Molecular conformational analyses of dehydroalanine analogues

Carlos Aleman * Departament d 'Enginyeria

Quimica Molecular Conformational E. 1. S. d'Enginyers Industrials

de Barcelona Analyses of Dehydroalanine Universitat Politecnica de Analogues

Catalun ya Av. Diagonal 647

Barcelona E-08028, Spain

Jordi Casanovas Departament de Quimica-Fisica

Facultat de Quimica Universitat de Barcelona

Martii Franques 1 Barcelona E-08028, Spain

The conformational preferences of dehydroalanine (AAla) were examined through ah initio calculations. The geometries of the minimum energy conformations for N-formyldehydro ala- nilamide and N-acetyl-N-methylamide of dehydroalanine were determined by gradient optimization at the HF/6-31 G * level, and correlation corrections were examined with MP2 single- point energy calculations. Furthermore, HF/3-21 G ah initio geometry optimizations were performed on nine conformations of the model tripeptide N-acetyl-N'-methylamide of didehydroalanine. The results indicate that the C, is the lowest energy conformation at all levels of theory. However, the relative energy ofthe helix conformation decreases when the number of AAla residues in the peptide chain increases. On the other hand, significant variations of the geometry upon conformational change were observed for the three compounds investigated. These results permit to extract important conformationally dependent geometry trends. The results of this study were compared to x-ray diflraction data on single crystals of dehydroalanine-containingpeptides. 0 1995 John Wiley & Sons, Inc.

INTRODUCTION

High quality ab initio quantum mechanical calculations of peptides can in principle provide unique information not readily accessible to experiment. Thus, experimental structural information on peptides and proteins is only available for the con- densed phase. In vacuo calculations allow one to determine conformation maps of molecules free of

bulk medium effects, which can be used to further understanding of the structure of proteins. Further- more, quantum mechanical calculations are useful for the evaluation of accurate force-field parameters (for a recent review, see Ref. 1 ). Thus, the results derived from empirical energy calculations, i.e., molecular mechanics, molecular dynamics, and Monte Carlo simulations, will depend criti- cally on the force field parameters.2-6 As a result,

Received August 1 1, 1994; accepted November 23, 1994. * To whom correspondence should be addressed.

Biopolymers, Vol. 36,7 1-82 (1995) 0 1995 John Wiley & Sons, Inc. CCC 0006-352519510 1007 I- 12

71

72 Aleman and Casanovas

ab initio calculations with large basis sets of some model peptides such as N-acetyl-”-methylamides of glyicine, alanine, and a-aminoisobutyric acid have been p e r f ~ r m e d . ~ - ~ ~

Dehydroalanine ( A Ala) is an a,@-unsaturated amino acid present in a number of naturally occur- ring peptide antibiotics of bacterial rigi in.^^-'^ The double bond of the side chain provides the residue with very interesting chemical features. Indeed, AAla has been found to play an active role in the catalytic activity of some yeastz6 or in bacterial enzymes, 27 probably due to the nucleophilic char- acter of the side chains. On the other hand, the con- version of a tetrahedral saturated to a trigonal de- hydro residue with a shortening of the C*-C’ dis- tance introduces strong and specific steric effects, which influence its conformational behavior.

H H \ /

CP I I o a

ii 0

I H

AAla

Several structures of short peptides containing AAla residues have been solved by x-ray crystallog- raphy in the In all cases the residue AAla exhibits an extended conformation. The same behavior has been observed from nmr33 and theoretical s t ~ d i e s . ~ ~ , ~ ~ - ~ ~ In addition, as a consequence of the preferred extended conformation, the A Ala constraints the conformational space of the preced- ing residue inducing an inverse In contrast to the small peptide results, theoretical studies using force field 34 and quantum mechanical 35 calculations have indicated the stability of the 310-helix conformation for A Ala homopolypeptides. The stabilization of the 310-helix with respect to the extended conformation when the number of AAla residues in the polypeptide chain increases can be rationalized in terms of cooperative energy effects.35 Thus, semiempirical AM 1 and single point ab initio SCF-MO 4-3 1G calculations on several A Ala oligopeptides showed a large cooperative energy effects for the helical conformations, whereas no cooperativity was observed for the extended conformations. Indeed, a comparative study between AAla, a-aminoisobutyric acid (Aib), and alanine ( Ala) residues suggested that both AAla and Aib have a similar intrinsic ten-

