J. Phys. Chem. 1996, 100, 11589-11595
11589
Ab Initio Molecular Orbital Calculations on Low-Energy Conformers of N-Acetyl-N′-methylprolineamide Young Kee Kang† Department of Chemistry, Chungbuk National UniVersity, Cheongju, Chungbuk 361-763, Korea ReceiVed: February 6, 1996; In Final Form: April 28, 1996X
The results of ab initio HF/SCF calculations on nine low-energy conformers of N-acetyl-N′-methylprolineamide (Ac-Pro-NHMe) with trans/cis imide bonds and down/up puckerings using the STO-3G, 3-21G, and 6-31G** basis sets are reported. Single-point MP2/6-31G** calculations were performed on the HF/6-31G** optimized conformations. In ab initio calculations at all levels, the intramolecularly hydrogen-bonded C7 conformer is found to be most preferred, which is consistent with the structures deduced from IR, CD, and NMR experiments in nonpolar solvents. From HF/3-21G to HF/6-31G**, the trend for the lowering of energies of Ac-ProNHMe appears to be quite similar to that found for alanine dipeptides, while the variations in backbone torsion angles φ and ψ (av ∆φ ≈ 2° and ∆ψ ≈ 9°) are different, which may be attributed to rigid constraints on the N-CR rotation imposed by pyrrolidine ring closure. The MP2 corrections increase the HF/6-31G** energies by about 1 kcal/mol, except for the conformer tCu. The down puckering seems to be about 1.5 kcal/mol more stable than the up puckering at the HF/6-31G** and MP2/6-31G** levels. The HF/6-31G** optimized bond lengths and bond angles as well as endocyclic torsion angles χ’s of the pyrrolidine ring are, in general, consistent with the corresponding values of X-ray structures of peptides, but the strong dependence of structural parameters on the conformation cannot be seen. The preference and population for down and up puckered structures with the trans and cis imide bonds calculated at the HF/6-31G** and MP2/6-31G** levels agree reasonably with the results obtained from the analysis of X-ray structures of proteins. The degree of puckering for each conformer is described by three puckering amplitudes, and the linear correlations between any two of them are discussed.
Introduction It has been well-known that proline (Pro) plays important roles in the structure and folding of proteins.1,2 The Pro residue is unique in that its side chain is covalently bonded to the nitrogen atom of the peptide backbone. This leads the backbone not to form a hydrogen bond and the N-CR rotation to be rigid.2 The pyrrolidine of the Pro residue is a five-membered ring, and its puckering has occasionally been described using the concept of pseudorotation.3-7 The ring may adopt two distinct puckered conformations that are almost equally favorable.3,4 They are distinguished by the displacement of the Cβ and Cγ atoms from the mean plane of the ring and are referred to as “up” and “down”8 or “exo” and “endo”,9 respectively. The Pro residue has a relatively high intrinsic probability of having the cis peptide bond preceding proline compared with other amino acids,10-12 since the configurations of atoms of the Pro residue adjacent to the R-carbon of the preceding residue are quite similar in either trans or cis conformation. Cis peptide bonds are found mainly in β-bends, and a specific structural role for cis imide bonds has been suggested.10,11 Recently, the cis-trans isomerization of the incorrect imide bond preceding proline has been suggested to be involved in the rate-determining slow steps for refolding and folding of proteins.13,14 In addition, the structural and dynamical roles of Pro residues in transmembrane segments of integral membrane proteins have been examined.15,16 Although many experimental and theoretical studies have been made on either the puckering of prolyl rings3-6,17-22 or the cis-trans isomerization of imide bonds10-14,23-28 of proline† Corresponding e-mail:
[email protected]. FAX: +82431-273-8328. X Abstract published in AdVance ACS Abstracts, June 1, 1996.
S0022-3654(96)00381-4 CCC: $12.00
containing peptides, only a few studies were established for the ring puckering of cis and trans proline residues by the analysis of X-ray crystal structures of peptides and proteins29 and by conformational energy calculations on proline-containing peptides.30,31 The development of the direct SCF32 and direct MP233 methodologies has recently made it possible to investigate the structural and energetic properties of the model dipeptides of alanine34-38 and glycine.35,36,38 However, only a few ab initio studies of N-acetylprolineamide (Ac-Pro-NH2)39,40 and N-acetylN′-methylprolineamide (Ac-Pro-NHMe)28 have been carried out. Peters and Peters39 found that at the STO-3G level the conformational energy of trans-Ac-Pro-NH2 is not largely affected by the puckering of the pyrrolidine ring. Sapse et al.40 reported that the prolyl ring in the C7 conformation is calculated to be almost planar at both the HF/STO-3G and HF/6-31G levels. They suggested the addition of polarization functions to basis sets to describe the ring puckering adequately. Recently, Fischer et al.28 determined the reaction path for the cis-trans isomerization of Ac-Pro-NHMe in terms of a virtual torsion angle to represent imide nitrogen pyramidalization and isomerization at the HF/6-31G**//HF/3-21G level. They reported the HF/3-21G optimized geometries of cis- and trans-Ac-Pro-NHMe with a down puckering. Head-Gordon et al.35 found that at the HF/3-21G level the structures and the energy ordering of the conformers of alanine and glycine dipeptide analogues are in reasonable agreement with the results of the larger basis sets. However, they have shown that relative energies between conformers are quite different at high levels from those determined at low levels. In the present work the results of optimized low-energy conformations of trans- and cis-Ac-Pro-NHMe with down and up puckering at the HF level with STO-3G, 3-21G, and 6-31G** © 1996 American Chemical Society
11590 J. Phys. Chem., Vol. 100, No. 28, 1996
Kang
TABLE 1: Relative Conformational Energies of N-Acetyl-N′-methylprolineamide by Various Methodsa conformer letter codeb tCd tAd tAu cAd tFd tFu cAu cFd cFu
ECEPP/3c
HF/STO-3Gd
HF/3-21Ge
HF/6-31G** f
MP2/6-31G** g
0.00 0.16 0.47 0.95 0.98 1.64 1.96 2.30 3.73
0.00 2.19 2.46 2.53 2.79 0.51j 2.32 4.10 5.26
0.00 6.21h 8.65 5.04i
0.00
0.00
4.42 3.01i
5.72 3.61i
2.51j 6.80 7.78 9.27
1.89j 4.19 5.68 6.55
1.71j 4.92 6.75 7.41
a All minimum-energy conformations are listed. All energies are in kcal/mol. b t and c denote the trans and cis Ac-Pro imide bonds, respectively. d and u correspond to the down and up puckerings, respectively. The conformational letter code of Zimmerman et al.45 was used to represent the backbone conformation. c Taken from ref 31. d Zero of energies -562.594 731 8 au. e -566.597 769 4 au. f -569.787 211 2 au. g MP2/6-31G**/ /HF/6-31G**, -571.580 663 6 au. h Optimized codes tBd. i cBd. j tCu.
