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Model Amyloid Peptide B18 Monomer and Dimer Studied by Replica Exchange Molecular Dynamics Simulations Volker Knecht* Max Planck Institute of Colloids and Interfaces, Science Park Golm, 14424 Potsdam, Germany ReceiVed: May 27, 2010; ReVised Manuscript ReceiVed: July 13, 2010
Peptide misfolding and aggregation are the early steps during the formation of amyloid fibrils. Understanding these processes in detail is crucial for the development of therapeutic strategies against amyloid diseases. Here I present temperature replica exchange molecular dynamics (TREMD) simulations of the model amyloid peptide B18 in the mono- and dimeric states in explicit aqueous solution. Both the monomer and the dimer involve β-sheets consisting of different residues in different registers with comparable statistical weight. The dimer forms intra- as well as intermolecular β-sheets. The average β-sheet content is in agreement with previous estimates from circular dichroism (CD) spectra for monomers and is lower for dimers. The tendency of B18 to form β-sheets likely contributes to its fibrillogenic property. For both the monomer and the dimer, individual peptides form U-shaped or other partially collapsed conformations. Combined with data from electron microscopy, this suggests that for higher aggregates during fibrillization B18 undergoes a transition from U-shaped to outstretched conformations. The tendency of B18 to form U-shaped conformations, intramolecular β-sheets, and intermolecular β-sheets with different register will contribute to the lag phase for fibril formation. Introduction Amyloid diseases including Alzheimer’s, Creutzfeldt-Jakob disease, and bovine spongiform encephalopathy are associated with the conversion of a given precursor protein from a soluble and functional form into high-order fibrillar aggregates rich in β-structure.1 Here, the β-strands are normal to the fibril axis, a structure denoted as a cross-β motif. The initial step is the misfolding or partial denaturation of the precursor protein leading to a state highly prone to aggregate. Understanding the structural properties of the misfolded monomer and low molecular weight aggregates is essential for understanding the origin of the disease. There is increasing evidence suggesting that not the mature fibrils but the early intermediates are the toxic entities which, hence, should be the target of therapeutic strategies.2 Amyloid formation appears to be a fundamental property of polypeptide chains in general. Various peptides not involved in diseases have been shown to form amyloid-like fibrils in vitro. Short peptides with this property are useful model systems to understand the fundamental principles of fibril formation. An example for a peptide known to form amyloid-like fibrils in aqueous solution is the peptide B18 with sequence LGLLLRHLRHHSNLLANI.3 This sequence corresponds to residues 103-120 of the sea urchin fertilization protein Bindin.3 Little secondary structure with some β-sheet content of soluble species is indicated from circular dichroism (CD) spectroscopy.4 Typical β-sheet/coil conformations with β-sheets formed by different sets of residues for B18 in water were indicated from previous molecular dynamics (MD).5 However, these simulations suffered from a sampling problem such that the population of observed conformations could not be determined, and many important conformations were possibly not even sampled. I have now used temperature replica exchange MD (TREMD) simulations to study B18 in mono- and dimeric form. In * To whom correspondence should be addressed. E-mail: vknecht@ mpikg.mpg.de.
