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1 Basic Research Program, SAIC-Frederick, Inc., Laboratory of Experimental and Computational Biology, National Cancer Institute at Frederick, Frederick, Maryland 21702, USA
2 Sackler Institute of Molecular Medicine, Department of Human Genetics and Molecular Medicine, Sackler School of Medicine, Tel Aviv University, Tel Aviv 69978, Israel
Reprint requests to: Ruth Nussinov, NCI-FCRF Building 469, Room 151, Frederick, MD 21702; e-mail: ruthn{at}ncifcrf.gov; fax: (301) 846-5598.
(RECEIVED February 13, 2003; FINAL REVISION June 13, 2003; ACCEPTED June 19, 2003)
Article and publication are at http://www.proteinscience.org/cgi/doi/10.1110/ps.0306103.
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Abstract |
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 TOP Abstract IntroductionResults and DiscussionMaterials and methodsReferences |
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-Helical instead of a ß-hairpin structure was the most stable form for the E2 isomer. However, no matter how much the sequence changes, for all variants studied, ideal "native" ß-hairpin topologies remain as minima (regardless of whether global or local) in the energy landscape. In general, we find that the energy landscape is dependent on the hydrophobic cluster topology and on the sequence. Our present study indicates that the key is the relative conformational energies of the different conformations. Changes in the sequence strongly modulate the relative stabilities of topologically similar regions in the energy landscape, rather than redefine the topology space. This finding is consistent with a population redistribution in the process of protein folding. The limited variation of topological space, compared with the number of possible sequence changes, may relate to the observation that the number of known protein folds are far less than the sequential allowance. Keywords: Protein folding; side-chain interaction; hydrogen bonding; hydrophobic interactions; ß-peptide; ß-hairpin
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Introduction |
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TOPAbstractIntroductionResults and DiscussionMaterials and methodsReferences |
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Protein topology and stability may define the space of allowed sequences (Koehl and Levitt 2002). Hence, sequence evolution is under structural constraints (Parisi and Echave 2001). The question is, then, how does the change in the sequence affect the protein structure.
ß-Hairpin structures may constitute suitable minimal systems for in-depth studies of fundamental issues in protein folding. In particular, Muñoz et al. (1997, 1998) have shown that a 16-residue ß-hairpin peptide captures the essential features of the folding of large proteins. The peptide folds rapidly and cooperatively into a conformation with a defined secondary structure and a well-packed hydrophobic cluster of aromatic side chains. The peptide they used (GEWTYDDATKTFTVTE, residues 41–56 from the protein G B1 domain, named G peptide below following the method of Honda et al. 2000) has a similar conformation in the isolated state (Blanco et al. 1994) compared with that observed in the protein (Gronenborn et al. 1991).
A particularly interesting feature of the G peptide is the topology of a four-residue hydrophobic cluster (W43, Y45, F52, and V54). Numerous experimental and theoretical studies indicate that this hydrophobic cluster is crucial for the stability of the G peptide. There are two points concerning the hydrophobic cluster: (1) how many residues are needed to form stable hydrophobic cluster in the G peptide, and (2) what are the effects of shifting the hydrophobic cluster (toward the turn or toward the terminus) in the ß-hairpin structure. Both lead to an intriguing sequence–topology relationship.
Previous studies have addressed some aspects of the sequence–topology relationship of the G peptide. Computationally, coarse-grained (Kolinski et al. 1999; Guo et al. 2000; Klimov and Thirumalai 2000) and atomistic (Dinner et al. 1999; Pande and Rokhsar 1999; Roccatano et al. 1999; Bryant et al. 2000; Ma and Nussinov 2000; Garcia and Sanbonmatsu 2001; Lee and Shin 2001; Zagrovic et al. 2001; Zhou et al. 2001; Zhou and Linhananta 2002) models were used to study the folding/unfolding and the energy landscape of the peptide. The G peptide also serves as a reference for ß-hairpin design and for mutational studies (Kobayashi et al. 2000; Cochran et al. 2001; Espinosa et al. 2001). From molecular dynamics simulations, Ma and Nussinov (2000) proposed that three out of the four hydrophobic residues are sufficient to form a stable hydrophobic cluster in the ß-hairpin structure. Experimental mutational studies confirmed that V54A, and possibly W43A, mutants still fold as a ß-hairpin. However, either a Y45A or a F52A mutation strongly destabilizes the ß-hairpin structure (Kobayashi et al. 2000).
