Energy landscape of a peptide consisting of α-helix, 3₁₀-helix, β-turn, β-hairpin, and other disordered conformations

Abstract

The energy landscape of a peptide [Ace-Lys-Gln-Cys-Arg-Glu-Arg-Ala-Nme] in explicit water was studied with a multicanonical molecular dynamics simulation, and the AMBER parm96 force field was used for the energy calculation. The peptide was taken from the recognition helix of the DNA-binding protein, c-Myb. A rugged energy landscape was obtained, in which the random-coil conformations were dominant at room temperature. The CD spectra of the synthesized peptide revealed that it is in the random state at room temperature. However, the 300 K canonical ensemble, Q(300K), contained α-helix, 3₁₀-helix, β-turn, and β-hairpin structures with small but notable probabilities of existence. The complete α-helix, imperfect α-helix, and random-coil conformations were separated from one another in the conformational space. This means that the peptide must overcome energy barriers to form the α-helix. The overcoming process may correspond to the hydrogen-bond rearrangements from peptide–water to peptide–peptide interactions. The β-turn, imperfect 3₁₀-helix, and β-hairpin structures, among which there are no energy barriers at 300 K, were embedded in the ensemble of the random-coil conformations. Two types of β-hairpin with different β-turn regions were observed in Q(300K). The two β-hairpin structures may have different mechanisms for the β-hairpin formation. The current study proposes a scheme that the random state of this peptide consists of both ordered and disordered conformations. In contrast, the energy landscape obtained from the parm94 force field was funnel like, in which the peptide formed the helical conformation at room temperature and random coil at high temperature.

The thermodynamic stability and the folding process of a polypeptide chain are determined by the energy landscape of the system. One picture for the landscape is a funnel-like surface, which has the advantage of quickly folding the chain into a unique tertiary structure. The other picture is a rugged surface, in which a number of energy local minima are widely spread, and the chain thermally fluctuates among the minima at a given temperature.

The folding funnel has been studied with simplified models (Bryngelson et al. 1995; Chan and Dill 1998; Dill 1999; Istrail et al. 1999; Nakamura and Sasai 1999), in which the chain was designed to fold into a unique, stable structure at the ground state or at a low temperature. An advantage of the simplified model is that the thermodynamically important states can be counted relatively precisely, and thus the free energies of the states are evaluated. The simplified model is also used to specify the determinant factors to fold the chain into unique tertiary structures (Irback and Potthast 1995; Li et al. 1996; Tatsumi and Chikenji 1999). A β-sheet protein, β-lactoglobulin, is known to pass through α-helical intermediates in the refolding process (Hamada et al. 1996), which cannot be explained with the simple funnel-like landscape. A simplified model by Chikenji and Kikuchi (2000) suggested the possibility that this protein kinetically moves down the slope of the free-energy landscape from the random-coil state to the α-helical state in the early stage of folding, and the thermal fluctuation in the helical state plays the role of a driving factor to carry the chain to the β-structure. However, due to simplicity of and adjustable parameters included in the model, the model itself cannot produce realistic discussions without the support of the atomic-level simulations or experiments.

A molecular dynamics (MD) simulation is a technique to trace the folding or unfolding process of a protein at an atomic resolution, and can complement experiments (Wong et al. 2000). The MD simulations (Boczko and Brooks 1995; Lazarids and Karplus 1997) implied that the funnel-like landscape is assigned to proteins with well-defined tertiary structures. Unfolding simulations (Tsai et al. 1999; Wang et al. 1999a) demonstrated that β-hairpin regions in proteins were considerably stable after the disruption of the other regions, due to the high stability of the β-turn.

Recently, the denatured states of proteins have been studied with unfolding simulations (Bond et al. 1997; Kazmirski and Dagget 1998; Wong et al. 2000). The long unfolding-simulation trajectories demonstrated that the denatured states involve residual structures consisting of thermally fluctuating secondary-structure elements. The residual structures also have been experimentally detected, and are considered to be important for protein folding (Neri et al. 1992; Shortle 1993, Shortle 1996; Blanco and Serrano 1995; Frank et al. 1995; Searle et al. 1996; Gillespie and Shortle 1997a,b; Wang and Shortle 1997; Blanco et al. 1998; Kamatari et al. 1999; Sinclair and Shortle 1999). Some proteins or protein segments are intrinsically unstructured in the native state (Wright and Dyson 1999), and this property was considered to be biologically important because the unstructured segments may have the ability to bind to several different targets.

