J. Phys. Chem. B 2007, 111, 5351-5356
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Folding of the 25 Residue Aβ(12-36) Peptide in TFE/Water: Temperature-Dependent Transition from a Funneled Free-Energy Landscape to a Rugged One Narutoshi Kamiya,†,| Daisuke Mitomo,‡ Joan-Emma Shea,§ and Junichi Higo*,‡ Clinical Genome Informatics Center, Kobe UniVersity, Graduate School of Medicine, 1-5-6 Minatojima-Minami-machi, Chuo-ku, Kobe 650-0047, Japan, Laboratory of Bioinformatics, School of Life Science, Tokyo UniVersity of Pharmacy and Life Sciences, 1432-1 Horinouchi, Hachioji, Tokyo, 192-0392, Japan, and Department of Chemistry and Biochemistry, UniVersity of California, Santa Barbara, California 93106 ReceiVed: October 27, 2006; In Final Form: February 10, 2007
The free-energy landscape of the Alzheimer β-amyloid peptide Aβ(12-36) in a 40% (v/v) 2,2,2-trifluoroethanol (TFE)/water solution was determined by using multicanonical molecular dynamics simulations. Simulations using this enhanced conformational sampling technique were initiated from a random unfolded polypeptide conformation. Our simulations reliably folded the peptide to the experimental NMR structure, which consists of two linked helices. The shape of the free energy landscape for folding was found to be strongly dependent on temperature: Above 325 K, the overall shape was funnel-like, with the bottom of the funnel coinciding exactly with the NMR structure. Below 325 K, on the other hand, the landscape became increasingly rugged, with the emergence of new conformational clusters connected by low free-energy pathways. Finally, our simulations reveal that water and TFE solvate the polypeptide in different ways: The hydrogen bond formation between TFE and Aβ was enhanced with decreasing temperature, while that between water and Aβ was depressed.
1. Introduction The folding of a protein is governed by the structure of its underlying free energy landscape.1-4 It has been suggested that the energy landscape of proteins is minimally frustrated, with an overall funneled shape, and simulations have played a key role in characterizing these landscapes.5 Go-models (models in which only native contacts experience an attractive interaction) serve to emulate an idealized funneled landscape, in which energetic frustration is minimized, and folding is governed by topology.6 These simplified models have been successful in reproducing the folding kinetics7 and the folding transition-state ensemble of fast-folding proteins.8-13 Coarse-grained models with non-Go potentials have been used to explore how energetic frustration affects the roughness of the folding landscape.14,15 Fully atomic simulations have thus far mostly been limited to the study of small peptides,16-21 and a precise free-energy landscape of a medium or large protein with an accurate allatom model in an explicit solvent has yet to be obtained. The extent to which the energy landscape of such a “real” protein resembles a funneled landscape remains an open question. Recently, generalized ensemble methods (see ref 22 for a review), such as replica exchange sampling23,24 or multicanonical molecular dynamics (MCMD) simulation,25-27 have been developed to enhance the conformational sampling of polypeptides. We have shown that MCMD simulations can generate precise free-energy landscapes for short peptides with an all* Author to whom correspondence should be addressed. Phone: +8146-276-5498. Fax: +81-46-276-5351. E-mail:
[email protected]. † Kobe University. ‡ Tokyo University of Pharmacy and Life Sciences. § University of California. | Current address: Graduate School of Medicine, Osaka University, Open Laboratories of Advanced Bioscience and Biotechnology, 6-2-3, Furuedai, Suita, Osaka 565-0874, Japan.