By using a statistical mechanical model, Muñoz et al. (1998) first characterized two variants of the original ß-hairpin: moving the hydrophobic cluster one residue closer to the center of the peptide (W44, Y46, F51, V53) and one residue closer to the ends (W42, Y44, F53, V55). The results indicated that the ß-hairpin is stabilized and the folding rate is enhanced if the hydrophobic cluster is moved closer to the turn and opposite if moved toward the ends. Kolinski et al. (1999) also simulated the two variants (with a Monte Carlo lattice model) and found similar trends. Klimov and Thirumalai (2000) tested other possibilities of shifting the hydrophobic cluster two residues toward the turn and two residues closer to the ends. They also found that a shift changes the folding rate and cooperativity of ß-hairpin formation. At least two experimental studies have also been devoted to the moving of the hydrophobic cluster along the ß-hairpin strands (Santiveri et al. 2000; Espinosa et al. 2001). Santiveri et al. (2000) found that the bending rigidity of the turns alters the side-chain interactions. Based on studies of a series of isomers of a 20-residue peptide (derived from the G peptide), Espinosa et al. (2001) concluded that the separation between the loop segment and the hydrophobic cluster strongly influences the ß-hairpin size and stability, with a smaller separation leading to a greater stability.
To further understand the structure–sequence relationship of the G-related peptides, we investigated the energy landscapes and dynamics of the ß-hairpins, changing the size and position of the hydrophobic cluster. The peptides investigated (Fig. 1
) include three isomers corresponding to moving the hydrophobic cluster toward the inside, that is, toward the turn region (T1, AGEWTYDDKTFTVTET; T2, GEDTWDYATFTVTKTE; T3, GEDDWTYATFTVTKTE), and three isomers shift the hydrophobic cluster outside, toward the end region (E1, EWTYDDAGETKTFTVT; E2, WEYTGDDATKTETFTV; E3, WTYEGDDATKTETFTV). For each peptide isomer, we generate the folded structures (ß-hairpin and -helix), partially folded and random conformations by using high temperature molecular dynamics simulation. The free energy surfaces are constructed by using the free energies of the generated conformers. The free energy terms include molecular mechanics energy, Poisson-Boltzmann electrostatic solvation energy, surface area solvation energy, and conformational entropy estimated by using normal mode analysis.
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Results and Discussion |
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TOPAbstractIntroductionResults and DiscussionMaterials and methodsReferences |
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In the present study, we adopt the Klimov and Thirumalai’s permutation (Klimov and Thirumalai 2000; M1 is T2, and M2 is E2; Fig. 1
) and select other permutations to ensure that we have both similarity and diversity. Our goal is to carry out a meaningful comparison between changes in sequence and topology. Our T1 and T2 are similar to Kolinski’s (1999) S1 and S2, however, with a lesser turn conservation. T3 has more sequence conservation than does T2, with YTW and FTV moving together inside the turn region. E3 has the highest sequence similarity to the wild type, with YTW and FTV moving together outside toward the end, keeping the turn region of DDATKT unchanged.
Changes in the sequence can alter the secondary structure preference of the peptide to different extents. By using the PSIPRED protein structure prediction server (http://bioinf.cs.ucl.ac.uk/psipred; Jones 1999), we tested the secondary structure preference changes upon shifting the hydrophobic cluster along the ß-hairpin strands. For the wild-type G-peptide sequence, the server correctly predicted one of the two ß-strands, with the sequence GEWTYDDAT to be random and KTFTV to be a ß-structure. When shifting the hydrophobic cluster one residue closer to the turn, the resulting peptide (T1) has a similar secondary structure preference as the wild type. However, when shifting two residues closer to the turn (T2 and T3), additional residues are predicted to be in an extended structure, with a turn region. Note that in the T2 and T3 permutations, the turn residues have mostly changed. For the shifting of the hydrophobic cluster one residue closer to the end (E1), the predicted structural preference is again similar to the wild type. For the larger moving steps (two residues closer to the end, E2 and E3), all sequences are predicted to be random (Fig. 1), even for the E3 sequence, which has the highest sequence identity compared with the wild-type G peptide.
