM22 + CMAP tend to over-stabilize α-helical structures in model peptides (Best, Buchete, & Hummer, 2008). Based on these previous studies, we set out to determine the most effective force field for modeling a difficult target, the Aβ40 peptide, as our findings serve not only to evaluate the ability of MM force fields to describe conformational transitions, but also to provide a recommendation for conducting simulations that have implications for elucidating the molecular mechanism of AD. Methods Force fields The five MM force fields chosen for the present work were AMBER03 (Duan et al., 2003), CHARMM22 with energy correction maps (CMAP) (Foloppe & MacKerell, 2000; MacKerell et al., 2001; MacKerell et al., 1998; MacKerell et al., 2004), OPLS-AA (Kaminski et al., 2001), GROMOS96 53A6 (Oostenbrink et al., 2004), and GROMOS96 54A7 (Schmid et al., 2011). These force fields include both all-atom (AMBER03, CHARMM22 + CMAP, and OPLS-AA) and united-atom (GROMOS96 53A6 and 54A7) parameter sets. AMBER03 and CHARMM22 + CMAP both represent recent revisions of earlier force fields that include modifications to backbone torsional terms. The parameters in CHARMM22 protein force field include so-called CMAP corrections (MacKerell et al., 2004) to the previous edition of the force field (MacKerell et al., 1998). GROMOS96 54A7 is a revision of GROMOS96 53A6 that weakens repulsive interactions between backbone atoms and modifies backbone torsional terms in an effort to improve helical stability (Schmid et al., 2011). These five force fields represent different parameterization strategies, with AMBER03, CHARMM22 + CMAP, and OPLS-AA originating with QM geometry optimizations, while the GROMOS96 parameter sets were derived from model compounds whose thermodynamic properties were fitted empirically. The most recent version of OPLS-AA also involved fitting liquid thermodynamic properties and thus makes use of QM and empirical parameterization. Molecular dynamics The structure used for modeling Aβ40 (PDB code 1BA4) was taken from an NMR structure determined at pH 5.1 in the presence of sodium dodecyl sulfate micelles


MM Force Field Evaluation Using Aβ (Coles, Bicknell, Watson, Fairlie, & Craik, 1998). Topologies for Aβ40 were generated under each force field, assigning canonical protonation states at pH 7 for each titratable residue. Aβ40 was centered in a dodecahedral unit cell with a minimum solute-box distance of 1.0 nm. The unit cells of each system were filled with the water models indicated in Table 1. Since each peptide bears a net 3 charge at pH 7, three Na+ ions were added to neutralize the systems. Energy minimization was carried out using the steepest descent method. All simulations were carried out with GROMACS, version 4.5.4 (Hess et al., 2008; Pronk et al., 2013). Long-range electrostatic interactions were calculated using the smooth particle mesh Ewald (PME) method (Darden, York, & Pedersen, 1993; Essmann et al., 1995). The short-range nonbonded cutoffs (rvdw for van der Waals interactions and rc for Coulombic interactions within the real-space contribution to PME) employed are shown in Table 1. Neighbor lists were updated every five simulation steps within a radius of rlist, which was set equal to rc in all cases (Table 1). Dispersion correction was applied to energy and pressure terms to account for truncation of van der Waals interactions. Periodic boundary conditions were applied in all three spatial dimensions. All bonds in Aβ40 were constrained using the P-LINCS method (Hess, 2008) and all water molecules were kept rigid using the SETTLE algorithm (Miyamoto & Kollman, 1992), allowing an integration time step of 2 fs. Equations of motion were integrated using Langevin dynamics with stochastic temperature coupling (van Gunsteren & Berendsen, 1988), using an inverse friction coefficient of 1.0 ps 1. All systems were equilibrated in two stages, applying position restraints to all heavy atoms in Aβ40. The first phase employed a canonical (NVT) ensemble for 100 ps. Temperature was maintained at 298 K. The second phase of equilibration employed an isothermal–isobaric (NPT) ensemble for 100 ps. Temperature was again maintained at 298 K and the pressure was maintained at 1 bar using the Parrinello–Rahman barostat (Nosé & Klein, 1983; Parrinello & Rahman, 1981). Production MD simulations were carried out in the absence of any restraints at 298 K and 1 bar. Three independent trajectories for each simulaTable 1. Water models and short-range nonbonded parameters for each force field. Force field AMBER03 CHARMM22 + CMAP GROMOS96 53A6 GROMOS96 54A7 OPLS-AA

Water model

rc and rlist (nm)

rvdw (nm)

TIP3P TIP3P

.8 1.2

.8 1.2

SPC SPC TIP4P

.9 .9 1.0

1.4 1.4 1.0

3

tion set were produced by generating different random velocities at the outset of NVT. Simulations were allowed to run until the backbone root-mean-square deviation (RMSD) showed no systematic upward or downward trends or major changes over 100 ns, thus serving as a preliminary indicator of convergence. Data analysis RMSD clustering was carried out using the method described by (Daura, Gademann, Jaun, Seebach, & van Gunsteren, 1999), using a cutoff of 0.2 nm to define structural similarity. Clustering was accomplished by creating sub-trajectories of the original MD simulations that covered the last 100 ns of each of the three replicate simulations for each system. These sub-trajectories were pooled to create 300 ns of sampling time for each force field. Secondary structure features were calculated over the last 100 ns of each trajectory according to DSSP (Kabsch & Sander, 1983). NMR shifts were calculated by running CamShift (Kohlhoff, Robustelli, Cavalli, Salvatella, & Vendruscolo, 2009) on 100 frames from the final 100 ns of simulation time at 1 ns intervals, averaged together to yield the chemical shift data for each force field. Similarly, / backbone dihedral configurations were characterized by calculating 3JHNHα coupling constants from the final 100 ns of each trajectory using coefficients in the Karplus equation according to (Vuister & Bax, 1993). Statistical analyses were performed using a two-tailed t-test with significance being established if p < .05. Results Assessment of convergence To assess the completeness of each simulation, we monitored backbone RMSD as a preliminary indicator of convergence. Once this quantity had stabilized over 100 ns (as determined by block averaging of windows over the final 100, 75, 50, and 25 ns with RMSD values not differing by more than one standard deviation), simulations were stopped. Simulations conducted using OPLS-AA and GROMOS96 53A6 reached stable backbone RMSD values in the shortest amount of time, but AMBER03 and CHARMM22 + CMAP stabilized only after more than 400 ns of simulation and GROMOS96 54A7 took almost twice as long as the other simulations (Table 2). Since backbone RMSD values are degenerate measures, we further assessed the convergence of the trajectories by carrying out RMSD clustering to analyze the different structures that were produced. The structures in Figure 1 are the central structures of the five largest clusters for each of the force fields. AMBER03 and GROMOS96 54A7 produced helical structures persisting most frequently from residues 15 to 25. CHARMM22 + CMAP produced a large amount of helical structure that

4

S.R. Gerben et al.


