J. Am. Chem. SOC.1994,116, 3967-3972
3967
Interrelationship between Conformation and Theoretical Chemical Shifts. Case Study on Glycine and Glycine Amide Horst M. Sulzbach,'qb Paul v. R. Schleyer,'JP*b and Henry F. Schaefer III*Ja Contribution from the Center for Computational Quantum Chemistry, The University of Georgia, Athens, Georgia 30602, and Institut fur Organische Chemie der Universitat Erlangen-Niirnberg, Henkestrasse 42, 91 054 Erlangen, Germany Received December 10, 1993. Revised Manuscript Received February 23, 1994"
Abstract: The gauge independent atomic orbital (GIAO) method was used to explore the change in the chemical shift (As) with respect to the dihedral angle for glycine, H2NCH2COOH ( l ) ,and glycine amide, H2NCH2CONH2 (2), a t the GIAO-SCF/6-3 1lG**//RHF/6-3 1G*, GIAO-SCF/6-3 1 lG**//MP2/6-31G*, and GIAO-MP2/6-3 1lG**// MP2/6-3 1G* levels of theory. The absolute chemical shielding depends strongly on the geometry and the level of theory at which the N M R chemical shielding is calculated. The change of the chemical shifts as a function of the backbone angle J., however, depends only slightly on the level of theory. Both 1 and 2 are able to reproduce the difference in the chemical shifts for the methylene carbon (C,) that is found for the e-helix and the @-pleatedsheet. The chemical shifts of the diastereotopic hydrogens, that are bound to C,, depend strongly on the positions of the carboxyl and carbamide moieties.
Introduction The solution structure of a protein or peptide is in many cases identical to the biologically active structure that is found in vivo, because living cells exist in an aqueous environment.2 Until about 15years ago, X-ray crystallography was the only method to obtain structural information. Moreover, as discussed in detail by Kessler for cyclic peptides,3 the structure in the crystal can differ considerably from that in solution for biomolecules. The structures of peptides in solution are now obtained by N M R methods including two- and three-dimensional Fourier-transform (FT) N M R experiment^.^ In a typical structure determination the N M R signals are assigned first. The nuclear Overhauser enhancement (NOE) effects between protons that are located a t a shorter distance than approximately 5.0 A from each other but belong to different parts of the amino acid sequence are determined next. In a possible structure of the peptide the above pairs of protons must becloser than 5 A to each other. Distance-geometry algorithms, which use relatively simple force fields, perform a restricted geometry optimization to find possible spatial structures that contain the required H H distance^.^ Finally, using the Karplus equation, dihedral angles are deduced from vicinal coupling constants (35).5,6 N M R chemical shift information is not normally used to help deduce structural information, because the dependency of the N M R chemical shifts on the conformation is not well-known. Only in specific cases, e.g. to determine if a proline residue contains a cis or trans amide linkage, are chemical shifts To establish this conformation-NMR shift relationship, two experimental approaches have been taken. The first is to measure the solid-state N M R shifts of proteins, whose X-ray structures areavailable.sl1 The second is to assume that the crystal structure
* Correspondence should be addressed to the Center for Computational Quantum Chemistry, Athens, GA 30602. Abstract published in Advance ACS Abstracts, April 1, 1994. (1) (a) University of Georgia. (b) UniversitPt Erlangen-Niirnberg. (2) Streyer, L. Biochemistry; W. H. Freeman: New York, 1988. (3) Kessler, H. Angew. Chem. 1982, 94, 509. (4) Wiithrich, K. N M R of Proteins and Nucleic Acids; Wiley: New York, 1986. (5) (6) (7) (8)
Karplus, M. J. Chem. Phys. 1959, 30, 11. Karplus, M. J. Am. Chem. SOC.1963,85, 2870. McFarlane, W. Chem. Commun. 1970, 418. Smith, I. C. P. In Topics in Carbon-13 NMR-Spectroscopy; Levy, G. C., Ed.; Wiley: New York, 1976; pp 1-80. (9) Saita, H. Magn. Reson. Chem. 1986, 24, 835. ( 10) Teng, Q.;Iqbal, M.; Cross,T. A. J . Am. Chem. SOC.1992,114, 53 12.
