Polyproline II conformation is one of many local conformational states and is not an overall conformation of unfolded peptides and proteins

Abstract

The alanine-based peptide Ac-XX(A)₇OO-NH₂, referred to as XAO (where X, A, and O denote diaminobutyric acid, alanine, and ornithine, respectively), has recently been proposed to possess a well defined polyproline II (P_II) conformation at low temperatures. Based on the results of extensive NMR and CD investigations combined with theoretical calculations, reported here, we present evidence that, on the contrary, this peptide does not have any significant amount of organized P_II structure but exists in an ensemble of conformations with a distorted bend in the N- and C-terminal regions. The conformational ensemble was obtained by molecular dynamics/simulated annealing calculations using the amber suite of programs with time-averaged distance and dihedral-angle restraints obtained from rotating-frame nuclear Overhauser effect (ROE) volumes and vicinal coupling constants ³J_HNΗα, respectively. The computed ensemble-averaged radius of gyration R_g (7.4 ± 1.0) Å is in excellent agreement with that measured by small-angle x-ray scattering (SAXS) whereas, if the XAO peptide were in the P_II conformation, R_g would be 11.6 Å. Depending on the pH, peptide concentration, and temperature, the CD spectra of XAO do or do not possess the maximum with positive ellipticity in the 217-nm region, which is characteristic of the P_II structure, reflecting a shifting conformational equilibrium rather than an all-or-none transition. The “P_II conformation” should, therefore, be considered as one of the accessible conformational states of individual amino acid residues in peptides and proteins rather than as a structure of most of the chain in the early stage of folding.

The structures of proteins under denaturing conditions have received considerable attention from experimentalists (1–19) and theoreticians (20–32). The dominating model has been the statistical coil (erroneously called a random coil) developed by Flory (20) and corroborated by Tanford (1). However, recent work (9, 10) suggests that the end-to-end distances in denatured proteins need not conform to statistical-coil polymer-like distributions.

Recently, Kallenbach and coworkers (11) carried out CD and NMR studies of an alanine-based peptide Ac-XX(A)₇OO-NH₂ (where X, A, and O denote diaminobutyric acid, alanine, and ornithine, respectively), hereafter referred to as XAO, and proposed that XAO has a dominant polyproline II (P_II) structure at 2°C and that the content of the β-strand is increased by ≈10% at 55°C relative to that at 2°C. Based on the temperature dependence of the CD spectra of XAO, they stated that there is a transition from the low-temperature P_II conformation to a β-structure; in other words, the P_II conformation at low temperatures is the state of most residues of the whole peptide rather than the state that pertains to a subset of individual amino acid residues. Subsequently, the XAO peptide has been considered as a model of P_II structure. This peptide seems to be an appropriate and simple model for determining whether the common description of denatured proteins as structureless statistical coils is accurate, because its amino acid sequence is too short to form an α-helix and its side chains are too short to interact with each other. Therefore, based on CD and NMR measurements on XAO, Kallenbach and coworkers (11, 16, 19) proposed that the P_II conformation might generally be characteristic of unfolded proteins.

On the other hand, later theoretical (30, 31) and experimental (18) work suggested that the P_II conformation is not characteristic of alanine-based peptides in aqueous solution. Vila et al. (30) carried out a theoretical conformational study and showed that the XAO peptide appears to consist of an ensemble of conformations with only a few residues (≈30%) in the P_II region. Four of its seven alanine residues show a downfield ¹³C^β chemical shift in water, indicating a conformational preference to form a β-strand or extended structure (30). Ramakrishnan et al. (31) used the gromos force field to compute the conformational ensemble of Ac-A₈-NHMe in water. They found that, although 40% of the individual amino acid residues of the conformational ensemble at 298 K are found in the region of conformational space characteristic of P_II, the largest cluster (18%) of conformations corresponds to a β-hairpin. Recently, Pande and coworkers (18) used the small-angle x-ray scattering (SAXS) technique to determine the experimental radius of gyration of the XAO peptide. They obtained a value of R_g = 7.4 ± 0.5 Å (18), which is <11.6 Å for an all-trans P_II conformation or 13.0 Å for a fully extended conformation of XAO.