Table 2. Simulation times (in ns) for all trajectories. Replicate

AMBER03

CHARMM22 + CMAP

GROMOS96 53A6

GROMOS96 54A7

OPLS-AA

1 2 3 Average

250 375 800 475

900 225 200 442

200 300 200 233

725 775 725 742

200 275 275 250

is largely reflective of the original NMR structure, indicating very little change over the course of the simulations. Trajectories run using OPLS-AA and GROMOS96 53A6 both showed β-strands near the N- and Ctermini, with short helices persisting in the middle of the peptide. AMBER03, GROMOS96 54A7, and OPLS-AA showed a large percentage of structures in the first five clusters (Figure 1), an outcome that indicates that these force fields produce a reasonably homogenous ensemble of structures. CHARMM22 + CMAP and GROMOS96 53A6, in contrast, show much smaller individual clusters, indicating that the force fields sample a wide range

of structures, even when the backbone RMSD showed no systematic changes. For CHARMM22 + CMAP, the different structures were attributed mostly to the formation of small bend and coil regions within the long helix that encompasses most of the Aβ40 sequence, as well as random coil motions towards the N-terminus (Figure 1). In the case of GROMOS96 53A6, many different configurations were sampled that manifested a mixture of secondary structure elements (Figure 1). Secondary structure analysis Structures from the last 100 ns of each replicate were analyzed and averaged to determine the overall secondary

Figure 1. Central structures from each of the first five clusters for each force field, along with the percentage occupancy of that cluster. The central structures are from pooled sub-trajectories and thus are representative of all simulations conducted using each force field. The peptides are colored by secondary structure, and N- and C-termini are indicated by blue and red spheres, respectively.


MM Force Field Evaluation Using Aβ structure formation for each force field (Table 3). Secondary structure formation for AMBER03 and CHARMM22 + CMAP are statistically indistinguishable from one another, with both stabilizing large amounts of helical structure and showing no β-strand formation. Simulations under GROMOS96 54A7 produced a statistically indistinguishable amount of helical formation as compared to AMBER03, though it was significantly different from CHARMM22 + CMAP (p < .002), which showed more helical structure, and GROMOS96 53A6 (p < .02), which showed less helical structure. Helix formation was indistinguishable between OPLS-AA, GROMOS96 53A6, and GROMOS96 54A7, though the helical content produced by OPLS-AA was significantly different (p < .05) from AMBER03. GROMOS96 53A7, GROMOS96 54A7, and OPLS-AA all produced statistically indistinguishable amounts of β-strand structure. Simulations using AMBER03 and CHARMM22 + CMAP produced no β-strand at all. To provide a more in-depth characterization of the secondary structure content of Aβ40 produced in these simulations, we calculated the propensity of helices, strands, and random coil elements as a function of amino acid residue within the Aβ40 sequence (Figure 2). Both GROMOS96 53A6 and OPLS-AA produced a short helical segment in the vicinity of residues 12–20 and β-strand elements towards the N- and C-termini. The overall appearance of β-strands was more uniform across the peptide sequence in the GROMOS96 53A6 simulations, with short strands appearing throughout Aβ40. GROMOS96 54A7 produced a similar set of structures, though helical elements were more prominent than in the simulations using GROMOS96 53A6 and OPLS-AA. Two helical segments persisted in the GROMOS96 54A7 simulations, extending from residues 12 to 28 with a small break in the middle, and residues 33–37. Strand and coil elements generally persisted towards the termini of Aβ40. The results of the simulations carried out using the AMBER03 and CHARMM22 + CMAP force fields were characterized by prominent helical structures and little, if any, β-strand content. The simulations using AMBER03 produced an N-terminal helix from residues 2 to 12 and

5

another, longer, helix from residues 14 to 36. Random coil elements largely accounted for the structures adopted by the intervening residues and termini. The frequency of helical structures was even greater in the simulations conducted using CHARMM22 + CMAP. Residues 14–36 were almost exclusively helical, with an additional helical region extending from residues 7 to 14. As with the results of the AMBER03 simulations, β-strand configurations were negligible, and random coil elements accounted for the remainder of the structures in terminal residues. Compactness of the Aβ40 structure Having examined the secondary structure content of the Aβ40 peptide under different force fields, we next analyzed the tertiary structure of each peptide in terms of its radius of gyration, Rg, over the final 100 ns of each simulation. The value of Rg is an indicator of how compact the Aβ40 structure was during the trajectories. Results are listed in Table 4. The CHARMM22 + CMAP force field produced the most elongated structures, with an average Rg value that was significantly larger (p < .02) than that of all the other force fields studied here. The other four force fields produced more compact structures, with statistically indistinguishable values of Rg. The Rg values produced by AMBER03, OPLS-AA, and both GROMOS96 parameter sets were in good agreement with available experimental evidence that suggests the Rg of monomeric Aβ40 in solution is .9 ± .1 nm (Nag et al., 2011). NMR chemical shifts The ensemble of structures generated during an MD simulation allows for the calculation of properties related to the local chemical environments of the atoms being simulated. For this reason, we further characterized the tertiary structure of Aβ40 by calculating NMR shifts from the data generated in these simulations. Experimental studies have shown that Hα atoms experience an upfield (lower ppm) shift, relative to random coil values, when the peptide adopts a helical conformation and a downfield (higher ppm) shift when there is β-strand formation (Wishart, Sykes, &

Table 3. Secondary structure content of Aβ40, given in percent. Values are averaged over the final 100 ns of simulation time, with standard deviations shown. Force field AMBER03 CHARMM22 + CMAP GROMOS96 53A6 GROMOS96 54A7 OPLS-AA

Coil

β-stranda

Bend

Turn

Total helixb

29 ± 4 21 ± 2 32 ± 7 34 ± 4 31 ± 4

0±0 0±0 32 ± 12 14 ± 7 16 ± 4

13 ± 4 9±3 17 ± 6 21 ± 6 23 ± 5

19 ± 7 8±4 12 ± 5 11 ± 6 18 ± 5

39 ± 12 58 ± 5 4±2 20 ± 4 12 ± 5

β-strand includes both isolated β-bridge and extended strand configurations. Total helix includes the sum of α-, 310-, and π-helical configurations.

a

b

S.R. Gerben et al.


6

Figure 2. Secondary structure as a function of amino acid residue within Aβ40. Frequencies are calculated as the fraction of frames within the final 100 ns of three replicate trajectories that produced the indicated secondary structure elements.

