J. Phys. Chem. 1982, 86,3956-3962
3956
C-terminal of the neutral molecule. The peptide linkage of the dipeptide, however, has considerable double bond character owing to the resonance structures.
Thus,as a first approximation, the carbonyl of the peptide bond may be considered to be similar to that of the amino acid zwitterion. From previous calculations on Gly-Gly, the order of ionization of 1s electrons was1' 0: N:
IPC terminal IPpeptide
'IPpeptide 'IPN
bond
bond
terminal
Therefore, the proton affmity of the oxygen at the peptide bond is predicted to be greater than that of the carboxylate group. Conversely, protonation at the nitrogen of the peptide bond is predicted to be less favorable than that at the N terminal. Hence, given the assumption above and the calculated proton affinities of the nitrogen of neutral glycine and the oxygen of the glycine zwitterion, the interaction energy of a proton with the peptide bond would be expected to be greater at the oxygen. This conclusion, arrived at through the use of eq 1and the present work on the amino acid glycine, is consistent with experimental fmdings that 0 protonation is favored during protonation of the peptide linkage2 and the limited calculations on Gly-Gly presented above.
A similar analysis of the zwitterionic dipeptide cannot be performed here as there is only one nitrogen capable of protonation and no trend can be established. However, in a polypeptide where the central bonds are not significantly influenced by the charged terminals, the conclusions drawn above may be applicable. In a previous theoretical investigation,' it was found that the inductive effects of the side chains in alanine, serine, cysteine, and threonine influenced the proton affinity relative to glycine. Electron donating groups (e.g., -CHJ tended to increase the interaction energy of a proton with an attack site while electron-withdrawing groups (e.g., -OH) had the opposite effect. From the relationship given in eq 1,therefore, the ionization potential of, for example, the lsNof the peptide bond of Gly-Ala should be calculated (or determined) to be less than that of Gly-Gly. Results from a previous theoretical study predict this to be the c8se.l' It must be stressed that quantitative results for peptides cannot be made on the limited amount of data presented here, but only qualitative trends of protonation based on the results of theoretical studies of amino acids. The use of eq 1has resulted in at least a limited number of predictions which have been shown to be accurate. Theoretical calculations may therefore be useful in determining both proton affinities and preferred sites of attack in molecules containing oxygen and nitrogen atoms, such as amino acids and peptides. This approach may be especially important in cases where proton affinities are difficult to determine experimentally.
Ab Inltlo Self-Conslstent Field Studies of the Peptldes Gly-Gly, Gly-Ala, Ala-Gly, and GIy-Gly-Gly Lance R. Wrlght and Raymond F. Borkman" School of Chemlsby, &wg& Institute of Technoey, Atlanta, GsOrgla 30332 ( R w h d : January 26, 1982; In Flnal Form: June 21, M82)
Ab initio self-consistentfield calculations have been performed on the three smallest dipeptides: glycylglycine, glycylalanine, and alanylglycine. SCF energies are reported for the neutral and zwitterionic forms of the molecules by using a 2slp Gaussian basis set. The quality of this basis set was tested by calculating a conformationsurface for the model compound N-formylglycylamideand comparing this map with those from previous calculations in the literature. The energy surfaces were found to be parallel to within a few kcal/mol. The barrier to rotation about the peptide bond was computed for each of the dipeptides studied; these values ranged from 22.9 f 0.4 kcal/mol for the neutral species to 23.9 f 1.8 kcal/mol for the zwitterionic forms. All of the neutral dipeptides, and also the zwitterions +Gly-Ala-and +Ala-Gly-were found to be most stable with the peptide bond in the trans orientation. The cis conformation, however, was calculated to be preferred in the +Gly-Gly-zwitterion. In addition to determining the energy minimum associated with rotation about the peptide bond, rotation barriers were determined for the other torsion angles of neutral Gly-Gly. Six metastable conformations of Gly-Gly were found which were less than 4 kcal/mol above the most stable conformation. Dipole moments and ionization potentials were also computed for each of the dipeptides; the average values for these properties were calculated to be 2.8 f 0.1 D and 10.7 f 0.1 eV for the neutral molecules and 26.0 f 1.4D and 5.2 f 0.2 eV for the zwitterionic species, respectively. Finally, SCF energies were calculated for the neutral and zwitterionic forms of the tripeptide Gly-Gly-Gly in the extended trans conformation.
