Determination of the Three-Dimensional Structure of a New

A large elliptic curve for the dihedral angles for the Gly residue was drawn from the interatomic distance of rCN = 3.43 Å (II) (Figure 7b). An addit...
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J. Phys. Chem. 1996, 100, 14995-15004

14995

Determination of the Three-Dimensional Structure of a New Crystalline Form of N-Acetyl-Pro-Gly-Phe As Revealed by 13C REDOR, X-Ray Diffraction, and Molecular Dynamics Calculation Akira Naito,*,† Katsuyuki Nishimura,† Shigeki Kimura,† Satoru Tuzi,† Misako Aida,‡ Noritake Yasuoka,† and Hazime Saitoˆ *,† Department of Life Science, Himeji Institute of Technology, Harima Science Garden City, Kamigori, Hyogo, Japan, 678-12, and Biophysics DiVision, National Cancer Center Research Institute, Tsukiji 5-chome, Chuo-ku, Tokyo, Japan 104 ReceiVed: January 17, 1996; In Final Form: June 12, 1996X

The interatomic distances in the crystalline specimen of 13C,15N doubly labeled peptides [1-13C]N-acetylPro-[15N]Gly-Phe (I), N-acetyl-[1-13C]Pro-Gly-[15N]Phe (II), and [1-13C]N-acetyl-Pro-Gly-[15N]Phe (III) evaluated from rotational echo double resonance (REDOR) data were compared with those from X-ray diffraction studies and justify our novel approach. The minimization of B1 inhomogeneity was critical to obtain accurate distances, which were achieved by confinement of the samples in the central portion (50% of the total filling volume of the rotor). The effect of the finite length of the π pulse was found to be negligible as long as the pulse length is less than 10% of the rotor cycle. The 13C‚‚‚15N distances obtained from 13C REDOR were thus 3.24 ( 0.05, 3.43 ( 0.05, and 4.07 ( 0.05 Å for I, II, and III, respectively. The REDORderived conformation of this peptide was β-turn type I, consistent with our X-ray diffraction study (orthorhombic crystal). The maximum deviation of the distances determined by NMR and X-ray diffraction is 0.08 Å despite the complete neglect of the dipolar interactions with the labeled nuclei of neighboring molecules and natural abundance nuclei. The precision and accuracy given by 13C REDOR experiments are on the order of (0.05 Å. Distinction between the two types of β-turn forms including the β-turn type II found in the monoclinic crystal of this peptide whose interatomic distances are different by about 0.57 Å is made possible only by the very accurate REDOR measurement. Finally, we found that the three-dimensional structure of this peptide was well reproduced by a molecular dynamics simulation by taking into account all the intermolecular interactions in the crystals.

Introduction Elucidation of the three-dimensional (3D) structure of biologically active peptides such as hormones or ligands of receptor proteins is crucially important in relation to understanding their structure-function relationship. This approach, however, is not always a straightforward way in which to arrive at the biologically active conformation, because in the solution state these molecules are usually too flexible to take any unique structure. Instead, such a conformation is available when they are bound to a membrane or receptor molecule.1 For this purpose, very accurate interatomic distances can be determined by a variety of solid state NMR techniques which recouple the magnetic dipolar interaction, under the magic-angle spinning condition.2 Rotational resonance (RR)3,4 and RF-driven dipolar recoupling (RFDR)5,6 techniques are based on the magnetization exchange between the two homonuclearly labeled atoms. Dipolar recovery at the magic angle (DRAMA)7,8 recouples the homonuclear dipolar interaction by employing rotor synchronizing π/2 pulses. Rotational echo double resonance (REDOR)9 and transferred echo double resonance (TEDOR)10 are based on the interference of the averaging weak heteronuclear dipolar interactions. These techniques have proved to be useful for the elucidation of the conformation of small peptides,11 membrane peptides, proteins,12 and enzyme-inhibitor complexes,13 because the size or quality of the crystalline samples is not so stringent †Himeji

Institute of Technology. National Cancer Center Research Institute. X Abstract published in AdVance ACS Abstracts, August 15, 1996. ‡

S0022-3654(96)00179-7 CCC: $12.00

for NMR work in contrast to X-ray diffraction, and samples involving the membrane-bound state can be equally used. Undoubtedly, it is essential to be able to determine the interatomic distances as accurate as possible, if one aims to utilize the distance constraints thus determined to construct the 3D structures of peptides or proteins. REDOR9 and RR3,4 are the most well studied techniques for this purpose. Particularly, it is expected that the most accurate distances could be obtained by REDOR experiments9 in view of its simplicity for processing the experimental data. There remain, however, two major possible sources of errors in REDOR experiments, other than the instrumental conditions, which arise from the dipolar contributions from the labeled nuclei of neighboring molecules and nuclei of natural abundance in the same molecule. The presence or absence of the former contribution can be readily recognized as a systematic deviation of experimental points14 from the theoretical line, which was obtained by analysis of a two-spin system, in a plot of ∆S/S0 against NcTr, where S0, ∆S, and NcTr stand for the peak intensity of full echo, its difference from REDOR, and the product of the number of rotor cycles and its period, respectively. It appears that the previous REDOR studies on peptides by Schaefer et al.11a,d and Garbow et al.,11e,f however, seem to have some drawbacks in the treatments of these points as follows. First, excess dilution of the labeled sample up to 1:4911e may cause errors in the distance determination owing to REDOR signals with poor S/N ratio, even if the intermolecular contributions could be completely removed by this procedure. Second, measurement of ∆S/S0 (which should be preferably larger than 0.5) at a single set of Nc and Tr does not necessarily lead to an accurate distance free from © 1996 American Chemical Society