Richards, 1992). Similarly, Cα atoms experience an upfield shift when located in β-strands and a downfield shift when located in α-helices (Saitô, 1986; Wishart & Sykes, 1994). Additionally, Hα shifts are more sensitive to changes in β-strand content, whereas Cα shifts are more sensitive to changes in α-helical formation (Wang & Jardetzky, 2002). In the present work, NMR shifts were calculated from MD trajectories for

each force field using CamShift (Kohlhoff et al., 2009). The simulated data were then plotted against experimental Hα and Cα shifts (Hou et al., 2004), as shown in Figures 3 and 4. Regions along the Aβ40 sequence where the simulations show chemical shifts consistently higher or lower than the experimental shifts were used to identify areas where each simulation failed to accurately model Aβ40.

MM Force Field Evaluation Using Aβ

7

Table 4. Rg values, averaged over the last 100 ns of each trajectory, with standard deviations shown. Force field

Rg (nm)


AMBER03 CHARMM22 + CMAP GROMOS96 53A6 GROMOS96 54A7 OPLS-AA

1.03 ± .03 1.30 ± .07 1.05 ± .06 .98 ± .07 .96 ± .02

AMBER03 showed downfield Cα shifts between residues 3–11 and residues 15–28, which correspond to areas of helical structure (Figure 3). CHARMM22 + CMAP showed consistent downfield Cα shifts starting around residue 12 and lasting through to the C-terminus (Figure 4), which is consistent with the extended helix formed throughout that sequence (Figure 1). GROMOS96 53A6 showed downfield Cα shifts compared to the experimental data from residues 15 to 19, which is the one area of helical structure, and upfield Hα shifts from the N-terminus to residue 14 and from residues 32 to the C-terminus, which corresponds to the formation of β-strands near the termini (Figures 3 and 4). GROMOS96 54A7 showed downfield Cα shifts from residues 10 to 29, corresponding to the helical structure in the middle of the peptide (Figure 3). OPLS-AA showed downfield Hα shifts from residues 3 to 7 and upfield shifts from residues 14 to 18 corresponding to areas of helical structure (Figure 4). To quantify how well the simulation results matched the experimental data, we calculated the total difference and average difference for Cα and Hα shifts for each residue, as well as the RMSD of these values (Tables 5 and 6). The total and average differences between the simulated and experimental shifts were used to determine any

Figure 4. Calculated experimental data.

Hα

NMR

shifts

plotted

against

systematic upfield or downfield tendencies of the force field (Tables 5 and 6). The RMSD provides an unsigned metric for how well each force field performs, and thus is independent of any systematic biases. Using the RMSD of Hα shift data to determine how well each simulation predicted β-sheet formation, the force fields rank, from best to worst: GROMOS96 54A7, GROMOS96 53A6, OPLS-AA, AMBER03, CHARMM22 + CMAP. GROMOS96 54A7, AMBER03, and CHARMM22 + CMAP all showed systematic upfield shifts, indicative of smaller amounts of β-sheet formation than the experimental data, while GROMOS96 53A6 and OPLS-AA both show systematic downfield shifts, indicative of more frequent emergence of β-strands (Table 6). By evaluating the RMSD of the Cα chemical shifts, the five force fields were ranked, in order from best to worst: GROMOS96 53A6, OPLS-AA, GROMOS96 54A7, AMBER03, CHARMM22 + CMAP. CHARMM22 + CMAP, AMBER03, and GROMOS96 54A7 all showed systematic downfield shifts, indicative of greater helical formation. Simulations conducted with OPLS-AA showed a systematic upfield shift, indicative of a decreased α-helical structure. GROMOS96 53A6 showed a very small trend in upfield Cα shifts, but no systematic bias towards helical structures, as the average difference in Cα shifts was zero for all residues (Table 6). J-coupling constants

Figure 3. Calculated experimental data.

Cα

NMR

shifts

plotted

against

To further characterize the backbone configurations, we computed 3JHNHα coupling constants over the last 100 ns of each trajectory and compared them to experimentally determined values to assess / backbone dihedral dynamics in the MD simulations. Two experimental NMR datasets were used for this comparison, the first determined using HSQC (Yan, McCallum, & Wang, 2008) and a more recent study using SOFAST-HMQC (Rosenman,

8

S.R. Gerben et al.

Table 5. Deviations in Cα chemical shifts (ppm) for each force field.


Residue 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

Experimental 52.80 56.39 57.53 55.62 56.28 53.96 58.93 45.32 58.15 56.38 62.80 55.79 56.03 56.20 56.35 55.04 61.87 57.31 57.23 52.51 56.29 53.97 62.86 45.40 58.47 53.39 56.57 45.09 52.56 61.01 61.02 45.09 55.17 55.54 62.51 45.16 45.00 62.32

Average difference Total difference RMSD

AMBER03

CHARMM22 + CMAP

GROMOS96 53A6

GROMOS96 54A7

OPLS-AA

.72 .54 1.06 3.11 1.22 1.40 1.17 .29 1.38 .70 .91 .93 .10 1.53 2.09 2.37 1.98 3.24 2.56 1.93 1.75 2.19 .70 1.15 1.46 1.34 .53 .09 .52 2.80 1.59 .49 .03 .10 .62 .07 .44 1.40

1.50 .32 .06 .02 1.35 1.42 .46 .86 .41 1.09 .32 .42 .00 1.90 2.45 2.37 3.43 3.43 3.37 1.83 2.79 2.90 2.34 2.18 2.03 2.26 1.22 1.81 1.40 2.76 3.32 2.78 2.09 2.95 1.65 .82 .70 .59

.13 .44 .03 .37 .64 .00 .01 .29 .02 .34 .89 1.04 .60 1.48 1.18 1.05 2.25 1.31 .85 1.70 1.01 .14 .37 .75 1.29 .82 .99 .37 .01 .31 1.00 .67 1.07 .85 1.12 .75 .27 .30

.46 .13 .91 .45 1.35 1.59 .50 .54 .42 .96 .46 .72 .16 1.43 2.23 1.68 2.71 2.46 1.59 1.04 .91 .14 1.59 1.17 1.03 1.23 .32 .84 .98 .23 .04 .97 .88 .05 .25 .38 .02 .00

1.51 .91 .58 .23 .25 .17 .29 1.01 1.77 .54 .62 2.89 2.19 .53 1.49 1.07 .74 .16 .47 .51 .11 .89 .03 .80 .10 .16 1.42 .93 .49 .46 .06 .75 .76 .09 .39 1.22 1.21 .05