dency to adopt helical conformations, 37 being the Aib an experimentally well-known helix former, 38-41 and resulting greater than that of Ala. These results may have a comparison in the case of the dehydrophenilalanine ( APhe) residue. Thus, experimental and theoretical studies have indicated that APhe strongly prefers a @-turn structure in small pep tide^.^^-^^ However, in peptides containing several APhe residues separated by amino acid residues, a 310-helical conformation was ob- ~ e r v e d . ~ ~ - ~ ’

These results indicate that the AAla residue can be considered a useful building block for de novo protein design. High quality ab initio calculations could certainly help to characterize the A Ala residue, and this is the intent of the present study. In this work we wish to provide a rigorous and sys- tematic study of the structural and energetic properties of three small AAla derivatives (see Figure 1 ): (a ) N-formyldehydroalanylamide ( I ) ; (b) N- acetyl-N’-methylamide of dehydroalanine or A Ala dipeptide analogue (11); and (c) N-acety1-N’- methylamide of didehydroalanine or A Ala tripeptide analogue (111). Furthermore, a comparison has been made with x-ray diffraction results on single crystals of AAla derivatives.

COMPUTATIONAL PROCEDURE

The program HONDO 7.04’ running on the com- puters IBM 3090/600 and IBM/RISK-6000 was used in the calculations. Geometry optimizations of I and I1 were performed at the Hartree-Fock (HF) level with the 3-21G49 and 6-31G*50 basis sets. The optimizations were continued until a maximum energy gradient dropped below 0.0005 kcal/mol. All optimized structures were checked by analysis of harmonic vibrational frequencies obtained from diagonalization of force constant ma- trices at both 3-21G and 6-31G* levels. Excluding translational and rotational motions, only positive eigenvalues of the Hessian matrix were obtained, proving that the calculated conformer geometries are minima on the HF/3-21G and HF/6-31G* potential energy surfaces of I and 11. The sum of zero-point energies for all normal-mode vibrations scaled by a recommended factor of 0.95’,52 approx- imates the ZPE contribution. The fully optimized HF/6-31G* structures of I were used for single point calculations with the TZP53 basis set. Fur- thermore, the Msller-Plesset ( MP) perturbation treatment 54 was used to compute electron correla-

Analyses of AAla Analogues 73

H8 I

/N2\ /c4\ ,HI1

O6 D1 I I HI2

N5 I c3

H7 \

14

HI9 / l i H 20

FIGURE 1 Atom numbering scheme for the molecules: N-formyldehydroalanine (I) , N- acetyl-N'-methylamide of dehydroalanine (II), and N-acetyl-N'-methylamide of didehydroalanine ( 111).


tion corrections to the energy. MP2 corrected energies for I were computed from 6-3 1G * and 6-3 1 G basis sets. The good agreement between them per- mits us to stimulate the effect of the electron correlation for I1 at the 6-3 1G

Analogue I11 was considered in nine conformations. The structures selected for investigation are not the result of a complete conformational search. Rather, they were selected because their geometries represent characteristic regions of the conformational space that are of interest, as discussed below. Geometry optimizations were performed at the HF/ 3-2 1G level. As for I and 11, the optimizations were continued until the maximum energy gradient was less than 0.0005 kcal/mol. Due to the size of the molecule, the calculation of the second-order derivatives was not possible.

RESULTS AND DISCUSSION

N-Formyldehydroalanylamide

The results from ab initio HF optimizations on two conformations of I using 3-2 1G and 6-3 lG* basis sets are shown in Table I. A comparison of the structural parameters, i.e., bond lengths, bond angles, and dihedral angles, for a given conformation indicates that the agreement between HF/ 3-2 1G and HF/ 6-3 1 G * geometries is quite good ( rms deviation bond lengths = 0.010 A; rms bond angles = 0.9"; and rms dihedral angles = 4.0'). Thus, HF/ 3-2 1 G bond lengths and bond angles were not included in Table I. The lowest energy conformation found is the extended conformation (cp = - 179.6", $ = 179.9"), also named C5. It is characterized by an intramolecular hydrogen bond with < N2H8OI0 = 126.1' and RHgOl0 = 2.092 A. Due to the sp2 nature of the a-carbon in the AAla residue, the C7,e, ( c p = -65.9", $ = 20.7") and C7,ax ( c p = 66.2", $ = -20.7") are in fact one twofold degenerate minimum with corresponding dihedral angles cp, $ = - cp, - $. The C7 intramolecular hydrogen-bond geometry is characterized by RH1 106 = 2.038 A and