In view of the conflicting evidence as to the existence of alanine-based peptides in the P_II conformation, we carried out a conformational study of XAO in water and in aqueous acetate buffer to determine the conformational characteristics of the ensemble, using the NMR technique to determine the ensemble-dependent observables and molecular dynamics (MD) simulations with simulated annealing (SA), the amber99 force field, and time-averaged distance and dihedral-angle restraints derived from the NMR measurements. Such a theoretical approach led to an ensemble of conformations that satisfy the NMR data. We also recorded CD spectra under various conditions to determine the effect of concentration and environment on their appearance. We present here only those results that address the issue of the P_II conformation of XAO.

Results

CD Spectra.

The P_II conformation is characterized by a negative band around 200 nm and by a weaker positive band at ≈217 nm in CD spectra (33). The spectral features of the P_II structure are quite characteristic and, therefore, are easily distinguished from structures such α-helices, β-sheets, β-turns, or statistical coils. The CD spectra of XAO in water indicate a partial P_II structure (Fig. 1A). The CD spectra of XAO depend strongly on pH, peptide concentration, and on the kind of buffer (Fig. 1B). The CD spectra of XAO in phosphate buffers are partially characteristic of the statistical-coil structure but exhibit a shallower minimum around 200 nm compared to the CD spectrum in water (Fig. 1A). At low concentration of XAO in acetate buffer and at pH = 3, the CD curves are indicative of a significant content of P_II structure (Fig. 1B). At higher values of pH, i.e., 7 and 9, and higher concentrations of XAO in phosphate buffers, a higher amount of statistical-coil structure is observed (Fig. 1A). The shape of the CD curves depends on the amount of acetate and phosphate ions in the solution. The CD spectra of XAO in water showed the complete absence of α-helical features; similar absence of α-helical features were seen in methanol and trifluoroethanol (data not shown). The CD spectra also were obtained at different temperatures (at 1°C and over a range of 5–80°C; data not shown). As in previous work (11), the spectra were temperature-dependent with the amount of P_II structure decreasing with temperature in favor of β-strand and statistical-coil structure. An isodichroic point (where the CD curves obtained under different conditions intersect) was observed at ≈208 nm, as shown in Fig. 1B for concentration-dependent CD spectra. A similar effect was observed for the temperature-dependent CD spectra (data not shown). These observations suggest the presence of a concentration- and temperature-dependent equilibrium between different conformations. Therefore, we interpret the temperature dependence of the CD spectra as a shift in the conformational equilibrium with temperature and not as an indication of a conformational transition.

Fig. 1.

CD spectra of the XAO peptide. (A) XAO peptide at 0.2 mM in 0.2 M acetate buffer at pH = 3 and 5°C, 0.2 mM in water at 5°C, and in phosphate buffers (0.007 M–0.25 M) at pH = 5, 6, 7, 9, and 11 at 5°C. (B) XAO peptide in 0.2 M acetate buffer at pH = 3 with peptide concentrations of 0.2 mM, 0.1 mM, and 0.05 mM and in phosphate buffers (0.01 M and 0.15 M) at pH = 7 and pH = 9 with peptide concentrations of 0.2 mM, 0.1 mM, and 0.05 mM at 1°C.

NMR Chemical Shifts.

The observed chemical shifts for ¹³C, ¹⁵N, and ¹H for the XAO peptide are almost identical in water and in the acetate buffer. Therefore, the 3D structures of this peptide should be very similar in both solvents. The ¹H chemical shifts in acetate buffer are in a good agreement with those reported by Kallenbach et al. (11).