1.02 38.62 1.50

1.50 57.14 1.98

.00 .13 .87

.69 26.34 1.10

.12 4.39 .93

Connors, Chen, Wang, & García, in press). Results are shown in Figure 5 and Tables 7 and 8. We note that not all residues were assigned 3JHNHα values in the NMR studies, thus we restrict our analysis to only those residues that could be unambiguously assigned experimentally. Comparing the 3JHNHα values with the HSQC data (Table 7) shows that the GROMOS96 54A7 force field produced the best agreement with experimental data in terms of average difference, total difference, and RMSD. The AMBER03 force field was the next best in these categories. The remaining force fields produced larger deviations from experimental data, with CHARMM22 + CMAP showing the largest RMSD. While 3JHNHα values

in the N-terminal region were in reasonable agreement with experimental data (Figure 5), the 3JHNHα values for residues 18–40 were generally considerably lower than the experimental data-set. Whereas CHARMM22 + CMAP produced a predominantly helical structure across these residues, the other force fields produced mixtures of disordered and β-strand configurations, which are more likely to be present in vitro and in vivo in an aqueous environment. The results of the comparison with SOFAST-HMQC data (Table 8) indicate a similar pattern. The OPLS-AA force field fared the best in terms of average and total difference with respect to experimental results, but the GROMOS96 54A7 force field had the best RMSD value,


9

Table 6. Deviations in Hα chemical shifts (ppm) for each force field.


Residue 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

Experimental 4.30 4.19 4.55 4.25 4.53 4.63 4.37 3.88 4.51 4.19 3.92 4.59 4.56 4.26 4.26 4.33 4.03 4.57 4.56 4.21 4.20 4.65 4.15 3.98 4.43 4.74 4.26 3.93 4.31 4.15 4.15 3.92 4.34 4.54 4.12 4.00 3.94 4.18


AMBER03

CHARMM22 + CMAP

GROMOS96 53A6

GROMOS96 54A7

OPLS-AA

.07 .10 .01 .54 .19 .21 .14 .05 .44 .17 .36 .10 .14 .31 .14 .16 .17 .33 .28 .23 .03 .26 .31 .16 .13 .24 .12 .10 .06 .34 .12 .10 .09 .13 .02 .10 .14 .07

.13 .21 .07 .06 .21 .06 .12 .12 .16 .04 .06 .30 .20 .37 .28 .25 .30 .32 .32 .05 .12 .28 .42 .20 .12 .19 .08 .10 .08 .33 .37 .14 .25 .42 .20 .08 .09 .24

.03 .08 .07 .30 .06 .13 .06 .13 .02 .20 .29 .23 .13 .11 .14 .06 .08 .11 .03 .39 .03 .00 .18 .02 .07 .07 .15 .12 .01 .26 .22 .38 .16 .27 .12 .32 .18 .03

.09 .04 .05 .24 .01 .24 .05 .03 .02 .09 .02 .02 .06 .15 .14 .09 .25 .28 .21 .07 .06 .04 .33 .20 .01 .11 .11 .09 .21 .08 .11 .05 .24 .10 .06 .10 .14 .15

.13 .16 .20 .15 .29 .08 .06 .04 .34 .22 .26 .18 .18 .20 .16 .32 .18 .11 .17 .01 .26 .20 .05 .13 .17 .29 .14 .00 .10 .10 .10 .00 .22 .04 .04 .04 .28 .31

.11 4.24 .21

.15 5.72 .22

.08 3.16 .17

.05 1.78 .14

.06 2.24 .19

indicating that both of these force fields represent the structure reasonably well. GROMOS96 53A6 had the next lowest RMSD. As with the comparison to HSQC data, CHARMM22 + CMAP performed poorly, as indicated by the large average and total differences, as well as the highest RMSD of any of the force fields examined here. Discussion In the present work, we have applied a systematic analysis of five common MM force fields in the context of simulating Aβ40. A wide body of literature describes simulations of Aβ, but different force fields are often applied

(Lee & Ham, 2011; Luttmann & Fels, 2006; Olubiyi & Strodel, 2012; Sgourakis et al., 2007; Yang & Teplow, 2008), making interpretation and comparison of these results difficult. The evaluation of these force fields has implications for protein folding, as a thorough critique of the ability of each of these force fields to describe disordered peptides is largely missing from the literature. We sought to employ a variety of popular MM force fields that represent diverse parameterization strategies, such as dipeptide QM geometry and electrostatic properties in the condensed phase (AMBER03), QM water interaction energy and vibrational spectra (CHARMM22 + CMAP), and condensed-phase liquid structure, and thermodynamic properties (OPLS-AA, GROMOS96 53A6 and

S.R. Gerben et al.


10

Figure 5. 3JHNHα values for each of the force fields examined here plotted against available experimental data. Only residues for which unambiguous experimental values exist were plotted. Values from HSQC and SOFAST-HMQC experiments are presented with experimental errors, and error bars from MD simulations represent standard deviations from three replicates over an accumulated sampling time of 300 ns.


11

Table 7. Δ3JHNHα values (Hz) for each force field relative to HSQC experiments.


Residue 3 4 5 7 8 10 11 15 16 18 20 21 22 23 24 26 27 30 31 32 35 36 39 40

Experimental 6.43 6.61 6.97 5.80 6.10 5.94 6.20 5.10 6.30 7.78 7.55 5.37 5.91 6.21 6.48 6.50 6.70 5.41 7.24 7.48 6.68 7.21 7.66 8.87


AMBER03

CHARMM22 + CMAP

GROMOS96 53A6

GROMOS96 54A7

OPLS-AA

.07 .55 2.12 .59 .05 .06 1.29 .06 .79 2.46 1.83 .55 .65 .27 .24 .19 .39 .18 2.48 1.10 .51 .31 .43 1.19

.89 1.39 .56 .14 .55 .96 .13 .61 .99 2.80 2.42 .75 1.07 1.39 1.49 .80 .62 .21 1.61 2.50 1.77 .81 .25 .34

1.50 1.46 1.73 1.90 .67 2.08 .92 .04 .27 .94 .13 3.00 .13 1.19 .07 .45 .24 1.07 .47 1.37 1.69 1.66 .41 .32

.41 .04 .12 1.26 .42 .73 .26 .29 1.10 2.46 .45 .02 .71 .75 1.87 .67 .38 1.50 1.33 .54 .30 .21 .72 .40

1.48 1.83 .84 .44 .21 1.68 1.23 1.32 .05 .67 .37 1.92 1.39 .32 1.85 1.04 .83 1.39 .09 2.29 1.58 .28 .98 .04