Introduction The conformations of peptides play a fundamental role in determining the structures and hence the biological properties of proteins.' As a result, numerous theoretical (1) G.N.Ramechandran and V.Sasisekjaran,Adv. Protein Chem., 23, 283-438 (1968). 0022-3654182120863956$0 1.2510
investigations have been performed in an effort to characterize the peptide bond unit. In vacuo calculations allow one to determine conformation maps of molecules free of bulk medium effects and can be used to further the understanding of the structure of proteins. In many previous studies, "model peptides" of t h e type RCONHCH,CONHR, where R is usually a hydrogen or 0 1982 American Chemical Society
Ab Initio SCF Studles of Dipeptides
methyl group, were examined theoretically. Due to the large size of these model compounds, empirical and semiempirical calculations have been the most common theoretical methods used to determine the conformation energie~.~-'~ These calculations are dependent upon experimentally determined parameters, however, and as such may not provide reliable predictions of in vacuo potential surfaces. Consequently, nonempirical theoretical methods have also been used recently on model peptides; these include ab initio self-consistent field theory1"l9 and the use of molecular fragments.20v21 While there have been numerous calculations on the conformations of the above-mentioned model peptides, there have been no theoretical studies on the conformations of peptides composed of sequences of the 20 biological amino acids, the simplest of these being the dipeptide glycylglycine, NH2CH2CONHCH2COOH.These dipeptide conformation studies are of interest for their own sake, but it may also be noted that the dipeptides provide a reasonable model for the behavior of the ends of long peptide chains where the -(RICH- group is flanked by only one peptide bond. This is in contrast to the model compounds, such as NFGA, which model the central regions of peptide chains. It was of interest, therefore, to compare the conformation surface of glycylglycine with those obtained from model peptide studies. In the current work are presented the results of ab initio self-consistent field (SCF) calculations on the conformations of the three smallest dipeptides: glycylglycine (Gly-Gly), glycylalanine (Gly-Ala), and alanylglycine (Ala-Gly);also included are preliminary calculations on the smallest tripeptide, glycylglycylglycine (Gly-Gly-Gly). SCF energies are presented for the nonionic and zwitterionic forms of the molecules; dipole moments, the ionization potentials calculated from Koopmans's theorem, are also given for the calculated stable conformations of the peptides studied. (2)J. Caillet, P. Claverie, and B. Pullman, Theor. Chim. Acta, 47, 17-26 (1978). (3)J. L. DeCoen and E. Raleton, Jerusalem Symp. Quantum Chem. Biochem. 5,41-9 (1973). (4)G. Govil and A. Saran, J. Chem. SOC. A, 3624-7 (1971). (5) A. Imamura, M. Kodama, Y. Tagashira, and C. Nagata, J. Theor. Biol., 10,356-69 (1966). (6)B. Maigret, B. Pullman, and M. Dreyfw, J. Theor. Biol., 26,321-33 (1970). (7)A. K.Mitra, Int. J. Pept. Protein Res., 11, 166-78 (1978). (8) K. Niehikawa, F. A. Momany, and H. A. Sherage, Macromolecules, 7,797-806 (1974). (9)A. Pullman and H. Berthod, C. R. Acad. Sci. Paris, Ser. D,277, 2077-9 (1973). (10)B. Pullman and B. Maigret, Jerusalem Symp. Quantum Chem. Biochem., 5, 13-39 (1973). (11)B. Pullman and A. Pullman, Adu. Prot. Chem., 28, 347-526 (1974). (12)V. Renugopalakrishnan, S. Nir, and R. Rein, Jerusalem Symp. Qwntum Chem. Biochem., 8, 109-33 (1976). (13)K. Sundaram and A. R. Srinivaean, Int. J. Quant. Chem., 12, 671-81 (1977). (14)S. S. Zimmerman and H. A. Sheraga, Biopolymers, 17,1871-84 (1978). (15)A. T.Hngler, L. Leiserowitz, and M. Tuval, J.Am. Chem. SOC., 98,4600-12 (1976). (16)I. H. Hillier and B. Robson, J. Theor. Biol., 76, 83-98 (1979). (17)D. Peters and J. Peters, J. Mol. Struct., 53, 103-19 (1979);62, 229-47 (1980);64,249-63 (1980). (18)B. Robeon, I. H. Hillier, and M. F. Guest, J. Chem. SOC.,Faraday Tram. 2,74,1311-8 (1978). (19)S. Scheiner and C. W. Kern, J. Am. Chem. SOC.,100, 7539-48 (1978). 95, (20)L.L. Shipman and R. E. Christoffersen, J. Am. Chem. SOC., 1408-16 (1973). 95, (21)L. L. Shipman and R. E. Christoffersen. J. Am. Chem. SOC.. 4733-44 (1973).