TREMD simulations, several replica of the same system are simulated at different temperatures, and configurations between neighboring temperatures are exchanged according to a probabilistic criterion. Hence, the enhanced sampling at the highest temperature is coupled to the correct Boltzmann distribution at all other temperatures. In my simulations, B18 monomers are found to form various coil or β-strand-loop-β-strand conformations, with various antiparallel β-sheets consisting of different sets of residues with comparable statistical weights. In dimers, the β-sheet content is decreased, and intermolecular β-sheets are found more often than intramolecular ones. Dimerization is found to result from a competition between solvation favoring and conformational entropy of the peptide opposing dimerization. Results and Discussion TREMD simulations of B18 monomers or dimers in explicit aqueous 100 mM NaCl solution were carried out. The initial configurations for the different replica were obtained from trajectories at 1000 K created to randomize the peptide configurations and (for the dimer system) the mutual orientation and position of the peptides; these initial configurations contained neither any R-helical nor β-sheet structures. Each replica was simulated for 200 ns. The analyses were focused on the trajectory for 290 K. Figure 1 shows running averages over 200 ps windows for the energies corresponding to the shortrange electrostatic interactions (interatomic distances below 1 nm) (a) within the peptide for the monomer and (b) within and between the peptides for the dimer at 290 K. The data indicate that after 150 ns the simulations are converged. Therefore, further analyses were focused on the period between 150 and 200 ns. Structure. Neither the monomer nor the dimer showed R-helical conformations. The average β-sheet fraction was 16 ( 2% for the monomer and 7 ( 2% for the dimer. Previous CD spectroscopy experiments suggested 4 ( 3% helical and 32 ( 17% β-sheet conformations for B18 in aqueous buffer at
10.1021/jp1048698 2010 American Chemical Society Published on Web 09/14/2010
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Figure 1. Convergence of simulations. Shown are running averages over 200 ps windows for the energies E corresponding the short-range electrostatic interactions (a) within the peptide for the monomer and (b) within and between the peptides for the dimer at 290 K. The vertical dashed lines mark the beginning of the period considered for the structural and thermodynamic analyses (sampling period). The horizontal dash-dotted line indicates the average of E over the sampling period, and the dotted lines give the corresponding standard error.
similar conditions.4 The standard error for the experimental estimates reflects the dependence of the values obtained on the preparation procedure and the method used to estimate the structure content from the data. It is likely that the experimental data mainly reflect the structure of monomers. The agreement of the β-sheet (and helical) fraction between the available experimental estimates and my simulations of monomers suggests that my model predicts the correct secondary structure of the peptide in water. Furthermore, our previous simulations reproduced the experimentally known tendency of water to induce β-sheet and apolar environments to stabilize R-helical conformations for this peptide.5 Finally, the force field used here has been shown to be able to reproduce the experimental fold of a number of structurally unrelated peptides as illustrated by four examples given in a review by van Gunsteren et al.6 These findings give confidence that the force field represents the underlying tertiary structure of the peptide accurately. The secondary structure of B18 in the mono- and dimeric state shows that β-sheet conformations are accessible to the peptide which likely facilitates their formation in the fibril state. Aggregation of amyloid peptides is often argued to involve an increase in β-sheet content. The present results suggest that aggregation is not required to explain β-sheet conformations for B18 but can even lead to a decrease in the β-sheet content. Though the β-sheet content for fibrils is expected to be larger than for monomers, aggregation might not lead to a monotonous increase in β-sheet content as a function of the degree of oligomerization but could lead to a decrease for intermediate stages. To study the conformational distribution of the monomers, the 2500 configurations of the sampling period were clustered based on the rmsd of the main chain of residues 104-119 using the method by Daura et al. with a cutoff distance of 0.2 nm yielding 83 clusters. The probabilities of the conformations represented by these clusters are shown in Figure 2; here, the clusters or conformations are ranked and indicated according to their size. The figure reveals that the peptide neither folds to a single predominant conformation nor is a random coil, but its properties are somewhere in between. Two conformers are more probable than all others but together only appeared 23% of the time. The 17 largest clusters form 72% of the ensemble, and the locations of β-sheets for these clusters are shown in Table 1. Conformer 1 does not show any β-sheet conformation. Conformer 2 exhibits a β-sheet with five residue β-strands
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Figure 2. Population of configurational clusters for B18 monomers at 290 K. For the 17 largest clusters, the location of β-sheets is given in Table 1, and the three-dimensional structure of the respective central configuration is depicted in Figure 3.