14996 J. Phys. Chem., Vol. 100, No. 36, 1996 any systematic errors and is insensitive to the presence of the intermolecular contributions mentioned above, if any.14 Third, the dipolar interactions either with the labeled nuclei of neighboring molecules or from nuclei of natural abundance in the same molecule require data analysis in terms of at least the three-spin system14 instead of a simple addition of the isolated two-spin systems. Otherwise, such effects could accumulate and may cause errors, especially in the case of 15N REDOR measurements. We previously showed14 that no correction for the dipolar interactions with nuclei of natural abundance is necessary as far as the 13C REDOR experiment is concerned. Fourth, it is not always possible to assume an 8-10% reduction of the C-N dipolar interactions11a,d-f by motional modulation without specific experimental verification, because such correction, if any, depends on the flexibility of molecules and the distances under consideration. It is also possible that such systematic reduction of the dipolar interaction could be accompanied by a variety of experimental conditions such as the effect of B1 inhomogeneity and pulse lengths. To clarify the above-mentioned points in more detail, we propose here an alternative but more simple approach to these problems based on some considerations of the experimental conditions and a new means to reveal the 3D structure of peptides and proteins based on the interatomic distances determined by REDOR measurements. To this end, it is crucially important to justify our new approach for the data analysis of the REDOR experiment and critically examine some experimental conditions so far not yet fully analyzed, including the B1 inhomogeneity and the length of π pulses as viewed from the achieved precision and accuracy of the determined interatomic distances. Acquisition of accurate data is very important for the construction of 3D structures, because only a limited number of distance constraints are available in the solid state. Currently, the precision and accuracy of distance data available from RR have been recently estimated as on the order of 0.1 and 0.2-0.3 Å, respectively.15 In the present paper, we have applied the REDOR technique to determine the three sets of interatomic distances of a simple tripeptide, N-acetyl-Pro-Gly-Phe, in order to demonstrate usefulness of our new approach for determination of the 3D structure of peptides: (1) the distance measurements and recognition of the existence of the intermolecular dipolar interactions by means of a plot of ∆S/S0 vs NcTr; (2) complete neglect of the dipolar contributions from natural abundant nuclei for 13C REDOR; (3) examination of the B1 inhomogeneity and the finite length of the 15N π pulse; (4) use of 13C and 15N chemical shifts to distinguish polymorphism, if any. This peptide was chosen because the secondary structure is known from previous X-ray diffraction studies16 (β-turn type II structure; monoclinic crystal), but the orthorhombic crystals available for the present NMR measurements turned out to be β-turn type I form. In addition, several types of relaxation parameters for a variety of time scales were examined in order to gain insight into how the 13C‚‚‚15N pairs under consideration are involved in different types of internal motions. We found that both types of the β-turn structures were not always stabilized by the intramolecular hydrogen bonds alone but mainly by the intermolecular hydrogen bonds with neighboring molecules as revealed by means of molecular dynamics (MD) simulation for the molecules in the crystals. Experimental Section Sample Preparation. Three doubly labeled tripeptides, [1-13C]N-acetyl-Pro-[15N]Gly-Phe (I), [1-13C]N-acetyl-Pro-Gly[15N]Phe (II), and N-acetyl-[1-13C]Pro-Gly-[15N]Phe (III), and

Naito et al.

Figure 1. Pulse program for the REDOR experiment used in this study.

unlabeled peptide (IV) were synthesized using an ABI-430A peptide synthesizer. Fmoc-amino acids were purchased from the Peptide Institute, Osaka, Japan. Fmoc isotopically labeled amino acids (99% enriched) were synthesized by the reaction of Fmoc-Osu with the labeled amino acids ([1-13C]Pro, [15N]Gly, and [15N]Phe from CIL, Cambridge) following the method of Paquet.17 N-acetylation was carried out with 13C-labeled acetic anhydride in dimethylformamide. These peptides were purified by reversed-phase high-pressure chromatography (Waters) on a Bondasphere C-18 column. The purity of the synthesized peptide was checked by recording both 1H and 13C NMR spectra in solution state. Polycrystalline samples for the NMR studies were grown from ethanol solutions. 13C NMR and REDOR Measurements. 13C and 15N NMR spectra were recorded on a Chemagnetics CMX-400 spectrometer by employing cross polarization-magic-angle spinning (CPMAS). Repetition and contact times were usually 4 s and 1 ms, respectively. 13C and 15N chemical shifts were measured with respect to TMS and the NH4+ signals of ammonium nitrate, respectively, as external references. 13C spin-lattice relaxation times in the laboratory frame and proton spin-lattice relaxation times in the rotating frame were measured by the methods of Torchia18 and cross-polarization dynamics,19 respectively. All of the NMR measurements were carried out at ambient temperature (23 °C). 13C REDOR spectra were recorded on the same spectrometer equipped with two types of triple-resonance probes (7.5 and 5.0 mm o.d. rotors). The π/2 pulses for the 13C and 15N nuclei were typically 8.0 and 14.2 µs, respectively, for the former probe. However, the π/2 pulse lengths of the latter probe for 13C and 15N nuclei were typically 5.0 and 7.0 µs, respectively. The rf fields of the latter for the 1H, 13C, and 15N channels were, therefore, 60, 50, and 36 kHz, respectively. Prior to the REDOR experiments in the latter probe, we examined the length of the π pulse by changing the sample volume in order to check the B1 inhomogeneity. As a result, about 30 mg of [1-13C, 15N]glycine sample was packed in the center part of a zirconia rotor (6 mm length and 50% of the total possible filling volume). The pulse sequence used for the REDOR experiment is shown in Figure 1 and an xy-4 compensated pulse sequence20 was employed in the irradiation channel to minimize off-resonance effects and the effect of rf power fluctuation during the REDOR measurement. These compensation pulses were not applied to the observation channel so as not to disperse the magnetization to the proton reservoir. The normalized echo difference, ∆S/ S0, was obtained for a number of echo intervals by taking into account all of the sidebands to remove the orientation effects. The spinning frequency for the REDOR experiment was 4000 Hz. X-ray Diffraction. A colorless plate-type single crystal suitable for the X-ray diffraction study was grown from mixed solvents consisting of ethanol, acetone, and petroleum ether (2:

3D Structure of a New Form of N-Acetyl-Pro-Gly-Phe

J. Phys. Chem., Vol. 100, No. 36, 1996 14997

1:4). A colorless plate-type crystal of C18H23O5N3 having approximate dimensions of 0.10 × 0.20 × 0.30 mm was mounted on a glass fiber. All X-ray measurements were made on a Rigaku AFC5R diffractometer with a 12 kW rotating anode generator that produced graphite monochromated Cu KR radiation. The powder X-ray diffraction pattern for polycrystalline samples was recorded on a Phillips X’Part-MPD diffractometer. Computational Method Analysis of REDOR Data. REDOR and full echo spectra were acquired for a variety of NcTr values, where Nc is the number of rotor cycles and Tr is the rotor period. Therefore, the normalized echo difference, ∆S/S0, was calculated from

∆S/S0 ) (S0 - Sf)/S0

(1)

where S0 and Sf are the echo amplitude of the full echo and REDOR experiments, respectively. The rotational echo amplitudes under the full echo and REDOR conditions were evaluated by considering the time evolution of the density operator under the average Hamiltonian with magic-angle spinning and the finite length of the π pulse train from the following equations:

1 2π π ∫ ∫0 sin β dβ dR 2π 0

(2)

1 2π π ∫ ∫ 〈I (T )〉 sin β dβ dR 2π 0 0 y r

(3)

S0 ) and

Sf )

(21xa + b T )

〈Iy(Tr)〉 ) cos

2

2

(4)

r

respectively, where

a)

D {sin2 β[sin(2R+ωrtw) + sin(2R-ωrtw) 4π 2 sin 2R] - 2x2 sin 2β[sin(R+ωrtw/2) + sin(R-ωrtw/2) + 2 sin R] - sin2 β[sin(2R+ωrtw) +

4ωr2tw2 1 sin(2R-ωrtw)] 2 2 + x2 sin 2β sin R+ ωrtw + 2 2 4ωr tw - π

[ (

)