The chemical shifts (δ) depend on the backbone dihedral angles (φ and ψ) and on the local chemical environment. The conformational shift (Δδ), defined as the deviation of the observed chemical shifts (δ_obs) from those of statistical-coil (δ_coil) values (Δδ = δ_obs − δ_coil), is a very sensitive indicator of the secondary structure of peptides and proteins (34). We used values of the reference statistical-coil chemical shifts (δ_coil) determined under similar conditions as those of our experimental NMR studies [pH, aqueous solution, and 2, 2-dimethylsilanpentane-5-sulfonic acid (DSS) as a reference standard] (6, 35–38).

Because the chemical shifts are temperature-dependent (38), it was necessary to recalculate the δ_coil values at different temperatures. The proton (H^α) and carbon (C^α and C^β) chemical shifts in the range of 5–28°C were found to change with temperature by 0.1 and 0.01 ppm, respectively; i.e., the temperature dependence of the H^α, C^α, and C^β chemical shifts was negligible. The sequence correction for the δ_coil values of the H^α and C^α chemical shifts, proposed by Schwarzinger et al. (6, 39) was implemented. There is evidence that the chemical shifts for both the H^N and ¹⁵N nuclei are strongly temperature- and sequence-dependent (35–37, 39, 40). Hence, a sequence and temperature correction was included for these nuclei. The corresponding corrections for the temperature and sequence dependence for the δ_coil values were computed by using the procedures in refs. 35, 37, and 39–41 and were taken into account in the determination of the conformational shifts (Δδ = δ_obs − δ_coil) shown in Fig. 2 A and B.

Fig. 2.

Values of the conformational shifts (Δδ) based on different sets of statistical-coil values as reference for H^N (A) and ¹⁵N (B) chemical shifts of the XAO peptide. The bars indicate the reference set used, namely white (36), light gray (6), and dark gray (37) in A and white (6), light gray (37), and dark gray (35) in B.

The Diaminobutyric Acid and Ornithine Residues.

The trend of the observed conformational shift values indicates that the N- and C-terminal residues (X₁, X₂, and O₁₁) behave differently from the middle part of the peptide. In particular, the observed ΔδH^N and Δδ¹⁵N values, which in the literature are >0.29 and 1.2 ppm (42), respectively, indicate a tendency toward formation of β-structure. For β-structure, the observed ΔδC^α and ΔδC^β values (data not shown) are negatively shifted by more than −1.4 ppm (42). Formation of β-strand is more evident for the X residues than for the O₁₀ residue (see Fig. 2). The O₁₀ residue could be in an equilibrium among β-strand, P_II structure, and statistical-coil conformation because some of the Δδ values (ΔδH^N and ΔδC^β) indicate a slight bias toward β-strand conformation and some (ΔδH^α, Δδ¹⁵N, and ΔδC^α) toward the statistical-coil conformation.

The Alanine Residues.

Homonuclear and heteronuclear NMR spectra were collected in both water and acetate buffer. Our results indicate that all chemical shifts are very similar in both solvents. In particular, we observed that the C^α and C^β chemical shifts of alanines are strongly overlapped. The chemical shifts in the 2D NMR spectra of the H^N and ¹⁵N nuclei have better dispersion than the H^α, H^β, C^α, and C^β chemical shifts for all seven alanines. Therefore, the deviations of the chemical-shift values ΔδH^N and Δδ¹⁵N are better indicators to discriminate the differences in conformation of each alanine in the XAO peptide (Fig. 2).

All alanines have very small values for the ΔδH^α, ΔδC^α, and ΔδC^β chemical shifts (data not shown), indicating that the alanines may exist as an ensemble of statistical-coil conformations.

The H^N and ¹⁵N chemical shifts corresponding to P_II and β-structure are shifted downfield relative to those of a statistical coil, whereas those of the α-helical structure are shifted upfield (34). In Fig. 2 A and B, the deviations of the ΔδH^N and Δδ¹⁵N chemical shift values of the seven alanine residues are different from each other. The Δδ values of the alanines in Fig. 2 decrease continually from the N terminus to the C terminus. In addition, it can be seen (Fig. 2) that the diaminobutyric acid residues have stronger positive-shifted values of ΔδH^N and Δδ¹⁵N than both the alanines and the ornithines; this effect could be a consequence of the shorter side chain of X compared with that of O. It can, therefore, be concluded that the conformational states of the alanine residues in XAO are not uniform.