atom model in explicit water, with our simulations producing a thermodynamically stable conformational cluster (i.e., nativestructure cluster) in good agreement with experimentally observed structures.28-31 Furthermore, these studies have shown the existence of conformational clusters other than the native one present in conformational space. It would be very interesting to see if this multicluster feature (i.e., rugged free-energy landscape) is specific only to short-peptide systems, or whether it applies to longer polypeptide sequences as well. In this work, we use MCMD to probe the nature of the freeenergy landscape of a 25-residue fragment of the Alzheimer’s β-amyloid peptide, Aβ(12-36). An NMR experiment has shown that this polypeptide adopts a unique tertiary structure in a 40% (v/v) 2,2,2-trifluoroethanol (TFE)/water solution.32 We prepared the polypeptide in the same condition as the experimental one, and started the MCMD simulation from a random conformation. Our simulations successfully reproduce the experimental NMR structure as the most thermodynamically stable conformation at 300 K and reveal that the shape of the landscape strongly depends on temperature. 2. Materials and Methods The Aβ originally consists of 40 (or 42) amino acid residues and a fragment consisting of residues n-m cut from the fulllength Aβ is generally expressed as Aβ(n-m). The experimental structure32 (pdb code 1AML; 20 NMR models deposited) of Aβ(1-40) in a 40% (v/v) TFE/water solution at 298 K is composed of two helices, helix 1 (residues 12-22) and helix 2 (residues 31-36), and a coil region (residues 23-30) linking the helices. Eleven residues at the N-terminal and four at the C-terminal are disordered in the NMR models. In our simulations, we only considered the ordered regions and the computed segment is thus Aβ(12-36) with sequence [Ace-12Val-13His-
10.1021/jp067075v CCC: $37.00 © 2007 American Chemical Society Published on Web 04/17/2007
5352 J. Phys. Chem. B, Vol. 111, No. 19, 2007 14His-15Gln-16Lys-17Leu-18Val-19Phe-20Phe-21Ala-22Glu-23Asp24Val-25 Gly-26 Ser-27Asn-28 Lys-29 Gly-30Ala-31Ile- 32 Ile-33Gly34Leu-35Met-36Val-Nme],
where Ace and Nme are the Nterminal acetyl and C-terminal N-methyl groups, respectively, introduced to cap the termini. We set up the simulation system as follows. First, a sphere (sphere 1; diameter ) 47.0 Å) consisting of water molecules was prepared. The water molecules in sphere 1 have been configurationally equilibrated at a density of 1 g/cm3 at 300 K in advance. Then, Aβ(12-36) was immersed in sphere 1 with the geometrical center of Aβ(12-36) set at the center of sphere 1. Water molecules overlapping polypeptide atoms were removed. We then randomly replaced 372 water molecules sited within a sphere (sphere 2; diameter ) 40.0 Å centered at the center of sphere 1) by 101 TFE molecules. In this replacement, average excluded volumes of 0.019 and 0.070 L/mol for water and TFE, respectively, were considered to set the TFE/water concentration in sphere 2 at the experimental value (i.e., 40% (v/v)).32 The final system consisted of 5098 atoms (101 TFE and 1264 water molecules, and 397 polypeptide atoms). The force field parameters for Aβ(12-36) and water molecule were taken from an AMBER-based hybrid force field33 and the flexible TIP3P water model,34 respectively. The hybrid force field was defined as a mixture of AMBER parm9435 (E94) and parm9636 (E96) force fields as (E94 + E96)/2. The difference between E94 and E96 exists only in the main-chain torsion angle energy terms. Thus, the hybrid force field was computed by simply hybridizing the torsion terms of E94 and E96. The force field for TFE was determined as follows. A bond parameter for C1-Fx (x ) 1, 2, 3), angle parameters for FxC1-Fy (y ) 1, 2, 3; x * y) and Fx-C1-C2, dihedral parameters for Fx-C1-C2-O and Fx-C1-C2-Hz (z ) 1, 2), and nonbond parameters for C1 and Fx were taken from http:// pharmacy.man.ac.uk/amber/, where C1 and C2 are carbon atoms covalently bonding to fluorine atoms Fx and C1, respectively, and Hz is the hydrogen atom attached to C2. The other bond and nonbond parameters were taken from the dataset in AMBER parm96.36 Partial charges for TFE were calculated with the charge fitting procedure of the RESP program37 after a geometric optimization with the Gaussian 98 program38 using the HF/631G* basis set. Version 325 of the program PRESTO39 was used for the MCMD simulation with the following simulation conditions: time step ) 1 fs; the SHAKE method40 to constrain covalent bonds between heavy atoms and hydrogen atoms; the cell multipole expansion method41 to compute electrostatic interactions; and temperature control by a constant-temperature method.42 To avoid evaporation, a harmonic potential was applied to water-oxygen atoms only when they were outside sphere 1. Another harmonic potential was applied to the heavy atoms of Aβ(12-36) and TFE only when they were outside sphere 2. The TFE/water concentration in sphere 2 then fluctuated around 40% (v/v) during the simulation. To keep Aβ(12-36) at the sphere center, the momentum and angular momentum of Aβ(12-36) were constrained to zero during the simulation. The MCMD simulation method25 is briefly summarized below. A modified potential energy is defined as EMCMD ) E + RT0 ln[P(E,T0)], where E is the original potential energy of the system, T0 the simulation temperature, and P(E,T0) the canonical energy distribution at T0. T0 is usually set to a high value (700 K in this work) so that the conformation can overcome high potential-energy barriers. EMCMD is used to calculate forces acting on atoms: force ) -grad EMCMD. If