2ωr2tw2 1 sin R- ωrtw 2 ωr2tw2 - π2

)]

(

D {sin2 β[cos(2R+ωrtw) + 4π 2πωrtw 1 - x2 sin 2β cos R+ ωrtw + cos(2R-ωrtw)] 2 2 2 2 4ω t - π

b)

[ (

r w

)

2πωrtw 1 cos R- ωrtw 2 ωr2tw2 - π2

(

D)

)]

γIγSh 2πr3

where R is the azimuthal and β is the polar angle defined by the internuclear vector in a coordinate system with the z axis parallel to the rotor axis. The constants, γI and γS are the gyromagnetic ratios for the spins I and S, respectively, h is Planck’s constant, and r is the length of the I-S internuclear

vector, which is spinning at a frequency ωr about the axis at the magic angle with the direction of the static magnetic field. Pulse length, tw, is also considered in the calculations for the analysis of REDOR results. When the length of tw is zero, eq 3 is the same form as derived previously.9 Values of rCN were determined by inspecting the best fit of the experimentally obtained REDOR data with the theoretically evaluated values using eq 3. Contributions to the REDOR effect from the natural abundant nuclei and labeled nuclei of neighboring molecules were not taken into account since the effect is not significant as far as 13C REDOR is concerned.14a,b Conformational Analysis of the Peptide. To determine the 3D structure of the peptides, the distance information thus obtained was converted to the dihedral angles of each amino acid residue. The possible combinations of the dihedral angles (Φi, Ψi) at the peptide unit i are not necessarily unique but yield a number of possibilities that are shown in the conformational map of the ith amino acid residue. The conformational map for the ith amino acid residue was calculated by the procedure that varied the Φi and Ψi angles by 1° increments from -180° to 180° to give the same C-N distance of atoms four bonds apart, determined from REDOR experiments by using a program CONF4 written in FORTRAN 77 language. Standard values of C-N, N-CR, and CR-C bond lengths were employed, namely, 1.33, 1.46, and 1.51 Å, respectively.21 The ω value for the Pro residue was assumed to be either 180° or -175°. The conformational map for the interatomic distance of atoms seven bonds apart was calculated from Φi, Ψi, and ωi+1 by varying Φi+1 and Ψi+1 values by 1° increments using the program CONF7. Energy Minimization and Molecular Dynamics Calculations. The energy minimization and molecular dynamics (MD) calculations were performed using the KGNMD program from the MOTECC package,22 with the ab initio potentials for the solute intra- and intermolecular interactions.23 The total energy of a system was described as the sum of the solute nonbonded and the solute bonded interaction energies.22 For the energy minimization, the SUMSL (secant-type unconstrained minimization solver) routine24 was used. The equations of motion were solved using the leap-frog algorithm with a time step of 0.5 fs. In all cases, periodic boundary conditions were applied. For the MD simulation of the single peptide in Vacuo, all possible nonbonded interactions were taken into account and all the energy terms are explicitly evaluated using a large enough simulation box to ensure that any atom in the box was far away from its periodic images. The energy-minimized structure was used as an initial structure for the MD simulation in Vacuo at 100 K. The molecule was equilibrated during 50 ps, followed by a 50 ps run without velocity rescaling, since the average temperature remained essentially constant around 100 K. The final 50 ps simulation was used for analysis; coordinates and velocities were stored every 50 fs. Two kinds of systems were simulated at 293 K in the crystallographic cells: the orthorhombic and monoclinic crystals.16 For each of the systems, we used the simulation box, which was composed of a certain number of crystallographic cells, as will be described below, to ensure that a large enough value can be set for the cutoff radius for the nonbonded interactions. The long-range Coulomb term was computed with the Ewald sum correction.25 One simulation box in the orthorhombic crystal was composed of 6 crystallographic cells: 2 cells along the a axis, 1 cell along the b axis, and 3 cells along the c axis. Four molecules per cell were placed in a crystallographic cell with the symmetry

14998 J. Phys. Chem., Vol. 100, No. 36, 1996

Naito et al. TABLE 1: 13C and 15N Chemical Shifts of N-Acetyl-Pro-Gly-Phe 13C

chemical shiftsa (ppm)

acetyl Pro Gly Phe peptides CdO CdO CdO COOH I II III IV

173.7

a

13C

15

N chemical shifts (ppm) Pro Phe Gly 81.6

174.2 173.7 173.8 173.8 171.5

171.5

113.9

100.2 100.2 100.3

81.5

Other chemical shifts: Phe Cγ, 138.3; Phe Cζ, 127.6; Pro Cδ, 62.2; Phe CR, 56.5; Pro CR, 48.0; Gly CR, 42.9; Phe Cβ, 37.9 ppm.

Figure 2. 13C and 15N NMR spectra of N-acetyl-Pro-Gly-Phe in the crystalline state.

of the space group P212121. The X-ray structure revealed in this paper was used as an initial conformation. In total, 24 molecules were included in a simulation box. A cutoff radius of 9.4 Å was adopted with the Ewald sum correction for the long-range Coulomb term. One simulation box in the monoclinic crystal was composed of 18 crystallographic cells: 3 cells along the a axis, 3 cells along the b axis, and 2 cells along the c axis. Two molecules per cell were placed in a crystallographic cell with the symmetry of the space group P21. The published X-ray strucure15 was used as an initial conformation. In total, 36 molecules were included in a simulation box. A cutoff radius for this simulation was 11.5 Å. For each of the simulations, the system was equilibrated over 50 ps, followed by a 10 ps run without velocity rescaling, since the average temperature remained essentially constant around 293 K. The final 50 ps simulation was used for analysis; coordinates and velocities were stored every 50 fs. Results 13C

and 15N Chemical Shifts. Figure 2 shows the 13C and CP-MAS of unlabeled N-acetyl-Pro-Gly-Phe (IV) in the polycrystalline state. Resonance lines were assigned with reference to the chemical shifts in the solution state27 as summarized in Table 1. We found that the 13C and 15N chemical shifts of the three kinds of doubly labeled peptides, I, II, and III, were identical with those of the unlabeled peptide. It has been shown that the 13C chemical shifts of the CR, Cβ, and carbonyl carbons vary up to 8 ppm depending upon the secondary structures of peptides.26 Therefore, it was shown that the crystal structures of these three kinds of labeled peptides used for REDOR measurements were the same in view of the conformation-dependent displacements of the 13C chemical 15N