³J_HNHα Values of XAO.

The values of ³J_HNΗα measured at 5°C are summarized in Fig. 3. These values are very similar in both water and acetate buffer and agree with the values reported by Kallenbach et al. in acetate buffer (11). The values of the observed coupling constants at 5°C are smaller for the alanines than for the X and O residues. Because of the degeneracy of the Karplus relation (43), the possible values of the dihedral angles φ that satisfy this equation are: −165°, −70°, +30°, and + 100°, for all amino acid residues of the XAO peptide. These values can correspond to α-helix, β-strand, P_II structure, or β-turn type I, I′, II, or II′. As reported by Kallenbach et al. (11), we found that the values of ³J_HNΗα are mostly temperature-dependent (data not shown). However, we interpret this observation as a shift in the conformational equilibrium and not as conformational transitions, as already concluded in CD Spectra in Results.

Fig. 3.

ROE pattern (d_XN, where X = N, α and β), the vicinal coupling constants (³J_HNΗα) (all at 5°C), and the temperature coefficients for H^N (Δδ/ΔT), observed in NMR spectra for the XAO peptide. Some experimental values were difficult to obtain and are indicated by the letter d. The ROE patterns, the vicinal coupling constants, and the temperature coefficients in water and acetate buffer were all very similar, i.e., with differences ranging in values of 10%, 0.3 Hz, and 0.3 parts per billion (ppb)/K, respectively.

Rotating-Frame Nuclear Overhauser Effect (ROE) Effects Observed in NMR Spectra.

Fig. 3 summarizes the ROE pattern measured for XAO. In contrast to the results of Kallenbach et al. (11), who found no H_i^N–H_i+1^N cross-peaks, three such cross-peaks were found in our experimental ROE spectroscopy (ROESY) spectra. Weak H_i^N–H_i+1^N ROE signals exist between the amide protons of X₁–X₂, A₆–A₇, and A₉–O₁₀. These observations suggest that the XAO peptide cannot exist in the P_II structure because no H_i^N–H_i+1^N ROE signals should be observed in the P_II structure (44).

The weak H_i^N–H_i+1^N and the strong H_i^α-H_i+1^N signals between X₁ and X₂ indicate that these amino acid residues exist in the β-strand conformation (45). The cross-peaks found in the ROESY spectrum, between the H^α protons of X₂ and the H^N protons of A₃, A₄, and A₅, may be characteristic of a β bend structure in this region (45). Similarly, the weak H_i^N–H_i+1^N signal for A₆–A₇ also may indicate a turn in this fragment. However, all other ROE patterns, which could have confirmed this observation, are strongly overlapped (overlapped signals of A₃–A₉ are not shown in Fig. 3). The signals between the H^β protons of A₆ and the H^N proton of A₇ (shown as an open rectangle in Fig. 3) was reported by Kallenbach et al. (11). This signal may confirm the existence of a β-turn in this region. The weak H_i^N–H_i+1^N and H_i^β-H_i+1^N ROE signals, in connection with a strong H_i^α-H_i+1^N ROE pattern between A₉ and O_10, indicate the possibility of forming another half-turn structure at the C terminus of the XAO peptide.

The absence the same ROE pattern in every residue is consistent with the existence of a statistical-coil structure with a tendency for formation of a bend at the N and C termini and in the middle part of the XAO peptide in this ensemble.

Hydrogen Bonds.