basis sets are presented. In addition, the relative stability of the conformers obtained by the single-point MP2/6-31G** calculations at the HF/6-31G** optimized structures is reported. The results obtained here at the higher level of basis sets, used to date, may provide more extensive information for structures and energetics of the proline residue. Methods All ab initio calculations were carried out using the Gaussian 9041 and Gaussian 9242 molecular orbital packages run on the HP/A 9000/735 workstation and the Cray YMP C90 supercomputer of the System Engineering Research Institute (SERI), Korea. Full geometry optimization was performed at the direct HF/SCF level32 with the STO-3G, 3-21G,43 and 6-31G**44 basis sets. The latter two basis sets have been successfully used for conformational analysis of alanine and glycine dipeptides.35-38 The nine low-energy conformers of Ac-Pro-NHMe obtained by the ECEPP/3 force field31 were used as initial structures for full geometry optimization with the STO-3G basis set. These nine conformers consist of three trans-down, two trans-up, two cis-down, and two cis-up puckered conformations. There are two reasons to choose minimum-energy conformations from the ECEPP/3 calculations as starting conformations. First, they include all possible combinations of the conformations, i.e., the trans and cis imide bonds and the down and up puckerings. Second, the ECEPP/3 force field predicted reasonably the structures and energetics of proline-containing peptides.31 Each conformation is denoted in terms of the conformational letter code for the backbone torsion angles φ and ψ, defined by Zimmerman et al.45 Thus, in nine starting conformers transdown puckered conformers can be denoted as C (C7eq), A (RR), and F (PII) and the other conformers as A and F. Hence, a code tCd corresponds to the trans-down puckered C conformation, etc. The optimized structures at the HF/STO-3G and HF/3-21G levels were used as starting points for the HF/3-21G and HF/ 6-31G** optimizations, respectively. Full geometry optimizations of all degrees of freedom were then carried out. Singlepoint MP2 calculations were performed on the HF/6-31G** optimized conformations with the same basis set. In Figure 1 the geometry of Ac-Pro-NHMe is defined according to the recommendations of the IUPAC-IUB Commission on Biochemical Nomenclature.46 The pyrrolidine ring puckering can be described in terms of the puckering amplitude and the phase angle.47 For each puckered conformation, the puckering amplitudes χm of Altona and Sundaralingam,48 qz of Cremer and Pople,49 and qR of Han and Kang7,50 were calculated.
Figure 1. Geometrical definition of Ac-Pro-NHMe. The torsion angles are defined as follows: ω′ ) ∠CC′NCR, φ ) ∠C′NCRC′, ψ ) ∠NCRC′N, χ0 ) ∠CδNCRCβ, χ1 ) ∠NCRCβCγ, χ2 ) ∠CRCβCγCδ, χ3 ) ∠CβCγCδN, and χ4) ∠CγCδNCR.
Results Conformational Energies. In Table 1 the relative conformational energies of Ac-Pro-NHMe from the ab initio calculations at the HF/STO-3G, HF/3-21G, HF/6-31G**, and MP2/ 6-31G**//HF/6-31G** levels and the ECEPP/3 calculations31 are listed. The corresponding values of backbone torsion angles ω′, φ, and ψ are shown in Table 2. In all ab initio calculations, the conformer tCd is the most preferred followed by the conformer tCu, of which each has an intramolecular C7 hydrogen bond between the carbonyl oxygen of the acetyl group and the amide hydrogen of the carboxylic group. The computed distances r(C′dO‚‚‚H-N) are 2.09 and 2.11 Å at the HF/631G** level for the conformers tCd and tCu, respectively. The ordering of conformational energies calculated at the HF/ STO-3G level remains the same as that obtained by the ECEPP/3 calculations, except for the conformers tFu and cAu. In particular, the conformer tFu is no longer a local minimum and converges to the second lowest-energy conformer tCu after optimization. Its conformational energy is only 0.51 kcal/mol higher than that of the global minimum tCd. At the HF/3-21G level a local minimum tFd disappears, and the two local minima tAd and cAd at the HF/STO-3G level shift to the conformers tBd and cBd, respectively. There is a remarkable shift of the torsion angle ψ to ψ ≈ 0° by about 40° from the HF/STO-3G optimized values for these two conformers (see Table 2). The energies of local minima relative to the conformer tCd become higher than those obtained from the HF/ STO-3G and ECEPP/3 calculations. This may be ascribed to the potential well at the global minimum tCd becoming deeper at the HF/3-21G level. The order of conformational energies of local minima is quite different from the orders obtained by the HF/STO-3G and ECEPP/3 methods. The energy of the second global conformer tCu is 2.51 kcal/mol less stable than that of the global minimum tCd.