shifts,17,28 consistent with our finding based on the powder diffraction study. This is one of advantage of the NMR method, because it is easy to distinguish the crystal structures by monitoring the chemical shift values of the individual carbon and nitrogen resonances with reference to those of the known structure. It is interesting to note that both the Cδ and C signals of Phe side chain are completely suppressed in Figure 2a. This happens when the rate constant of the flip-flop or oscillatory motion of the Phe side chain is close to the proton-decoupling frequency.29 In addition, it is noticed from the expanded dipolar dephased difference spectrum (inset of Figure 2) that the Pro Cγ signal is substantially broadened and appears as a shoulder of the Pro Cβ signal.29 This finding can be explained in terms of the presence of ring-puckering motion between the Cγ-exo and Cγ-endo forms, whose rate interferes with the protondecoupling frequency (104 Hz). The difference of the 13C chemical shifts between the Pro Cβ and Pro Cγ signals, ∆βγ ()δβ - δγ), thus obtained is -1.9 ppm.30 Determination of the Interatomic Distances by the REDOR Experiment. First, we examined how the π pulse length for a 5 mm probe is influenced by a plausible B1 inhomogeneity within the rotor using 20% [1-13C, 15N]Gly as a standard sample. We found that the confinement of the sample at the central 50% volume (6 mm of the total 12 mm length) resulted in the homogeneous 15N π/2 pulse length of 7.0 µs, whereas the fully packed sample (12 mm length) resulted in the π/2 pulse length of 9.0 µs using the same rf power from the transmitter. We found that further reduction of the sample volume from 50% volume (to 3 mm length) did not change the pulse length, although the sensitivity of signals was considerably reduced. In Figure 3, the REDOR parameter ∆S/S0 as measured for 20% [1-13C,15N]Gly was plotted for the lengths of the 15N π pulse of 13.0 µs for this particular experiment and 24.6 µs (chosen to satisfy 10% rotor cycle) as a function of NcTr with the calculated lines using the δ pulse length (solid line) and finite length (13.0 and 24.6 µs for the broken and dotted lines, respectively) of the π pulse for the partially packed sample (6 mm length). It turned out that the finite length of the 15N π pulse does not affect the REDOR effect provided the pulse length is less than 10% of the rotor cycle at the rotor frequency of 4000 Hz.31 The observed REDOR parameter, ∆S/S0, as measured for III was plotted against NcTr32 as shown in Figure 4. The solid circles, solid squares, and open circles in Figure 4 were obtained from the experiments employing the confinement of the samples to 50% of the total filling volume of the 5 mm rotor and the fully packed state of the 5.0 and 7.5 mm rotors, respectively. It was found that the best fit C-N internuclear distances were 4.07 Å (solid circles), 4.37 Å (solid squares), and 4.45 Å (open circles) for these three kinds of arrangement. In any case, the precision of these distances was on the order of (0.05 Å. Nevertheless, only the distance obtained using the 5 mm rotor with 50% of the total filling volume is in good agreement with that determined by X-ray diffraction of the orthorhombic crystal

3D Structure of a New Form of N-Acetyl-Pro-Gly-Phe

Figure 3. 13C REDOR and full echo spectra of [1-13C, 15N]glycine as recorded by the rotor frequency of 4000 Hz and an NcTr of 4 ms (top) and plots of the REDOR parameters vs NcTr (bottom). Solid and open circles denote the experimental points recorded using a 15N π pulse of 13.0 and 24.6 µs, respectively. Calculated lines: solid line (δ pulse), broken line (13.0 µs), and dotted line (24.6 µs).

(3.99 Å), as will be described later. As mentioned above, the difference in the 15N π pulse length between the samples of 6 and 12 mm length in the 5 mm probe is not serious for any discrepancies in these interatomic distances. Therefore, the B1 inhomogeneity due to the sample size can cause serious systematic errors ranging from 0.19 to 0.39 Å depending on the distances to be measured as listed in Table 2. Peerson et al. also reported inhomogeneity effects on the sample coil of the RR experiment,15 in which a decrease of sample volume caused an increase of the effective decoupling field. It is pointed out that the inhomogeniety effect for REDOR is much more serious than for RR, because the number of π pulses lead to an accumulation of the errors. If dipolar contributions from the labled 15N nuclei of nearby molecules are present, a significant deviation of the experimental points from the theoretical line, when they were analyzed by the two-spin system, could be observed, as demonstrated for I in our previous paper.14 Such a deviation, if any, can be minimized when the dilultion experiment is carried out or the intermolecular dipolar contribution is explicitly taken into account by analysis of the dipolar interactions as a three-spin system.14 In contrast, it appears that such intermolecular dipolar interactions can be ignored for II and III, because no significant deviation from the theoretical lines of the two-spin system was noted on the level of (0.05 Å, as demonstrated in Figure 4.14a Therefore, it was not necessary to perform the dilution experiment for all samples I, II, and III as far as the present crystalline form involving β-turn conformation is concerned. This is not always true, however, when any crystalline form involving the

J. Phys. Chem., Vol. 100, No. 36, 1996 14999

Figure 4. 13C REDOR and full echo spectra of III with an NcTr of 16 ms (top) and plots of the REDOR parameters vs NcTr (bottom). Solid circles, solid squares, and open circles denote the experimental points from the samples filled in the central 50% of the total filling volume of a 5 mm o.d. rotor, and the fully packed state of 5.0 and 7.5 mm rotors, respectively. The resulting interatomic distances were determined as 4.07, 4.37, and 4.45 Å, respectively.

β-sheet conformation is involved, as in the case of the β-amyloid fibril,33 since the dipolar contributions from the labled nuclei of nearby molecules can no longer be neglected. Nevertheless, the precision for the distance measurement could be further improved to the order of (0.02 Å, when the dilution experiments to minimize the contribution from the dipolar interactions with the labeled neighboring molecules were performed.14 It seems, however, not easy at present to achieve the accuracy of this level, as described later. The interatomic distances for the three differently labeled peptides thus obtained are summarized in Table 2. Spin-Lattice Relaxation Times. Table 3 summarizes the 13C spin-lattice relaxation times in the laboratory frame (T ) 1 and the carbon-resolved 1H spin-lattice relaxation time in the rotating frame (T1F) of the peptide. It is found that the 13C T1 value (18 s) of the acetyl methyl carbon is unusually longer than that of the corresponding methyl group in other peptides undergoing rapid C3 rotation (0.5 s).34 This finding indicates that the crystals are so tightly packed that the molecular backbone is rigid enough (T1 of 80-140 s) to prevent the C3 rotation of the methyl group. It is also interesting that the T1 value of Pro Cβ is so very long (26.4 s) that there appears no fast puckering motion in the pyrrolidine ring of the Pro residue, as would be detected by the appreciable reduction in the T1 value (1-3 s).34d Nevertheless, it appears that the observed 1H T 1F values were rather short as compared with the similar data of other peptides,35 indicating the presence of slow motion with the correlation time of 10-4 s. It is difficult, however, to locate which residue undergoes such local motions, because spin diffusion tends to level off all the relaxation times of the individual residues. Instead, such information is available from

15000 J. Phys. Chem., Vol. 100, No. 36, 1996

Naito et al.