Kamiya et al. P(E,T0) is accurately estimated in a range of potential energy, the MCMD simulation provides a flat energy distribution in the range. Since P(E,T0) is unknown a priori, iterative runs are required through which P(E,T0) gradually converges to an accurate distribution. Conformations sampled in the last run (i.e., the productive run) of the iteration are used for the conformational analysis. The density of states n(E) and the canonical distribution P(E,T) at any temperature T in the energy range are derived from P(E,T0) with the reweighting technique28-31 as follows: n(E), where n(E) dE is the number of microscopic states of the system in an energy interval [E, E + dE], is related to P(E,T0) as: P(E,T0) ) n(E) exp[-E/RT0]/Z(T0), where Z(T0) is a partition function at T0. P(E,T) is then derived as: P(E,T) ) n(E) exp[-E/RT]/Z(T) ) P(E,T0) exp[E/RT0]/exp[-E/RT] Z(T0)/Z(T). The term Z(T0)/Z(T) can be regarded as a normalization factor to calculate P(E,T). Choosing conformations with a statistical weight of P(E,T) from the whole of the sampled conformations, we can generate a thermodynamically equilibrated conformational ensemble S(T) at T. The starting conformation of Aβ(12-36) for the first run was a random conformation; the starting one for the ith run was the last conformation of the (i-1)th run. After 22 iterative runs, the productive run of 3.6 × 108 steps (360 ns) was done yielding a flat energy distribution in the temperature range 280-700 K. We stored a snapshot every 1 000 steps (360 000 snapshots stored in total). To analyze the free-energy landscape, the principal component analysis (PCA) was applied on the obtained conformational ensemble, as follows. The minimum distance (dij) between residues i and j was calculated in each sampled conformation in S(T) (number of residue pairs ) 253 with the condition of |i - j| g 3). Then, every conformation was represented by a vector as q ) [q1, q2, ..., q253], where q1 ) d12,15, q2 ) d12,16, ..., q253 ) d33,36. Next, a variance-covariance matrix, C, was calculated: Cmn ) 〈qmqn〉T - 〈qm〉T〈qn〉T, where Cmn is the (m,n)th element, and 〈...〉T represents the ensemble average over the conformations in S(T). By diagonalizing C, a set of eigenvectors and eigenvalues were obtained: the kth eigenvector and eigenvalue are denoted as Wk(T) and λk(T), respectively. The eigenvectors satisfy the equation Wi(T)‚Wj(T) ) δij. The eigenvectors construct a high-dimensional conformational space as coordinate axes. We designated a three-dimensional (3D) subspace constructed by Wi(T), Wj(T), and Wk(T) as Γ(i,j,k;T). The conformations in S(T) were then projected on Γ(1,2,3;T), where the position [c1,c2,c3] of a conformation, q′, in Γ(1,2,3;T) was given by the equation: ci ) Wi(T)‚(q′ - 〈q〉T). Finally, the distribution was expressed in a form of the potential of mean force: F(W1,W2,W3;T) ) -RT ln[F(W1,W2,W3;T)], where R is the gas constant and F is the density at position [W1,W2,W3] in Γ(1,2,3;T) (i.e., probability of finding a conformation at the position). We set F so that the highest density is equal to 1.0: Flowest ) 0. This distribution can be regarded as an image of a free-energy landscape. 3. Results Overall View of Free-Energy Landscape. To analyze the conformations generated by the MCMD simulation, we determined the number of native contacts for each structure. A native contact is defined as follows: if the minimum distance between heavy atoms belonging to different residues is less than rnc ()5.0 Å) in the NMR structure,32 this residue pair is registered as a candidate for the natively contacting residue pair (NCRP). In calculating the minimum distances, we used only the atomic positions in residues 12-36 of the deposited NMR models. Then, any candidate found in more than two-thirds (66.7%) of
Free-Energy Landscape of Aβ Peptide
J. Phys. Chem. B, Vol. 111, No. 19, 2007 5353
Figure 1. Dependence of Q on energy (E). The axis for temperature (T) is shown parallel tothe E axis; a tip mark at T corresponds to a value of 〈E(T)〉 ) ∫ EP(E,T) dE. Distribution is expressed in the potential of mean force: -RT ln[F(Q,E)], where F(Q,E) is the density at Q and E on the Q-E plane. The potential of mean force is given in kcal/mol and indicated by color.