formed by residues 106-110 and 115-119. Conformations including a β-sheet formed by the same residues were also observed in our previous simulations.5 The other conformers show either no β-sheet conformation or β-sheets with β-strands located at different positions and comprising between two and four residues. The loops between the strands have a length between three and nine residues. The three-dimensional structure of these clusters is shown in Figure 3, revealing that all β-sheets are antiparallel ones. The tendency of B18 to form coil and β-sheet conformations in the monomeric state resembles the behavior of other fibrillogenic peptides of similar length in previous simulation studies.7–21 The configurations of the dimers formed 100 clusters whose population is shown in Figure 4. Similar to the monomer, the dimer is neither folded nor a random coil. The 2 or 17 largest clusters comprise 21% or 80% of the ensemble, respectively. The location of β-sheets for the 17 largest clusters is shown in Table 2. β-sheets are present in most of the conformers. The length of the β-strands is between two and seven residues; hence, the dimer tends to exhibit more extended β-sheets than the monomer. The three-dimensional structure of the predominant conformers is shown in Figure 5. The individual peptides mostly form U-shaped or other partially collapsed conformations. Intermolecular β-sheets as for conformers 1, 2, 4, 5, 6, 8, 9, 10-14, and 17 are formed more often than intramolecular β-sheets (conformers 4, 11, 12, 14, and 15). Intramolecular β-sheets are always antiparallel, whereas intermolecular ones are more often parallel (conformers 1, 2, 4, 5, 6, 9, 10, 14, and 17) than antiparallel (conformers 5, 11-13). The number of strands in a β-sheet is mostly two (conformers 1, 5, 6, 8, 9, 10, 13, 15, and 17), but it may also be three (conformer 12 and 14) or four (conformer 11). Conformer 14 shows an interesting topology where one of the peptides forms a two-stranded β-sheet that is extended by another strand from the other peptide which, however, forms a second β-sheet that is stacked on top of the first one. Stacked β-sheets were also observed for Aβ (10-35) trimers in simulations using implicit solvent.22 Conformer 4 represents a side-by-side placement of β-hairpins as observed previously for (i) a generic lattice model of an amyloid species, (ii) the full length Alzheimer Aβ peptide or its 10-35 or 1-28 fragments in studies using coarse-grained descriptions for the peptides or implicit solvent, and (iii) for the Aβ (25-35) peptide in explicit solvent.7,22–25 Side-by-side placement of β-hairpins was proposed as a structural model for protofibrils of the viral model amyloid peptide LSFD.26 Intertwined-hairpin-like β-sheets as for β2 -microglobulin (83-99)27 or Aβ (25-35)25 are not observed.
Model Amyloid Peptide B18 Monomer and Dimer
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TABLE 1: Location of β-Sheets (“B”) in Predominant Conformations Together Comprising 70% of the Ensemble for B18 Monomers at 290 Ka Leu 103 Gly 104 Leu 105 Leu 106 Leu 107 Arg 108 His 109 Leu 110 Arg 111 His 112 His 113 Ser 114 Asn 115 Leu 116 Leu 117 Ala 118 Asn 119 Iso 120 a
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
. . . . . . . . . . . . . . . . . .
. . . B B B B B . . . . B B B B B .
. . . . . . . . . . . . . . . . . .
. . . B B . . . . . . B B . . . . .
. B B B B . . . . . . B B B B B . .
. . . . . . . . . . . . . . . . . .
. . B B B . . . . . . . . . B B B .
. . . . . . . . . . . . . . . . . .
. . B B B B . . . . . . B B B B . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . B B . . . B B . . . . . . . .
. . B B . . . . B B . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . B B . . . . . . . B B . . . . .
The abundance of these conformations is shown in Figure 2, and their three-dimensional structure is indicated in Figure 3.
Figure 3. Central configurations of predominant clusters together comprising 70% of the ensemble for B18 monomers at 290 K. The peptide backbone is shown in ribbon representation; the nitrogen atom at the N-terminus is shown as a sphere. Side chains, ions, and water are not shown for clarity. The location of β-sheets in these configurations is given in Table 1, and the population of clusters is shown in Figure 2.