The dependence of bond lengths on the conformation is very small. The largest change of a bond length occurs for RN2C3r which varies from 1.398 A (C,) to 1.428 A (C7). In contrast, large changes with the conformation were observed for bond angles. More specifically, < N2C3C4 varies from 109.7' (C,) to 12 1.2" (C,). These results show that in the C5 conformation the value of the < N C T '

< N5H1106 = 138.6".

angle is considerably shorter than the expected values of 120" in a trigonal configuration, suggesting the key role ofthis valence angle in determining the structure of A Ala-containing peptides.

Table I1 presents the HF relative energies determined at different theory levels, as well as various electron correlation and ZPE contributions. All electron correlation contributions were calculated at the HF/6-31G* geometries with both the 6- 31G* and 6-31G basis sets. Clearly, the C5 is the most stable conformation at all the theoretical levels. Simultaneously, the relative stability of the C7 conformer presents a very small dependence with the basis set and correlation energy. Thus, the C7 conformation has a relative energy of 3.9 kcal/mol at HF/6-31G*//HF/6-31G*; improvement ofthe theoretical level changes this number to 4.6 kcal/ mol and 4.0 kcal/mol at HF/TZP//HF/6-31G* and MP2/6-3 lG*//HF/6-3 1G*, respectively. It should be noted that the ZPE corrections calculated at both HF/3-21G and HF/6-31G* geometries stabilize the relative energy of the C5 conformation by 1.5 and 0.7 kcal/mol, respectively. Comparison between MP2/6-3 lG*//HF/6-3 lG* and MP2/6-3 lG//HF/6-3lG* relative energies suggests that the latter correctly represent the effect of the electron correlation contribution.

N-Acetyl-N'-Methylamide of Dehydroalanine

Five minima were found for I1 at both HF/ 3-2 1G and HF/ 6-3 lG* levels: C, , C7,eq, C7,ax, aR, and a ~ . Note that for 11, C7,eq and C7,ax as well as aR and aL are indeed twofold degenerate minima with corresponding dihedral angles cp, $ = cp, -+. The optimized geometrical parameters for the cs, C7, and a conformations are shown in Table 111. The HF/ 3-21G bond lengths and angles are in good agreement with the HF/6-31G* data for the three conformers (rms bond lengths = 0.0 10 A and rms bond angles = 1.5"), and therefore they were not included in Table 111. Plots of the minimized structures of I1 are given in Figure 2.

The lowest energy structure found is the C5 conformation with cp = - 179.9" and $ = 178.7". The C, strained intramolecular hydrogen bond is characterized by < N3HI2Ol4 = 110.0" and RH12014 = 2.069 A. The C7 conformation is slightly less stable. The C7 intramolecular hydrogen bond is characterized by < N6Hl5Ol1 = 148.7' and RH15011 = 2.003 A. The last minimum is located in the a- helical region of the potential energy surface with

Analyses of AAlu Analogues 75

Table I Equilibrium Geometrical Parameters of N-Formyldehydroalanylamide (I) Conformations"

HF/3-2 IG optimized geometries H7-CI-N2-C3 (mi) CI-N2-C3-C4 (p) N2-C3-C4-C5 ('P) C3-C4-N5-H11 ( ~ 2 )

AE

CI-N2 N2-C3 c3-c4 C4-N5 06-C 1 H8-N2 c9-c3 0 10-C4 H I3-C9 H 14-C9 CI-N2-C3 N2-C3-C4 c3-c4-c5 06-C 1 -N2 H8-N2-C3 c9-c3-c4 OIO-C4-N5 H I3-C9-C3