For both statistical-coil and P_II structures, highly negative values of the temperature coefficients (Δδ/ΔT) for NH protons involved in hydrogen bonds are observed (45, 46). The values of the temperature coefficients of the XAO peptide, which are shown in Fig. 3, are very negative (approximately −8.2 ppb/K) and very close to the values characteristic of a statistical-coil structure [literature values (40) of −8.20 ± 0.21 ppb/K for alanine (A) and −7. 87 ± 0.20 ppb/K for lysine (K)]. Based on the data for the temperature coefficients of the amide proton chemical shifts, published by Cierpicki and Otlewski (47), the values of our observed temperature coefficients (Δδ/ΔT) for H^N indicate that each of the amide protons of XAO resides in an intramolecular hydrogen-bonded state for only 9% of the ensemble. In addition, the correlation between the backbone amide H^N chemical shift temperature gradients (Δδ/ΔT) with the deviation of the H^N protons from the statistical-coil reference chemical shift (ΔδH^N), proposed by Andersen et al. (48), confirms that no persistent hydrogen bonds are present in the XAO peptide. The observed high negative temperature coefficients (Δδ/ΔT) for H^N, together with the absence of the same ROE pattern in every residue, support the view that the alanines exist mainly in statistical-coil conformations.

Conformational Ensemble Generated by MD SA with Time-Averaged Restraints.

The conformational ensemble obtained by MD SA simulations with time-averaged restraints from NMR experiments (see Materials and Methods) was clustered into families. Ten families were found with an rms deviation cut-off of 3.0 Å per family, of which three were dominant (Fig. 4). The conformations from these main families have two common features: (i) the central part of the structure is better defined then the C- and N-terminal parts and (ii) these conformations have a tendency to form a bend structure in the A₆-A₇ region (see Fig. 4).

Fig. 4.

Superposed conformations of three major families of the conformations of XAO found by MD SA with time-averaged NMR restraints. The C^α rms deviation from the mean structure over residues from A₄ to O₁₀ is 2.80 ± 0.37 Å (for a family of 36 conformations) (A); 3.17 ± 0.49 Å (for a family of 22 conformations) (B); and 3.16 ± 0.50 Å (for a family of 24 conformations) (C).

A collective scatter plot of the conformational states of each amino acid residue of all of the conformations of XAO generated with the time-averaged-restrained MD SA simulations is presented in Fig. 5. It can be seen that the conformational states are clustered about three vertical lines at φ = −160°, −70°, and 60°, respectively, the last one being least populated. The first cluster contains mainly extended states, the second cluster contains the P_II states and the type I, II, and III β-turn states, and the third one the type I′, II′, and III′ β-turn states. The scatter plot characterizes the dominant conformations in the ensemble of unfolded states.

Fig. 5.

Scatter plot of the dihedral angles (φ and ψ) of all residues and all 193 conformations of XAO calculated by MD SA with time-averaged restraints.

We calculated the average value of R_g for the MD SA-generated and clustered conformation of the XAO peptide by using crysol (49) software. We generated simulated SAXS scattering profiles for the computed conformational ensemble and, subsequently, computed the ensemble-averaged radius of gyration. We obtained R_g = 7.4 ± 1.0 Å, which is in excellent agreement with that obtained by Pande and coworkers (18) by SAXS measurements (7.4 ± 0.5 Å). The highest and lowest values of R_g for the computed structures of XAO under study here are 10.8 Å and 5.6 Å, respectively.

Discussion

The results of our conformational study demonstrate that the alanine-based XAO peptide exists in an ensemble of interconverting conformations rather than in a well defined P_II conformation even at low temperature. The conformational ensemble generated by the MD SA method with time-averaged restraints is consistent with the experimental ROE intensities, ³J_HNΗα coupling constants, chemical shifts, and temperature coefficients. The calculated ensemble-averaged radius of gyration (7.4 ± 1.0 Å) is in excellent agreement with that determined experimentally by Pande and coworkers (18) from SAXS measurements (7.4 ± 0.5 Å).