.44 10.55 1.09

.62 14.84 1.30

.86 20.59 1.27

.33 8.04 .94

.63 15.09 1.23

54A7). It was not our intent to exhaustively evaluate all possible force fields, rather to examine a representative cross-section of the available parameter sets. Newer versions and subtle revisions to these force fields exist, and continuing to test and evaluate all of them remains an important goal, but for the purposes stated here, we believe the present cross-section to be a useful reference point in comparing MM force fields. To this end, we have analyzed metrics related to the secondary and tertiary structure of Aβ40 and have made comparisons to existing experimental evidence, including data produced by techniques such as CD spectroscopy, fluorescence correlation spectroscopy, dynamic light scattering, and NMR. AMBER03 and CHARMM22 + CMAP both produced large amounts of helical content (39 ± 12 and 58 ± 5%, respectively) that were significantly higher than the other force fields examined here. AMBER03 and CHARMM22 + CMAP also failed to reproduce experimental NMR chemical shift data by producing dramatic downfield Cα shifts (Table 5). These results agree with a previous study showing both of these force fields tend to over-stabilize helical structures (Best et al., 2008). Our results show that CHARMM22 + CMAP consistently produced helices throughout most of the Aβ40 sequence

(residues 7–37, most prominently between residues 17 and 37). AMBER03 produced shorter helices with slightly lower frequency (Figure 2). Some helical content was produced very close to the N-terminus, from residues 2 to 12, an outcome that was different from all other force fields studied here. The formation of helices and β-strands was comparable among GROMOS96 53A6, GROMOS96 54A7, and OPLS-AA, though GROMOS96 54A7 produced significantly more helical structure than GROMOS96 53A6 (Table 3). The location of these helices within the Aβ40 sequence was similar, generally occurring around residues 12–20, though the simulations using GROMOS96 54A7 produced helices within residues near the C-terminus (Figure 2). Experimental studies on Aβ in water suggest that α-helical content is negligible, perhaps less than 3% (Hou et al., 2004; Kirkitadze et al., 2001; Soto et al., 1995), indicating that, in the context of secondary structure, GROMOS96 53A6 and OPLS-AA may be good choices for modeling Aβ40. GROMOS96 53A6, GROMOS96 54A7, and OPLS-AA all produced β-strand content that agrees well with two experimental studies (Hou et al., 2004; Kirkitadze et al., 2001), though none of the force fields examined here produced β-strand content as high as has been predicted by an earlier CD study (Soto

12

S.R. Gerben et al.

Table 8. Δ3JHNHα values (Hz) for each force field relative to SOFAST-HMQC experiments.


Residue 3 4 5 10 11 12 15 16 17 18 19 20 21 22 23 24 26 31 32 34 35 36 39 40

Experimental 6.4 7.0 7.4 6.3 6.2 6.5 6.4 5.9 6.5 8.4 7.5 7.8 5.3 5.8 6.6 6.9 5.8 7.7 7.4 6.7 7.2 7.5 8.1 8.9


AMBER03

CHARMM22 + CMAP

GROMOS96 53A6

GROMOS96 54A7

OPLS-AA

.1 .2 2.6 .3 1.3 1.5 1.4 .4 .2 3.1 2.7 2.1 .5 .8 .7 .7 .5 2.9 1.0 .4 .0 .6 .9 1.2

.9 1.0 .1 .6 .1 .2 .7 .6 1.3 3.4 2.5 2.7 .7 1.0 1.8 1.9 .1 2.1 2.4 1.2 2.3 1.1 .7 .4

1.5 1.1 1.3 1.7 .9 2.0 1.3 .7 .2 1.6 .1 .1 3.1 .0 .8 .4 .3 .0 1.5 1.3 1.2 1.4 .0 .3

.4 .3 .6 .4 .3 .0 1.0 .7 .8 3.1 1.5 .7 .1 .8 .4 2.3 .0 1.8 .5 1.1 .8 .5 1.2 .4

1.5 1.4 .4 1.3 1.2 .2 .0 .5 1.5 .0 .3 .6 2.0 1.5 .1 2.3 1.7 .4 2.2 1.4 1.1 .0 .5 .0

.68 16.38 1.44

1.00 23.99 1.57

.64 15.44 1.23

.68 16.25 1.11

.44 10.66 1.21

et al., 1995). Despite our efforts to produce sufficiently long, converged simulations, the timescale over which these structures emerge experimentally may still remain inaccessible to atomistic MD simulations in the absence of enhanced sampling methods such as temperature and Hamiltonian replica exchange. The prominent β-strands that appeared in the simulations using GROMOS96 53A6 (residues 10–15 and 34–38) agree well with the results of a previous MD/ NMR study that found a β-hairpin formed in Aβ40 involving residues 9–13 and 35–37 (Ball, Phillips, Wemmer, & Head-Gordon, 2013). β-strands involving residues 35 – 37 were also produced in simulations using GROMOS96 54A7 and OPLS-AA. The work of Ball et al. used the AMBER99SB force field (Hornak et al., 2006; Wickstrom, Okur, & Simmerling, 2009), and the fact that our results using GROMOS96 53A6 qualitatively agree with this previous study provide further evidence that GROMOS96 53A6 models Aβ40 effectively. Given that the formation of β-strands, especially towards the C-terminus of the peptide sequence, is a defining feature of higher-order aggregates (Roychaudhuri, Yang, Hoshi, & Teplow, 2009), this outcome is very important in the assessment of the ability of these force fields to reproduce biological reality. Given that GROMOS96 53A6, GROMOS96 54A7, and OPLS-AA produced β-

strand structures in regions that are known to drive Aβ aggregation (Figure 2), it appears that these force fields are better suited to modeling Aβ40 than AMBER03 and CHARMM22 + CMAP in the context of understanding its structural transition, and ultimately its aggregation in aqueous solution. Previous studies have suggested that the GROMOS96 53A6 parameter set favors extended configurations at the expense of helical stability (Best et al., 2008; Project, Nachliel, & Gutman, 2010). In contrast, work by Olubiyi and Strodel suggests that GROMOS96 53A6 may be an optimal parameter set for studying Aβ40 and Aβ42, but their comparison only involved GROMOS96 53A6 and GROMOS96 43A2 (Daura, Mark, & van Gunsteren, 1998), indicating that the former represents an improvement over the latter (Olubiyi & Strodel, 2012). GROMOS96 53A6, GROMOS96 54A7, and OPLSAA all reproduce the experimental NMR chemical shift data (both Cα and Hα shifts) reasonably well, in agreement with previous work that utilized an older GROMOS96 parameter set (Sgourakis et al., 2007) and work by Olubiyi and Strodel that used GROMOS96 53A6 (Olubiyi & Strodel, 2012). It is interesting to note that while GROMOS96 54A7 better reproduced Hα chemical shifts than GROMOS96 53A6, showing that