A diversity of dimeric structures similar to that for B18 has been observed recently for Aβ (25-35).25 In particular, Aβ (25-35) also formed various dimer conformations in which the individual peptides adopted U-shaped or partially collapsed conformations. In addition, a small fraction of conformations existed in which both peptides were fully stretched and formed an extended intermolecular β-sheet; such conformations were proposed to be similar to the conformation of the peptide in protofibrils. Outstretched conformations were not observed for B18 dimers but seem to be relevant for B18 fibrils. The width of B18 protofibrils from B18 observed by electron microscopy was about 5 nm.28 In general, the length per residue is da ) 0.347 nm for an antiparallel and dp ) 0.325 nm for a parallel β-sheet or dt ) 0.15 nm for a turn. If the peptides in the fibril were in β-hairpin conformation (involving an antiparallel β-sheet), the protofibrils would have a width of 8da + dt ) 3.3
nm. If the peptides would adopt an outstretched conformation and form an in-register intermolecular β-sheet, the width of the protofibrils would be 5.8 nm for a parallel and 6.2 nm for an antiparallel β-sheet. From these simple geometrical considerations, it seems likely that B18 in fibrils adopts outstretched conformations forming (possibly slightly out-of-register) parallel intermolecular β-sheets. That would imply that during fibrillization B18 undergoes a transition from U-shaped to outstretched conformations. Such a transition is not observed for dimers but should occur for higher-order aggregates. A transition from U-shaped to outstretched conformations upon aggregation at a water/air interface is suggested for the model amyloid peptide LSFD.19,29 The tendency of B18 to form β-sheets likely contributes to its fibrillogenic property. On the other hand, the tendency of B18 to form U-shaped conformations, intramolecular β-sheets,
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TABLE 2: Location of β-Sheets (“B”) in Predominant Conformations at 290 K Together Comprising 70% of the Ensemble for B18 Dimers at 290 Ka Leu 103 Gly 104 Leu 105 Leu 106 Leu 107 Arg 108 His 109 Leu 110 Arg 111 His 112 His 113 Ser 114 Asn 115 Leu 116 Leu 117 Ala 118 Asn 119 Iso 120 Leu 103 Gly 104 Leu 105 Leu 106 Leu 107 Arg 108 His 109 Leu 110 Arg 111 His 112 His 113 Ser 114 Asn 115 Leu 116 Leu 117 Ala 118 Asn 119 Iso 120 a
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
. B B . . . . . . . . . . . . . . . . . . . . . . . . . . . . B B B . .
. . . . . . . . B B B . . . . . . . . . . B B B B B B . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . B B B . . . . . . . . . B B . . . B B B B B . . . B B B B B B B .
. . . B B . . . . . . . . . . . . . . . B B . . . . . . . . . . . . . .
. . . . . . . B B . . . . . . . . . . . . . . . . . . . . . . . B B . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. B B B B . . . . . . . . . . . . . . . . B B . . . . . . . . . . . . .
. . . . . . . B B B . . . . . . . . . . . . . B B B B B . . . . . . . .
. . B B B B B . . . . . . . . . . . . . . . . . . . . . B B B B B . . .
. . B B . . . . . B B . . B B . . . . . . . . . . . . . . . . . B B . .
. B B . . . B B B . . . . . . . . . . . . . . . . . . . . . . B B B . .
. . . . . . . . . . B B B B B B B . . . . B B B B . B . . . . . . . . .
. . . B B B B B . . . . B B B B . . . . B B . . . . B B . . . . . B B .
. . . . . . . . . . . . . . . . . . . . B B B B B . . . . . B B B B B .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . B B B B . . . . . . . . . . . . . . . . . B B B . . . . . . . .
The abundance of these conformations is shown in Figure 4, and their three-dimensional structure is indicated in Figure 5.