N-Acetyl-N′-methylprolineamide
J. Phys. Chem., Vol. 100, No. 28, 1996 11591
TABLE 2: Conformations of N-Acetyl-N′-methylprolineamidea conformer letter codeb tCd tAd tAu cAd tFd tFu cAu cFd cFu
ω′
ECEPP/3c φ
ψ
176.8 -179.3 178.6 -3.9 179.7 177.0 -7.7 -2.9 -7.4
-68.8 -68.8 -53.0 -68.8 -68.8 -53.0 -53.0 -68.8 -53.0
79.9 -23.9 -37.9 -26.1 159.2 150.2 -41.5 159.4 145.9
ω′
HF/STO-3Gd φ
ψ
-165.0 -168.6 -170.0 34.5 171.4 -170.7 33.4 -33.9 27.8
-84.0 -91.8 -72.9 -95.3 -57.0 -77.0 -87.2 -53.8 -83.0
81.8 -38.0 -44.5 -41.4 163.5 86.5 -45.4 179.2 163.3
ω′
HF/3-21Ge φ
ψ
ω′
HF/6-31G** f φ
-173.3 -171.9 -175.4 10.9
-85.3 -97.2 -67.1 -90.9
70.0 8.0 -28.8 -1.5
-172.9
-86.3
75.3
-171.3 10.9
-71.6 -91.0
-20.8 -4.4
-175.1 9.2 -2.9 -3.1
-83.2 -75.0 -70.3 -64.7
72.8 -22.5 174.1 176.6
-174.9 7.5 -3.4 -4.4
-82.7 -76.5 -71.8 -57.9
84.1 -20.4 160.2 156.4
ψ
a Torsion angles ω′, φ, and ψ are defined in Figure 1. b See footnote b of Table 1. c Fixed values of torsion angle φ ) -68.8° and -53.0° for the down and up puckerings, respectively; see ref 31. d-f See footnotes h-j of Table 1.
Figure 2. HF/6-31G** optimized conformations tCd, tCu, cBd, and cAu from left to right.
At the HF/6-31G** level the energy ordering of local minima is almost the same as that obtained at the HF/3-21G level. However, a local minimum tBd at the HF/3-21G level disappears and the conformer tAu is more preferred than the conformer cFd. The resulting order of conformational stabilities is tCd > tCu > cBd > cAu ≈ tAu > cFd > cFu. In general, the energies of local minima relative to the global conformer tCd are lower by about 2 kcal/mol at the HF/6-31G** level than the HF/321G level. In particular, the energy of the second global minimum tCu is 1.89 kcal/mol higher than that of the global conformer tCd, which is 0.6 kcal/mol lower than the value obtained at the HF/3-21G level. This suggests that the HF/631G** potential surfaces may be flatter than the HF/3-21G surfaces. The trend for the ordering and lowering of conformational energies of Ac-Pro-NHMe at the HF/6-31G** and HF/ 3-21G levels is quite similar to that found for alanine dipeptides at both levels.35,37 However, the variations in torsion angles φ and ψ (av ∆φ ≈ 2° and ∆ψ ≈ 9°) of Ac-Pro-NHMe on going from HF/3-21G to HF/6-31G** are different from those of alanine dipeptides (av ∆φ ≈ 10° and ∆ψ ≈ 10°).35 The smaller variation in φ appears to be due to rigid constraints on the N-CR rotation imposed by pyrrolidine ring closure. The four lowenergy conformations tCd, tCu, cBd, and cAu optimized at the HF/6-31G** level are shown in Figure 2. In Table 1 the MP2/6-31G** single-point energies obtained at the HF/6-31G** geometries are compared with the HF/321G and HF/6-31G** energies. It can be seen that the energies computed at the HF/6-31G** level are more consistent with the MP2 single-point energies than the HF/3-21G energies. The MP2 corrections increase the HF/6-31G** energies by 0.61.3 kcal/mol, except for the second global conformer tCu being lowered by 0.2 kcal/mol. These are in accord with the previous MP2 results on alanine dipeptides.35,37 Because the backbone structures of each pair of the conformers (tCd, tCu) and (cBd, cAu) appear to be similar to each other, the energy difference of each pair of conformers may correspond to that of the down and up puckerings. These values are calculated to be 1.9 and 1.2 kcal/mol at the HF/6-31G** level and 1.7 and 1.3 kcal/mol at the MP2/6-31G** level for the trans and cis imide bonds, respectively. Thus, the down puckering seems to be about 1.5 kcal/mol more stable than the up puckering.