0002-786319411516-3967$04.50/0
is maintained if the protein is dissolved and measure the N M R spectrum in solution.12 Both methods provide information on the dependence of the N M R chemical shieldings on geometrical changes. However, the chemical shifts also depend on the sidechain conformation and crystal-packing effects, which complicate the analysis of the factors that influence 6 . 9 If the N M R is taken in solution, the structure is not known well enough to determine structure-shift dependencies reliably. The problem is that small structural changes cannot be excluded. Finally, an experimental correlation between the chemical shifts and the conformation is limited to those secondary, or backbone, conformations that are represented in the actual molecule. An alternative approach is to compute the dependencies of the N M R chemical shifts on the conformation using ab initio theory. Methods like IGLO,I3-l7 LORG,l8-20 GIAO,21-25 and GIAOMP226927allow the prediction of the N M R chemical shifts and have been used successfully to elucidate the structures of boranes and c a r b ~ r a n e s , ~ ~have - ~ I helped to reconfirm unusual N M R shifts,32 and have elucidated long known N M R effects on a theoretical basis.33 Furthermore, the absolute N M R chemical (1 1) Gerald, R.; Bernhard, T.; Haeberlen, U.; Rendell, J.; Opella, S. J . Am. Chem. SOC.1993, 115, 777. (12) Williamson, M. P. Biopolymers 1990, 29, 1423. (13) Kutzelnigg, W. Isr. J. Chem. 1980, 19, 193. (14) Schindler, M.; Kutzelnigg, W. J . Chem. Phys. 1982, 76, 1919. (15) Schindler, M.; Kutzelnigg, W. J. Am. Chem. SOC.1983, 105, 1360. (16) Fleischer, U.; Schindler, M. Chem. Phys. 1988, 120, 103. (17) Kutzelnigg, W.; Fleischer, U.; Schindler, M. N M R Basic Principles and Progress; Springer-Verlag: Berlin Heidelberg, 1990; Vol. 23. (18) Hansen, A. E.; Bouman, T. D. J. Chem. Phys. 1985, 82, 5035. (19) Bouman, T. D.; Hansen, A. E. Chem. Phys. Lett. 1988, 149, 510. (20) Hansen, A. E.; Bouman, T. D. J . Chem. Phys. 1989, 91, 3552. (21) Ditchfield, R. J . Chem. Phys. 1972, 56, 5688. (22) Ditchfield, R. MTP International Review of Science Physical Chemistry Series I . Molecular Structure and Properties; Butterworth: London, 1972. (23) Ditchfield, R. Mol. Phys. 1974, 27, 789. (24) Ditchfield, R.; Ellis,P. D. In Topicsin Carbon-13NMRSpectroscopy; Levy, G. C., Ed.; Wiley: New York, 1974. (25) Pulay, P.; Wolinski, K.; Hinton, J. F. J . Am. Chem. SOC.1990, 112, 825 1. (26) Gauss, J. Chem. Phys. Lett. 1992, 191, 614. (27) Gauss, J. Chem. Phys. 1993, 99, 3629. (28) Hnyk, D.; Vajda, E.; Biihl, M.; Schleyer, P. v. R. Inorg. Chem. 1992, 31, 2464. (29) Biihl, M.; Schleyer, P. v. R. J. Am. Chem. SOC.1992, 114, 477. (30) Biihl, M.; Schleyer, P. v. R. Struct. Chem. 1993, 4, 1. (31) Mebel, A. M.; Charkin, 0. P.; Schleyer, P. v. R. Inorg. Chem. 1993, 32, 469.