Figure 4. Population of clusters for B18 dimers at 290 K.
and intermolecular β-sheets with different register will contribute to the lag phase of this peptide. In particular, the register for intermolecular β-sheets may require dissociation of the peptides as found for the amyloid peptide NFGAIL.30 Alternatively, the change in register may occur without dissociation due to reptation as observed in coarse-grained31 or fully atomistic simulations.32 Experiments have shown that for the prion peptide H1 both mechanisms are possible and that the reorganization pathway depends on the peptide concentration.33 Independent of the reorganization pathway, the transition from out-of-register to in-register will likely involve a significant free energy barrier. Thermodynamics. A second cluster analysis based on all peptide atoms was used to determine the difference in peptide entropy between the dimer and the monomer, ∆Sp, according
to eq 3, yielding ∆Gp ≡ -T∆Sp ) +9.1 ( 0.3 kJ/mol. Hence, the configurational entropy of the peptide disfavors dimerization. Interestingly, there is evidence that the loss in configurational entropy upon aggregation may play a significant role for diseaserelated amyloid peptides. In particular, differences in configurational entropies of respective monomers have been proposed to determine which of the two major forms of the amyloid β peptide is dominant in senile plaques found in the brain of Alzheimer patients.34 In contrast, dimerization is expected to be favored by the hydrophobic effect arising from a decrease in water entropy at nonpolar surfaces at ambient conditions. The hydrophobic and the hydrophilic solvent-accessible surface area (SASA) for a dimer and two monomers is given in Table 3. In both states, the hydrophobic SASA exceeds the hydrophilic one. Upon dimerization, the hydrophilic SASA decreases by 2.3 nm2 and the hydrophobic one by 4.3 nm. The solvation energy for two monomers or a dimer, ∆Gm+m, respectively, based on the SASA of individual peptide atoms was determined using atomic solvation parameters from free energies of transfer following the approach by Eisenberg and McLachlan.35 Hence, I obtain a change in solvation free energy upon dimerization by ∆Gsasa ) ∆Gd - ∆Gm+m ) -28 ( 2 kJ/mol. Hence, for dimerization of B18, the partial desolvation of the peptide overcompensates the decrease in configurational entropy, leading to a net contribution of ∆Gps ≡ ∆Gsasa + ∆Gp ) -19 ( 2 kJ/mol.
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Figure 5. Central configurations of predominant clusters together comprising 70% of the configurations for B18 dimers at 290 K. The representation is similar to that chosen for Figure 3. Colors distinguish between the peptides. The location of β-sheets in these configurations is given in Table 2, and the population of clusters is shown in Figure 4.
TABLE 3: Solvent-Accessible Surface Area (SASA) for Two Monomers (M + M) or a Dimer (D) at 290 K system M+M D D - (M + M)
hydrophobic SASA (nm) hydrophilic SASA (nm) 21.26(8) 17.0(2) -4.3(2)
13.4(1) 11.14(8) -2.3(1)
Summary and Conclusion B18 monomers and dimers in aqueous NaCl solution have been studied using TREMD simulations. The monomers are found to form various coil or β-strand-loop-β-strand conformations, with various antiparallel β-sheets consisting of different sets of residues with comparable statistical weights. A single predominant conformation is not detected. The average β-sheet content of the monomers is in agreement with estimates from CD spectroscopy. In dimers, the β-sheet content is decreased, and intermolecular β-sheets are found more often than intramolecular ones. Both the monomer and the dimer involve β-sheets consisting of different residues in different registers with comparable statistical weight. β-Sheets involving the same residues as those in fibrils in the right register might act as nucleation points for fibril-relevant β-sheets, whereas out-of-register β-sheets may act as kinetic traps contributing to the lag time for fibril formation. Dimerization is favored by the partial desolvation of the peptide, in particular, a decrease in hydrophobic surface area. However, dimerization is disfavored by a decrease in the configurational entropy of the peptides. Hence, I provide direct evidence that, although formation of amyloid fibrils or toxic oligomers is