The Journal of phvsical Chemistry, Vol, 86, No. 20, 1982 3Q57
The present study is the second in a series of calculations on amino acids and peptides with ab initio SCF techniques; the first in this series reported on the structure and properties of the five amino acids glycine, alanine, serine, cysteine, and threonine.22 The conformation calculations presented herein are believed to be the first on biological dipeptides obtained by using ab initio techniques. To the authors' knowledge, only one other ab initio calculation exists on a dipeptide: Ryan and in their study of the bonding in glycine, used SCF and limited CI methods on the +Gly-Gly- zwitterion. Only one energy point was computed, however, with the dipeptide in the extended trans form, which was presumed by them to be the most stable orientation of the molecule.
Method of Calculation The molecular orbital calculations were performed on a Control Data Cyber 70, Model 74, computer. The HONDO (Version 5.0) program written by Dupuis et al.24was used for all calculations to obtain restricted SCF energies. A number of Gaussian basis sets were tested on the free amino acid glycine, including the STO-NG (N = 3-6) series, before initiating the conformation calculations on the dipeptides. A (6s3p/3s) Gaussian basis set contracted to [2slp/ ls], developed by Ditchfield, Hehre, and P0ple,2~ was chosen for the heavy atoms and hydrogen. This basis set gave the lowest SCF energy for glycine, as compared to the other basis sets tested, while retaining a reasonable computing time of 1600 CPU seconds per energy. Bond lengths and bond angles were taken from the standard values given by Pople and Gordon;26the C-0 bond length of the zwitterion was taken to be 1.29 A. Following IUPAC-IUB d on vent ion,^' the dihedral angles @I and $ are defined to be zero when the C' atoms are cis about the N-C" bond and the N atoms are cis about the Ca-C' bond, respectively; the dihedral angle corresponding to the peptide bond, o,is defined to be zero when the peptide is in the cis conformation. The neutral peptide possesses an additional dihedral angle: rotation of the hydroxyl group about the C'-0" bond. This angle is designated 6' and is defined here as zero when the 0'42'0"-H atoms in the cis conformation. Positive values for the dihedral angles are given for clockwise rotation about the bonds; these values range from -180 to +180°. Structures I and I1 depict the neutral and zwitterionic dipeptides studied in the present work including the dihedral angles as described above. These molecules possess a single peptide bond and two each of the torsion angle @I and $. Results N-Formylglycylamide. To ascertain the ability of the present basis set to accurately determine the conformations of the dipeptides studied, test calculations were performed on N-formylglycylamide (HCONHCH2CONH2,hereafter referred to as NFGA) in order to compare with the previous ab initio calculations of Robson et a1.18 who used a (22)L. R. Wright and R. F. Borkman, J. Am. Chem. SOC.,102,6207-10 (1980). (23)J. A. Ryan and J. L. Whitten, J. Am. Chem. SOC.,94,2396-400 (1972). (24)M.Dupuis, J. Rys, and H. F. King, J. Chem. Phys., 65, 111-6 (1976). ~~(25)R. Ditchfield, W. J. Hehre, and J. A. Pople, J. Chem. Phys., 52, 5001-7 (1970). (26)J. A. Pople and M. Gordon, J. Am. Chem. SOC.,89, 4253-61 (1967). (27)IUPAC-IUB Commision on Biochemical Nomenclature, Biochemistry, 9,3471-9 (1970). -I
3958
The Journal of Physical Chemistry, Vol. 86, No. 20, 1982
Wright and Borkman i180
H
HH
I 90
0'
+ HI
li,
I
H
0'
s "I1