Although the conventional MD technique provided valuable information about protein refolding, a full description of the protein folding process is still difficult because of the limitation of computation time and the inaccuracy in the force-field parameters (Brooks 1998). Thus, the full description was first attempted for short peptides. The folding mechanism of the α-helix has been studied for many years (Zimm and Bragg 1959). With the recent development of computer power, folding simulations of peptides are now achievable. Takano et al. (1999) observed the helix-coil transitions with an MD simulation of a 15-residue polyalanine peptide in explicit water. Daura et al. (1999) observed the folding and unfolding of the helix of a β-heptapeptide in methanol. The weighted histogram analysis method was used to provide more statistically reliable data on the helix propagation for the hydrophobic peptides Ace-(Ala)_n-Nme, in which n = 4-15 (Yong and Brooks 1996). Duan and Kollman (1998) performed a 1-μs folding simulation of a 36-residue helical peptide in explicit water. In contrast, the folding mechanism of β-structures has not been well characterized (Munoz et al. 1997). Recently, the formation of β-structures was studied experimentally (Ramirez-Alvarado et al. 1996; Munoz et al. 1997; Alba et al. 1999; Honda et al. 2000). The MD simulations of the β-hairpin, the minimal β-structure element, were done and possible folding mechanisms were discussed (Dinner et al. 1999; Roccatano et al. 1999; Wang et al. 1999b; Bonvin and van Gunsteren, 2000). Galzitskaya et al. (2000) preformed the simulated annealing of a 16-residue peptide, which was taken from the β-hairpin region of the src SH3 domain, in explicit water starting from random conformations, and observed the formation of stable β-hairpins, in which the β-turn was first formed. Unfolding simulations of the β-hairpin (Pande and Rokhser 1999) showed that the unfolding process consisted of four distinguishable states.

A drawback of the conventional MD method is the sampling inefficiency in the conformational space, in which high-energy barriers are complicatedly distributed. Even then it is still difficult to obtain data statistically reliable for deriving the energy landscape even for the short peptides. Thus, to develop an effective sampling method is a key to describe precisely the energy landscape. Caves et al. (1998) reported that the integration of 10 short (120 ps) conventional MD runs provides a better sampling efficiency than a long (5 ns) conventional MD run. This exemplifies the fact that the sampling efficiency strongly depends on the sampling algorithm, although the study with the conventional MD simulation focused only on the conformational fluctuations around the native structure at 300 K. Recently, some powerful sampling methods have been developed to enhance the sampling of dense systems; multicanonical Monte Carlo sampling (Berg and Neuhaus 1992), entropic sampling (Lee 1993), replica-exchange Monte Carlo sampling (Hukushima and Nemoto 1996), simulated tempering (Lyubartsev et al. 1992), the 1/k-ensemble method (Hesselbo and Stinchcombe 1995), and Tsallis statistics (Tsallis 1988). These methods were applied to biological systems (Hansmann and Okamoto 1993, Hansmann and Okamoto 1997a,b; Kidera 1995; Andricioaei and Straub 1996; Hansmann et al. 1996; Bartels and Karplus 1997, Bartels and Karplus 1998; Bartels et al. 1998, 1999; Schaefer et al. 1998). The multicanonical algorithm was expanded to the simplified protein model (Iba et al. 1998; Chikenji et al. 1999; Kikuchi et al. 2000). Sugita and Okamoto have coupled the replica-exchange algorithm with the MD method (Sugita and Okamoto 1999, Sugita and Okamoto 2000a,b; Sugita et al. 2000).

Recently, Nakajima et al. (1997a) developed a multicanonical MD method. This method was applied to the structural prediction of CDR loops in antibodies (Shirai et al. 1998; Kim et al. 1999), the flexible docking between the CH3 domain and a pro-rich peptide (Nakajima et al. 1997b), and the evaluation of the free-energy landscape of peptide dimers in explicit water (Nakajima et al. 2000). This method was extended by dividing the total energy into two or more terms (Higo et al. 1997; Nakajima 1998), in which the sampling enhancement was done differently. Furthermore, the method was coupled with the weighted histogram analysis method to accurately evaluate high-energy barrier regions (transition states) in the conformational space (Ono et al. 1999). The advantage of the multicanonical method is that the canonical ensemble at any temperature can be derived from the sampling. Thus, we used this method for the conformational sampling of a peptide in explicit water to obtain the energy landscape, and measured the CD spectra for the synthesized peptide.

Results

The peptide we studied is [¹Ace-²Lys-³Gln-⁴Cys-⁵Arg-⁶Glu-⁷Arg-⁸Ala-⁹Nme], in which Ace and Nme are, respectively, the N-terminal acetyl and C-terminal N-methyl groups. This sequence is derived from the recognition helix (third α-helix; the 128'th to 134'th residues) of the DNA-binding protein c-Myb, as determined by Ogata et al. (1995). The residue ⁸Ala is Phe in the original pdb data. This residue was replaced to reduce the system size. The amino acid residues ²Lys, ⁵Arg, ⁷Arg, and ⁶Glu were treated as charged. Note that the carbonyl oxygen (¹O) in ¹Ace and the hydrogen (⁹HN) of the amide group in ⁹Nme can participate in hydrogen bond (H-bond) formation. The peptide was immersed in an explicit water sphere with a radius = 17 Å (see Materials and Methods). The number of atoms in the system was 1818 (135 peptide atoms and 561 water molecules).