We also used the PHD server (Rost and Sander 1993). Because the query sequences are too short (16 residues) for the PHD algorithm, we added two XX to our query sequences (e.g., for the native peptide we seek XXGEWTYDDATKTFTVTEXX). The predicted secondary structures are also reported in Figure 1. In general, the PHD algorithm predicted more extended structures for the isomers.
The secondary structure predictions only indicate that the permuted sequences may still be able to form ß-strands. However, because the turn propensity is not addressed, their ß-hairpin propensities are unknown from the secondary structure predictions. In general, the stability of a ß-hairpin structure depends on three factors: the turn propensity, the stability of the hydrophobic cluster, and the interactions between backbone hydrogen bonding, dictated by strand propensities. In all permutations, the hydrophobic core appears closely packed. However, the turn and strand propensities change: The T1 and E1 permutations are the most likely to keep the ß-hairpin structure, because their strand propensity is still preferred and the turn region is predicted to be a coiled structure. E2 and E3 also appear to have a good probability to be in a ß-hairpin conformation due to the high conservation of the turn sequences. However, from the PSIPRED prediction, their strand propensities may have changed too much (Fig. 1). As for the T2 and T3 sequences, their hydrophobic cores are very close to the turn and are expected to stiffen the turn region. Indeed, both PHD and PSIPRED predict continued extended structures around the turn region, which is unfavorable for a ß-hairpin structure.
The size and position of the HP cluster change the energy landscape
Experiments and computational studies (Veitshans et al. 1997) show that much of the complexity seen in the folding of proteins is captured in peptides with well-defined low-energy structures. Characterization of the folding free energy surface of small peptides may provide an insight into peptide stabilities and folding pathways. Bursulaya and Brooks (1999 Bursulaya and Brooks (2000) examined the potential of mean force (PMF) surface of the three-stranded ß-sheet protein Betanova. They found that the overall shape and location of the global minimum are relatively less sensitive to the solvation models (explicit and implicit GB models) used. In the present study, we explored the free energy landscapes for the wild type and its variants.
Initially, we tested three types of reaction coordinates to characterize the free energy surface of the wild type peptide. Two obvious reaction coordinates are the intrastrand hydrogen bonds and the fraction of the native contacts. In the present study, we use a measure to follow the closeness of the hydrophobic clusters, the HP cluster index (see Materials and Methods). Our concerns are largely the stability of the hydrophobic cluster, how this stability affects the overall peptide topology, and what are the sequence effects. The question is which combination to use: HP cluster with native contacts or with intrastrand hydrogen bonds as reaction coordinates.
As may be seen in Figure 2, the free energy surface shows a well-defined global minimum with the HP cluster index and the native contact fraction (Fig. 2A,B), centered near a native contact fraction of 0.5 to 1 and the HP index around zero (the smaller the HP index, the more compact the HP cluster). When using the HP index and the number of hydrogen bonds to characterize the free energy surface, we see an L-shaped valley (Fig. 2C,D), favoring a more compact HP cluster and, to a lesser extent, hydrogen bonds. The L-shaped distribution is very similar to the potential energy surface previously characterized by Pande et al. (Pande and Rokhsar 1999; Zagrovic et al. 2001) for the wild-type peptide. The free energy surface characterized by the native contact fraction and the hydrogen bonds (Fig. 2E,F) is much less defined compared with the native contact fraction and the HP cluster index.