associated with protein disorder, disorder may also stabilize monomeric species. Methods Simulation Setups. The Bindin B18 peptide was studied in explicit water under periodic boundary conditions using molecular dynamics simulations. The systems contained either a single (“Monomer”) or a pair (“Dimer”) of solvated B18 molecules. The protonation state of the peptide was chosen to mimic pH 7-7.5. In particular, the histidine side chains were modeled in a deprotonated state. Full deprotonation of the histidine side chains at pH 7.5 is suggested from the pKa of isolated histidines and indicated from Hε1 chemical shifts for B18 in water/TFE.36 The initial peptide configuration was a strand-loop-strand conformation (including an antiparallel β-sheet between residues 106-107 and 118-119) and was obtained from a previous simulation of B18 in water.5 The systems are specified in Table 4, and the simulations are summarized in Table 5. For both systems, octahedral boxes were used. For the “Dimer1” system, the peptide configuration was repeated in z direction with a center of mass distance between the peptides of 3.29 nm. For the Monomer and the Dimer1 systems, the box size was chosen such that the distance between the peptide and the boundary of the box was at least 1.2 nm. The box was filled with a pre-equilibrated box of water molecules, and all water molecules that overlapped with peptide atoms were removed. Water molecules at energetically favorable positions were replaced by chloride ions to counterbalance the positive charge of the peptide(s) and excess chloride and sodium
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TABLE 4: Systems Simulated, Consisting of a Single (Monomer) or a Pair of B18 Molecules (Dimer1 or Dimer2) in Water Containing 100 mM NaCla system
nw
nNa
nCl
a (nm)
Monomer Dimer1 Dimer2
2896 7205 3656
5 13 7
7 17 11
4.89 6.63 5.34
a The number of water molecules, nw, sodium ions, nNa, and chloride ions, nCl, as well as the initial edge length of the simulation box, a, are given. For the Dimer1 system, the initial configuration consisted of two separated B18 monomers. After aggregation of peptides, the box was reduced in size yielding the Dimer2 system. For Monomer and Dimer2, simulations at 1000 K were conducted yielding the initial configurations of respective replica exchange MD simulations.
TABLE 5: Simulations Conducted in This Worka simulation
system
nrep
T (K)
t (ns)
MHOT D1HOT D2HOT MREP DREP
Monomer Dimer1 Dimer2 Monomer Dimer2
1 1 1 42 47
1000 1000 1000 290-406 290-406
15.3 2.0 16.8 200 200
a The simulated systems are specified in Table 4. MHOT, D1HOT, and D2HOT were conventional MD simulations, while MREP and DREP were temperature replica exchange MD (TREMD) simulations. For the conventional simulations, the corresponding temperature, T, and simulated time scale, t, are given. For the TREMD simulations, the number of replica, nrep, the temperature range, T, and the time scale per replica, t, are given. For the latter simulations, the temperatures were chosen to form a geometrical sequence. The initial peptide configuration chosen for MHOT and D1HOT was a strand-loop-strand conformation from a previous simulation of B18 in water.5 D1HOT was started from two separate monomers; in its final configuration, the monomers were aggregated. This dimer structure was re-solvated in a smaller box yielding the initial configuration for the simulation D2HOT. MHOT and D2HOT were conducted to randomize the monomer and dimer configurations yielding the initial configurations for the corresponding TREMD simulations.
to mimic 100 mM NaCl. To remove overlap between nonbonded atoms, each system was relaxed to a local potential energy minimum using steepest descent. Subsequently, the systems were simulated for 15.3 ns (Monomer) or 2 ns (Dimer1) at 1000 K. These and all subsequent simulations were conducted at constant volume. In the final configuration of the Dimer1 trajectory, peptides were aggregated. Here, water and ions were removed; the box size was reduced; and the peptide dimer was (re)solvated in a procedure similar to that chosen above yielding the system “Dimer2”. This system was also energy minimized and simulated at 1000 K for 16.8 ns. The simulations of the Monomer and Dimer2 systems at 1000 K were conducted to randomize the peptide configurations and (for Dimer2) the mutual orientation and position of the peptides. Omitting the initial 3 ns for equilibration, configurations of the trajectories for Monomer and Dimer2 systems every 300 ns were taken as initial configurations for the TREMD simulations. For Monomer 42 and for Dimer2 47 replicas were run at temperatures forming a geometrical sequence between 290 and 406 K. Exchanges of configurations between neighboring replica were attempted every 5 ps. The time scale for each replica was 200 ns. The temperature range for the two systems was similar to the range chosen in a previous TREMD simulation study of Aβ (10-35) dimers.22 The time scale for each replica was chosen as a factor 1.3 larger than that in the previous work.