Two force fields, AMBER parm94 (Cornell et al. 1995) and parm96 (Kollman et al. 1997), were examined for the simulation (see Materials and Methods). The number of multicanonical iterative runs was 38 for the parm94 simulation, and 46 for the parm96 simulation. The number of MD steps in the last multicanonical run (i.e., sampling run) was 16.8 × 10⁶ (16.8 ns) for parm94 and 50.4 × 10⁶ (50.4) for parm96, and flat energy distributions (Fig. 1 ▶) were obtained. The parm96 simulation covered the range of 230–600 K, and the parm94 simulation covered 290–1000 K. As shown later, only the results from parm96 agreed with the experiment. Thus, we mainly describe the results from parm96.

Fig. 1.

Flat distribution (natural logarithm of probability P) of potential-energy (E) from the last multicanonical run. Top: parm94 simulation; bottom: parm96 simulation. In both, the dotted lines are the canonical distribution at T₀ (see text), and the broken lines at 300 K.

Figure 2A ▶ represents the relation between the potential energy (E) and the radius of gyration (R_g) of the peptide obtained from parm96: The R_g was widely distributed at any energy. Figure 2B ▶ is the relation between E and the main-chain root mean square deviation (rmsd), which was calculated between the sampled conformations from parm96 and the α-helix conformation (q_cMyb) in the pdb data of c-Myb. The rmsd was distributed between 2.5 Å and 4.0 Å at any energy, and rarely approached 1 Å. Figure 3 ▶ is the conformational distribution from parm96 on the plane of rmsd and R_g at 300 and 500 K. The main conformational feature was the random-coil conformations at both temperatures, although the probability of the α-helix increased as temperature decreased.

Fig. 2.

(A) Relation between potential energy, E, from parm96 and radius of gyration, R_g. (B) Relation between E from parm96 and the main-chain root mean square deviation, rmsd, between the sampled conformations and α-helix (q_cMyb) in c-Myb.

Fig. 3.

Distribution of conformations from parm96 on plane of rmsd and R_g at 500 K (A) and 300 K (B). Solid contour lines represent probabilities from 0 to 0.2, with a spacing of 0.02, and broken lines from 0.2 to 1, with a spacing of 0.1.

To obtain an image of the energy landscape from the sampled conformations, we did the following procedure: First, conformations were picked from the whole sampled conformations with the weight of the canonical energy distribution, P(E,T), at a temperature T. Note that the picked conformations generate a canonical ensemble Q(T), in which the probability of existence assigned to a conformation of energy E is P(E,T) in Q(T), and the energy distributions of Q(T₀) and Q(300K) correspond to the dotted and broken lines, respectively, in Figure 1 ▶. Next, we combined the canonical ensembles at different temperatures and added q_cMyb to them (i.e., Σ Q(T) + q_cMyb). This combined ensemble covers a wide energy range. Last, we applied the principle component analysis (see Materials and Methods) to the ensemble. The eigen values were arranged in descending order. The conformation distribution on the principle axes gives the image of the potential energy landscape. The landscape from parm96 was rugged, as shown in Figure 4A ▶, in which the low-energy as well as the high-energy conformations were widely distributed on the plane of the first and second axes. The distribution (Fig. 4B ▶) on the plane of the first and fourth axes indicated the existence of a small α-helical cluster around q_cMyb. This cluster is shown more clearly later. The quantity λ_iΣ_jλ_j represents the width of the distribution along the i'th principle axis, in which λ_i is the eigen value assigned to the i'th axis. The value was 22% for the first principle axis, 12% for the second, 10% for the third, 7% for the fourth, and so on. Afterward, we will see that not only the α-helix but also other secondary structures exist in the rugged landscape. In contrast, the landscape from parm94 was funnel like, and the α-helix was located at the bottom of the funnel (Fig. 4C ▶).

Fig. 4.

Potential-energy landscape of peptide on the first and second principle axes from parm96 (A), the first and fourth axes from parm96 (B), and the first and second axes from parm94 (C). Point labeled cMyb represents location of q_cMyb. We did not use all of the conformations for the figures because the number (∼10⁵) of conformations in Q(T) at each temperature is too large to show. Conformations were then picked randomly from Q(T). The numbers of the conformations shown in A and B are 207 (at 300K), 219 (350K), 253 (400K), 270 (450K), 302 (500K), 283 (550K), and 272 (600K), and those in C are 184 (at 300K), 199 (350K), 203 (400K), 191 (450K), 238 (500K), 263 (550K), and 259 (600K).