Structural Parameters. In Table 3 we list the structural parameters of the HF/6-31G** optimized conformers of AcPro-NHMe and the corresponding values of the ECEPP/3 force field31 used as the initial geometry for optimization. The ECEPP/3 values were derived from 12 crystal structures of proline-containing noncyclic peptides with a crystallographic R factor below 0.05. In general, the dependence of bond lengths on the conformation at the HF/6-31G** level appears to be very weak. However, the largest change of a bond length is found for r(NCR), which varies from 1.444 Å (cFd) to 1.470 Å (tCu). For the down and up puckered conformations, the bond length r(CβCγ) remains almost constant, while the bond length r(Cγ-Cδ) of the down puckered is a little longer than that of the up puckered (i.e., av ∆r(Cγ-Cδ) ≈ 0.004 Å). It can be seen that the HF/6-31G** optimized bond lengths are in very close agreement with the ECEPP/3 results, i.e., the averaged values of crystal structures. However, the average bond lengths r(CβCγ) and r(Cγ-Cδ) are longer by about 0.03 Å than the ECEPP/3 values, while the average bond length r(C′dO) is shorter by about 0.03 Å. On the other hand, although the weak dependence of bond angles on the conformation is likely to exist as found for bond lengths, there are somewhat larger variations in bond angles around the CR atom. The largest change of a bond angle occurs in ∠NCRC′, varying from 110.6° (tCu) to 116.6° (tAu). For ∠CRC′O and ∠CRC′N, the variations are about 4°. For the down and up puckered structures, the variations in bond angles seem to be quite small, which may be attributed to the closure of the pyrrolidine ring. As seen in bond lengths, there is good agreement between the HF/6-31G** optimized bond angles and the ECEPP/3 values, except for ∠CβCRH and ∠C′CRH. Puckering of Proline Ring. In Table 4 we list average torsion angles and puckering parameters of the pyrrolidine ring of Ac-Pro-NHMe with the trans and cis imide bonds and the down and up puckerings obtained by the HF/3-21G, HF/631G**, and ECEPP/3 methods. Those values for the HF/631G** optimized conformations are shown in Table 5 separately. At both the HF/3-21G and HF/6-31G** levels, the trend for calculated endocyclic torsion angles appears to be similar to each other. However, it is observed, in general, that the values at the HF/6-31G** level are somewhat less than those obtained at the HF/3-21G level. The largest magnitudes of the torsion angles χ2 and χ3 are found for the trans-down, cis-down, and cis-up conformations, and for the trans-up conformation, respectively. The calculated results at both levels reveal that the down puckered structures have larger changes in torsion angles χ’s than the up puckered structures. The dependence of the trans and cis imide bonds on the puckering is likely to be very weak. The differences in torsion angles χ’s of the HF/6-
11592 J. Phys. Chem., Vol. 100, No. 28, 1996
Kang
TABLE 3: Ab Initio Structural Parameters (HF/6-31G**) of N-Acetyl-N′-methylprolineamidea parameterb
tCd
tAu
cBd
C′-Nd N-CR CR-Cβ Cβ-Cγ down Cβ-Cγ up Cγ-Cδ down Cγ-Cδ up Cδ-N CR-C′ C′dOe C′-Ne CR-H Cβ-H Cγ-H Cδ-H N-H
1.350 1.469 1.528 1.529
1.362 1.464 1.539
1.364 1.458 1.538 1.530
1.465 1.537 1.205 1.342 1.082 1.083 1.083 1.086 0.996
1.527 1.464 1.523 1.201 1.348 1.082 1.084 1.085 1.084 0.991
CR-C′-Nd CR-C′-Od O-C′-Nd C′-N-CR d trans C′-N-CR d cis C′-N-Cδ d trans C′-N-Cδ d cis CR-N-Cδ N-CR-Cβ N-CR-C′ Cβ-CR-C′ down Cβ-CR-C′ up N-CR-H down N-CR-H up Cβ-CR-H C′-CR-H down C′-CR-H up CR-Cβ-Cγ down CR-Cβ-Cγ up CR-Cβ-H Cγ-Cβ-H H-Cβ-H Cβ-Cγ-Cδ down Cβ-Cγ-Cδ up Cβ-Cγ-H down Cβ-Cγ-H up Cδ-Cγ-H down Cδ-Cγ-H up H-Cγ-H N-Cδ-Cγ down N-Cδ-Cγ up N-Cδ-H down N-Cδ-H up Cγ-Cδ-H down Cγ-Cδ-H up H-Cδ-H CR-C′-Ne CR-C′-O O-C′-Ne C′-N-CR e
117.2 120.9 121.9 121.0
117.8 121.3 121.0 118.9
125.4
125.7
112.3 103.0 111.1 112.2
112.2 103.7 116.6
tCu bond length, Å 1.350 1.470 1.539
1.527 1.530
1.532 1.525 1.460 1.539 1.204 1.343 1.082 1.082 1.085 1.083 0.996
1.467 1.532 1.203 1.343 1.082 1.083 1.085 1.084 0.992 177.7 121.4 120.9
1.358 1.444 1.542 1.530
1.360 1.448 1.548
1.528
109.9 111.2
1.462 1.533 1.199 1.351 1.085 1.085 1.084 1.083 0.992
1.523 1.459 1.529 1.199 1.350 1.088 1.084 1.085 1.083 0.993