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) also shows that the folding has no apparent enthalpic barrier. However, there is a possible entropy barrier from the extended state, with a large hydrophobic cluster separation and an absence of native contacts. Note that the energy landscape with the HP cluster index and a native contact fraction forms a rugged funnel for the wild-type peptide. The folding funnel concept (Bryngelson and Wolynes 1989; Frauenfelder et al. 1991; Baldwin 1994; Bozko and Brooks 1995; Karplus et al. 1995; Onuchic et al. 1995; Wolynes et al. 1995; Dill and Chan 1997; Lazaridis and Karplus 1997; Gruebele and Wolynes 1998; Dill 1999) indicates that the most realistic model of two-state proteins is a minimally frustrated heteropolymer with a rugged funnel-like landscape biased toward the native structure (Shea et al. 1999). In constructing an energy landscape, a smooth surface would be preferred, especially when one wants to fold a protein ab initio. In the current study, we are mostly interested in the change of the energy landscape with the sequences. Therefore, we need reaction coordinates that can provide a well-defined fold location and with the changes progressively moving toward the folded region. In this sense, the combination of the HP cluster index and the native contact fraction is ideal for this purpose. For the rest of the isomers studied, we mainly use the HP cluster index and the native contact fraction to characterize the free energy surface.
A comparison of Figure 3A (for the T1) with Figure 2A shows that when shifting the hydrophobic cluster one residue inside toward the turn region (T1, AGEWTYDDKTFTVTET), the free energy landscape does not change too much. For both the wild type and the T1 isomer, the narrow valley corresponds to the ß-hairpin conformations. As may also be seen in Table 1, ß-hairpin structures dominate the top 10 most stable conformers for the wild type and the T1 isomer. These results are consistent with our expectation from secondary structure analysis.
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), with a few isolated valleys corresponding to larger hydrophobic residue separations. No native (ß-hairpin) contacts appear. For the T2 sequence, the energy landscape is diffusive. Indeed, a fully extended structure (Fig. 4B; Table 1) was identified as the most stable conformer for the T2 isomer. For the T3 isomer, a partially folded -helix (at the N-terminal portion; data not shown) is ranked number three (Table 1). Note that for the T2 and T3 isomers, the hydrophobic residues are close in sequence (at the turn); therefore, the HP cluster indices are relatively smaller than those of the wild-type G peptide and of the T1 isomer. Still, all three isomers (T1, T2, and T3) share similar landscape features. From the wild type to T1, then T3, and finally T2, we see a progressively changing energy landscape toward less stable ß-hairpin structures. This behavior is due to the change in the sequence reflected in the turn topology and in the position of the HP cluster. The prediction that the T2 should be less stable than the wild type is in accord with the conclusions of Klimov and Thirumalai (2000).
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) ranks two random conformers in the top three conformations. Still, there is a deep valley centered around the ideal ß-hairpin structure and the most stable conformer is a hairpin structure with a long loop (Table 1; Fig. 4D). Moving the hydrophobic cluster to the very end (E2, WEYTGDDATKTETFTV; E3, WTYEGDDATKTETFTV) also leads to an interesting free energy landscape (Fig. 3E,F). For the E2 isomer, a completely folded -helix structure was the most stable conformer (Fig. 4E). There is only a small valley corresponding to the ideal ß-hairpin structure. Even though the ß-hairpin structure appears in the top 10 conformers, the top-ranking conformers are dominated by extended and random structures (Table 1).
The change in the HP cluster size also provides insight into its role in stabilizing the ß-hairpin structure. We investigated the energy landscape of three GB1 peptide variants, replacing W43 by Gly, replacing W43 and V54 by Gly, and mutating Y44 and F53 to Gly (Fig. 5). In our previous study (Ma and Nussinov 2000), we named the three variants P4, P7, and P8, respectively. The P4 peptide still has a similar landscape as the wild type. However, when an additional hydrophobic residue is mutated out (P7; Fig. 5B), conformations with large hydrophobic separations (Y–F for P7; and W–V for P8) become energetically accessible.
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Correlation of the free energy landscape and peptide conformation dynamics
Molecular dynamics simulations of the wild-type G peptide have been reported extensively in the literature (Dinner et al. 1999; Kolinski et al. 1999; Pande and Rokhsar 1999; Roccatano et al. 1999; Bryant et al. 2000; Guo et al. 2000; Klimov and Thirumalai 2000; Ma and Nussinov 2000; Garcia and Sanbonmatsu 2001; Lee and Shin 2001; Zagrovic et al. 2001), as well as the simulations of P4, P7, and P8 peptides (Ma and Nussinov 2000). In the present study, we have also conducted MD simulations for the six isomers (T1, T2, T3, E1, E2, and E3). For each isomer, two independent MD simulations are run with slightly different ideal ß-hairpin starting geometries.