HF/6-3 lG* optimized geometries

H I4-C9-C3 H7-CI-N2-C3 ( ~ 1 )

C 1 -N2-C3-C4 (p) N2-C3-C4-C5 ('P) C3-C4-N5-H 1 1 (4 AE

179.9

179.9 -179.9

0.0

1.353 I .398 1.511 1.345 1.194 0.997 1.323 1.204 1.072 1.075

-179.5

127.7 109.7 118.5 126.6 114.1 124.5 121.9 121.2 121.5 179.9

- 179.6 179.9

-179.9 0.0

-173.5 -55.6

23.9 179.2

4.9

1.348 1.428 1.513 1.35 1 1.197 0.996 1.319 I .200 1.072 I .075

127.3 121.2 117.3 125.9 115.6 118.4 122.9 1 19.9 121.6

-172.9 -65.9

20.7 172.6

3.9

a Bond lengths in A. Bond angles and dihedral angles in degrees. Rela- tive energies in kcal/mol.

torsion angles cp and $ of -74.4" and -7.7", respectively. The largest deviation from planarity of the peptide groups occurs for the helical conformation with w1 = -170.1" and o2 = 173.9".

The present results are in poor agreement with those reported by Aj6 et al.57 The authors, using empirical calculations, predicted a peculiar conformation with dihedral angles (a, + = - 140", 10" as the lowest energy structure. Furthermore, the energy order for the remaining conformers differs from that found at the ab initio level. Thus, the a (cp, $ = -60", -lo"), the extended (two semiextended conformations were characterized as minimum: cp, + = - 150", - 140"), and a unusual conformation with cp, $ = -30", 140" were found 1.5

kcal/mol, 2.5 kcal/mol (3.0 kcal/mol for the second semiextended structure) and 3.8 kcal/mol respectively, less stable than the absolute minimum. The origin of the discrepancies between the present ab initio results and empirical calculations reported by Aj6 et al.57 must be attributed to important deficiencies in the force field parameterization. However, a better description of the force field parameters for AAla residue has been recently reported by several a ~ t h o r s . ~ ~ , ~ ~ , ~ ~

The variation of bond lengths and angles upon conformational change is very similar to that of I. The largest change of a bond length occurs for RN3C4, which varies from 1.397 A ( C , ) to 1.429 (C,) and 1.425 A ( a ) . On the other hand, a large


Table I1 Relative Energies (kcal/mol) of N-formyldehydroalanylamide (I) Conformations"

Level of energy calculation/ Level of Geometry Optimization

HF/3-21/G//HF/3-2 1G ZPE (HF/3-21G)b HF/3-21G//HF/3-21G + ZPE(HF/321G) HF/6-3 lG*//HF/6-3 lG* ZPE (HF/6-31G*)b HF/6-3 lG*//HF/6-3 lG* + ZPE(HF/6-3 1G*) HF/TZP//HF/6-3 1 G* MP2/6-3 lG*//HF//6-3 lG* MP2/6-3 lG*//HF/6-3 lG* + ZPE(HF/6-3 1G*) MP2/6-3 lG//HF/6-3 1 G*

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

4.9 1.5 6.4 3.9 0.7 4.6 4.6 3.9 4.6 4.1

a The total energies of conformer Cs (in au) at all levels oftheories are the following: HF/3-2 IG//HF/3- 21G, -41 1.289625; HF/3-21G//HF/3-21G + ZPE(HF/321G), -41 1.190709; HF/6-31G*//HF/6-31G*, -413.596629; HF/6-31G*//HF/6-3 IG* + ZPE(HF/6-31G*), -413.497619; HF/TZP//HF/6-31G*, -413.739916; MP2/6-31G*//HF//6-3 IG*, -414.799698; MP2/6-31G*//HF/6-31G* + ZPE(HF/6- 31G*), -414.700688; MP2/6-31G//HF/6-3 1G*, -414.223434.