117.6 121.2 121.2
117.6 121.3 121.0
118.2 120.8 121.1
125.4
126.8
127.2
110.9 104.4 110.6
119.5 112.3 103.7 116.1
119.5 113.3 102.5 113.0 110.4
119.8 112.9 103.6 114.0
112.1
109.4
127.0 118.8 112.6 103.1 115.3 110.6
110.7 105.3
110.4 112.3 108.3 103.3
102.9 111.3
108.4 112.3
111.6 110.0
109.0
106.0
111.8
105.1 110.1 111.6 108.2
103.9 110.6 112.1 107.6
103.0
102.9
111.8 107.7 103.6
103.3 110.9 111.2
111.0 108.1
111.3 108.0
102.6
103.1
104.0 110.6 111.7 108.0 102.8 111.5
108.2 103.7
111.5 108.1 102.7
110.1 110.9
107.4 117.5 119.2 123.4 121.5
110.8 112.0 108.1 103.5
111.3
110.2
112.7 111.7 107.9 117.5 118.8 123.5 120.6
109.3
111.6
110.3
111.6
110.6 110.1
111.3
111.3 111.1 108.1
110.8 108.8 103.0
111.6
111.1
109.1 111.3
103.1 103.7 110.7 112.0 107.8
1.528
1.525 1.466 1.525 1.202 1.345 1.083 1.084 1.085 1.083 0.992
bond angle, deg 117.9 120.4 121.7 120.7
105.5
108.1 114.9 121.8 123.3 121.2
1.367 1.460 1.545
112.0
103.3
108.5 103.6
cFu
1.529
110.1 109.0
110.6 111.6 109.0 103.5
cFd
1.528
126.2
112.8 108.7
cAu
110.3 112.5
112.0 108.4 114.8 121.9 123.3 120.9
112.7 107.8 116.9 119.5 123.6 121.8
107.8 114.6 122.5 122.9 121.8
112.7 108.1 114.0 122.2 123.7 123.1
ECEPP/3c 1.340 1.465 1.530 1.502 1.524 1.501 1.520 1.475 1.520 1.230 1.325 1.090 1.090 1.090 1.090 1.000 118.0 120.5 121.5 121.0 127.3 127.3 121.0 111.7 103.7 112.3 111.8 111.6 110.2 110.1 114.0 105.1 105.2 103.7 103.4 111.6 111.6 107.0 105.3 102.9 111.2 111.8 111.2 111.8 107.0 103.4 102.8 111.6 111.8 111.6 111.8 107.0 115.0 120.5 124.5 121.0
a The order of conformations is the same as in Table 1. b Refer to Figure 1 for atom labeling. Same for the down and up puckerings, except where indicated separately. c Taken from ref 31. d X-Pro. e Pro-X.
31G** and ECEPP/3 methods vary from 0.9° (χ3) to 5.7° (χ0) for the down puckering and from 0.3° (χ3) to 6.2° (χ1) for the up puckering. The results obtained from the HF/6-31G** optimized structures (Table 5) indicate that the dependence of backbone torsion angles φ and ψ on endocyclic torsion angles is notable for the trans-up and cis-down conformers, of which variations are estimated to be 1.9° (χ3) to 8.5° (χ0) and 0.5° (χ2) to 2.6° (χ4), respectively. The puckering of the pyrrolidine ring of the Pro residue has occasionally been described using the concept of pseudo-
rotation.3-7 We need an appropriate geometrical parameter to describe the pseudorotation along the phase angle.47 This parameter is usually called a puckering amplitude, since it measures the degree of puckering. In this work we compare three puckering amplitudes to examine the degree of puckering for each conformer and the preference of puckering for the trans and cis preceding imide bonds. Altona and Sundaralingam48 suggested the puckering amplitude χm as the maximum value attainable by endocyclic torsion angles χ’s along the phase angle. Cremer and Pople49 defined the puckering amplitude qz as the distance perpendicular to the
N-Acetyl-N′-methylprolineamide
J. Phys. Chem., Vol. 100, No. 28, 1996 11593
TABLE 4: Average Torsion Angles and Puckering Parameters of Pyrrolidine Ring of N-Acetyl-N′-methylprolineamidea HF/3-21G down parameter
b
χ0 χ1 χ2 χ3 χ4 χm, deg qz, Å qR, deg Φ, deg
ECEPP/3c
HF/6-31G** up
down
up
trans
cis
trans
cis
trans
cis
trans
cis
-17.5 35.0 -40.1 29.4 -7.6 40.3 0.398 11.4 83.4
-15.1 33.8 -40.3 31.0 -10.1 40.2 0.400 11.4 87.0
-3.3 -19.2 33.7 -35.1 24.4 38.4 0.374 10.7 292.1
0.9 -23.8 37.3 -36.1 22.5 38.9 0.384 10.9 285.9
-14.8 32.2 -38.0 28.7 -8.8 37.9 0.371 10.6 85.6
-15.7 32.6 -37.7 28.1 -7.8 37.9 0.372 10.6 84.4
-2.3 -20.3 34.5 -35.3 23.8 37.9 0.367 10.6 290.2
1.3 -23.5 36.4 -35.1 21.5 37.8 0.369 10.6 285.1
down
up
-9.6 27.4 -35.6 29.3 -12.1 35.3 0.338 9.8 92.1
6.3 -28.1 39.3 -34.9 18.1 39.6 0.386 11.1 278.5
a Angles are in degrees. b Torsion angles are defined as χ0 (Cβ-CR-N-Cδ), χ1 (N-CR-Cβ-Cγ), χ2 (CR-Cβ-Cγ-Cδ), χ3 (Cβ-Cγ-Cδ-N), and χ4 (Cγ-Cδ-N-CR). The puckering amplitudes χm, qz, and qR are computed by using the expressions in refs 48-50, respectively. Φ represents the phase angle. The phase angle P defined in ref 48 corresponds to Φ + 90°. c ECEPP/3 assumes the same puckering for the trans and cis conformers; see ref 31.