MM Force Field Evaluation Using Aβ GROMOS96 53A6 over-stabilized β-structures, GROMOS96 53A6 more accurately reproduced the Cα chemical shifts. Since the main differences between GROMOS96 54A7 and GROMOS96 53A6 in this context relate to different //ψ torsional terms and a weakened repulsion between backbone NH and C=O groups, our results suggest that this recalibration actually biases helical configurations in the context of disordered peptides. AMBER03 and CHARMM22 + CMAP both performed poorly in terms of reproducing NMR shifts for both Hα and Cα atoms. A similar outcome was observed in terms of 3JHNHα values, which were used as a further characterization of backbone configurations and dynamics. We compared the calculated 3JHNHα values from MD simulations against two data-sets, one produced by HSQC experiments (Yan et al., 2008) that has served as a reference in other MD studies of Aβ (Ball et al., 2011, 2013) and a more recent set of J-coupling values resolved using the SOFAST-HMQC pulse sequence (Rosenman et al., in press). As with the chemical shift analysis, GROMOS96 53A6, GROMOS96 54A7, and OPLS-AA generally performed the best in all categories (average and total Δ3JHNHα and RMSD). CHARMM22 + CMAP performed poorly in these comparisons, a result that can be attributed to the large α-helical content produced in residues 18–40. We assessed the tertiary structure of Aβ40 by measuring Rg over time. We found that CHARMM22 + CMAP produced extended structures that were incompatible with experimental measurements regarding the size of Aβ40 in solution (Nag et al., 2011). The other four force fields examined here produced Rg values that were similar to one another and in good agreement with experimental results. This outcome indicates that AMBER03, OPLS-AA, GROMOS9653A6, and GROMOS96 54A7 produce compact structures of Aβ40 that are compatible with the experimentally determined “collapsed coil” state (Zhang et al., 2000). Collapsed structures with compact hydrophobic cores are necessary to serve as a nucleation point for higher-order aggregation in vivo (Roychaudhuri et al., 2009), thus in this regard it appears that four of the force fields examined here are capable of modeling this element of the Aβ40 structure. Considering both secondary and tertiary structure metrics, it is clear that OPLS-AA, GROMOS96 53A6, and GROMOS96 54A7 all adequately model Aβ40 in water. The work of Sgourakis et al. determined that OPLS-AA was superior to an older version of the GROMOS96 force-field family, parameter set 43A1 (Sgourakis et al., 2007), but our results suggest that newer versions of the force field represent an improvement such that the results may be equal in quality to those obtained with OPLS-AA. Using RMSD clustering as a way to evaluate of these force fields, we observed that while

13

OPLS-AA and GROMOS96 54A7 showed more homogeneous ensembles, GROMOS96 53A6 produced more varied structures between different simulations. These findings indicate that more thorough sampling needs to be applied when using GROMOS96 53A6, since no single simulation is definitive. Individual simulations may converge in terms of relatively homogeneous sampling, but each trajectory may be very different. The unitedatom parameter sets (GROMOS96 53A6 and 54A7) may be preferable because the simulation systems will contain fewer atoms, thus making simulations faster. In this regard, we noted that individual trajectories conducted using OPLS-AA and GROMOS96 53A6 both converged very quickly (Table 2), while other force fields took longer to reach a stable state. Ultimately, the goal of any biomolecular simulation is to shed light on some biologically relevant phenomenon, and in the case of Aβ, most simulations are conducted in an attempt to understand aggregation behavior or toxicity. The aim of our study then, in part, is to illustrate which biomolecular force field is best suited to this task, and our results have implications not only for Aβ but for simulations of other disordered peptides. Monomeric Aβ is generally regarded as nontoxic (Cleary et al., 2005), thus any extrapolation from our data to observed toxicity associated with a disease state would be inappropriate. Oligomeric species of Aβ are widely believed to be the most toxic entities in the disease state (Kayed et al., 2003, 2004), and though the exact structure of oligomers remains unknown, details are slowly emerging (Gu, Liu, & Guo, 2013; Pan, Han, Borchers, & Konermann, 2012). The Aβ aggregation cascade can broadly be described as an increase in β-strand structure as the monomer aggregates into higher-order structures (Roychaudhuri et al., 2009). The β-strands that give rise to aggregation are principally located within two regions of the Aβ sequence, residues 12–24 and the hydrophobic C-terminal region (Tycko, 2003), structural features that were observed in our simulations using GROMOS96 53A6 and GROMOS96 54A7. Conclusions Here, we have shown that OPLS-AA, GROMOS96 53A6, and GROMOS96 54A7 are superior to AMBER03 and CHARMM22 + CMAP for the purpose of simulating Aβ40. These findings may have implications for simulations of other disordered proteins or for studies on protein folding. The three most successful MM force fields (OPLS-AA, GROMOS96 53A6, and GROMOS96 54A7) have common parameterization strategies that involve fitting to thermodynamic observables, such as free energies of hydration. This outcome implies that they may be well suited to studying highly dynamic systems in which the constituent residues of the

14

S.R. Gerben et al.


protein may be exposed to ever-changing microenvironments, given that enthalpic and entropic driving forces have been incorporated in the theory of the underlying force field and influence the dynamics during MD simulations. Future studies on a more diverse set of disordered proteins should be carried out to corroborate or refine our findings here, and likely even more force fields should be considered. A recent revision of the CHARMM force field, called CHARMM22⁄ (Piana, Lindorff-Larsen, & Shaw, 2011), has been shown to be useful in studying the protein folding by eliminating most of the CMAP corrections from CHARMM22 + CMAP and reparameterizing several dihedrals and side chain charges. All of these factors should be taken into account as the field moves forward in assessing and refining existing force fields for the purpose of improving the accuracy of MD simulations.

Abbreviations Aβ Aβ40 Aβ42 AD CD HSQC MM MD NMR PME QM Rg RMSD SOFASTHMQC

amyloid β-peptide 40-residue amyloid β-peptide 42-residue amyloid β-peptide Alzheimer’s disease circular dichroism spectroscopy heteronuclear single quantum coherence molecular mechanics molecular dynamics nuclear magnetic resonance spectroscopy particle mesh Ewald quantum mechanics radius of gyration root-mean-square deviation band-selective optimized flip-angle shorttransient heteronuclear multiple quantum coherence

Acknowledgments The authors thank Prof Michael Zagorski at Case Western Reserve University for providing the experimental NMR chemical shifts, David Rosenman, and Prof Chunyu Wang at Rensselaer Polytechnic Institute for providing J-coupling data, and the administrators of Virginia Tech Advanced Research Computing for providing computing time on the SystemX and HokieOne supercomputers. J.A.L. and D.R.B. designed research. S.R.G. performed simulations. S.R.G., J.A.L., and A. M.B. analyzed data. J.A.L., S.R.G., A.M.B., and D.R.B. wrote the paper.

References Alzheimer’s Association. (2013). 2013 Alzheimer’s disease facts and figures. Alzheimer’s & Dementia, 9, 1–68. Ball, K. A., Phillips, A. H., Nerenberg, P. S., Fawzi, N. L., Wemmer, D. E., & Head-Gordon, T. (2011). Homogeneous and heterogeneous tertiary structure ensembles of amyloidβ peptides. Biochemistry, 50, 7612–7628.