Figure 5 ▶ shows the CD spectra of the aqueous solution of this peptide at various pH values at 10°C. The large negative peak around 197 nm is typical of the disordered structure, and the peaks corresponding to α-helices or β-structures were absent. Neither raising the temperature to 25°C, nor the addition of salt (up to 0.5 M NaCl) changed the spectra significantly (data not shown). These results strongly suggest that the peptide does not adopt a rigid secondary structure under these conditions. Thus, parm96 is more plausible than parm94.

Fig. 5.

CD spectra of synthesized peptide at pH 6.0 (solid line), 7.0 (broken line), and 8.0 (dotted line). Temperature was 10°C and no salt was added.

Below, we describe the secondary structures included in Q(300 K) from parm96. The α-helix of the peptide is specified by the five intra-mainchain H-bonds; ¹O-⁵HN (designated by HB1), ²O-⁶HN (HB2), ³O-⁷HN (HB3), ⁴O-⁸HN (HB4), and⁵O-⁹HN (HB5). Here, we designate a helical conformation with three bonds, HB2, HB3, and HB4, by HLX(2,3,4), for example. As shown later, the conformations HLX(2,4), HLX(2,3,4), HLX(1,2,3,4), and HLX(1,2,3,4,5) are close to q_cMyb and generate a cluster. Thus, we call these conformations complete α-helix. In HLX(2,4), the helical conformation was well maintained by HB2 and HB4, although the central H-bond (HB3) was not formed. The other conformations (partly disordered helices) with more than two H-bonds, such as HLX(1,2,3), were located apart from the complete helix cluster, as also shown later. We call the partly disordered helices imperfect α-helices. In this study, an H bond was assigned to the pair of a donor and an acceptor when the distance between them was shorter than 2.5 A.

For β-hairpins, we considered two types, HPN1 and HPN2; the turn region of HPN1 is in residues 4–7, with the possible H-bonds of ²O-⁹HN, ³HN-⁸O, ³O-⁸HN, ⁴HN-⁷O, and ⁴O-⁷HN, and that of HPN2 is in residues 3–6 with ¹O-⁸HN, ²HN-⁷O, ²O-⁷HN, ³HN-⁶O, and ³O-⁶HN. The H-bond (⁴O-⁷HN for HPN1 or ³O-⁶HN for HPN2) to form the β-turn is called a β-turn H-bond, and the other H-bonds are called inter-strand H-bonds. We defined a conformation as a hairpin when it contained both the β-turn H-bond and one or more inter-strand H-bonds. Although five H-bonds are possible for the hairpins, the maximum we observed was three (the β-turn and two inter-strand H-bonds) in HPN1 and two (the β-turn and one inter-strand H-bonds) in HPN2. We designate HPN1 with three H-bonds as HPN1(3), for example.

The principle component analysis was applied to Q(300K). The distributions of the α-helix, β-hairpin, random-coil conformations, as well as those only with HB3 (HB3 conformations), are shown in Figure 6 ▶. The complete helix, imperfect helix, and HB3 conformations were isolated from one another. This indicates that the energy barriers should be overcome for the transitions from the HB3 conformations to the imperfect helix, as well as from the imperfect helix to the complete helix. Note that the HB3 conformations were located in the random-coil ensemble. This suggests that the transitions from the random-coil to the HB3 conformations do not require jumps of energy barriers. Figure 6 ▶ also shows that the β-hairpin conformations were embedded in the ensemble of the random-coil conformations. We calculated the partial partition function Z at 300 K for each of the ordered structures and the disordered (i.e., random-coil) conformations, using the canonical distribution at 300 K, and estimated the partial free energy F = -RT ln[Z] of these structures, in which R is the gas constant and T = 300 K. Here, we define the partial free energy of each secondary structure relative to the random-coil conformations by ΔF = F(each ordered structure) - F(random-coil): ΔF(complete α-helix) = 2.617 kcal/mol [the probability of existence to Q(300K) = 1.18%], ΔF(imperfect α-helix) = 2.622 (1.17%), ΔF(HB3 conformations) = 1.67 (5.82%), ΔF(HPN1) = 2.58 (1.27%), ΔF(HPN2) = 3.09 (0.54%), and ΔF[HPN1(3)] = 3.89 (0.16%). The ΔF(complete α-helix) was smaller than ΔF[HPN1(3)], although it was slightly larger than that of ΔF(HPN1), in which HPN1 = HPN1(2) + HPN(3). In the estimation of ΔF, the random-coil conformations were defined by the conformations in Q(300K), except for the α-helices and β-hairpins. The probability of existence for the random coil was 95.84% of Q(300K) and that for the secondary structures was 4.16%.