The zero-point energies (uncorrected) ofconformer Cs (in au) are the following: HF/3-2 lG, 0.0989 16; HF/6-3 lG*, 0.099010.

change was observed for the < N3C4C5 bond angle, which varies from 109.5' (C,) to 120.8' (C,) and 119.4 ( a ) . These results permit to extract important conformationally dependent geometry trends. Thus, in the C5 conformation the < N C T ' bond angle adopts a value similar to those frequently observed in peptides, i.e., glycine, alanine, and a-aminoisobutyric acid, 7-22 whereas in the C7 and a conformations the computations point out an unusu- ally large value. This suggests that standard force field parameters must be modified in order to provide a suitable description of the conformational behavior of a,gunsaturated amino acids and peptides.

Energy differences are shown in Table IV. In all cases the C5 is the most stable conformation. The HF/ 3-2 1 G method seems to overestimate the Cs stability as compared to HF/6-3 lG*. Thus, the relative energies of C7 and a conformations are over- estimated 1.1 and 2.3 kcal/mol, respectively, at the HF/3-21G//HF/3-21G level. In fact, the HF/6- 3 1G* results suggest that the true surfaces may be more flat than the HF/3-21G surfaces. It can be noted that the ZPE corrections stabilize the relative energy of Cs conformer by 0.6 kcal/mol (C,). Since MP2 calculations at the 6-31G* level are computationally prohibited for us, we evaluate the electron correlation contributions using the 6-3 1 G basis set. The preceeding section states that calculations at the MP2/6-3 lG level provide reasonable

relative energies. The results indicate that also in this case the most stable conformer is the C,, being the relative energies of the C7 and a conformations 3.1 and 5.3 kcal/mol, respectively.

N-Acetyl-N'-Methylamide of Didehydroalanine

It is an interesting question as to how the essential conformational properties of the dipeptide deviate when the polypeptide chain growth. In order to as- certain this, we select AAla tripeptide (111) as the simplest model. Even though it is not as advanced as one might desire, it may be noted that I11 provide a reasonable model for the behavior of the ends of long peptide chains.

The results reported in previous sections indicate that the 3-2 1 G basis set provides an acceptable description of the molecular conformation, therefore geometry optimizations of I11 were performed at this level. Calculated dihedral angles and energies of the nine selected conformations are presented in Table V. Each of the structures with angles pl , p2, q2 has a degenerate enantiomeric conformation with angles - pI , - + I , - p 2 , - $2.

As it can be noted the CsCs is considerably more stable than any other conformation. In contrast to the dipeptide energy pattern, the (YR-cIR is more stable than the C7eqC7q conformation. Thus, for I1 the a conformation was found 2 kcal/mol higher in en-


Table I11 Equilibrium Geometrical Parameters of N-Acetyl-N'-Methylamide of Dehydroalanine (11) conformations'

HF/3-2 1G optimized geometries Cl-C2-N3-C4 ( ~ 1 )

C2-N3-C4-C5 (cp ) N3-C4-C5-N6 ('I!) C4-C5-N6-C7 ( ~ 2 )

AE

C2-N3 N3-C4 c4-c5 C5-N6 01 1-c2 H 12-N3 C 13-C4 0 14-C5 H 15-N6 H 19-C 13 H20-C 13 C 1 -C2-N3 C2-N3-C4 N3-C4-C5 C4-C5-N6 C5-N6-C7 0 1 1 -c2-c 1 H 12-N3-C2 C 13-C4-N3 0 14-C5-C4 H 15-N6-C5 H 19-C 13424 H20-C3-C4 Cl-C2-N3-C4 ( w I )

C2-N3-C4-C5 (cp ) N3-C4-C5-N5 (\k) C4-N5-N6-C7 ( ~ 2 )

AJT

HF/6-3 1G* optimized geometries

179.7 179.6

-178.2 -179.8

0.0

1.362 1.397 1.514 1.341 1.198 0.997 1.324 1.200 0.990 1.068 1.072

11 3.8 127.9 109.5 118.6 121.0 122.2 118.7 126.1 119.4 120.2 121.5 121.3 179.5

- 179.9 -178.7

179.3 0.0

- 176.3 -62.7

32.5 -179.5

5.3

1.356 1.429 1.514 1.343 1.202 0.995 1.318 1.203 0.996 1.075 1.072

114.5 127.1 120.8 117.0 120.0 122.4 117.2 120.3 119.8 117.8 121.6 210.1

- 174.4 -70.1

32.2 176.5

4.2

-171.7 -72.0 -5.4 176.8

7.3

1.369 1.425 1.510 1.347 1.195 0.995 1.318 1.202 0.992 1.075 1.072

114.8 122.9 119.4 116.2 121.8 122.9 117.8 121.8 120.3 117.8 121.7 119.8

- 170.3 -74.4 -7.7 173.9

5.0

a Bond lengths in A. Bond angles and dihedral angles in degrees. Relative energies in kcal/mol.