Ball, K. A., Phillips, A. H., Wemmer, D. E., & Head-Gordon, T. (2013). Differences in β-strand populations of monomeric Aβ40 and Aβ42. Biophysical Journal, 104, 2714–2724. Best, R. B., Buchete, N.-V., & Hummer, G. (2008). Are current molecular dynamics force fields too helical? Biophysical Journal, 95, L07–L09. Chiti, F., & Dobson, C. M. (2006). Protein misfolding, functional amyloid, and human disease. Annual Review of Biochemistry, 75, 333–366. Cleary, J. P., Walsh, D. M., Hofmeister, J. J., Shankar, G. M., Kuskowski, M. A., Selkoe, D. J., & Ashe, K. H. (2005). Natural oligomers of the amyloid-β protein specifically disrupt cognitive function. Nature Neuroscience, 8, 79–84. Coles, M., Bicknell, W., Watson, A. A., Fairlie, D. P., & Craik, D. J. (1998). Solution structure of amyloid β-peptide(1–40) in a water-micelle environment. Is the membrane-spanning domain where we think it is? Biochemistry, 37, 11064–11077. Danielsson, J., Andersson, A., Jarvet, J., & Gräslund, A. (2006). 15N relaxation study of the amyloid β-peptide: Structural propensities and persistence length. Magnetic Resonance in Chemistry, 44, S114–S121. Darden, T., York, D., & Pedersen, L. (1993). Particle mesh Ewald: An N· log(N) method for Ewald sums in large systems. Journal of Chemical Physics, 98, 10089–10092. Daura, X., Gademann, K., Jaun, B., Seebach, D., & van Gunsteren, W. F. (1999). Peptide folding: When simulation meets experiment. Angewandte Chemie International Edition, 38, 236–240. Daura, X., Mark, A. E., & van Gunsteren, W. F. (1998). Parametrization of aliphatic CHn united atoms of GROMOS96 force field. Journal of Computational Chemistry, 19, 535–547. Duan, Y., Wu, C., Chowdhury, S., Lee, M. C., Xiong, G., Zhang, W., … Kollman, P. (2003). A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase quantum mechanical calculations. Journal of Computational Chemistry, 24, 1999–2012. Essmann, U., Perera, L., Berkowitz, M. L., Darden, T., Lee, H., & Pedersen, L. G. (1995). A smooth particle mesh Ewald method. Journal of Chemical Physics, 103, 8577–8593. Foloppe, N., & MacKerell, A. D. Jr. (2000). All-atom empirical force field for nucleic acids: I. parameter optimization based on small molecule and condensed phase macromolecular target data. Journal of Computational Chemistry, 21, 86–104. Gu, L., Liu, C., & Guo, Z. (2013). Structural insights into Aβ42 oligomers using site-directed spin labeling. Journal of Biological Chemistry, 288, 18673–18683. Haass, C., & Selkoe, D. J. (2007). Soluble protein oligomers in neurodegeneration: Lessons form the Alzheimer’s amyloid βpeptide. Nature Reviews: Molecular Cell Biology, 8, 101–112. Hardy, J. A., & Higgins, G. A. (1992). Alzheimer’s disease: The amyloid cascade hypothesis. Science, 256, 184–185. Harper, J. D., & Lansbury, P. T. (1997). Models of amyloid seeding in Alzheimer’s disease and Scrapie: Mechanistic truths and physiological consequences of the time-dependent solubility of amyloid proteins. Annual Review of Biochemistry, 66, 385–407. Hess, B. (2008). P-LINCS: A parallel linear constraint solver for molecular simulation. Journal of Chemical Theory and Computation, 4, 116–122. Hess, B., Kutzner, C., van der Spoel, D., & Lindahl, E. (2008). GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation. Journal of Chemical Theory and Computation, 4, 435–447.


MM Force Field Evaluation Using Aβ Hornak, V., Abel, R., Okur, A., Strockbine, B., Roitberg, A., & Simmerling, C. (2006). Comparison of multiple Amber force fields and development of improved protein backbone parameters. Proteins: Structure Function, and Bioinformatics, 65, 712–725. Hou, L., Shao, H., Zhang, Y., Li, H., Menon, N. K., Neuhaus, E. B., … Zagorski, M. G. (2004). Solution NMR studies of the Aβ(1–40) and Aβ(1–42) peptides establish that the Met35 oxidation state affects the mechanism of amyloid formation. Journal of the American Chemical Society, 126, 1992–2005. Jarrett, J. T., & Lansbury, P. T. (1993). Seeding “OneDimensional Crystallization” of amyloid: A pathogenic mechanism in Alzheimer’s disease and Scrapie? Cell, 73, 1055–1058. Kabsch, W., & Sander, C. (1983). Dictionary of protein secondary structure: Pattern recognition of hydrogen-bonded and geometrical features. Biopolymers, 22, 2577–2637. Kaminski, G. A., Friesner, R. A., Tirado-Rives, J., & Jorgensen, W. L. (2001). Evaluation and reparametrization of the OPLS-AA force field for proteins via comparison with accurate quantum chemical calculations on peptides. Journal of Physical Chemistry B, 105, 6474–6487. Kayed, R., Head, E., Thompson, J. L., McIntire, T. M., Milton, S. C., Cotman, C. W., & Glabe, C. G. (2003). Common structure of soluble amyloid oligomers implies common mechanism of pathogenesis. Science, 300, 486–489. Kayed, R., Sokolov, Y., Edmonds, B., McIntire, T. M., Milton, S. C., Hall, J. E., & Glabe, C. G. (2004). Permeabilization of lipid bilayers is a common conformation-dependent activity of soluble amyloid oligomers in protein misfolding diseases. Journal of Biological Chemistry, 279, 46363–46366. Kirkitadze, M. D., Condron, M. M., & Teplow, D. B. (2001). Identification and characterization of key kinetic intermediates in amyloid β-protein fibrillogenesis. Journal of Molecular Biology, 312, 1103–1119. Kohlhoff, K. J., Robustelli, P., Cavalli, A., Salvatella, X., & Vendruscolo, M. (2009). Fast and accurate predictions of protein NMR chemical shifts from interatomic distances. Journal of the American Chemical Society, 131, 13894–13895. Lee, C., & Ham, S. (2011). Characterizing amyloid-beta protein misfolding from molecular dynamics simulations with explicit water. Journal of Computational Chemistry, 32, 349–355. Luttmann, E., & Fels, G. (2006). All-atom molecular dynamics studies of the full-length β-amyloid peptides. Chemical Physics, 323, 138–147. MacKerell, A. D.Jr., Banavali, N., & Foloppe, N. (2001). Development and current status of the CHARMM force field for nucleic acids. Biopolymers, 56, 257–265. MacKerell, A. D.Jr., Feig, M., & Brooks, C. L.III (2004). Extending the treatment of backbone energetics in protein force fields: Limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. Journal of Computational Chemistry, 25, 1400–1415. MacKerell, A. D.Jr., Brooks, B. R., Brooks, C. L.III, Nilsson, L., Roux, B., Won, Y., & Karplus, M. (1998). CHARMM: The energy function and its parameterization with an overview of the program. In P. V. Schleyer, N. L. Allinger, T. Clark, J. Gasteiger, P. A. Kollman, H. F. Shaefer III, & P. R. Schreiner (Eds.), Encyclopedia of computational chemistry (pp. 271–277). Chichester: Wiley.