Fig. 6.

Distributions of secondary structures and random-coil conformations in Q(300 K) from parm96, on the plane of the second and third principle axes. Point labeled cMyb represents location of q_cMyb. Points labeled conf. with HB3 represent the conformations with only HB3. This plane most clearly showed the separation of the complete helix, imperfect helix, and random-coil conformations. Quantity λ_iΣ_j λ_j (see text) was 32% (i = 1), 21% (i = 2), and 14% (i = 3).

We calculated the partial internal energy ≤E> for each of the ordered structures and random conformations, and defined the relative internal energy as Δ≤E> = ≤E>(each ordered structure) - ≤E>(random-coil): Δ≤E>(complete α-helix) = -7.6 kcal/mol, Δ≤E>(imperfect α-helix) = -5.8, Δ≤E>(HB3 conformations) = -1.9, Δ≤E>(HPN1) = -2.6, and Δ≤E> (HPN2) = -4.2. The reference value, ≤E>(random-coil), was 5528.6 kcal/mol, and the internal energy ≤E>[Q(300K)] for the whole ensemble Q(300K) was −5528.7 kcal/mol. Note that the summation of ≤E> over the partial internal energies is not equal to ≤E>[Q(300K)]: ≤E>(complete α-helix) + ≤E>(imperfect α-helix) + ≤E>(HB3 conformations) + ≤E>(HPN1) + ≤E>(HPN2) ≠ ≤E>[Q(300K)] because the normalization of the partial internal energy for each ordered structure was done by the partial partition function. Remember that the probability of existence was nearly the same between the complete and imperfect α-helices. The result of ≤E> shows that the stabilizing factor is different between them, that is, ≤E>(complete α-helix) was lower than ≤E>(imperfect α-helix). Therefore, the complete α-helix is stabilized by the internal energy, and the imperfect α-helix is done by the entropy. This result is reasonable because the terminal region of the imperfect α-helix is more flexible than that of the complete α-helix.

To investigate the structural differences between the complete and imperfect helices, snapshots of HLX(2,3,4) and HLX(1,2,3), picked up from Q(300K), are drawn in Figure 7A and B ▶, respectively, in which water molecules near the peptide atoms ⁴O or ⁸HN are shown together with the peptides. In HLX(1,2,3), ⁴O and ⁸HN were exposed to the solvent and formed H-bonds with water molecules (Fig. 7B ▶). In contrast, in HLX(2,3,4) ⁴O and ⁸HN formed an H-bond (HB5), and water molecules could not penetrate between ⁴O and ⁸HN (Fig. 7A ▶). A similar situation was found in the comparison of HLX(2,3,4) and HLX(3,4,5) (data not shown). This means that the imperfect helices, in which two sequential H-bonds (HB1 and HB2, or HB4 and HB5) at the N- or C-terminal were absent, were stabilized by the peptide-water H-bonds. The H-bond rearrangement from the peptide–water to peptide–peptide interactions may correspond to the process of overcoming the energy barriers. The absence of one H-bond (HB1 or HB5) at the N- or C-terminal did not largely affect the helical conformation, and water molecules could not penetrate into the packed peptide.

Fig. 7.

(A) Ten conformations randomly picked from HLX(2,3,4), and (B) those from HLX(1,2,3). In both A and B, water molecules close to ⁴O or ⁸HN with distances < 3.5 Å are shown. Bold bonds in the peptide are the covalent bonds ⁴C-⁴O and ⁸N-⁸HN. Broken lines represent hydrogen bonds.

All of the conformations of HPN1(3) contained the same intra-mainchain H-bonds, for example, ²O-⁹HN, ⁴HN-⁷O, and ⁴O-⁷HN. However, they were clearly classified into two groups (Fig 8 ▶); one was characterized by the type I β-turn and the other by the type II' turn. Nakajima et al. (2000) recently performed the multicanonical MD simulation of a short peptide, and found that the energy barrier between the I and II' turns is relatively low. Another difference between the two groups was also found in the twisting of the strands (Fig. 8 ▶). Note that the peptide sequence is highly hydrophilic, so that a hydrophobic core cannot be formed. This property of the sequence may prevent the formation of the inter-strand H-bonds, ³HN-⁸O and ³O-⁸HN.

Fig. 8.

Stereo drawing of HPN1(3) picked up from Q(300K). Peptides in yellow are those characterized by type I β-turn and those in blue by type II'. Broken lines represent hydrogen bonds, ²O-⁹HN, ⁴HN-⁷O, and ⁴O-⁷HN. β-turn regions (residues 4–7) were superimposed among the conformations.