The trajectories of the hydrophobic cluster index are reported in Figure 6. In general, shifting the HP cluster by just one residue toward the inside (T1) or outside (E1) can still keep a stable ß-hairpin structure, whereas no stable ß-hairpin structure is observed in the course of the simulations for T2, T3, E2, and E3. Such conformational dynamics are consistent with what we can expect from their free energy landscapes. The energy landscape for T2 (Fig. 3B) shows a broad distribution of low-lying conformers. For the E2 isomer, there is only a small valley for the compact HP cluster, with most low-lying conformers located in other regions (Fig. 3F). In the MD simulations, the starting ß-hairpin structures for both the T2 and E2 isomers quickly changed into random states, which also show a large separation between the hydrophobic residues (Fig. 6, green lines).
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-helix was found to be the lowest lying conformer for the E2 isomer. We also simulated the stability of the -helical E2 isomer. At the 278 K (1.4 nsec) and, subsequently, the 300 K (1 nsec) simulations, the central portion of the E2 isomer keeps the -helical structure well, whereas both the N- and C-terminal residues fluctuate.
The hydrophobic clusters of the T3 and E3 isomers are relatively more compact than those of the T2 and E2 isomers. The sole difference between the T2 and T3 conformers (and between the E2 and E3 conformers) is that T3 and E3 retain slightly more of the wild-type character (i.e., WTY matches FTV in T3 and E3) than do T2 and E2 (Fig. 1). However, as may be seen in Table 1 and Figure 3, the absolute free energies of these isomers are all much higher than that of the wild-type peptide. These elevated free energy surfaces lead to unstable ß-hairpin structures in the T3 and E3 isomers.
In molecular dynamics simulations, kinetic barriers often trap specific conformations. This may be the case for our simulations of the E1 and P8 peptides. Examination of the energy landscape for the E1 isomer (Fig. 3D) indicates large conformational fluctuation. However, the MD simulation shows a consistent ß-hairpin structure and a well-defined hydrophobic cluster (Fig. 6B, blue lines). In our previous simulations of the P4, P7, and P8 peptides (Ma and Nussinov 2000), we found that P4 and P8 are consistently stable, whereas P7 showed an unfolding and refolding transition. Experimental evidence indicated that P4 might be stable in solution (experiment W43A mutation; see Kobayashi et al. 2000; P4 is the W43G mutant), whereas P8 should be random in solution. Examination of the energy landscapes for the P4, P7, and P8 (Fig. 5) peptides indicates that P4 (with a funnel-like landscape similar to the wild type) is stable in solution, whereas P8 may be random, consistent with experimental studies. Apparently, the previous simulations of P8 were caught in a kinetic trap, and the additional simulations with multiple trajectories may have revealed its true stability.
Conclusions
Through a study of two peptides with similar topologies (three-stranded antiparallel ß-sheet) and a low sequence identity (15%), Ferrara and Caflish (2001) have shown that the overall shape of the free-energy surface is defined primarily by the native-state topology, whereas the sequence determines the statistically predominant order of the events. In our present study, we have revealed the gradual changes of the free energy surface with the size and position of the hydrophobic cluster for the G-peptide variants.
Shifting the HP cluster along the ß-strands introduces sequence changes as well. As for the six isomers studied, two (T1 and E1) share high sequence identity with the wild-type G peptide (87.5%). Although shifting the HP cluster one residue inside toward the turn region (T1) preserves the characteristics of the energy landscape the most, the landscape changes dramatically when the HP cluster shifts one residue outside toward the end region (E1). Isomers T2, T3, E2, and E3 share little sequence identity with the G peptide. In terms of topology, all these sequences can form a ß-hairpin structure with a variable position of the HP cluster with respect to the turn and end regions. Indeed, the energy landscape for T2, T3, and E3 are also topologically similar to the wild-type G peptide (Fig. 3), consistent with the recently increasing general agreement regarding the role of native topology. However, we also see the critical effects of the sequence, best illustrated by the energy landscape of the E2 isomer. Six central residues (D46–T51) in the E2 and E3 isomers are identical to those of the turn region of the G peptide, and E2 and E3 isomers only differ by an exchange of the residue positions of E42 and T44. Yet, the energy landscape for E2 is unique and strongly prefers an -helical conformation instead of the dominant ß-hairpin of the related isomers.