ergy than the C7 (at the HF/3-21G//HF/3-21G), whereas for I11 the latter is unestabilized by around 2.6 kcal/mol with respect to the former. These results are in good agreement with our previous cal- c u l a t i o n ~ . ~ ~ ~ ~ ~ Thus, they indicate that the helix conformation is stabilized when the number of residues in the polypeptide chain increases. On the other hand, it must be noted that all three conformations-C5, C7, and a-are minima also when they are combined between them. This illustrates the large flexibility of peptide chains, which is re- tained in the restricted, a,&unsaturated residues.

All these structures were obtained without taken into account solvent interactions, which can change the order of the energy minima relative to that found in vacuum calculations.

Although one must consider how the results change with the level of theory, it is apparent that, even at single levels such as HF/ 3-2 lG, conformational geometry trends are well reproduced from a qualitative point of view. Table VI shows the main geometrical parameters for the nine computed conformations of 111. It can be noted that the variation of bond lengths and angles happens in a sim-


0 / n

FIGURE 2 Molecular structure of the three low-energy conformations C5 (a), C7 (b), and a (c) of N-acetyl- N'-methylamide of dehydroalanine. Nonpolar hy- drogens were omitted for simplicity.

ilar way to that of I and 11. The largest change of a bond length occurs for RN3,--, which varies from 1.397 A (C5-aR) to 1.432 A (C7eq-C7ax). On the other hand, the largest change of a bond angle occurs for < N6C7C8, which varies from 108.4" ((2,-

C,) to 123.1" (C7eq-C7ax). Thus, in structures with a C5 conformational pattern the < N C T ' bond angle adopts a tetrahedral value, whereas in structures with a C7 and/or a pattern a trigonal value is obtained.

Survey of A Ala Derivatives

The structure of noncyclic AAla derivatives was obtained from the Cambridge Structural Data Base." The main features found in these compounds that have been studied by x-ray crystallog- raphy are shown in Table VII. In all cases AAla residue adopts an extended conformation. It should be noted the excellent agreement between the geometrical parameters computed for the C5 conformation of 1-111, and those found in the structures determined by x-ray analysis. More specifically, it can be seen that in the crystallyzed compounds the < N C T ' bond angle appears at values close to those computed in the present work. This is specially remarkable in I1 for which both experimental and quantum mechanical data are available.

Unfortunately, the conformational dependence observed for the < N C T ' bond angle cannot be directly confirmed on A Ala-containing polypeptides with a helix conformation due to the lack of x-ray data. Thus, although force field and quantum mechanical calculations predict that polypeptides with several AAla residues adopt a 310-helix conformation, experimental data are only available for small peptides with only one AAla residue. How- ever, we compare the present results with those derived from the crystal data of APhe-containing polypeptides with a 3 ,o-helix conformation. The mean geometrical parameters found for the APhe residues in these compounds are very similar to those found in the present work for the a conformation of I1 and 111. More specifically, an average < N C T ' bond angle value of 1 17" was found for the helical APhe residues, whereas a value of 1 19.4" was found for I1 at the HF/6-3 lG* level.