It is interesting to examine whether Q(300K) contained the 3₁₀-helix. By picking up conformations with H-bonds ⁱO-ⁱ⁺³HN from Q(300K), we detected the imperfect 3₁₀-helix conformations with H-bonds ³O-⁶HN and ⁴O-⁷HN. The probability of existence for the 3₁₀-helix was small, 0.52% of Q(300K), which corresponded to ΔF = 3.09 kcal/mol. Note that the H-bond ³O-⁶HN is the β-turn H-bond of HPN2 and, ⁴O-⁷HN is that of HPN1.

We also detected conformations that have the inter-strand H-bonds but lack the β-turn H-bond. We call them closure conformations. The closure is generally classified as the random coil. The probability of existence in Q(300K) was 12.9% (ΔF = 1.19 kcal/mol): 7.3% (ΔF = 1.53) for HPN1, and 5.6% (ΔF = 1.68) for HPN2. Note that the free energy is not additive: ΔF(states A + B)≠ ΔF(A) + ΔF(B). The β-turn conformations, which include only the β-turn H-bond, had the probability of 6.64% (ΔF = 1.58); 1.93% (ΔF = 2.31) for HPN1 and 4.7% (ΔF = 1.78) for HPN2. The probability of the closure only with the H-bond ²O-⁹HN was 0.8% (ΔF = 2.87), and that only with ¹O-⁸HN was 0.16% (ΔF = 3.81).

The distributions of the above structured conformations (i.e., β-hairpin, imperfect 3₁₀-helix, β-turn, and closure) may provide some scheme for the β-hairpin formation. Thus, we picked up these conformations from Q(300 K), and applied the principle component analysis to them, λ_iΣ_j λ_j = 34.3% (for i = 1), 18.6% (i = 2), 13.1% (i = 3), and so on. Figure 9 ▶ is the distribution on the plane of the first and third axes, in which the separation of HPN1 and HPN2 were most clearly shown. It is clear that the structured conformations did not form separated clusters from one another. This means that the transitions among them have no energy barriers. Note that HPN1 and the HPN1 closure are distributed in the same area, and the β-turn 4–7 conformations contact them. The HPN2 is distributed in a small region of the area of the HPN2 closure, and then the closure is spaced between the β-turn 3–6 conformations and HPN2. The imperfect 3₁₀-helix is located in a restricted region of the area of the β-turn 3–6 conformations, and has no contact with the β-hairpins.

Fig. 9.

Distribution of structured conformations and the other disordered conformations in Q(300K) on the plane of the first and third principle axes. Conformations are designated as follows: β-hairpin conformations are designated by HPN1 and HPN2, imperfect 3₁₀-helix by 3_10 helix, β-turn conformations by turn 4–7 and turn 3–6, which are the conformations with β-turn H-bonds only in residues 4–7 and 3–6, respectively, and closure conformations by HPN1 closure and HPN2 closure.

Discussion

The canonical ensemble Q(300K) from parm96 was subjected to the random state, which inherently consists not only of disordered conformations but also of several kinds of ordered ones. Accordingly, the potential-energy landscape was rugged, covering the wide variety of conformations. This result is expected, because the thermal fluctuations in the random state are larger than those in a state characterized by a well-defined structure. The current study may be useful to investigate the residual structures observed experimentally in the denatured state of proteins (Neri et al. 1992; Shortle 1993, Shortle 1996; Blanco and Serrano 1995; Frank et al. 1995; Searle et al. 1996; Gillespie and Shortle 1997a,b; Wang and Shortle 1997; Blanco et al. 1998; Kamatari et al. 1999; Sinclair and Shortle 1999), or help to interpret the unstructured segments in proteins in the native state (Wright and Dyson 1999). Remember that the current fragment is helical in the protein cMyb, but the actual conformation in water is random coil for the synthesized peptide fragment. The small cluster for α-helix in Q(300K) indicates that the peptide has a slight tendency to fold into the helix. Our study shows that the peptide can adopt different conformations, depending on the environment. This work supports the scheme proposed by Wright and Dyson (1999) that unstructured fragments are structured when functioning.

Although the conventional MD technique is becoming a powerful tool to study biomolecules, it is difficult to obtain statistically reliable data to view the energy landscape. Our multicanonical study provides a successful example that the simulation technique complements insufficient experimental data: The sampling covered a variety of secondary structures, which are not detectable experimentally because of the small probabilities of existence.

Because the multicanonical simulation provides an equilibrated picture, it is difficult to discuss precisely the kinetic process of chain folding. However, the potential-energy landscape yielded the information about energy barriers between the conformations. Our study showed that the propagation of helical content is achieved by the jumps between energy barriers from the HB3 conformations to the imperfect helix, and from the imperfect helix to the complete helix (Fig. 6 ▶). On the other hand, the HB3 conformations were accessible from the random-coil conformations without requiring jumps. The analysis of the snapshots suggested that the jumping over the barriers corresponds to the H-bond rearrangement from the peptide–water to the peptide–peptide interaction.