TABLE 2: C-N Interatomic Distances (Å) Determined for REDOR Experiments As Compared with Those by X-Ray Diffraction and MD experimental labeled peptides

REDOR orthorhombic

I II III

3.24 ( 0.05 (3.43 ( 0.05)a 3.43 ( 0.05 (3.66 ( 0.05) 4.07 ( 0.05 (4.45 ( 0.05)

a

calculated

X-ray orthorhombic monoclinicb 3.19 3.35 3.99

MD energy- minimizedc

orthorhombic

monoclinic

3.17 3.57 4.17

3.22 ( 0.10 3.32 ( 0.10 3.92 ( 0.12

3.63 ( 0.10 3.33 ( 0.10 3.83 ( 0.10

3.76 3.21 3.91

Data from ref 14 based on fully packed 7.5 mm rotor system. b Reference 16. c Energy-minimized structure based on REDOR data.

TABLE 3: 13C Spin-Lattice Relaxation Times (T1’s) in the Laboratory Frame and 1H Spin-Lattice Relaxation Times (T1G’s) in the Rotating Frame

T1 (s) T1F (ms)

acetyl (CdO) Pro (C)O)

Gly (CdO) Phe (COOH)

Phe Cγ

Phe Cζ

Pro Cδ

Phe CR

Pro CR

Gly CR

Phe Cβ

Pro Cβ

acetyl (Me)

104.4 2.88

131.8 3.00

87.6 2.89

163.8 3.25

115.7 3.05

144.9 3.57

144.9 3.10

103.5 3.08

86.2 3.61

26.4 2.95

18.2 3.24

TABLE 4: Crystal Data for N-Acetyl-Pro-Gly-Phe mol formula mol wt color habit density(calc), g cm-3 m(Cu Ka), cm-1 space group lattice Parameters a, Å b, Å c, Å b, deg V, Å3 no. of reflections R factors a

orthorhombica

monoclinicb

C18H23O5N3 361.40 colorless plate 1.343 8.24 P212121 10.455(6) 22.93(1) 7.452(4)

C18H23O5N3 361.18 white needle 1.244 6.20 P21 8.915 8.458 13.216 104.8 963.47

1786(1) 1450 0.058

This work. b Reference 16.

the change of 13C NMR line widths: the flip-flop motion of the aromatic side chain in the Phe residue and the ring puckering in the pyrrolidine ring in the Pro residue (interconversion between Cγ-exo-Cβ-endo and Cγ-endo-Cβ-exo forms)36 were manifested from the selective peak suppression of C and Cδ signals and substantial broadening of the Cγ signal, respectively (Figure 2). These findings indicate that no appreciable backbone motion, which may seriously deteriorate accuracy of the measured interatomic distances, if any, was present in this peptide. Fortunately, it is also pointed out that the presence of the above-mentioned puckering motion in the pyrrolidine ring of the Pro residue does not seriously affect the accuracy of the measured interatomic distances, as revealed by our MD simulation of this peptide in the crystalline state.37 X-ray Diffraction of the Orthorhombic Crystal. Table 4 compares the crystal data for the orthorhombic crystal studied in this paper with those of the monoclinic crystal reported previously.16 As illustrated in Figure 5, the molecular conformation of the orthorhombic crystal turned out to be β-turn type I, although the monoclinic crystal of this peptide shows β-turn type II.16 The C, N interatomic distances to be compared with those of I, II, and III are summarized in Table 2. The thermal factors of the orthorhombic crystal show that there are some motions around both the Pro and Phe rings, consistent with the 13C NMR observation mentioned above. It is noteworthy from the crystalline structure (Figure 6) that the intermolecular hydrogen bond is very weak for the orthorhombic crystal as compared with that of the monoclinic crystal, despite the increased density in the former and only one hydrogen bond is formed with a nearby molecule, as will be indicated later in Figure 9. In addition, the intramolecular hydrogen bond between the carbonyl oxygen of the N-acetyl group and the

Figure 5. ORTEP drawing for conformation of the orthorhombic crystal of N-acetyl-Pro-Gly-Phe.

amide nitrogen of the Phe residue is much weaker than that of the monoclinic crystal, as manifested from the differences in the distances for III (Table 2). We also proved that the cell parameters of all the orthorhombic crystalline samples used for the REDOR experiment were different from those of the monoclinic crystal, despite our continued efforts to crystallize the sample in the latter form, and turned out to be identical to those of the orthorhombic crystals, as manifested from the powder X-ray diffraction study (data not shown). Discussion Precision and Accuracy of the Interatomic Distances Measured by REDOR. We found that the crystalline forms of I-IV are identical judging from the conformation-dependent displacements of the 13C and 15N chemical shifts (Table 1) and the powder X-ray diffraction data (data not shown). Further, their crystal structures turned out to be not monoclinic but orthorhomic, as judged from the X-ray diffraction study. In addition, there appears to be no appreciable internal motion for various time scales, as judged by the spin-relaxation times and chemical exchange processes. Thus, the interatomic distances determined from the REDOR experiment can be used without any corrections for motional modulation as starting data to construct the 3D structure of the peptide. The maximum deviation of the interatomic distances determined from REDOR data from those by X-ray diffraction was 0.08 Å. Therefore, it is concluded that the precision and accuracy of our REDOR

3D Structure of a New Form of N-Acetyl-Pro-Gly-Phe

J. Phys. Chem., Vol. 100, No. 36, 1996 15001

Figure 6. Stereoview of the crystalline structure of N-acetyl-Pro-Gly-Phe (orthorhombic crystal). The intra- and intermolecular hydrogen bonds are connected by thick lines.

measurements are at present on the order of (0.05 Å, as combined with a precision of (0.05 Å. Obviously, these measurements seem to be not yet completely free from other systematic errors, because the distances measured from REDOR are always longer than those determined by X-ray diffraction (Table 2). It is worthwhile to perform the dilution experiments to minimize the contributions from the dipolar interactions with the labeled nuclei in order to improve further the accuracy of measurements. It seems to be also very important to take into account of the change of the bond length by thermal fluctuations (factor). This can be simply estimated by considering the averaging of the 1/r3 value rather than the r value for the direct dipolar interactions by taking into account the thermal factor. A simple model was considered for evaluating the effective interatomic distances in the presence of displacements of the atomic position characterized by thermal factors. We denote that w and u and V are small displacements along and perpendicular to the interatomic vector, respectively. The averaged interatomic distances determined from the REDOR experiments are obtained as38