the 20 NMR models was judged as a native contact. We then counted the number (Nnt) of native contacts in the NMR structure. Next, we defined the reproduction rate of native contacts (Q) of a sampled structure belonging to the conformational ensemble S(T) as follows: If the minimum heavy atom-heavy atom distance between two residues belonging to the native contact list was less than 1.2rnc () 6.0 Å), we considered a native contact to be formed. The multiplication of 1.2 has been used in estimating Q by other researchers.10,43 Assuming the atomic radius for protein heavy atoms to be 2 Å, the remaining space between two natively contacting residues in a snapshot is less than 2 Å. Thus, a water molecule (diameter ) 3 Å) cannot penetrate between the residues. Finally, Q was defined as Q ) Nsnap/Nnt, where Nsnap is the number of the reproduced native contacts in the snapshot. The dependency of Q on the energy E is shown in Figure 1 for different temperatures. It is clear that the lower the temperature, the larger the Q value. As well, the greater the number of native contacts in a conformation, the lower the internal energy (i.e., 〈E(T)〉). This result supports a picture in which the free-energy landscape of Aβ(12-36) in the TFE/ water solution is funnel-like in nature. We note, however, that while Q is a very useful reaction coordinate for idealized Gomodel systems, it may not be a suitable reaction coordinate for the fully atomic system considered here. Indeed, highly structurally dissimilar conformations can have the same Q,44 indicating that the Q value does not have sufficient resolution to discriminate conformational differences in fully atomic systems. To analyze the nature of these conformational differences, we used PCA, projecting conformations in the ensemble (S(T)) at a temperature T on the 3D subspace Γ(1,2,3;T), constructed from the first three eigenvectors W1(T), W2(T), and W3(T) (see Materials and Methods). We designate this projected distribution as D(T). Although a three-dimensional description cannot capture all the details of the full-dimensional conformational distribution, it can nonetheless provide very useful insight into some essential features of the free-energy landscape.28-31 Figure 2 displays D(T) at three temperatures. One can visually infer from this figure that the lower the temperature, the more rugged the landscape: At 500 K, D(500K) presents a simple landscape
Figure 2. Conformational distribution, D(T), at 500 (a), 400 (b), and 300 K (c). The 3D subspace, Γ(1,2,3;T), was constructed by eigenvectors computed from S(T) at each T. The distribution is expressed in potential of mean force F (see Materials and Methods). In part c, blue and magenta contours respectively represent levels of F ) 1.0 and 3.0 kcal/mol, which correspond to densities of F1 ) exp[-1 × 0.59] and F2 ) exp[-3 × 0.59], respectively. The blue and magenta contours in parts a and b are given so that density levels are equal to F1 and F2, respectively. Consequently, the blue contours represent F ) 1.67 kcal/ mol in part a and 1.33 kcal/mol in part b, and the magenta contours represent F ) 5.0 kcal/mol in part a and 4.0 kcal/mol in part b. Three panels are drawn with the same axis scale, although the orientations are slightly different from one another.
(Figure 2a) with no clear cluster separation seen and the high density (i.e., low free energy) region located in the center of the distribution. The distribution at 400 K D(400K) is more complex than D(500K) with some clusters present (Figure 2b), while the distribution at 300 K D(300K) is clearly rugged, with several conformational clusters present (Figure 2c). With using the value of F2 ) exp[-3 × 0.59] for the magenta contours, the clusters were connected by the magenta contours as shown
5354 J. Phys. Chem. B, Vol. 111, No. 19, 2007
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Figure 3. Temperature (T) dependence of xmin.