In their earlier study of XAO, Kallenbach and coworkers (11) assumed that there is a “folding–unfolding” transition between the low-temperature P_II conformation and the β conformation at higher temperatures. This assumption does not consider the fact that, unlike proteins, peptides usually exist as an ensemble of interconverting conformations. Moreover, to derive the low-temperature conformation, they deduced the P_II conformation based on the absence of H_i^N–H_i+1^N nuclear Overhauser effects (NOEs), whose presence, on the other hand, was demonstrated here for A₆–A₇ and on the value of φ = −70° obtained from the coupling constants without considering the degeneracy of the Karplus equation (43). Using the morass software (50, 51), we calculated the H_i^N–H_i+1^N NOE intensities for the XAO peptide in the ideal P_II conformation and in the ideal right-handed α-helical conformation. The ratio of the H_i^N–H_i+1^N NOE intensity computed for an all-P_II conformation to that computed for an α-helical conformation is 1:4, which suggests that NOEs should be observed if the whole chain were to adopt the P_II conformation, even though such NOEs are weak.

The assumption of Kallenbach and coworkers (19) that a well defined conformational transition occurs was based mainly on the temperature dependence of the CD and NMR spectra of XAO. However, we have demonstrated here that these CD spectra depend not only on temperature but also on the concentration of XAO, pH, and the kind of ions in solution (phosphate or acetate) as shown in Fig. 1 A and B. Therefore, the dependence of the CD spectra on temperature and on other factors should be attributed to a shift in the equilibrium between many interconverting conformations rather than to an all-or-none conformational transition. In agreement with this conclusion, recent simulations of denatured structures of polypeptides using a simplified five-state model, steric restrictions, and a simplified solvation-free energy function (32) also suggest that, although the conformational space of amino acid residues is severely restricted even in a denatured state, the P_II conformation should be considered as one of sterically feasible and favorable conformational states. Finally, the emphasis in the literature on a well defined P_II conformation as the characteristic of a denatured protein is in contrast to a model of an ensemble of states, in which the P_II conformation is only one of these.

Materials and Methods

Peptide Synthesis.

The XAO peptide was synthesized on a 0.19 mmol scale by the solid-phase method using the fluorenylmethoxycarbonyl (Fmoc) strategy with an automated 9050 Plus PepSynthesizer (Millipore). N^α-Fmoc amino acids, with natural-abundance isotopic content, were in a 4-fold excess over the required amount of peptide, and diisopropylcarbodiimide (DIPCI) was used as the coupling agent. Purification was carried out on a Kromasil-5-C8 preparative HPLC column (Eka Chemicals, Bohus, Sweden) by using a linear gradient of an aqueous solution of acetonitrile and 10% trifluoroacetic acid. The yield was 46.8% (fast atom bombardment MS: [M+H]⁺ = 985.5; the calculated mass of an observed singly protonated XAO is 985.2 g/mol). The purity of the peptide was also checked by HPLC chromatography, resulting in a chromatogram with a single peak.

CD Spectroscopy.

CD spectra were recorded on a Jasco J-20 automatic recording spectropolarimeter with 1-mm quartz cuvettes. CD measurements were made at 0.05 mM, 0.1 mM, and 0.2 mM peptide concentration in water (pH = 6), in aqueous sodium acetate (pH = 3), and in phosphate buffers (pH = 5, 6, 7, 9, and 11) from 1° to 80°C. The spectra were recorded from 193 nm to 260 nm, with a sensitivity of 5 mdeg/cm and a scan speed of 2 cm/min. The CD spectra were measured three times and plotted as mean ellipticity Θ (degree × cm² × dmol⁻¹) vs. wavelength λ (nm).

NMR Spectroscopy.