0 1994 American Chemical Society
3968 J . Am. Chem. SOC..Vol. 116. No. 9. 1994
Sulzboch er al.
shieldings have been computed for a large number of molecules.'' In general, the relative chemical shifts that are obtained show good agreement with experimental data. Chemical shifts have already been computed ab initio for peptide structures. De Dios. Pearson, and Oldfield found good agreement between C I A O N M R chemical shifts and the experimental values for the C.- and Cscarbons a s well a s for nitrogen ("N) and fluorine (I9F) atoms of selected residues in protein models." In addition, they claim that the various parameters, which affect the chemical shifts (bond length, bond angle, and dihedral angle) are not coupled and can therefore be treated separately.'' Laws et al. reproduced the chemical shifts of the C,-carbon using the C I A O 1nethod.3~Jiao. Barfield, and Hruby showed that IGLO calculations can reproduce the shift difference between the syn- and anti-conformation for the N-methyl group in simple amides." They also used the IGLO program to obtain the chemical shielding surface for C, of N-acetyl-N'-methylglycinamideand are able to reproduce the experimentalvaluesforCa but not forC0.I8 Chestnutand Phung pointed out that the N M R chemical shieldings of glycinedipeptide. computed with the C I A O method, are affected by intra- and intermolecular hydrogen bonding. Furthermore, they showed that an NMR-shift computation that uses large basis sets for the atoms of interest and small basis sets for all other atoms (the 'locally dense" approach) can give acceptable The molecular geometries that are used in the N MR-shift calculations may be obtained either from ab initio calculation^^^^^^^^^^ or from crystal structures.15 Wechose the simplest aminoacid, glycine (1 ),as well a s glycine amide (2). because it contains the amide moiety found in all peptides for thisstudy. W e haveevaluated thedependenceof the N M R chemical shieldings on the conformations of 1 and 2
(4. ,,
1
2
employingboth CIAO-SCF and GIAO-MP2. The usefulnessof such knowledge for conformational assignments was shown by (12) Quart. H.:Ach. M.: Kindcrmann. M. K.; Radcmaehcr. P.:Schindlcr. M. Chrm. Et?. 1991. 126. 503. (33) Imarhiro. F.; Maruda.Y.; Honda. M.;Obara.S. J . Cho"oe.. Perkin rronr. 2 1993. 151s. (34) De Dios. A. C.: Pearson. J. G.:Oldfield. E. Science 1993,260, 1491 (35) De Dior. A . C.; Pearson. J. G . :Oldfield. E. J. Am. Chem. Soc. 1993, 115. 9169. (36) Laws. D. D.; de Dim. A. C.; Oldfield. E. J . Eiomol. NMR 1991. 3. 601. (17) Jiao. D.: Barfield. M.: Hruby. V. Mogn. Reson. Chem. 1993.31.75. (38) J i m . D.: Barfield. M.: Hruby. V. J. J . Am. Chrm. Sor. 1993. 115. 10881. (39) Chestnut. D. E.: Phung. C. G. C h m . Phyr. LPlt. 1991. 183. 505. (40) Chestnut. D. E.: Phung. C. G . In Nuclear Magnelic Shieldings and Mokrulor Srrurture: Torrcll. J. A.. Ed.; Kluwer Academic Publishers: Dordrecht. The Netherlands. 1993.
(4I)Chcstnut.D.B.:Rurilaski.B.E.:Mmrc.K.D.;Egolf.D.A.J.Compur. Chem. 1993. I I . 1364. (42) SchPfcr. L.; Newton. S. Q.:Momany. F. A,; Klimkowski. V. J. T H E O C H E M 1991. 232. 215. (41) Bdhm. H.-J.; Brcde. S. J . Am. Chrm. Soc. 1991. 113. 7129. (44) Kollman. P. A,: Gould. 1. R. J . Phyr. Chrm. 1992, 96. 9255. (45) Schalcr. L.: Newton. S. Q.: Ming. C.: Peelers. A,; Van AIsenoy. C.; Wolinski. K.; Momany. F. A. J. Am. C h o n Soc. 1993. 115. 281.