in Figure 2c. On the other hand, the cluster-cluster connection was rapidly broken when a smaller density (i.e., a higher freeenergy level) was used for F2 (data not shown). Thus, the barrier height measured from the periphery of the clusters (regions surrounded by the blue contours) at 300 K was calculated as ∆F ) 300 K × R ln[F1/F2] ) 2 kcal/mol. We cannot obtain a reliable rate constant for overcoming the free-energy barriers from the current work as simulation times generated by enhanced sampling techniques such MCMD are not meaningful. To analyze the temperature dependence of D(T) more quantitatively, a one-dimensional distribution function F1D(p;T) was generated by projecting the 3D distribution F(W1,W2,W3;T) onto the first PCA axis W1, where p is the component along the W1 axis. We then calculated a correlation function: c(x;T) ) 〈F1D(p+x;T)F1D(p;T)〉p, where the average 〈...〉p was taken with sliding p. At any temperature, c(x;T) presented a maximum at x ) 0 before decaying as x increased, and finally reaching a minimum. We designated the value of x at the minimum as xmin. After reaching the minimum, c(x;T) repeatedly increases and decreases with gradually decaying amplitude. Figure 3 displays the temperature dependence of xmin. Since xmin corresponds to an average distance between a peak of F1D(p;T) and the nearest bottom of the peak along the first PCA axis, xmin can be approximately regarded as an average size of the conformational clusters on the first PCA axis at each temperature. Figure 3 thus indicates that the cluster size changes abruptly at 325 K. In other words, the free-energy landscape goes from funnel-like above 325 K to rugged below 325 K. Figure 3 also implies that the free-energy barriers separating the clusters (Figure 2c) vanish at 325 K. Conformational Distribution at 300 K. Figure 4 displays the distribution of conformations with Q g 0.7 in D(300K). Conformations with Q g 0.7 are distributed over the entire region of D(300K), and the average, 〈Q(300K)〉, of Q at 300 K was 0.75 (standard deviation ) 0.12). Thus, the majority of the conformations in D(300K) had considerable similarities with the NMR structure32 (which consists of two helices linked by a coil region). We note that the dots assigned to be close to each other in Figure 4 correspond to similar conformations because the patterns of the residue-residue distances are similar between them. Hence, two conformations that may have largely different Q values can be similar when they are close in Figure 4. Note that a small conformational change may cause a large change in Q because a residue-residue contact can vanish with the
Figure 4. Conformations with large Q in D(300K). Conformations with Q g 0.9 are indicated in red, those with 0.9 > Q g 0.8 in yellow, and those with 0.8 > Q g 0.7 in gray. Free-energy contours are the same as those in Figure 3c. Nine conformations, P1-P9, are displayed; character “N” represents the N-terminal.
Figure 5. Eight conformations chosen randomly around P6 and P7 in D(300K). The positions of P6 and P7 in D(300K) are shown in Figure 6. The main chains of the chosen conformations are displayed. Residues 25-35 (indicated as a stick model) of the picked conformations are superimposed. The black lines are H-bonds.
small conformational change. Figure 4 displays nine conformations chosen from D(300K). Conformations P1, P2, P5, and P9 possess both helices 1 and 2, although the relative positioning between the helices varied. This variety was also observed in the NMR structure.32 It is clear that the variety is due to the structural flexibility of the linker between helices 1 and 2 (the freedom for motion of the polypeptide chain is limited to the linker part when the two helices are formed). In the other conformations (P3, P4, P6, P7, and P8), helix 2 was disordered. This disordering of helix 2 is supported by our previous study45 of unfolding simulations of the NMR structure, in which we found that helix 2 was less stable than helix 1, and that the lesser stability of helix 2 correlated well with a theoretically computed φ value. These results indicate that the C-terminal part around helix 2 has more structural variety than the part around helix 1. Interestingly, the C-terminal part (residues 29-34) of P6 and P7 adopted a hairpin-like structure. We randomly chose conformations from a zone around P6 and P7 in Figure 4 and found that the hairpin-like structure was seen in most of the conformations in the zone. Figure 5 displays eight
Free-Energy Landscape of Aβ Peptide
Figure 6. Energy (E) and temperature (T) dependence of nHB.