larger Gaussian basis set. SCF energies were computed at 30° intervals of 4 and $. Figure 1presents the energy contour diagram resulting from these calculations;contour lines are expressed in 1kcal/mol intervals relative to the most stable conformation, 4 = H E W 0 and $ = f180'. The regions defined by parallel lines and hatching are 10 and 20 kcal/mol, respectively, above the same reference point. This contour diagram is similar to that of Robson et al.18 and also to the one generated by Peters and Peters1' who used a STO-3G basis set. Table I compares some specific values for the SCF energies of NFGA obtained by using the present basis set with the 3s2p Gaussian basis set of Robson et al.18 Also tabulated are the results of the 4-31G basis set calculations of Hillier and Robson16 on Nformylglycyl-"-methyhide. The conformation surfaces are seen to agree within a few kcal/mol with one exception. The present work calculates a 7 kcal/mol lower value for the barrier to rotation about the C"-C' bond (see Table I, = 180°,$ = OO). This discrepancy may be a result of the different initial orientations of the amine hydrogens between the present work and that of Robson et a1.18 Only two unique minima are found in the potential surface of NFGA, denoted by the symbols and A in Figure 1. The most stable conformation is predicted to be the extended form which is characterized by a fivemembered hydrogen-bonded ring; this form is designated as Cs (w). A secondary minimum occurs at 4 = -goo, $ = 60°, giving rise to a seven-membered hydrogen-bonded ring, the C, structure (A). The existence of both of these hydrogen-bonded structure has been experimentally confirmed in solution.28 Gly-Gly, Gly-Ala, and Ala-Gly. The SCF energies for the neutral and zwitterionic dipeptides in their most stable conformations, as well as for the glycine and alanine monomers, as presented in Table 11. Also given are the SCF energies for the neutral and zwitterionic forms of the tripeptide Gly-Gly-Gly; these energies are for the tripeptide in the extended trans conformation, the only orientation studied in the present work. The gaseous zwitterions of (28) M.Avignon and J. Lascombe, Jerusalem Symp. Quantum Chem. Biochem., 5,97-105 (1973).
-90
iiao 2180
-90
0
+ Figure 1. SCF energy contour diagram of N-formylglycylamide. Contour lines are expressed in 1 kcal/moi intervals about the most stable conformation, 4 = f180°, fi = f180° (m). The regions designated by parallel lines and hatching are 10 and 20 kcal/mol above the same reference point. Secondary minima occur at 4 = -goo, = 60' and symmetric point 4 = goo, $ = -60' (A).
+
TABLE I : Comparison of Ab Initio Conformation Results on N-Formylglycylamide with Previous Calculations
dihedral angle: deg @ - 90 - 90
$
energy relative to the most stable conformation, +180",j, = +180", = - kcal/mol @
this work
3s2pb
4-31GC
120 90 60 30 0
4.7 4.1 3.8 3.2 2.1 - 90 3.3 2.7 1.4 - 90 4.5 5.1 6.3 - 90 5.5 7.8 7.5 - 60 - 60d 8.9 11.0 9.6 -120 -120 8.1 9.9 -120 i180 3.9 4.5 +180 0 13.0 20.4 +180 - 60d 7.5 8.5 7.6 t180 -120 6.1 6.5 i180 t180 0.0 0.0 0.0 -120 120 5.0 4.6 3.5 -150 150 2.2 2.9 0 90 21.7 21.9 19.2 - 60 60e 25.7 22.8 25.3 Two energy minima occur in the conformation surface: one at 6 = -go", j, = 60" (the C , structure) and the other at 6 = *180",$ = t180" (the C , structure). These conformations are denoted in Figure 1 by the symbols A and .,respectively. Reference 18. Calculations on model from ref 16. compound N-formylglycyl-N'-methylamide Previous calculations used $ = - 50". e Previous calculations used $ = 50".