For NMR measurements, the peptide was dissolved in 90% H₂O/10%D₂O and in 30 mM sodium acetate buffer (pH 4.5 in 10% D₂O), respectively. The peptide concentration in each sample was 4 mM. The NMR experiments were carried out on a Varian Unity 500 Plus spectrometer. All 2D NMR spectra were recorded at 5°C except for the temperature coefficients of the chemical shifts, which were measured throughout the temperature range 5–44°C. The ¹³C-¹H heteronuclear sequential quantum correlation (HSQC) spectra were obtained at 5°C and 28°C. The proton chemical shifts were referenced to the H₂O frequency measured with respect to 2, 2-dimethylsilanpentane-5-sulfonic acid (DSS). The ¹³C and ¹⁵N chemical shifts where indirectly referenced to DSS following the procedure of Wishart and Nip (52). NMR sample temperatures were determined from the known temperature dependence of the NMR spectra of 100% methanol for temperatures below 25°C or 100% ethylene glycol above 25°C. NMR data were processed with the nmrpipe program (53) and analyzed with xeasy software (54). Sequential backbone resonance assignments were achieved in the following experiments: TOCSY (55) with mixing times of 10 and 80 ms; NOESY (56) with a mixing time of 300 ms; ROESY (57) with a mixing time of 300 ms; and HSQC (¹³C-¹H) (58) and (¹⁵N-¹H) (59). The solvent peak was suppressed by a flip-back pulse sequence (60).

The ³J_HNΗα vicinal couplings constants were determined by 1D ¹H-NMR experiments. The estimated experimental error was 0.3 Hz. The distance constraints and coupling constants were used in the program habas of the dyana package (61) to generate φ, ψ, and χ¹ dihedral angle restraints and stereospecific assignments. The dihedral angle restraints were calculated from the Karplus equation (43), ³J_HNΗα = 6.4 cos² θ − 1.4 cos θ + 1.9, with θ = |φ − 60°| (62).

ROE intensities were determined from the ROESY spectrum of XAO measured in water and in acetate buffer. The ROE volumes were integrated and calibrated with xeasy software (54). The strongly overlapped cross-peaks (seven H^α–H^N and seven H^β–H^N cross-peaks of A₃–A₉) were not integrated. The ROE integrated volumes showed an error below 10%. After internal calibration, the cross-peaks obtained from the ROESY experiment were converted into upper distance limits by the caliba program of the dyana package (61).

Because experimental data were not available for the statistical-coil chemical shifts and temperature coefficient of the H^N protons of both ornithine and diaminobutyric acid, the corresponding values for lysine were adopted.

MD SA Simulations with Time-Averaged Restraints.

MD simulations were carried out with the amber 99 force field (63). The nonstandard residues (O and X) were parameterized by using the RESP method (64) based on HF/6–31G* calculations carried out with gaussian 98 (65). The SA model of the amber program was used to speed up the conformational search. The time-averaged restraint method (63, 66, 67) was used to include interproton-distance (a total of 40) and dihedral-angle (a total of 16, pertaining to φ angles for Ala residues, φ and χ angles for O residues, and φ, ψ, and χ angles for X residues) restraints determined from the ROE intensities and coupling constants, respectively. Because of overlapping of the peaks of the H^α and H^β protons, it was not possible to determine the dihedral angles ψ and χ angles alanines and ψ for ornithines. The interproton distances were restrained with the force constant k = 20 kcal/(mol × Å²), and the dihedral angles with k = 2 kcal/(mol × rad²), respectively. The dihedral angles ω were restrained to 180° with k = 10 kcal/(mol × rad²). The improper dihedral angles centered at the C^α atoms (defining the chirality of amino acid residues) were restrained with k = 50 kcal/(mol × rad²). With a P_II starting conformation, 193 SA cycles were carried out. The starting structure for every next cycle was the last structure from the previous cycle, with retention of the conformation at the end of each cycle, i.e., a total of 193 conformations. Each SA cycle consisted of 30, 000 MD steps (30 ps each). The system was heated in 1 ps over 1, 000 steps from 10 K to 1200 K and then annealed at 1200 K for 2 ps over 2, 000 steps. During the SA time-averaged refinement, the system was cooled from 1200 K to 10 K in 27 ps over 27, 000 steps, the first 19, 000 iterations corresponding to slow cooling, the next 4, 000 iterations to faster cooling, and the last 4, 000 iterations to very fast cooling. The set of the final conformations was clustered with the molmol program (68). An rms deviation cut-off of 3.0 Å over the A₃–A₉ conformations was used for the clustering.