TABLE 5: Torsion Angles and Puckering Parameters of Pyrrolidine Ring of N-Acetyl-N′-methylprolineamide from HF/ 6-31G** Calculationsa parameterb χ0 χ1 χ2 χ3 χ4 χm, deg qz, Å qR, deg Φ, deg a
tCd
tAu
cBd
tCu
cAu
cFd
cFu
-14.8 32.2 -38.0 28.7 -8.8 37.9 0.371 10.6 85.6
6.2 -27.1 37.6 -33.4 17.2 37.9 0.371 10.6 278.1
-13.4 31.6 -38.2 29.8 -10.3 38.1 0.374 10.7 87.9
-10.7 -13.5 31.4 -37.2 30.4 37.9 0.362 10.5 302.3
2.6 -24.5 36.7 -34.7 20.3 37.8 0.369 10.6 283.1
-17.9 33.5 -37.2 26.3 -5.2 37.7 0.370 10.6 80.9
-0.1 -22.5 36.0 -35.4 22.6 37.7 0.368 10.6 287.0
The order of conformations is the same as in Table 1. b See footnote b of Table 4 for definition.
mean plane of the ring, which is an extension of the zdisplacement model of Kilpatrick et al.47 Recently, Han and Kang7,50 proposed a puckering amplitude qR defined by the angle Rj between the mean plane and the line joining the geometrical center and an atom j of the ring. The puckering amplitude qR of cyclopentane is found to be linearly proportional to the amplitudes χm and qz. At the HF/3-21G level, the amplitude χm is estimated to be about 40° and its least value is 38.4° for the trans-up conformers. The amplitude qz varies from 0.374 Å for the trans-up conformers to 0.400 Å for the cis-down conformers. The amplitude qR is estimated to be 11.4° and 10.8° for the down and up puckered conformers, respectively. At the HF/6-31G** level, the amplitude qz has the range of values between 0.367 Å for the trans-up conformers and 0.372 Å for the cis-down conformers. On the other hand, the amplitudes χm and qR are found to have constant values of 37.9° and 10.6°, respectively. Hence, three amplitudes appear to be constant at the HF/6-31G** level. The phase angles obtained at both the levels are similar to each other, i.e., Φ ≈ 85° and 288° for the down and up puckered conformers, and the linear correlations between any two of three amplitudes exist to a certain extent at each level, which can be found for cyclopentane.7,50 Furthermore, any significant preference for the degree of puckering cannot be seen at the HF/631G** level, while the up structure is more puckered than the down structure in the ECEPP/3.31 The phase angles are 92° and 279° for the down and up conformers in the ECEPP/3. From the HF/STO-3G and HF/6-31G calculations on AcPro-NH2, Sapse et al.40 reported that the prolyl ring in the C7 conformation is almost planar. They suggested the addition of polarization functions to the basis sets to describe the ring puckering adequately. Differing from these previous results,
each conformation is found to be sufficiently puckered and comparable to X-ray structures even in the case of the HF/STO3G results. Discussion Preferred Conformations Compared with Experimental Results. The most preferred conformation predicted by all ab initio computations at the HF/STO-3G, HF/3-21G, HF/6-31G**, and MP2/6-31G**//HF/6-31G** levels and by the ECEPP/3 force field is Ac-trans-Pro(down)-NHMe (i.e., tCd). This intramolecularly hydrogen-bonded C7 conformation has been confirmed to be dominant in nonpolar solvents by IR,51 CD,52 and NMR52 experiments. However, X-ray crystallographic studies on Ac-Pro-NHMe53 and Ac-Pro-NH254 indicated that the most preferred conformation is tAd, which has no intramolecular hydrogen bonds. The packing and intermolecular hydrogen bonds in the crystal appear to be dominant in stabilizing this conformer,53,54 which are not available for the molecule in nonpolar solvents. In addition, the φ-ψ analysis of X-ray structures of proteins revealed that the preferred conformations for the Pro residue are A and F.12,55 Because the conformation adopted by the Pro residue appears to be affected by the preceding and following residues,11,12,25,26,29 the C7 intramolecular hydrogen bond is not allowed for the Pro residues of proteins. Both the CD and 13C chemical shift observations indicated the dominant distribution of the trans form of Ac-Pro-NHMe over the cis form,52 which is in accord with our results obtained at the HF/6-31G** and MP2/6-31**//HF/6-31** levels. In the ECEPP/3 calculations on Ac-Pro-NHMe,31 the energies of the conformers cAd and cAu relative to the conformer tCd were estimated to be 0.95 and 1.96 kcal/mol, while the corresponding values are 3.01 and 4.19 kcal/mol from HF/6-31G** calculations and 3.61 and 4.92 kcal/mol from MP2/6-31**//HF/6-31**
11594 J. Phys. Chem., Vol. 100, No. 28, 1996 calculations, respectively. This is the reason why the population of cis conformers obtained by ab initio studies at higher basis sets here is lower than the populations obtained by the ECEPP/3 calculations31 and from experiments.52,56 Although solvent effects on the cis-trans equilibrium would appear to be negligible from NMR experiments on amides such as Nmethylformamide and N-methylacetamide in several solvents,57 the recent quantum mechanical calculations on the hydration free energy of Ac-Ala-NHMe38 imply that the relative stability of the conformer tCd of Ac-Pro-NHMe is likely to be to some extent decreased by including hydration. In addition, our recent studies on proline-containing tripeptides of RNase T1,25 AcPro-Xaa-NHMe,26 and +H2-Pro-Leu-Gly-NH258 may indicate that the intramolecular