the dipeptides were calculated to lie more than 100 kcal/mol above the neutral species, and the tripeptide zwitterion energy was calculated to be about 120 kcal/mol above the neutral molecule. These energy difference are about 25 kcal/mol per peptide bond greater than the corresponding values for the free amino acids. The neutral dipeptide Ala-Gly was calculated to be only slightly more stable (less than 0.2 kcal/mol) than its isomer, Gly-Ala. In the zwitterionic form, however, the dif-
The Journal of phvslcal Chemistry, Vol. 86, No. 20, 1982 3959
Ab Initio SCF Studles of Dipeptides
TABLE 11: Calculated SCF Energies, Dipole Moments, and Ionization Potentials of the Neutral and Zwitterionic Peptides and the Glycine and Alanine Monomers in the Gas Phase neutral zwitterion energy: au
dipole moment, D
IP,b eV
energy,a au
dipole moment, D
IP,b eV
AE,~ kcal/mol
1.61 1.60 2.88 2.70 2.79 4.32
11.11 11.08 10.75 10.75 10.74 10.22
-280.547 57 -319.265 45 -485.717 73 -524.429 0 5 - 524.432 79 -690.009 67
12.74 12.40 24.60 26.75 26.60 42.06
6.71 6.72 5.33 5.12 5.11 4.31
76.3 74.8 102.0 103.8 101.7 119.5
- 280.669 23
glycine alanine Gly-Gly Gly-Ala Ala-Gly Gly-Gly-Gly
-319.384 74 -485.880 35 -524.594 56 - 524.594 84 -690.200 1 2
With the molecule in the planar trans conformation for all peptides except Gly-Gly zwitterion which is planar cis. Calculated from Koopmans' theorem and the 8%rule. The gas-phase difference between the neutral and zwitterionic species, E('M-) - E(M).
I'
-
30
-e,
Y
-
15
'1- 20
E
0 Y
10
> c3
W
Z
w
i
-
0
v
6LT
t
25 -
20
1 '.
'I
15
-
(11
w 70z w
5 0 -180
-90
0
90
180
5t I
0
Figure 2. SCF energy variation as a functlon of w (rotation about the peptide bond with 4 = J, = 180') in neutral (-) and zwltterbnic (- -) Gly-Gly. Energies, in kcal/mol, are given relatlve to the most stable conformation (trans for Gly-Gly and cis for +Gly-GIy).
-180
I
I
1
-90
0
90
180
0
Flgure 4. SCF energy varlatbn as a function of w (rotation about the peptide bond with 4 = J/ = 180') in neutral (-) and rwltterbnic (--) Ala-Gly. Energies, in kcai/mol, are given relative to the most stable conformation (trans for both Ala-Gly and 'Ala-Gly-).
TABLE 111: Calculated Energy Differences between t h e Trans and Cis Isomers of the Neutral and Zwitterionic Dipeptides and the Calculated Bamers to Rotation about the Peptide Bond
A
a, 2 5 -
1 ' . 20 0
dipeptide
0
Y
>
15-
Gly-Gly 'Gly-Gly Gly-Ala 'Gly-AlaAla-Gly Ala-Gly -
(3
w w z
10-
W
+
-180
-90
0 m
90
180
Figure 3. SCF energy varlatbn as a function of w (rotation about the peptide bond wlth 4 = J, = 180') in neutral (-) and zwltterbnic (- -) Gly-Ala. Energies, in kcai/mol, are glven relative to the most stable conformatlon (trans for both Qly-Ala and 'Gly-Ala-).
ference in energy between these peptides was increased by a factor of 10 to 2.3 kcal/mol, with the +Ala-Glyzwitterion predicted to be the more stable of the two. Ionization potentials, calculated through the use of Koopmans' theore" and the 8% rule,30and dipole moments determined for the neutral and zwitterionic forms of the peptides, are also given in Table 11. For the neutral (29)T.Koopmans, Physica, l, 104-13 (1934). (30)C.R. Brundle, M.B. Robin, and H.Busch, J . Chem. Phys., 53, 2196-213 (1970).