15

Miyamoto, S., & Kollman, P. A. (1992). SETTLE: An analytical version of the SHAKE and RATTLE algorithms for rigid water models. Journal of Computational Chemistry, 13, 952–962. Nag, S., Sarkar, B., Bandyopadhyay, A., Sahoo, B., Sreenivasan, V. K. A., Kombrabail, M., … Maiti, S. (2011). Nature of the amyloid-β monomer and the monomer-oligomer equilibrium. Journal of Biological Chemistry, 286, 13827– 13833. Nosé, S., & Klein, M. L. (1983). Constant pressure molecular dynamics for molecular systems. Molecular Physics, 50, 1055–1076. Olubiyi, O. O., & Strodel, B. (2012). Structures of the amyloid β-peptides Aβ1–40 and Aβ1–42 as influenced by pH and a Dpeptide. Journal of Physical Chemistry B, 116, 3280–3291. Oostenbrink, C., Villa, A., Mark, A. E., & van Gunsteren, W. F. (2004). A biomolecular force field based on the free enthalpy of hydration and solvation: The GROMOS forcefield parameter sets 53A5 and 53A6. Journal of Computational Chemistry, 25, 1656–1676. Pan, J., Han, J., Borchers, C. H., & Konermann, L. (2012). Structure and dynamics of small soluble Aβ(1–40) oligomers studied by top-down hydrogen exchange mass spectrometry. Biochemistry, 51, 3694–3703. Parrinello, M., & Rahman, A. (1981). Polymorphic transitions in single crystals: A new molecular dynamics method. Journal of Applied Physics, 52, 7182–7190. Piana, S., Lindorff-Larsen, K., & Shaw, D. E. (2011). How robust are protein folding simulations with respect to force field parameterization? Biophysical Journal, 100, L47–L49. Project, E., Nachliel, E., & Gutman, M. (2010). Force fielddependent structural divergence revealed during long time simulations of calbindin d9k. Journal of Computational Chemistry, 31, 1864–1872. Pronk, S., Páll, S., Schulz, R., Larsson, P., Bjelkmar, P., Apostolov, R., … Lindahl, E. (2013). GROMACS 4.5: A highthroughput and highly parallel open source molecular simulation toolkit. Bioinformatics, 29, 845–854. Rosenman, D. J., Connors, C., Chen, W., Wang, C., & García, A. E. (2013). Aβ monomers transiently sample oligomer and fibril-like configurations: Ensemble characterization using a combined MD/NMR approach. Journal of Molecular Biology, 425, 3338–3359. Roychaudhuri, R., Yang, M., Hoshi, M. M., & Teplow, D. B. (2009). Amyloid β-protein assembly and Alzheimer disease. Journal of Biological Chemistry, 284, 4749–4753. Saitô, H. (1986). Conformation-dependent 13C chemical shifts: A new means of conformational characterization as obtained by high-resolution solid-state 13C NMR. Magnetic Resonance in Chemistry, 24, 835–852. Schmid, N., Eichenberger, A. P., Choutko, A., Riniker, S., Winger, M., Mark, A. E., & van Gunsteren, W. F. (2011). Definition and testing of the GROMOS force-field versions 54A7 and 54B7. European Biophysics Journal, 40, 843–856. Scott, W. R. P., Hünenberger, P. H., Tironi, I. G., Mark, A. E., Billeter, S. R., Fennen, J., … van Gunsteren, W. F. (1999). The GROMOS biomolecular simulation program package. Journal of Physical Chemistry A, 103, 3596–3607. Sgourakis, N. G., Yan, Y., McCallum, S. A., Wang, C., & Garcia, A. E. (2007). The Alzheimer’s peptide Aβ40 and Aβ42 adopt distinct conformations in water: A combined MD/ NMR study. Journal of Molecular Biology, 368, 1448– 1457.

16

S.R. Gerben et al.


Soto, C., Castaño, E. M., Frangione, B., & Inestrosa, N. C. (1995). The α-helical to β-strand transition in the amino-terminal fragment of the amyloid β-peptide modulates amyloid formation. Journal of Biological Chemistry, 270, 3063–3067. Tycko, R. (2003). Insights into the amyloid folding problem from solid-state NMR. Biochemistry, 42, 3151–3159. van Gunsteren, W. F., & Berendsen, H. J. C. (1988). A leapfrog algorithm for stochastic dynamics. Molecular Simulation, 1, 173–185. Vuister, G. W., & Bax, A. (1993). Quantitative J correlation: A new approach for measuring homonuclear three-bond J (HNHα) coupling constants in 15N-enriched proteins. Journal of the American Chemical Society, 115, 7772–7777. Wang, Y., & Jardetzky, O. (2002). Probability-based protein secondary structure identification using combined NMR chemical-shift data. Protein Science, 11, 852–861. Wickstrom, L., Okur, A., & Simmerling, C. (2009). Evaluating the performance of the ff99SB force field based on NMR scalar coupling data. Biophysical Journal, 97, 853–856.

Wishart, D. S., & Sykes, B. D. (1994). The 13C chemical-shift index: A simple method for the identification of protein secondary structure using 13C chemical-shift data. Journal of Biomolecular NMR, 4, 171–180. Wishart, D. S., Sykes, B. D., & Richards, F. M. (1992). The chemical shift index: A fast and simple method for the assignment of protein secondary structure through NMR spectroscopy. Biochemistry, 31, 1647–1651. Yan, Y., McCallum, S. A., & Wang, C. (2008). M35 oxidation induces Aβ40-like structural and dynamical changes in Aβ42. Journal of the American Chemical Society, 130, 5394–5395. Yang, M., & Teplow, D. B. (2008). Amyloid β-protein monomer folding: Free-energy surfaces reveal alloform-specific differences. Journal of Molecular Biology, 384, 450–464. Zhang, S., Iwata, K., Lachenmann, M. J., Peng, J. W., Li, S., … Lee, J. P. (2000). The Alzheimer’s peptide Aβ adopts a collapsed coil structure in water. Journal of Structural Biology, 130, 130–141.