Figure 1. Definition of the backbone angler d and +.shown for an alanine residue(Q= = 180O). ThedihedralangleCO-N-C.-COisdcsignated d. and thc dihedral angle N-C.-Co-N is designated +. The eclipsed conformer has d = Oo and = 0'. Rotation to the right is counted positive.
+
+
Buchanan. Morat. and Kirby.'6 Their C I A O computations of ethylene glycol revealed that 6 'IC changes over a range of 8 ppm when the torsional angle between the twocarbon atoms ischanged in 20-deg increments going from Oo to 1 8 0 O . Comparison with experimental N M R data confirmed their structural assignment for an 18-crown-6 ether derivative. The backboneconformationofpeptidesisdefinedby theangles $ and q. The dihedral angle N-C.-Co-N is called $,and the dihedral angle Co-N-C,Co is called $3' By definition. the eclipsed conformer has $ = 'O and $ = Oo. Rotation to the right iscountedpositive. Figure I showsthesedefinitionsforanalanine residue. For both $ and IP. several values exist that correspond to known minima structures for peptides. These define allowed regions in a Ramachandran plot.4' For I and 2 the torsional angle, $. which we used a s the reaction coordinate. was defined as the dihedral angle N-C.-Co-Oo~ for 1 and N-C.-Co-N for 2, in analogy to the backbone angle $ in peptides. The N M R chemical shieldings of I and 2 were evaluated a t theSCFlevelof theorywith theGlAOalgorithmas implemented in TX90 for each increment of $ of IO". In addition, GIAOMP2 shifts were computed with the A C E S 2 program48for the MP2/6-3IG8-optimized structures of both molecules with $ = Oo. 60°. and 120O. Since only the effect of $ was investigated, the influence of $ on the NMR chemical shifts is not known. Moreover, since the amino nitrogen in I and 2 is spl-hybridized and not planar a s in a peptide. some additional influence. that is not found in proteins.cannot beexcluded. However,our results indicate that the shifts of atoms that do not belong to the amino group are only moderately affected by changes in the orientation of the amino hydrogens. The questions we are interested in answering are ( I ) What is the magnitude of the changes in chemical shielding for the various atoms in our model compounds? (2) Is it sufficient to calculate the chemical shifts at the S C F level of theory, or d o correlated methods (CIAO-MP2) givedifferent results? (3) What level of theory should be used for the geometry optimizations? (4) Will the structures of our simple molecules with a dihedral angle $ that corresponds to a a-helix or a &pleated sheet show the same difference in thechemical shielding a s determined experimentally for peptide^?".'^ ( 5 ) To what extent does the relative position of thecarboxyl orcarbamidegroupinfluence the relativechemical shieldingand thedifferenceintheNMRchemicalshiftsbetween the diastereotopic protons a t the methylene carbon of the glycine moiety? This is of interest. because a correlation between the (46) Buchanan. G . W.; Moral. C.: Kirby. R. A.:Tre. J. S. Con. J . C h m 1991. 69. 1964.
(47) Ramachandran. G.N.: Ramakrirhnan. C.; Sarirckharan. V. J . Mol. B i d 1961. 7. 95.
1481 Stantan. J. F.: Gaurs. J.: Watts. D.: Laudcrdalc. W. 1.: Bartlctt. R. J. i h c ' A c E s ii ProGam sy;tek. ~ n rj. . Ch& 1992. s26.879. (49)Spera. S.: Bax. A. J . Am. Chem. Soe. 1991. 113. 5490. (50) Reily. M. D.; Thanabal. V.: Omccinrky, D. 0. J . Am. Chem. Soe.
Quantum
1992. 114. 6251.
Conformation and Theorefical Chemical Shi/ts
J . Am. Chem. SOC..Vol. 116. No. 9. 1994 3969
latter and the backbonestructureexists. which allowsa structural assignment."