AEdiff,(l kcal/mol 1.3
- 1.4 5.6 2.4 4.2 0.7
G u t .9
kcal/mol 23.2 25.7 22.4 23.1 22.9 23.0
Difference in energy between the trans and cis conformations, E(cis) - E(trans). Minimum barrier to rotation about the peptide bond.
molecules, these properties remained relatively constant, with only a slight increase in the dipole moments and a decrease in the ionization potentials in going from the free amino acids to the di- and tripeptides. The zwitterionic forms, however, displayed vastly different values for the computed dipole momenta and ionization potentials of the peptides when compared to the amino acids. Figures 2-4 present the SCF energy vs. angle of rotation about the peptide bond for each of the dipeptides studied, in both the nonionic and zwitterionic forms. For each of the neutral dipeptides, the minimum energy occurred at w = f180°, the planar trans conformation. Local minima occurred at w = ' 0 for Gly-Gly and w = *20° for Ala-Gly and Gly-Ala, respectively. The +Ala-Gly- and +Gly-Alazwitterions also had minimum energies at w = *180° and
3060
TABLE IV: Calculated Dipole Moments and Ionization Potentials of the Stable Conformations of Gly-Gly dihedral angle,a conformation 1 2 3 4 5 6 7
Wright and Borkman
The Journal of Physical Chemistty, Vol. 86, No. 20, 1982
$ I
180 180 180 180 180 180 180
w
180 0 180 180
&
180 180 -90 180 180 -90 0 -90 0 180
dipole A E , ~ moment,
deg
IP,~
$ z
kcal/mol
D
eV
180 180 180 0 15 180 0
0.0 1.3 1.4 2.1 3.4 3.6 3.7
2.88 3.35 3.02 3.18 2.82 3.33 2.67
10.75 10.63 10.76 10.75 10.72 10.76 10.61
fil axis when the peptide is cis. From the preceeding results, it has been determined that there exist two metastable conformations of neutral GlyGly which lie less than 1.5 kcal/mol above the extended form (1):cis Gly-Gly (2) and trans Gly-Gly with 42= -90° (3). These conformations are depicted in structures III-V, 0
e,
a = 180" and e = 0" assumed. Energies given are relative t o conformation 1. Calculated from Koopmans' theorem and the 8% rule.
local minima at w f20°, respectively, although the local minima were energetically much closer to the absolute minima in the zwitterions than in the neutral molecules. In the +Gly-Gly-zwitterion, however, the absolute minimum energy occurred at w = Oo, the planar cis conformation, with a local minimum at w = f180°. These data are summarized in Table I11 together with the barriers to rotation about the peptide bond for each of the dipeptide species. In addition to rotation about the peptide bond, the energy variation vs. the remaining dihedral angles of Gly-Gly was studied to determine these barriers to rotation. Prior to investigation of the central bonds, the rotation barriers of the N- and C-terminal groups (the amine and hydroxyl, respectively) were determined. From previous calculations on amino acids, these groups were calculated to be most stable when $1 = 180° and 0 = Oo, respectively.n This was also found to be the case for the dipeptide Gly-Gly. The barrier to rotation about the N1-C1" bond (&) was determined to be 7.3 kcal/mol, which compares favorably with the value of 8.1 kcal/mol calculated by Wright and Borkman for free glycine;22the rotation barrier for the hydroxyl group (e) was 4.6 kcal/mol. For all subsequent calculations on the neutral dipeptide, these groups were assumed to be in their most stable orientations. As shown above, the most stable conformation of neutral Gly-Gly with respect to the peptide bond is trans, with the cis orientation lying less than 1.5 kcal/mol above it. These conformations will subsequently be referred to as (1)and (2), respectively. Rotation about the remaining bonds was considered with the dipeptide initially as both trans (1) and cis (2). Whether Gly-Gly is in either conformation (1) or (2) should not affect the energy associated with the variation of & from 0 to f180°. This was found to