So then, how to understand the changes in the energy landscape? Our present study indicates that the key is the relative conformational energies of the different conformations. That is, changes in the sequence modulate the relative stabilities of the different topologies rather than redefine the topology space. In this regard, our current simulations yield two important observations. First, for all variants studied, ideal native ß-hairpin topologies remain as minima (regardless of whether global or local) in the energy landscape. Even for the most different landscape of the E2 isomer, the ideal ß-hairpin region has not vanished. This is especially interesting when we note that the free energies of all isomers are higher than that of the wild type (Table 1). This indicates that the entire energy landscape shifts while still preserving the topology space. Second, when the hydrophobic cluster size changes (Fig. 5), the near ideal ß-hairpin energy region does not change too much, whereas the other regions change dramatically. Previously, we have demonstrated the stabilizing role of the HP cluster for the G peptide. Here we further notice that the force keeping the hydrophobic residues together is not because they are attractive, that is, leading to deeper minima. Rather, it acts through destabilizing conformations with larger separations of the hydrophobic residues. The Z scores for the alternative sequences are perhaps less than that for the wild type. Clearly, this type of behavior is expected given the nature of hydrophobic interactions. Nevertheless, we see a gradual modification of the energy landscape by sequence and topology.
The recent work of Zhou et al. (2001) does not show evidence for helical intermediates. However, two other MD simulations have indicated that the native G peptide already has a tendency to form an -helical structure. By using a replica-exchange approach that combines MD trajectories with a temperature exchange Monte Carlo process, Garcia and Sanbonmatshu (2001) explored the energy landscape of the G peptide and located many helical structures. Semi-helical intermediates are also found in the folding pathway of the G peptide (Zagrovic et al. 2001). Therefore, the strong helical preference of the E2 isomer is simply a modification of the existing energy landscape.
Thus, the sequence changes do not lead to a complete redefinition of the topological space. Instead, they modulate the existing energy landscape, consistent with a population redistribution in the process of protein folding and binding (Ma et al. 2001, 2002). The ß-sheet structure reflects an interplay of many weak interactions (Searle 2001). A small perturbation may cause a large population shift. Consistent with the experimental shifting of a hydrophobic cluster along the ß-strands by Gellman and his colleagues (Espinosa et al. 2001), our energy landscape study and MD simulations also show that a smaller separation between the loop and the HP cluster tends to retain the wild-type energy landscape and thus has a greater stability. However, it appears that the native G-peptide sequence is optimized by nature. Any perturbation shifting the HP cluster leads to a higher energy landscape and lower stability compared with that of the native sequence.
The limited variation of the topological space compared with the number of possible sequence changes, may relate to the observation that the number of known protein folds are far less than the sequential allowance. Recently, Dokholyan et al. (2002) attempted to relate the limited protein folds to the early stage of evolution. Our study indicates a physically based explanation that might not be entirely new: Given a peptide/protein, the topology space is mostly defined by the Ramachandran plot, which defines the basic pool of conformers. For a long sequence, the topology may be extended through additional backbone and side-chain interactions. However, such interactions define the characteristic topologies, with only a limited number being energetically preferred.