hydrogen-bonded tC conformations of Ac-Pro-NHMe in aqueous solution are no longer dominantly feasible because of strong interactions between polar atoms of two end groups and water molecules. The φ-ψ analysis for X-ray structures of proteins with trans and cis proline residues shows that the preferred backbone conformation of the Pro residue is F followed by A for both trans and cis conformers.12 On the other hand, the results obtained at the HF/6-31G** level show the conformers C and A, and A and F to be preferred for trans and cis conformers, respectively. The discrepancy may arise from the effects of neighboring residues on the conformation of the Pro residue,11,12,25,26,29 which is not considered in Ac-Pro-NHMe, as discussed above. However, the calculated values (-72°, -21°), (-91°, -4°), and (-72°, 160°) of torsion angles φ and ψ for the conformers tAu, cBd, and cFd are close to the mean values (-61°, -35°), (-86°, 1°), and (-76°, 159°), respectively, obtained by the analysis of X-ray structures.12 The mean value (-65°, 150°) for the conformer tFd or tFu calculated from X-ray structures does not agree with the HF/6-31G** values (-86°, 75°) and (-83°, 84°) for the conformers tCd and tFu, respectively. In addition, the preferred conformations obtained at the HF/6-31G** level agree well with those determined by the ECEPP/3 force field,31 except for the conformation tF. Preference of Puckering for Trans and Cis Imide Bonds. From the analysis of X-ray structures of proteins, Milner-White et al.29 recently reported the average values of endocyclic torsion angles (χ1, χ2, χ3, χ4) of trans proline residues to be (22°, -30°, 25°, -11°) and (-21°, 29°, -31°, 16°) for down and up puckered conformations, respectively. The corresponding values for cis-down proline residues were reported as (30°, -36°, 24°, -8°). In addition, the average values obtained from X-ray structures of peptides are (18°, -29°, 17°, -4°), (-27°, 35°, -34°, 20°), (26°, -38°, 18°, -7°), and (-21°, 36°, -36°, 17°) for trans-down, trans-up, cis-down, and cis-up conformations, respectively.29 By comparison of the average values obtained at the HF/6-31G** level (see Table 4) with these two sets of X-ray values, it can be seen that ab initio HF/6-31G** values agree well with X-ray data within 5°, except for the trans-down conformation. The conformation tCd is a uniquely preferred trans-down conformation calculated at the HF/6-31G** level, as discussed in the previous section. Furthermore, the backbone conformation C is not favored for X-ray structures of proteins.12 These two facts seem to be crucial factors for the larger discrepancy between the HF/6-31G** values and X-ray data. As expected, the χ values obtained at the HF/6-31G** level are found to be consistent with X-ray data than those obtained at the HF/3-21G level. In addition, Milner-White et al.29 reported the preference of proline puckering for the trans and cis imide bonds: (1) trans Pro residues within R-helices and in extended conformations tend to have the up and down puckerings, respectively, and (2)
Kang cis Pro residues show a preference for the down puckering. Although the significance is not so strong here, the low-energy conformations tAu and tCd calculated at the HF/6-31G** (see Tables 1 and 2) agree reasonably with these observations. For cis Pro residues, the dominant population (90%, estimated by MP2 energies) of the down puckered conformers over the up puckered (see Table 1) is also in excellent agreement with the populations estimated by analyzing X-ray structures of proteins29 and by NMR experiments on Ac-cis-Pro-NH2 in solution.59 Use of Rigid Proline Geometry. The HF/6-31G** results on structural parameters (see Table 3) indicate that the dependence of bond lengths and bond angles on the conformation appears to be weak. The HF/6-31G** optimized bond lengths and bond angles are in very close agreement with the averaged values of X-ray structures of peptides, i.e., the ECEPP/3 values31 to within 0.02 Å and 3°, respectively. However, there are somewhat larger variations occurring in bond lengths r(CβCγ), r(Cγ-Cδ), and r(C′dO) by about 0.03 Å and in bond angles ∠NCRC′, ∠CRC′O, and ∠CRC′N around the CR atom by about 5°, as described above. Therefore, it may be said that the use of rigid proline geometry is to some extent valid for conformational energy calculations of proline-containing peptides and proteins provided that the set of bond lengths and bond angles is chosen properly.60 This does not mean that the rigid geometry can be safely applied to highly constrained peptides and proteins. However, several studies on a comparison of rigid and flexible force fields for the conformational analysis of Ac-Ala-NHMe36,61 and tandemly repeated peptide (Asn-Ala-Asn-Pro)962 showed that the extent of agreement and disagreement between these two kinds of force fields was not significantly different. Recently, Schmidt et al. reported the proline conformational equilibrium and dynamics in the cyclic decapeptide antamanide using the CHARMM force field,22 whose potential parameters for proline have been developed on the basis of ab initio calculations made on N-acetylprolineamide at the 6-31G* level. They noted