〈r〉REDOR ) 〈1/r〉-1/3 ) r0 + (1/2r0)(〈u〉2 + 〈V〉2 - 4〈w〉2) (5) where r0 is the distance in the absence of the thermal fluctuations and 〈u〉2, 〈V〉2, and 〈w〉2 indicate the mean averaged values of thermal displacements. It is noted that displacement of the atomic position along the interatomic vector decreases the distance determined from REDOR measurements. If the distance determined by X-ray diffraction without the thermal factor is r0, the corresponding distance obtained from a REDOR experiment is elongated by (1/2ro)(〈u〉2 + 〈V〉2 - 4〈w〉2). The maximum elongation of the interatomic distance of this crystal is 0.04-0.05 Å, evaluated by assuming a random motion characterized by the thermal factors determined by X-ray diffraction and ignoring the 〈w〉2 term. 3D Structure of the Peptide. Constraints of the three interatomic distances for the tripeptide thus obtained allowed us to determine the dihedral angles of the peptide plane of the individual residues systematically. Figure 7a shows the conformational map of the Pro residue as determined from the distance constraints from REDOR experiments. It is shown that many combinations of the dihedral angles of the two peptide

Figure 7. Conformation maps for the torsion angles in Pro (a) and Gly residues (b), respectively. The A and B regions were obtained from the intersections of the constraint of φ angles of the Pro residue. The C and D regions were then obtained by a cross section of the two types of conformation maps presented here.

planes exist as demonstrated by the ellipse, and the conformation cannot be uniquely determined from the information on the interatomic distances of I alone. It is possible, however, to narrow down the range of ΨPro from Figure 7 in view of the restricted areas of the ΦPro angle so far reported. We selected either the region A or B from the intersection of the ΦPro angle as -75°, in view of the data by a theoretical calculation (-75°),39 mean value of the observed data for a number of peptides (-69°), and X-ray diffraction study of the orthorhombic crystal (-76°). We selected only the region B (-75°, -28°) because the ΨPro value is close to the value determined by an empirical relationship between ∆βγ (-1.9 ppm) and the Ψ angle proposed by Siemion,40

∆βγ ) 0.036|θ| + 0.73, |θ| ) Ψ - 60°

(6)

where ∆βγ stands for the separation of 13C chemical shifts between Cβ and Cγ carbons41 as compiled from solution NMR data: -13° (-12° from the present X-ray diffraction) from ∆βγ of -1.9 ppm and in good agreement with that (-28°) of the B conformation as shown in Figure 7a. A large elliptic curve for the dihedral angles for the Gly residue was drawn from the interatomic distance of rCN ) 3.43 Å (II) (Figure 7b). An additional conformational map (III) as determined from the C-N internuclear distance constraint for seven bonds apart was drawn by a small ellipse, utilizing the already determined ΦPro and ΨPro and assuming ωGly as 180° and was superimposed on the conformatinal map for II.

15002 J. Phys. Chem., Vol. 100, No. 36, 1996

Naito et al.

TABLE 5: Dihedral Angles for N-Acetyl-Pro-Gly-Phe Converted from the Interatomic Distances by REDOR Experiments As Compared with Those by X-ray and MD in Crystals REDOR

energy-minimizedb X-ray

MD a

ΦPro

ΨPro

ΦGly

C

-75 ( 2

-28 ( 4

D

-75 ( 2

-28 ( 4

C, D monoclinicc β-turn II orthorhombicd β-turn I monoclinic orthorhombic

-46.8 -59

-22.4 128

-76

-12

-86

-47.1 ( 5.7 -52.4 ( 6.8

111.1 ( 7.3 -35.3 ( 8.4

90.4 ( 7.4 -90.8 ( 7.3

-112 ( 6 (-113 ( 6)a -68 ( 6 (-69 ( 6)a -108.6 81

ΨGly 48 ( 4 (37 ( 4)a -48 ( 4 (-37 ( 4)a 21.1 -6 -4.5 -11.7 ( 8.8 16.5 ( 9.0

ω angle was assumed to be -175°. b Based on REDOR data. c Reference 16. d This work.

Figure 8. Optimized conformation of N-acetyl-Pro-Gly-Phe as obtained by the minimization of energy from the initial form as deduced from the REDOR experiment (a) and a “snapshot” of the conformation deduced by MD simulation in Vacuo (at 100 K) (b).

Accordingly, the two conformations C and D were chosen from the crossing points of the two ellipses. The dihedral angles for the regions C and D are summarized in Table 5, together with the conformations determined by X-ray studies. The two conformations corresponding to the C and D regions were constructed as initial forms and then subject to the minimization of the conformational energy. Both conformations were found to yield the same energy-minimized form, as shown in Figure 8a. The interatomic distances and dihedral angles for the optimized structure thus obtained are summarized in Tables 2 and 5, respectively. It is emphasized that this sort of process is made possible only by the very accurate distance constraints as determined by the present REDOR experiments. Naturally, the backbone conformation for any given peptides can be determined by these systematic measurements of the interatomic distances. Fortunately, the distances of the C, N dipolar pairs were not seriously influenced by the presence of internal motions in the crystalline state. This is not always true for the side chains, however, because they undergo several kinds of internal motions as manifested from the relaxation parameters and 13C NMR spectral profile, and low-temperature REDOR experiments are required to avoid such effects. MD Simulation of the Single Peptide in Vacuo and Crystals.37,42 Starting from the optimized conformation as

Figure 9. A “snapshot” of the MD calculation in the crystalline (orthorhombic) state at 293 K as viewed from the c axis. Dotted lines denote the intra- and intermolecular hydrogen bonds.

described above, the MD simulation of the peptide in Vacuo was carried out at 100 K, to obtain the characteristics of the isolated peptide. During the MD simulation, the conformation of the peptide changed very much and turned into a completely different conformation. Three tight hydrogen bonds are formed in the peptide, as demonstrated in a “snapshot” (Figure 8b). The optimized conformation (Figure 8a) that reproduces the NMR-derived structure is consistent with the X-ray diffraction data. This conformation is one of the local minima of the peptide and is completely different from that observed during the MD simulation of the isolated molecule (Figure 9b). During the MD simulation in the crystals, the conformations of the molecules in the simulation box are not completely the same. On the average, however, those molecules show almost the same conformation for the peptide main chain. A “snapshot” of three peptide molecules in the orthorhombic crystal is shown in Figure 9. Note here that we dealt with an infinite system, and only a part of the system is shown in Figure 9. The average