be true; the barriers to rotation of the carboxylate group about the C2"-C; bond were 5.6 and 5.5 kcal/mol for (1)and (2), respectively. The resulting conformations are designated here as (4) and (7), respectively. For variation of &, however, with Gly-Gly in the trans form, there is considerable repulsion between the 0' atoms whe C#I~ = Oo, resulting in a rotation barrier of 264.0 kcal/mol. While in the cis conformation, this barrier is reduced to 49.2 kcal/mol. In both situations, however, metastable conformations exist when $2 = -9OO; these are denoted (3) when the peptide is trans and (6) when in the cis orientation. Rotation about fil required 7.6 kcal/mol with the dipeptide in the trans conformation. The corresponding value for the cis configuration was calculated to be 90.8 kcal/mol; the difference between these rotation barriers was attributed to the steric interference the amine group encounters with the Czahydrogens as it rotates about the
H0
S T " I11
I0
.5l"mv
cm,
= -goo, qJ2 = 180')
respectively. The dihedral angles of the latter conformation were subsequently varied in a further effort to determine stable orientations of the dipeptide. Rotation about the peptide bond of (3) in the positive direction was calculated to require 23.9 kcal/mol, slightly more than the 23.2 kcal/mol calculated for Gly-Gly in the extended trans form (1). The barrier to rotation in the negative direction was computed to be 25.3 kcal/mol. The cis conformation (6) and computed to be 2.2 kcal/mol less stable than the trans (3). The barriers to rotation of the carboxylate group (fi2) in the positive and negative directions of (3) were calculated to be 3.5 and 3.1 kcal/mol, respectively; these values were considerably lower than the 5.6 kcal/mol required with the dipeptide in the trans form (1). In addition, a local minimum was found to exist with fi2 = 1 5 O , designated here as (5). Variation of from 0 to f180' in (3) resulted in a rotation barrier of 9.3 kcal/mol. This compares to the 7.6 kcal/mol barrier of Gly-Gly in its most stable conformation (1).
There have been, therefore, calculated to exist in the neutral dipeptide Gly-Gly six metastable orientations which lie less than 4 kcal/mol above the most stable, the extended trans peptide (1). These conformations are summarized in Table IV and are given in order of decreasing stability, with energies relative to (1). Four of the five most stable have a trans peptide bond: (11, (3), (4), and ( 5 ) ; the remaining have the cis configuration. Also included in Table IV are the computed dipole moments and ionization potentials calculated from Koopmans' theorem and the 8% rule.
The Journal of Physical Chemistry, Vol. 86, No. 20, 7982 3961
Ab Inltlo SCF Studies of Dlpeptldes
TABLE V: Calculated Barriers to Rotation in the Neutral Dipeptide Gly-Gly conformationo A E , ~ dihedral final kcal/mol angle initial
1/11
1 1 2 3
W
1
W
3 3
@I $ 1
dJ. 7
'
W
@a
1 2 1
$2
2
$2
1
@Z @2
$ 2
1/12 1/12
2 3 3
1
7.3
1 2 3
7.7 90.8 9.3
2 6 6
23.2 23.gC 25.3d
3 6 1 2
4 7 5 5
1.8 2.9 264.0 49.2 5.6 5.5 3.5c 3.1d
1
-180
-90
0
90
180
9 Flgure 5. SCF energy varlatlon as a function of J/ in NFGA (-) and O l y G y (- -) with @ = f 180'. Energies, in kcal/md, are given relatlve to the most stable conformation (C, for NFGA and (1) for Gly-GIy).
1 1 4.6 a Conformation numbers refer to those given in Table IV. Energies given are relative to conformation 1. Rotation about dihedral angle in the positive direction. Rotation about dihedral angle in the negative direction. 8
Presented in Table V are the barriers to rotation which have been computed for each of the torsion angles in Gly-Gly. With the exception of the cases where there were intramolecular repulsions (noted earlier), the rotation barriers did not vary greatly within each group, despite the difference initial and f i i orientations of the molecule.