Table 1. Absolute Chemical Shielding for Some Atoms of Glycine ( I ) and Glycine Amide ( 2 ) O a n d e 1L
Computational Details Thegeomctria used in the NMRchemical shift studies wereoptimized using theself-consistent-field(SCF) analyticgradient method CADPAC 5.1.sz Harmonicvibrationalfrequenciawerecomputed withSCFanalytic second-derivativemethodr. Saddlepointswcrcloc'ated usingtheSchlegel method." Forglycine ( I ) thedihedral angle NH2-C.-Co-Oo~and for glycine amide (2) the dihedral NHx-C.-Co-N.,id, were used as the reaction coordinates. The potential energy surface, local minima. and transition states were computed fully. An RHF/6-3IG* structure was minimized for each dihedral angle increment of IOo. I n addition. a structure for J. = 0'. 60'. and 120° was optimized at the MP2/6-31G* level with Gaussian 92.y The SCF NMR chcmical shift calculations employed theTX9O program"with its implementationoftheGIAOz1-14 method and the standard 6-31 IG" basis set." The MP2 NMR shift calculations were performed with the ACES11 program pa~kagc~6.1'.~8 and employed the same basis set. The calculations were carried out on IBM RS-6000 workstations at the Center for Computational Quantum Chemistry and an I n d i p I r i s at the Department of Chemistry. University of Georgia. Athens. Geomctryoptimizations (RHF/6-31G1) twkca. 1-2 h. CIAO-SCFshift calculations 70 min, and GIAO-MP2 shift calculations 10 h each on an IBM RS-6000/580workstation. For an IBM RS-60M)/530 workstation these bcnchmarks must be multiplied by a factor of 2.5.
Results and Discussion Geometries. In agreement with recent result^.^^.^' the global minimum of glycine has C, symmetry and J. = 180'. A second minimum, a t a torsional angle of . ' 0 has C, symmetry and is I .9 kcal/mol higherinenergy. Theglobal minimum forglycineamide is located a t J. = 165". A second minimum, I .3 kcal/mol higher in energy, was found a t 2'. T h e structure with J. = 180° has Ct symmetry and resembles a distorted version of the global minimum. The main difference is that for J. = 165' the two hydrogens bound to the amino nitrogen form hydrogen bonds of a different length with the carbonyl oxygen. Up t o J. = 1 IOo a structure with one amino hydrogen oriented anti-coplanar to the c a r b o n s a r b o n bond is lowest in energy (2s). In the remaining structures both hydrogens form hydrogenbonds with thecarbonyl
C.
methodb
I
111
00
Glycine 153.2 150.6 150.3 20.9 9.5 27.5 -57.7 -88.2 -49.9
60'
I200
151.9 149.9 149.0 22.5 10.9 28.4 -75.6 -108.6 45.1
153.7 151.4 151.3 19.5 7.4 25.1 -54.5 -85.9 46.3
149.8 147.5 146.0 18.7 7.7 27.9 -87.2 - I 14.0 -81.8 180.6 171.6 179.8
150.9 148.7 148.3 18.3 7.3 26.9 42.0 -67.9 -39.8 176.9 168.2 177.5
Glycine Amide C.
I II
153.0 I50.5
111
CO
I II
I5O.I 20.0
10.1 30.5 41.7 -63.8 -38.7 179.6 170.9 179.8
111
oc-3
I I1 111
N.,id.
I II 111
The absolute chemical shielding is very dependent on the geometry and electron correlalion lor all atoms crccpt C.. However. the relative change in the chemical shielding with rspect to the torrionnl angle is almo\lthcsamcfor I . II.and 111. Thirruggcrtsihaioncethechcm~cal shifts have becncomputcdat a high l e ~ e l otheory f foroncconformattan. the chemical shifts for other conformations can bc obtamed unh lesq C X I C I ) I I ~ C computations. O t I ) CIAO-SCF 6-31 IG'*/ 1RtlFJ6-3lG.. ( I l l GIAO-SCt/6.3I IG**//MP2/6~3IG'. and (111) GIAO-MP2,6. 31 IC.', /MP2/6-31GV.
oxygen (Zb).
4