3D Structure of a New Form of N-Acetyl-Pro-Gly-Phe values of the bond distances and dihedral angles of the peptide main chain for one of the molecules in the orthorhombic and monoclinic crystals as summarized in Tables 2 and 5, respectively, are very close to those obtained by X-ray and REDOR experiments. Our calculation for the in Vacuo case and in the crystals revealed clearly that the conformations of the peptide in the crystal were determined not only by the intramolecular interactions but also by the intermolecular interactions. Naturally, we are tempted to rely on MD calculations to deduce the 3D structure, especially when a limited number of interatomic distances are available. It seems to be very difficult, however, to arrive at this goal, as far as a single molecule is taken into account for the calculation. In fact, we found that the intermolecular hydrogen bonds with neighboring molecules played an essential role in determining the β-turn forms, as manifested from the present MD simulations. It is also emphasized that this simulation correctly reproduced the manner of internal motions such as ring puckering for the Pro and oscillatory motions of the Phe side chain, consistent with the present NMR and X-ray diffraction studies. The detailed results will be published elsewhere shortly.36 Therefore, it seems to be essential to acquire sufficient sets of the accurately determined interatomic distances for a given peptide. Then, it is recommended that the optimized 3D structure of the peptide should be obtained by the energy minimization based on a conformation constructed from these experimentally determined distances. Concluding Remarks We found that the precision and accuracy of our distance measurements from REDOR experiments based on the present novel approach are on the order of (0.05 Å, as estimated by the comparative study on REDOR and X-ray diffraction on a new crystalline form of N-acetyl-Pro-Gly-Phe as the orthorhombic crystal. The most serious source of error for the accuracy is the inhomogeneity of the B1 field, and this effect was minimized by the confinement of the sample to the central 50% of the total filling volume. The effect of the finite pulse length, however, was effectively negligible for the distance measurements, unless it is too long. We proposed here the following protocol to determine the 3D structure of peptides by the distance measurements alone. Step 1: synthesize the 13C and 15N doubly labeled peptides at the carbonyl and amide nitrogen atoms which are four bonds or seven bonds apart. Step 2: record the 13C and 15N NMR spectra in order to examine whether these chemical shifts are unchanged among the samples used in which different 13C or 15N atoms were labeled in order to confirm that they adopt the identical polymorph under consideration. Step 3: examine T1, T1F, and chemical exchange processes in order to confirm that no dipolar pair under consideration is involved in any kind of internal motions. Step 4: determine the internuclear distances by REDOR experiments. Step 5: convert the distance data to the dihedral angles in the peptide plane. Step 6: refine the 3D structure thus obtained by the energy-minimization procedure. We must be careful about the use of the molecular dynamics simulation unless it is performed for the crystal condition taking into account all the possible intermolecular interactions from the nearest neighbors. Acknowledgment. This work was supported in part by Grants in Aid for Priority Area (06276215, 07268218, and 07208230) and Scientific Research (04554017, 06454666) from the Ministry of Education, Science and Culture, Japan. The energy minimization and the MD simulations were carried out

J. Phys. Chem., Vol. 100, No. 36, 1996 15003 on the IBM/RS6000 Powerstations at the National Cancer Center Research Institute and on the SP2 at the Computer Center of the Institute for Molecular Science, Okazaki, Japan. Supporting Information Available: A listing of positional parameters, bond distances, and bond angles (6 pages). Ordering information is given on any current masthead page. References and Notes (1) Moore, G. J. Trend Pharm. Sci. 1994, 15, 124. (2) (a) Gullion, T.; Schaefer, J. AdV. Magn. Reson. 1990, 13, 57-83. (b) Bennett, A. E.; Griffin, R. G. ; Vega, S. Solid-State NMR IV; Springer: Berlin, 1994. (3) Raleigh, D. P.; Levitt, M. H.; Griffin, R. G. Chem. Phys. Lett. 1988, 146, 71. (4) Levitt, M. H.; Raleigh, D. P.; Creuzet, F.; Griffin, R. G. J. Chem. Phys. 1990, 92, 6349. (5) Bennet, A. E.; Ok, J. H.; Vega, S.; Griffin, R. G. J. Chem. Phys. 1992, 96, 8634. (6) Sodickson, D. K.; Levitt, M. H.; Vega, H. S.; Griffin, R. G. J. Chem. Phys. 1993, 98, 6742. (7) Tycko, R.; Dabbagh, G. Chem. Phys. Lett. 1990, 173, 461. (8) Tycko, R.; Smith, S. O. J. Chem. Phys. 1993, 98, 932. (9) Gullion, T.; Schaefer, J. J. Magn. Reson. 1989, 81, 196. (10) Hing, A. W.; Vega, S.; Schaefer, J. J. Magn. Reson. 1992, 96, 205. (11) (a) Marshall, G. R.; Beusen, D. D.; Kociolek, K.; Redlinski, A. S.; Leplawy, M. T.; Pan, Y.; Schaefer, J. J. Am. Chem. Soc. 1990, 112, 963. (b) Spencer, R. G. S.; Halverson, K. J.; Auger, M.; McDermott, A. E.; Griffin, R. G.; Lansbury, P. T., Jr. Biochemistry 1991, 30, 10382. (c) Peerson, O. B.; Yoshimura, S.; Hojo, H.; Aimoto, S.; Smith, S. O. J. Am. Chem. Soc. 1992, 114, 4332. (d) Holl, S. M.; Marshall, G. R.; Beusen, D. D.; Kociolek, K.; Redlinski, A. S.; Leplawy, M. T.; McKay, R. A.; Vega, S.; Schaefer, J. J. Am. Chem. Soc. 1992, 114, 4830. (e) Garbow, J. R.; McWherter, C. A. J. Am. Chem. Soc. 1993, 115, 238. (f) Garbow, J. R.; Breslav, M.; Autohi, O.; Naider, F. Biochemistry 1994, 33, 10094. (12) (a) McDermott, A. E.; Creuzet, F.; Gebhard, R.; van der Hoef, K.; Levitt, M. H.; Herzfeld, J.; Lugtenburg, J.; Griffin, R. G. Biochemistry 1994, 33, 6129. (b) Hing, A. W.; Schaefer, J. Biochemistry 1993, 32, 7593. (c) Smith, S. O.; Hamilton, J.; Salmon, A.; Bormann, B. J. Biochemistry 1994, 33, 6327. (d) Thompson, L. K.; McDermott, A. E.; Raap, J.; van der Wielen, C. M.; Lugtenburg, J.; Herfeld, J.; Griffin, R. G. Biochemistry 1992, 31, 7931. (13) (a) Hing, A. W.; Tjandra, N.; Cottam, P. F.; Schaefer, J.; Ho, C. Biochemistry 1994, 33, 8651. (b) Auger, M.; McDermott, A. E.; Robinson, V.; Castelhano, A. L.; Billedeau, R. J.; Pliura, D. H.; Krantz, A.; Griffin, R. G. Biochemistry 1993, 32, 3930. (c) Beusen, D. D.; McDowell, L. M. M., Slomczynska, V.; Schaefer, J. J. Med. Chem. 1995, 38, 2742. (14) (a) Naito, A.; Nishimura, K.; Tuzi, S.; Saitoˆ, H. Chem. Phys. Lett. 1994, 229, 506. (b) Alternatively, it is possible to check whether our present view is justified or not, if interatomic distance from the nearest neighbor 15N nuclei, r 13 15 2 C1N2, and the angle ζ between the two types of C- N pairs involving 15N2 are available.14 The present X-ray diffraction study shows that the rC1N2 values are 5.506 and 5.840 Å for II and III, respectively, and the ζ angles are 92.11° and 140.00° for II and III, respectively. The simulated 13C-15N distances by this treatment as a three-spin system were found to be 3.46 and 4.12 Å, respectively. These data are obviously within the claimed level of error as (0.05 Å evaluated by the present two-spin system. (15) Peersen, O. B.; Groesbeek, M.; Aimoto, S.; Smith, S. O. J. Am. Chem. Soc. 1995, 117, 7228. (16) Brahmachari, S. K.; Bhat, T. N.; Sudhakar, V.; Vijayan, M.; Rapaka, R. S.; Bhatnagar, R. S.; Aranthanarayanan, V. S. J. Am. Chem. Soc. 1981, 103, 1703. (17) Paquet, A. Can. J. Chem. 1982, 60, 976. (18) Torchia, D. A. J. Magn. Reson. 1978, 30, 613. (19) Mehring, M. High Resolution NMR Spectroscopy in Solids; Springer: New York, 1983. (20) Gullion, T.; Schaefer, J. J. Magn. Reson. 1991, 92, 439. (21) Marsh, R. F.; Donohue, J. AdV. Protein Chem. 1967, 22, 235. (22) Corongiu, G.; Aida, M.; Pas, M. F.; Clementi, E. Modern Techiniques in Computational Chemistry: MOTECC-91E; Clementi, Ed.; ESCOM Science Publishers: Leiden, 1991; Chapter 21. (23) Aida, M.; Corongiu, G.; Clementi, E. Int. J. Quantum Chem. 1992, 42, 1353. (24) Dennis, J. E.; Gay, D. M.; Welsch, R. E. ACM Trans. Math. Software 1981, 7, 369. (25) De Leeuw, S. W.; Perran, J. W.; Smith, E. R. Proc. R. Soc. (London) 1980, A373, 27. (26) (a) Saitoˆ, H. Magn. Reson. Chem. 1986, 24, 835. (b) Saitoˆ, H.; Ando, I. Ann. Rep. NMR Spectrosc. 1989, 21, 209. (27) Howarth, O. W.; Lilley, D. M. J. Prog. NMR Spectrosc. 1978, 12, 1.