For β-hairpin formation, two mechanisms have been proposed as follows: (mechanism 1) the β-turn is formed first (Munoz et al. 1997; Alba et al. 1999; Wang et al. 1999b; Bonvin and van Gunsteren 2000; Galzitskaya et al. 2000), or (mechanism 2) the hydrophobic-core formation is formed first (Dinner et al. 1999). Because the current sequence is highly hydrophilic, a hydrophobic core cannot be formed. Thus, in the current case, the mechanism 2 should be replaced by a mechanism in which the closure conformations are formed first. Interestingly, Figure 9 ▶ implies that the formation process is different between HPN1 and HPN2. The HPN1 is accessible from either the β-turn conformations or the closure conformations, which suggests that both mechanisms 1 and 2 are possible. The HPN2 is accessible only from the closure conformations, which suggests mechanism 2. However, as the current peptide does not fold into a stable β-hairpin, due to the lack of hydrophobic-core residues, the folding mechanism proposed here does not provide enough information to develop a mechanism for the formation of stable hairpins. Studies should be done on other peptides that fold into thermally stable β-hairpins.

We observed an imperfect 3₁₀ helix in Q(300K). One may imagine that breaking the H-bond ⁱO-ⁱ⁺³HN initiates the formation of the β-hairpin. Figure 9 ▶ shows that the 3₁₀ helix is located in a restricted area in the β-turn conformations, and is isolated from the β-hairpin ensemble. This means that the 3₁₀ helix did not directly contribute to the growth of the hairpins.

The multicanonical simulations (Ono et al. 2000) of the short hydrophobic peptides Ace-(Ala)_n-Nme (n = 2 or 3), showed that parm94 had a high propensity to form the H-bonds ⁱO-ⁱ⁺³HN and ⁱO-ⁱ⁺⁴HN, and that parm96 was likely to form extended conformations. The peptide studied here was longer than those studied by Ono et al. (2000), and was more hydrophilic. Our parm96 results showed that the peptide has the ability to fold the chain into helix, hairpin, and random-coil conformations. The result on parm94, on the other hand, showed that the propensity of H-bond (ⁱO-ⁱ⁺⁴HN) formation leads the chain into the α-helix, which is located at the bottom of the funnel-like potential-energy landscape. The refolding study with the conventional canonical MD simulation of the 36-residue peptide (Duan and Kollman 1998) also showed that parm94 has a high ability to fold the peptide into helical conformations. Our multicanonical simulation revealed that parm96 is more appropriate than parm94. Of course, it does not mean that parm96 is the best force field, because force fields other than AMBER have not yet been examined.

The current study may raise the question of whether MD studies performed with an inappropriate force field are valid. However, we know that the various MD trajectories of a protein provide a similar pattern of atomic-positional fluctuations that agree well with the X-ray B-factors, when the study is focused on the thermal fluctuations around the well-defined native conformation. Using a simple protein model, Higo et al. (1997) have shown that the folded pattern of the protein main chain and the tight atom packing in the protein interior are important factors to determine the overall conformational fluctuations of the main chain. Thus, the serious force-field problem is caused when the chain folding is studied. In this sense, care should be taken to simulate the unfolded state in the free-energy perturbation method.

The thermodynamic stability of a peptide chain is governed by the free energy differences between the native and denatured states. Given a flexible fragment in a protein or a short flexible peptide, there should exist a number of different stable conformations characterized by similar free-energy values. Such systems can be analyzed only by the rugged energy landscape, to accurately compare the computations with the experiments. In addition, the rates and the paths of the conformational changes among the different stable and meta-stable states can be evaluated by analyzing the energy barriers among them. When the reaction path is correctly assumed, the umbrella sampling technique helps to estimate precisely the heights of the free-energy barriers. An example is the cis-trans imide isomerization, in which our new method, called multicanonical WHAM (Nakamura et al. 1999; Ono et al. 1999), revealed the free-energy barrier between the cis and trans isomers of Ace-Ala-Pro-Nme. Thus, when the conformational sampling is highly enhanced and the force field is sufficiently reliable, a precise analysis of the free-energy landscape for a realistic molecular model can yield a more complete understanding of the dynamic conformations and energetics of a peptide chain. Very recently, Higo et al. (2001) succeeded in reconstructing the precise canonical ensemble of an 8-residue peptide, which was designed for a β-hairpin (Ramirez-Alvarado et al. 1996), in explicit water with parm96 force field, from the multicanonical ensemble covering the wide temperature range between 290 and 700 K. They found that the β-hairpin conformations are predominant in the canonical ensemble at 300 K. Our simulation studies together with experiments are now underway, with longer peptides and proteins.