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Materials and methods |
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TOPAbstractIntroductionResults and DiscussionMaterials and methodsReferences |
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-helix), partially folded, and random conformations. The wild G-peptide ß-hairpin structure is taken from the protein structure (Protein Data Bank: 1gb1
[PDB]
). The ß-hairpin structures for the permutated sequences are generated from the wild G peptide by mutating the residues. The -helix structures are generated using Insight II modeling package (Accelrys). The partially folded and random structures are generated from molecular dynamics simulations starting from both the ß-hairpin and -helical structures. The conformations near the "native" states are taken from MD simulations with explicit waters. The random states are generated with high-temperature MD simulations in the gas phase (with distance-dependent dielectric constant 4*r). The conformations are then clustered by the native contact fraction and the hydrophobic (HP) cluster index. The native contacts are defined from the ideal ß-hairpin structure illustrated in Figure 1, with a C distance cutoff of 5 Å. The HP cluster index is a measure of the overall contact between the four hydrophobic residues, and is defined by
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The distances Rs are as follows: R1, between C
s of F and Y; R2, between Cs of F and W; R3, between C of W and C of V; and R4, between C of Y and C of V. The superscript o indicates the distances in the native states. Therefore, the smaller the HP index, the more compact the hydrophobic cluster.
The free energy landscapes are constructed by evaluating the free energies for individual conformers. The selected conformers are first subjected to energy minimization with a gradient less than 0.001 kcal/mole/Å with distance-dependent dielectric constant 4*r. Based on the minimized structure, the conformational free energies are evaluated using the formula
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where the Egas is the gas phase potential energy, Eelectrostatics is the electrostatic contributions to the solvation energy, Esurface is the cavity and exposed surface effect on the solvation energy, and GGvibration is solute vibrational free energy.
The vibrational free energy for a given conformation is
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All calculations are carried out at room temperature (298 K).
The vibrational contribution of the enthalpic and entropic components of the free energy are obtained in the standard way:
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where, N is the total number of atoms in the peptide, 
i is the vibrational frequency, h is Plank’s constant, K is the Boltzmann constant, and T is the temperature.
Estimation of the entropy contribution to the free energy surface is still a challenge. The G peptide is only marginally stable at most temperatures (Muñoz et al 1997). Thus, the conformational entropy could make a significant contribution to the free energy. Using vibrational entropy to estimate the conformational entropy is a good approximation (Wang et al. 2001). Vibrational energy and entropy are molecular properties and should be included in the energy evaluation. Further, flexible molecules have high conformational entropy due to the high number of energetically accessible states. At the same time, flexible molecules also have more low-energy vibrational states and therefore high vibrational entropy. In folding/unfolding of a peptide, by using a vibrational entropy estimation, we predicted cold denaturation of an -helix (Ma et al. 2000). The prediction of this phenomenon was subsequently confirmed by experiments (Kinnear et al. 2002). Even though the entropy estimation may yield some uncertainty in the ordering of the conformations in Table 1, the ranking of the native ß-hairpin structure as the most stable conformation for the wild-type G peptide provides confidence in the free energy evaluation of the system studied.
The Egas is evaluated with the CFF91 force field (Maple et al. 1998). The electrostatic solvation energy is obtained by solving the Poisson-Boltzmann equation by using the program Delphi (Gilson et al. 1988; Jayaram et al. 1989). Reaction field energy was used as the electrostatic solvation energy. The atomic radii and partial charges are taken from the CFF91 force field. The dielectric constants used are one for the solute and 80 for the water solvent. Grid spacing is 0.4 Å. The surface effects are calculated (Ma and Nussinov 1999) with Esurface = 0.05(ASAnonpolar - ASApolar). The computation of the polar and nonpolar ASA (accessible surface area) used the method described previously (Tsai and Nussinov 1997).
Molecular dynamics simulations were performed in the canonical ensemble (NVT) with cubic periodic boundary condition by using the program Discover 2.98. The system consisted of a peptide solvated with 1330 water molecules (for the native peptide; the number of water molecules slightly differs for different mutants) placed in a cubic box (with dimensions 35 x 35 x 35 Å3). The effective water density in the solvation box is 1.006 g/cm3. The overall charge of the system is -3. All atoms of the system were considered explicitly, and their interactions were computed by using the CFF91 force field (Maple et al. 1998). The time step in the MD simulations is 1 fsec, and snapshots from the trajectories were saved every 1 psec. The native peptide has the most folded conformation 
273 K, and the midpoint of the unfolding transition is 297 K. In our simulations, the temperature used is 278 K.
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Acknowledgments |
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References |
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TOPAbstractIntroductionResults and DiscussionMaterials and methodsReferences |
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