CONCLUSIONS

In this paper we have presented a detailed ab initio study of the conformational preferences of model dehydroalanine peptides: N-formyldehydroalanine ( I ) , N-acetyl-N'-methylamide of dehydroalanine (11) and N-acetyl-N'-methylamide of didehydroalanine (111). Our results


Table IV Relative Energies (kcal/mol) of Dehydroalanine Dipeptide Analogue (11) Conformations"

Level of Energy Calculation/ Level of Geometry Optimization c5

HF/3-2 1 G//HF/3-2 1 G ZPE (HF/3-2 lG)b HF/3-2 lG//HF/3-2 1G + ZPE(HF/32 1G) HF/6-3 lG*//HF/6-3 lG* ZPE (HF/6-3 lG*)b HF/6-3 lG*//HF/6-3 lG* + ZPE(HF/6-3 1G*) MP2/6-3 lG//HF/6-3 lG*

0.0 0.0 0.0 0.0 0.0 0.0 0.0

c7,eq

5.3 0.6 5.9 4.2 0.6 4.8 3.1

(YR

7.3 0.4 7.7 5.0 0.5 5.5 5.3

-

a The total energies of conformer C5 (in au) at all levels oftheories are the following: HF/3-2 IG//HF/3- 21G, -488.934593; HF/3-21G//HF/3-21G + ZPE(HF/32 IG), -488.782591; HF/6-3 IG*//HF/6-31G*, -491.671664; HF/6-31G*//HF/6-31G* + ZPE(HF/6-31G*), -491.520782; MP2/6-3 IG//HF/6-31G*, -492.447 137.

The zero-point energies (uncorrected) of conformer C5 (in au) are the following: HF/3-2 IG, 0.152002; HF/6-3IG*, 0.150882.

include ( a ) a detailed investigation of minima for both I and 11 peptides at higher levels of theory (HF/6-3 1G*) with inclusion of correlation effects (MP2) for relative energies; ( b ) a study of minima for I11 at a fairly low level of theory (HF/ 3-2 1 G ) . Our principal conclusions are as follows.

Optimized structures obtained for I and I1 at the HF/3-21G level are in generally good agreement with the HF/6-3 lG* results. The C5 conformation is the global minimum at all levels of theory, lying around 5 kcal/mol below C7 and a conformations. These results are in good agreement with both x-ray ~ r y s t a l l o g r a p h y ~ ~ - ~ ~

and nmr s p e c t r o ~ c o p y ~ ~ data, where an extended conformation have been observed in structures of short peptides containing one AAla residue. Regarding the results on 111, the C5-C5 conformations was also found as the most energetically favored minimum at the HF/ 3- 2 1G level. However, in this case the (YR-(YR conformation is 2.6 kcal/mol more stable that the C7eq-C7eq. Indeed, the results suggest that the helix is stabilized with respect to the extended conformation when the number of AAla residues increases. This is in excellent agreement with recent force field c a l c u l a t i o n ~ , ~ ~ where the 3,,,-helix was predicted as the most stable structure in

Table V Minimum Energy Structures" and Relative Energies (in kcal/mol) of N-Acetyl-N'-Methylamide of Didehydroalanine

a1 ' P I *I w2 (P2 *2 w3 AE

c5-c5 -179.5 -178.4 -178.3 -178.5 -178.8 -176.2 -179.5 O.Ob

C5-C7,eq -179.6 179.5 177.3 -174.9 -60.9 28.1 -178.3 6.7 ( Y R - ~ R - 170.9 -6 1.6 -18.9 176.4 -82.4 -3.7 179.1 7.0 G - a R - 179.9 180.0 -174.9 -173.3 -76.2 -2.2 178.2 7.2 C7,eq-C7,ax -173.0 -61.1 30.8 178.5 55.7 -27.5 179.4 9.2 C7,eq-C7,eq -172.1 -59.1 28.7 - 173.9 -64.0 27.0 -178.4 9.6 C 7 , e q - a ~ -172.7 -6 1.6 23.5 177.2 72.2 11.9 -179.0 10.7 C7,eq-O(R -173.5 -61.0 33.7 -175.1 -70.8 - 10.9 178.0 11.4 ~ R - C ~ L -170.1 -66.2 -18.2 172.9 72.9 7.2 -176.1 13.4

a The conformational angles are defined as follow: w, , CI-C2-N3-C4; (o,, C2-N3-C4-C5; q,, N3-C4-C5-N6; w2, C4-C5-N6-C7; ( o ~ , C5-N6-C7-C8; 'P2, N6-C7-C8-N9; wg , C7-C8-N9-C 10.

The total energy of C5C5 is -732.237872 au.