The peptide was modeled using the GROMOS96-43a1 force field37 in which CHi groups (i ) 1, 2, 3) are described using united atoms. Water molecules were represented by the threesite simple point charge (SPC) model.38–40 All simulations were performed using the GROMACS41 simulation code. The covalent bond lengths were constrained using the LINCS42 and SETTLE method42 for the peptide and water molecules, respectively. In addition, the masses of atoms attached to hydrogens were redistributed to increase the mass of the hydrogen atoms simulated explicitely. This eliminates high frequency motions of the hydrogens which allows the use of a time step of 4 fs.43 Although this slightly changes the kinetics of the system, it does not affect its structural properties. It has been observed that even the 5 fs time steps did not affect the populations of alternative conformational states of peptides significantly.44 The van der Waals interactions were treated using a twin-range cutoff; the forces between pairs of atoms were calculated every step if the distance between the atoms was less than 1 nm and together with the neighbor list updated every five integration steps if the distance was between 1 and 1.4 nm. Full electrostatic interactions were computed using the particle mesh Ewald technique45 with tinfoil boundary conditions.46 The temperature was controlled using a Berendsen thermostat47 with a relaxation time of 0.1 ps. Snapshots were saved every 20 ps for further analysis. All simulations were performed on AMD Opteron 2.4 or 3.0 GHz dual processor/dual core nodes. Analysis. The trajectory at 290 K was analyzed omitting the initial 150 ns for equilibration. The secondary structure of the peptide was determined based on the existence of main chain hydrogen bonds using the STRIDE program.48 Error bars were obtained by dividing the analyzed part of the trajectory into five segments. The tertiary structure of the peptide was analyzed based on the similarity of pairs of peptide configurations as follows. The trajectory consisted of a sequence of configurations as described by the positions ri(t) of all atoms i at time t using a time resolution of 20 ps. Either all atoms or only the positions of the main chain atoms of residues 104-119 were considered. To remove rigid body motions, the peptide configuration was rotated and translated yielding transformed coordinates r′i(t) such as to minimize (r′i(t) - ri(0))2. Hence, the root-mean-square deviation (rmsd) defined as
rmsd(t1, t2) )
[
N
∑
1 m |r' (t ) - r'i(t2)| 2 M i)1 i i 1
]
1/2
(1)
was determined where mi is the mass of atom i, and M ) ∑Ni)1mi. The configurations were analyzed using the Daura cluster analysis method.49 Here, pairs of configurations with an rmsd of less than 0.2 nm were considered to be neighbors. The configuration with the largest number of neighbors defines the central configuration. The latter configuration, together with its neighbors, was taken to form the first cluster and eliminated from the pool of structures. This process was repeated until no configurations remained in the pool. In the following, each cluster that has been obtained by this procedure will be viewed as a “conformation” of the peptide. In the figures, the location of β-sheets for these conformations are determined from the central configurations of the corresponding clusters. Likewise, the three-dimensional structure of these conformations are illustrated by the central configurations of the corresponding clusters and visualized using the software VMD.50 The probability pm,i of the conformation represented by cluster i of the monomer (m ) 1) or the dimer (m ) 2) was estimated
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from the respective number of configurations, km,i, and the total number of configurations considered, nm, via pm,i ) km,i/nm. Hence, the configurational entropy of the monomer or the dimer was estimated using
Sm ) -kB
∑ pm,i ln pm,i
(2)
i
where kB denotes Boltzmann’s constant. The entropy of a dimer, Spp, was estimated from Spp ) S2, that of two monomers from Sp+p ) 2S1, and the change in peptide entropy upon dimerization, ∆Sp, from
∆Sp ) Spp - Sp+p
(3)
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