Materials and methods

We used the multicanonical MD method (Nakajima et al. 1997a) to sample the peptide conformations in explicit water. Here, we briefly summarize the methodological advantage. This sampling is enhanced by introducing a modified energy function E_mod =E + RT₀ ln[P(E,T₀)], in which E is the potential energy of the system, R is the gas constant, T₀ is the temperature for the multicanonical MD simulation, and P(E,T₀) is the canonical energy distribution at T₀. The forces acting on the atoms are derived by -grad E_mod. The temperature T₀ is usually set high enough to overcome energy barriers in the potential energy surface during the prerun, as explained later. If P(E,T₀) is known in a wide energy range, then a flat energy distribution is obtained in the range through the multicanonical simulation. A benefit of the method is that the canonical ensemble, P(E,T), at any temperature is derived using a reweighting formula (Shirai et al. 1998).

The distribution P(E,T₀) is not known a priori, but is obtained through an iteration of the multicanonical MD runs. Prior to the multicanonical runs, a preparative canonical MD simulation (prerun) is done at T₀, and the distribution P₀(E,T₀) obtained from the prerun accurately covers only the high-energy range around T₀. Then, P₀(E,T₀) is extrapolated to the lower-energy direction, and the modified energy E_mod is reset by use of the extrapolated P₀(E,T₀). The first multicanonical run generates a flat energy distribution covering a wider energy range than the prerun. Then, P₁(E,T₀), derived from the flat distribution using the reweighting formula, is again extrapolated to the lower-energy direction, and E_mod is reset for the second run. This procedure is repeated until the sampling reaches the room-temperature region. Finally, the conformations sampled in the last multicanonical run are used for the analysis.

The peptide was immersed in a water sphere (radius = 17 Å) of the flexible TIP3P water model (Jorgensen et al. 1987). The sphere center was placed on the geometrical center of the peptide. A harmonic potential was applied to the water-oxygen atoms, but only when the water molecules were moving to the outside of the sphere, to confine the molecules within the sphere. The momentum and the angular momentum of the peptide were constrained at zero during the simulation, to keep the peptide position around the center of the water sphere. If the peptide assumed an extended conformation, then the methyl groups of ¹Ace and ⁹Nme may touch the spherical boundary, and this extended conformation may be stabilized because of the hydrophobic interaction with the vacuum (i.e., the outside of the sphere). Thus, a harmonic potential was applied to the atoms in ¹Ace and ⁹Nme, but only when these atoms were moving outside of a sphere (radius = 14 Å), for which the center was set to the water-sphere center. Due to this procedure, the space for the peptide fluctuations became smaller. However, the space was wide enough for the transitions among the random-coil and secondary structures, as shown in the Results section.

The computer program PRESTO (Morikami et al. 1992) with a modification for multicanonical MD (Nakajima et al. 1997a) was used for the sampling. The electrostatic interaction was calculated by using the cell-multipole expansion (Ding et al. 1992). The SHAKE algorithm (Ryckaert et al. 1977) was used to constrain the covalent bonds between hydrogen and heavy atoms. The time step of the MD simulation was 1 fs. The temperature was controlled by the constant-temperature method (Evans and Morriss 1983). The initial conformation of the peptide for the first multicanonical run was a random conformation, and the initial one for the (+1)'th run was the last one of the i'th run. Therefore, the sampled conformations were not influenced by the α-helix conformation (q_cMyb) in the original pdb data of c-Myb. The multicanonical simulation was examined with two force fields: AMBER parm94 (Cornell et al. 1995) and parm96 (Kollman et al. 1997). The temperature T₀ was 1000 K for the parm94 simulation, and 600 K for the parm96 simulation. We verified that T₀ is high enough to unfold q_cMyb into random-coil conformations with conventional canonical MD simulations in advance.

We used the principle component analysis in the same way as done by Shirai et al. (1998) to study the sampled conformations. Given an ensemble of n conformations, the main-chain rmsd was calculated for all conformation pairs in the ensemble, generating a distance matrix of [n × (n + 1)/2] elements. Next, the distance matrix was diagonalized, and a set of eigen vectors and eigen values were obtained. The eigen vectors construct a conformational space, in which the positions of the n conformations are assigned. An eigen vector with a larger eigen value corresponds to the principle axis along that the conformational distribution is wider.

We measured the CD spectra of this sequence to investigate the stable conformation in solution. The peptide was obtained from Kurabo (Osaka, Japan), and its purity was higher than 90%. The spectra were taken by use of a Jasco J-720 spectropolarimeter and a cell with a 1-mm path length. The sample concentration was 10 mM and pH was maintained by either 10 mM potassium phosphate buffer (pH 7.0 or 8.0) or 10 mM MES buffer (pH 6.0). Thirty two scans were accumulated for each spectra.