Table VI Equilibrium Geometrical Parameters of N-Acetyl-N'-Methylamide of Didehydroalanine (111) Conformations'

C2-N3 N3-C4 c4-c5 C5-N6 N6-C7 C7-C8 C8-N9 C 16-C4 C 19-C7 Cl-C2-N3 C2-N3-C4 N3-C4-C5 C4-C5-N6 C5-N6-C7 N6-C7-C8 C7-C8-N9 C8-N9-C 10 C 16-C4-N3 C 19-C7-N6

.362

.398 SO8 .345 .400 .510 .338 .320

1.320 131.1 127.2 109.0 117.4 126.7 108.4 11 8.8 120.1 126.4 126.7

1.359 1.398 1.5 10 1.341 1.436 1.515 1.340 1.321 1.316

113.3 126.8 109.2 118.0 127.4 122.5 1 17.6 1 19.6 126.2 119.7

1.37 1 1.423 1 SO2 1.359 1.425 1.505 1.340 1.315 1.313

114.1 122.2 119.0 114.8 122.0 118.4 115.8 120.7 122.7 122.9

1.364 1.397 1 SO8 1.355 1.430 1.502 1.343 1.32 1 1.314

1 13.2 126.9 108.8 117.8 122.1 119.5 1 16.6 120.2 126.4 122.1

1.359 1.432 1.514 1.339 1.428 1.515 1.341 1.317 1.318

114.2 127.9 122.4 116.7 127.7 123.1 117.9 119.4 120.2 119.6

1.360 1.43 1 1.514 1.338 1.434 1.514 1.342 1.317 1.316

114.0 128.2 123.1 117.3 126.2 122.3 116.9 120.0 120.0 1 19.9

1.359 1.432 1.513 1.362 1.423 1.499 1.345 1.317 1.314

114.2 127.4 122.3 116.3 120.9 118.6 115.7 120.1 120.4 122.9

1.358 1.380 1.432 1.422 1.514 1.501 1.353 1.362 1.424 1.425 1.503 1.501 1.344 1.345 1.316 1.315 1.314 1.314

113.9 113.9 128.1 121.4 122.5 118.9 116.7 115.4 121.3 121.5 119.1 118.9 115.7 116.4 120.7 120.2 120.1 124.2 122.5 122.4

a Bond lengths in A. Bond angles in degrees.

homopolypeptides with a large number of AAla residues. Unfortunately, these results cannot be confirmed experimentally due to the lack of x- ray and nmr data for homopolypeptides with a sufficient number of A Ala residues.

On the other hand, significant variations of the molecular geometry upon conformational changes have been observed for the three A Ala-containing compounds. Thus, in the C5 conformation the < NC"C' bond angle adopts a tetrahedral value similar to that found experimentally by x-ray crys- tallography, where in the C , and a conformations it takes an unusual large value that correspond to a

trigonal configuration. This induces strong changes in some bond distances, especially in RNPCa. The results presented here, particularly the HF/6-3 1 G * calculations, form a useful data base, which can be used to derived an accurate set of force field parameters for the conformational analyses of unsaturated residues.

We are indebted to Dr. M. Orozco and Professor F. Illas for computational facilities. The kind help of M. C. Vega and N. Irles is gratefully acknowledged. CA acknowl- edges support of the Centre de Supercomputacih de CA- talunya (CESCA) for supercomputer time.

Table VII Geometrical Parameters of Dehsdroalanine Derivatives (RAAlaR') in Crystals

CH3CO; OH 1.409 1.502 1.328 1.209 110.7 127.9 121.9 28 tBuOCONH-C(CH2Phe)-

CO; OCH3 1.396 1.486 1.328 1.189 109.9 126.6 122.5 30 CH3CO; NHCH; 1.400 1.502 1.322 1.231 11 1.4 124.7 119.7 31

CH,CO; NHCH3 (calculated) 1.397 1.5 14 1.324 1.200 109.5 126.1 1 19.4 This work HCO; NH2 (calculated) 1.398 1.511 1.323 1.204 109.7 124.5 121.9 This work

a The crystals of N-acetyl-dehydroalanine-N'-methylamide contain two molecules with slightly different geometrical parameters.

1.402 1.489 1.326 1.228 111.6 126.1 120.1


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Documents

Molecular conformational analyses of dehydroalanine analogues