that the inaccurate equilibrium distribution of puckered states in Pro2 of antamanide may be ascribed to the force field parameters, even though the results of the Langevin dynamics simulation of antamanide are in nearly quantitative agreement with NMR parameters. In the ECEPP force field,31 a representative structure was generated by averaging bond lengths, bond angles, and torsion angles for both up and down puckerings. However, very small adjustments in some bond angles are likely to occur in order to provide an exactly closed pyrrolidine ring for each puckering. This may result in some changes in conformational energy, which is not taken into account by the ECEPP force field. Therefore, the ab initio results at higher basis sets reported here are expected to be useful for improving the geometry and potential parameters of the proline residue. Conclusions In all ab initio calculations at the HF/STO-3G, HF/3-21G, HF/6-31G**, and MP2/6-31G**//HF/6-31G** levels, the C7 conformer is found to be the most preferred, which has a C7 hydrogen bond between terminal groups and is consistent with the structures deduced from IR, CD, and NMR experiments in nonpolar solvents. The trend for the lowering of energies of Ac-Pro-NHMe on going from HF/3-21G to HF/6-31G** appears to be quite similar to that found for alanine dipeptides, while the variations in backbone torsion angles φ and ψ (av ∆φ ≈ 2° and ∆ψ ≈ 9°) are different, which may be attributed to rigid constraints on the N-CR rotation imposed by pyrrolidine ring closure. The
N-Acetyl-N′-methylprolineamide MP2 corrections increase the HF/6-31G** energies by about 1 kcal/mol, except for the conformer tCu. The HF/6-31G** optimized bond lengths and bond angles as well as endocyclic torsion angles χ’s of the pyrrolidine ring are, in general, consistent with the corresponding values of X-ray structures of peptides, but the strong dependence of structural parameters on the conformation cannot be seen. The preference of puckering for the trans and cis imide bonds is likely to be weaker than that found for X-ray structures of proteins and peptides. This may be ascribed to the effect of neighboring residues on proline residues, which is absent for Ac-Pro-NHMe. However, the preference and population for down and up puckered structures with the trans and cis imide bonds calculated at the HF/6-31G** and MP2/6-31G**//HF/6-31G** levels agree reasonably with the results obtained from the analysis of X-ray structures. The degree of puckering for each conformer is described by three puckering amplitudes χm, qz, and qR, and the linear correlations between any two of them exist to a certain extent, as found for cyclopentane. In order to clarify the dependence of imide bonds on puckering, the potential surface of the proline puckering, expressed in terms of pseudorotation parameters, along the cistrans imide isomerization and its functional form is now being carried out. Acknowledgment. This work was partially supported by Institute for Molecular Science (IMS), Japan. The author thanks Professor I. Ohmine for the hospitality during his stay at IMS, the System Engineering Research Institute (SERI), Korea, for the use of the Cray YMP C90 supercomputer, and Dr. S. J. Han for his graphical assistance. References and Notes (1) Richardson, J. S. AdV. Protein Chem. 1981, 34, 167. (2) Creighton, T. E. Proteins: Structures and Molecular Properties, 2nd ed.; Freeman: New York, 1993. (3) Madison, V. Biopolymers 1977, 16, 2671. (4) DeTar, D. F.; Luthra, N. P. J. Am. Chem. Soc. 1977, 99, 1232. (5) de Leeuw, F. A. A. M.; van Kampen, P. N.; Altona, C.; Dı´ez, E.; Esteban, A. L. J. Mol. Struct. 1984, 125, 67. (6) Ma´di, Z. L.; Griesinger, C.; Ernst, R. R. J. Am. Chem. Soc. 1990, 112, 2908. (7) Han, S. J.; Kang, Y. K. J. Biomol. Struct. Dyn. 1995, 12, a084. (8) Momany, F. A.; McGuire, R. F.; Burgess, A. W.; Scheraga, H. A. J. Phys. Chem. 1975, 79, 2361. (9) Balasubramanian, R.; Lakshminarayanan, A. V.; Sabesan, M. N.; Tegoni, G.; Venkatesan, K.; Ramachandran, G. N. Int. J. Pept. Protein Res. 1971, 3, 25. (10) Ramachandran, G. N.; Mitra, A. K. J. Mol. Biol. 1976, 107, 85. (11) Stewart, D. E.; Sarkar, A.; Wampler, J. E. J. Mol. Biol. 1990, 214, 253. (12) MacArthur, M. W.; Thornton, J. M. J. Mol. Biol. 1991, 218, 397. (13) Schmid, F. X.; Mayr, L. M.; Mu¨cke, M.; Scho¨nbrunner, E. R. AdV. Protein Chem. 1993, 44, 25. (14) Nall, B. T. In Mechanisms of Protein Folding; Pain, R. H., Ed.; IRL Press: Oxford, 1994; p 80. (15) Williams, K. A.; Deber, C. M. Biochemistry 1991, 30, 8919. (16) von Heijne, G. J. Mol. Biol. 1991, 218, 499. (17) Venkatachalam, C. M.; Price, B. J.; Krimm, S. Macromolecules 1974, 7, 212. (18) London, R. E. J. Am. Chem. Soc. 1978, 100, 2678. (19) de Leeuw, F. A. A. M.; Altona, C.; Kessler, H.; Bermel, W.; Friedrich, A.; Krack, G.; Hull, W. E. J. Am. Chem. Soc. 1983, 105, 2237. (20) Sarkar, S. K.; Young, P. E.; Torchia, D. A. J. Am. Chem. Soc. 1986, 108, 6459. (21) Thomasson, K. A.; Applequist, J. Biopolymers 1992, 30, 437. (22) Schmidt, J. M.; Bru¨schweiler, R.; Ernst, R. R.; Dunbrack, R. L., Jr.; Joseph, D.; Karplus, M. J. Am. Chem. Soc. 1993, 115, 8747.
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JP960381W