conformations chosen from the zone with focus on the Nterminal part. When residues 25-35 were superimposed, the main-chain root-mean-square deviations among the conformations were at most 1.3 Å. Intra-main-chain H-bonds that frequently formed in the hairpin-like structure were Gly29:OLeu34:HN and Ala30:O-Gly33:HN. In some conformations, however, Gly29:O alternatively bonded to Gly33:HN or Ile32: HN. Thus, the structure of residues 29-34 was distorted from an ideal β-hairpin. We also found an alternative H-bond: Ser26: O-Gly29:HN or Ser26:O-Ile31:HN. Temperature Dependence of Hydrogen Bond Formation between Aβ and Solvent. The hydrogen bond (H-bond) formation between solvent and Aβ(12-36) may be important for evaluating effects of solvent on Aβ(12-36) structure. Here, we designate an H-bond between a TFE molecule and Aβ(1236) as HB[TFE-Aβ], one between a water molecule and Aβ(12-36) as HB[wat-Aβ], and an intra-Aβ(12-36) H-bond as HB[intra-Aβ]. The numbers of these H-bonds were designated as nHB[TFE-Aβ], nHB[wat-Aβ], and nHB[intra-Aβ], respectively. Figure 6 shows the temperature dependence of nHB. The nHB[TFE-Aβ] increased with a decrease in T across the entire temperature range. In contrast, nHB[wat-Aβ] was nearly constant from 700 to 450 K, then decreased with decreasing T below 450 K, before leveling off around 300 K. The sum nHB[TFE-Aβ] + nHB[wat-Aβ] increased with decreasing T, while nHB[intra-Aβ] increased monotonically with decreasing T. The increment of nHB[intra-Aβ] with decreasing T was slower than that of nHB[wat-Aβ] around 300 K. Therefore, the change of the total nHB ()nHB[TFE-Aβ] + nHB[wat-Aβ] + nHB[intraAβ]) around 300 K was primarily due to nHB[TFE-Aβ]. 4. Discussion If a simulation fails to reproduce a reliably determined experimental structure, then a detailed analysis on the energy landscape and sampled conformations may be irrelevant. In the current work, however, the lowest free-energy state at room temperature identified from MCMD simulation coincided well with the NMR structure. An interesting observation from our work is that the structural features of the free-energy landscape strongly depend on the coordinate axes used to express the
J. Phys. Chem. B, Vol. 111, No. 19, 2007 5355 landscape. Indeed, when plotted in the E-Q plane (Figure 1), the free energy landscape of our fully atomic protein in the explicit TFE/water solvent appears to be funneled. In contrast, when a PCA representation is used, the free-energy landscape switches from a funnel to more rugged shape at 325 K (Figure 3). Appearance of ruggedness with a lowering of the temperature may be a property found in many complicated systems: a number of potential-energy barriers exist in the conformational space and overcoming the barriers becomes more difficult with decreasing temperature. An important aspect derived from the current study is the abruptness of the transition between the funnel and the rugged landscapes. This result suggests a switching of the protein folding kinetics from entropy-limited to enthalpy-limited at 325 K. We note that even though the free-energy landscape becomes more rugged below 325 K, it does not entirely lose all funneled features. Indeed, even below 325 K, there is still a well-defined global minimum corresponding to the NMR structures. The conformational zone sampled below 325 K was restricted to this “funnel bottom” as indicated in Figure 1. The current work shows that clusters appear in the funnel bottom when the temperature is decreased. Since the MCMD simulation provides only the equilibrated distribution at each temperature, we do not have information outside the funnel bottom below 325 K. To investigate how the whole free-energy landscape is rugged below 325 K, the outside of the funnel bottom should be effectively sampled with a new sampling algorithm, where the simulations should start from random conformations at a temperature blow 325 K and reach the funnel bottom with providing the conformational distributions at the temperature. Now, we focus on the landscape at 300 K. The free-energy landscape is informative not only to predict the most stable conformation but also to expose details of pathways for conformational changes, which are undetectable experimentally. Figure 4 provides possible pathways among the clusters at 300 K. For instance, a direct movement from P4 to P6 requires overcoming a high free-energy barrier. So the conformation should take an indirect route for the movement between P4 and P6. In the current simulation, Aβ exhibited a conformational flexibility even though the native-contact patterns were similar with those in 1AML:32 the relative positioning between helices 1 and 2 had variety due to the flexibility of the linker part (see P1, P2, P5, and P9) in both the computational and NMR structures. The main focus for the current work is not to study the role of TFE in the polypeptide structure formation but to elucidate the free-energy landscape of the polypeptide that has a welldefined tertiary structure at room temperature. However, it is worth mentioning that TFE and water played different roles in hydration. Figure 6 clearly indicated that the water-Aβ H-bonds were replaced by TFE-Aβ H-bonds with a decrease in temperature. This result supports the preceding experimental46 and computational47 results that TFE induces the structure formation of polypeptide by displacing water molecules from hydrogenbondable sites around the polypeptide. Hong et al. have suggested that clusters of TFE and 3,3,3,3′,3′,3′-hexafluoroproponal (HFIP) molecules formed around a polypeptide may induce the helix-inducing property of TFE.48 Wei and Shea also have recently demonstrated that HFIP molecules preferentially hydrate Aβ(25-35) by performing a replica-exchange MD simulation.20 The transition of the free-energy landscape from funnel to rugged seen in our simulations is likely a feature of most peptides, rather than a specific characteristic of this particular
5356 J. Phys. Chem. B, Vol. 111, No. 19, 2007 fragment of the Aβ peptide. Indeed, potential energy barriers become more difficult to overcome at lower temperatures, leading to a rougher landscape. Therefore, the cluster separation seen here for Aβ(12-36) is likely a general property for many polypeptide systems. Interestingly, the presence of TFE would seem to reduce the roughness of the landscape compared to water (as can be seen by contrasting the results presented here to those from our recent simulations of this same peptide in water).49 It is difficult to assess whether the precise transition temperature seen here is the same for all peptides, or whether it varies with peptide length and sequence. Further simulations on other peptides would have to be performed. The validity of the force field is important in assessing the simulation results. The AMBER parm9636 is a better force field than parm9435 is in reproducing an experimentally determined tertiary structure for short peptides in explicit water.28,30,33,50 As a preliminary act, we performed an MCMD simulation of Aβ(12-36) using parm96 and found that parm96 considerably favors sheet conformations (data not shown). A combined study of quantum chemical and MCMD calculations showed that the hybrid force field is better than parm96 or parm94.33 In fact, the hybrid force field successfully reproduced the 1AML structure in the TFE/water solution, although this successful result does not necessarily mean that the force field used was perfect. The free-energy landscape generated at high temperatures (500 K) may not be fully accurate, as the force field was designed to reproduce the native structure of a polypeptide around 300 K. However, we believe that the current study provided an interesting property of the free-energy landscape in the physiological temperature range. 5. Conclusions The multicanonical molecular dynamics simulation provided the temperature dependence of the free-energy landscape of Aβ(12-36) in the explicit 40% (v/v) TFE/water solution. The shape of the free-energy landscape drastically changed at 325 K. Above 325 K, the overall shape of the free-energy landscape was funnel-like, with the bottom of the funnel coinciding exactly with the NMR structure. Below 325 K, on the other hand, the landscape became increasingly rugged, with the emergence of new conformational clusters connected by low free-energy pathways. Acknowledgment. We are grateful to Drs. Kei-ichi Yamaguchi (Center for Emerging Infectious Diseases, Gifu University, Japan) and Haruki Nakamura (Institute for Protein Research, Osaka University, Japan) for helpful discussions. J.H. was supported by Japan Science and Technology Corporation (JST), BIRD. References and Notes (1) Onuchic, J. N.; Luthey-Schulten, Z.; Wolynes, P. G. Annu. ReV. Phys. Chem. 1997, 48, 545. (2) Onuchic, J. N.; Wolynes, P. G. Curr. Opin. Struct. Biol. 2004, 14, 70. (3) Shea, J.-E.; Brooks, C. L., III Annu. ReV. Phys. Chem. 2001, 52, 499. (4) Brooks, C. L., III Acc. Chem. Res. 2002, 35, 447. (5) Bryngelson, J. D.; Onuchic, J. N.; Socci, N. D.; Wolynes, P. G. Proteins 1995, 21, 167. (6) Go, N. Annu. ReV. Biophys. Bioeng. 1983, 12, 183. (7) Munoz, V.; Eaton, W. A. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 11311. (8) Clementi, C.; Jennings, P. A.; Onuchic, J. N. Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 5871. (9) Clementi, C.; Nymeyer, H.; Onuchic, J. N. J. Mol. Biol. 2000, 298, 937.
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