15004 J. Phys. Chem., Vol. 100, No. 36, 1996 (28) We have recently shown that the conformational diversity of enkephalin crystals depending on solvent composition upon crystallization, humidity, and temperature is well monitored by displacements of the 13C chemical shifts: Naito, A.; Kamihira, M.; Tuzi, S.; Saitoˆ, H. J. Phys. Chem. 1995, 99, 12041. (29) Rothwell, W. P.; Waugh, J. S. J. Chem. Phys. 1981 74, 2721. (30) In many instances, the Cβ signal resonates at lower field than the Cγ signal.27,31,32 This is not the case, however, when the two peaks crossed over at certain Ψ angles. (31) This does not necessarily mean that the accurate REDOR parameters are available with a longer π pulse such as 50 µs even if the condition of 10% of the rotor cycle is satisfied. This is because utilization of a longer π pulse may cause an additional error caused by insufficient excitation range for the entire spin system. (32) Accumulation number has to be increased to give a spectrum with reasonable S/N ratios, as the NcTr values are increased. It should be taken into account that the amplitude of the rotational echo decreases appreciably when a molecule in question has a shorter T2 value. It is, therefore, essential to apply a strong spin-decoupling field to elongate the T2 value, because this parameter is very sensitive to the amplitude of the spin-locking rf field and the correlation times of the molecular motion.29 The measured T2 value for the carbonyl carbon was 27.4 ms under the present spectrometer condition. (33) Lansbury, P. T., Jr.; Costa, P. R.; Griffiths, J. M.; Simon, E. J.; Auger, M.; Halverson, K. J.; Kocisko, D. A.; Hendsch, Z. S.; Ashburn, T. T.; Spencer, R. G. S.; Tidor, B.; Griffin, R. G. Nature Struct. Biol. 1995, 2, 990-998. (34) (a) Naito, A.; Ganapathy, S.; Akasaka, K.; McDowell, C. A. J. Magn. Reson. 1983, 54, 226. (b) Saitoˆ, H.; Tabeta, R.; Yokoi, M. Magn. Reson. Chem. 1988, 26, 776. (c) Saitoˆ, H.; Yokoi, M. Macromolecules 1990, 23, 83. (d) Saitoˆ, H.; Yokoi, M. J. Biochem. (Tokyo) 1992, 111, 376. (35) Gil, A.; Masui, K.; Naito, A.; Tatham, T.; Belton, P. S.; Saitoˆ, H. Biopolymers, in press. (36) Aida, M.; Naito, A.; Saitoˆ, H. J. Mol. Struct. (THEOCHEM), in press. (37) It is pointed out that the manner of this particular puckering motion of the Pro residue was well reproduced by our recent MD simulation of

Naito et al. this molecule in the crystalline state,36 although the rate constant for such motion was obtained on the order of picoseconds. It is rather surprising, however, that the presence of such motion did not result in significant deviations of the C‚‚‚N distances under consideration (10.1 Å) as listed in Table 2, despite the resulting fluctuation of ΦPro angles (10°) caused by the ring-puckering motion.36 (38) The square of the interatomic distance with small displacements can be given by r2 ) r02(1 + 2w/r0 + [w2 + u2 + V2]/r02). The 1/r3 value is observable by solid state NMR, which is described as 1/r3 ) r0-3[1 + 2w/r0 + (w2 + u2 + V2)/ro2]-3/2. Because 2w/r0 + (w2 + u2 + V2)/r02 is much smaller than unity, the mean value of 1/r3 can be given by 〈1/r3〉 ) r0-3[1 + 3(2〈w〉2 - 〈u〉2/2 - 〈V〉2/2)/r02]. The values 〈w〉2, 〈u〉2, and 〈V〉2 are mean square values of small displacement and are correlated to thermal factors. Thus, the mean interatomic distance obtained from REDOR experiments can be approximated as 〈r〉NMR ) r0 + (1/2r0)(〈u〉2 + 〈V〉2 4〈w〉2). (39) Vasquez, M.; Nemethy, G.; Scheraga, H. A. Macromolecules 1983, 16, 1043. (40) Siemion, von I. Z.; Wieland, T.; Pook, K.-H. Angew. Chem. 1975, 87, 712. (41) The broadened shoulder peak was unequivocally assigned to the Cγ carbon in view of the present X-ray diffraction and MD simulation data. (42) It is well-known that the results of energy minimization and MD simulations depend on the quality of the force field. For the current energy minimization and MD simulation, we used here a set of ab initio potentials that were derived from ab initio molecular orbital calculations, with the aim of performing global simulations of biological systems.24 It has been demonstrated that the set of ab initio potentials represents well the distance and angle dependencies of the hydrogen-bonding interactions.43 Therefore, the force field used here is suitable for determination of the conformations of the peptide, which is very flexible. (43) Aida, M. Bull. Chem. Soc. Jpn. 1993, 66, 3423.

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