' - rl -180
I
I
I
I
-90
0
90
180
9
Discussion Theoretical calculations, in particular ab initio SCF methods, have provided valuable information on the allowed and disallowed orientations of proteins through the use of conformation surfaces of model peptides. These model peptides, however, are not accurate representations of biological dipeptides, or the terminal ends of polypeptides. In the model peptides, the torsion angles @ and $ are central to the molecule with a peptide bond adjacent to each. This is the situation which exists throughout most of the protein. However, at the terminal ends of the polypeptide, and in the dipeptide, only one peptide bond lies adjacent to the @,$pair. This has the effect of reducing the interdependence between @ and $. The difference between the model peptides and dipeptides can be illustrated by examining the rotation about the dihedral angle $ at fixed values of @. Potential energy curves for the variation of $ with @ = f180' and @ = -90" are presented in Figures 5 and 6, respectively, for the model peptide NFGA and the dipeptide Gly-Gly. For NFGA, the rotation of $, with @ = flWO(Figure 5), from ita most stable value of f180' results in a strongly disallowed region in the conformation map; the calculated rotation barriers vary from 13 kcal/mol in the present work to almost 32 kcal/mol for another model peptide, 2-formamidoacetamide." For Gly-Gly, however, rotation about q1required less than 8 kcal/mol. In both cases, the only stable conformation found is the C6 structure (@ = *180", J, = f180'). Variation of $2, however, resulted in two minima in the potential curve, conformations (1)(the C5structure) and (4). The minimum in the potential energy curve for NFGA in Figure 6 is the C7structure (@= -goo, $ = 60'). This conformation is a result of an intramolecular hydrogen bond formed between Ni+l-Hi+l and Ci-l'=Oi-{.ll This conformation lies 3.3 kcal/mol above the C5 structure (4
Flguro 6. SCF energy variation as a function of $ In NFGA (-) and Olyoly (--) with @ = -90'. Energies, in kcal/mol, are given relative to the most stable conformation (C, for NFGA and (1) for Gly-GIy).
= f180°,$ = f180'; see also Figure 5 ) . The dipeptide, however, cannot form the C7 structure as defined, and, as a result, no minimum is observed in this region. There are, however, two minima associated with the variation of $2 (@= -goo): conformations (3) and (5). Conformation (3) is predicted to be more stable than ( 5 ) by 2.0 kcal/mol. The resulta depicted in Figures 5 and 6 clearly illustrate the inability of the model peptide to accurately represent the dipeptide Gly-Gly in low-energy regions of the conformation surface. The only point in common to both NFGA and Gly-Gly is the planar trans orientation of the molecule, the C5 structure. In the determination of the barrier to rotation about the peptide bond, previous theoretical and experimental studies have usually limited their work to formamide and ita methylated deri~atives."*~l-~ The rotation barrier for these molecules about the peptide bond was determined to be 20 f 3 kcal/mol, the differences being dependent upon the theoretical method used and the experimental conditions.l' In the present work, the peptide bond rotation barrier was calculated to be about 23 kcal/mol for each of the dipeptides, in excellent agreement with the formamide studies. (31)P. R. Andrews, Biopolymers, 10, 2253-67 (1971). (32)W.A. Hiltner and A. J. Hopfinger,Biopolymers, 12, 1197-1202 (1973). (33)A. S.Kolaskar, A. V. Lakshminarayanan, K. P. Sarathy, and V. Sasisekjaran, Biopolymers, 14,1081-94 (1975). (34)M. Perricaudet and A. Pullman, Int. J . Pept. Protein Res., 5, 99-107 (1973). (35)S. Scheiner and C. W. Kern, J . Am. Chem. SOC.,99, 7042-50 (1977). ~~
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The Journal of Physical Chemistty, Vol. 86, No. 20, 1982
Rotation about the N-C' bond requires significantly more energy than rotation about the Ca-N bond. This is due to the partial double bond which is formed between the C' and N atoms, illustrated by the resonance structures _ I
-a
^ I
Thus, the peptide bond unit is predicted to be most stable in a planar conformation. However, small deformations from the planar structure are predicted to require little energy. Scheiner and Kern,35for example, have investigated the flexibility of the peptide bond in N-methylacetamide using the PRDDO method and determined that only 2 kcal/mol was required for the peptide bond to vary f20" from its planar orientation. In the present work, variation of w by f20° in Gly-Gly in the trans conformation required 2.4 kcal/mol. In the cis orientation, however, this value is reduced by 0.4 kcal/mol, which suggests that out-of-planetwisting of the peptide bond is more favorable when the peptide is cis. This observation was also made by Perricaudet and Pullmanu in their ab initio study using methylated formamides as models for the peptide bond unit. The relative ease of the peptide bond to exhibit nonplanarity may be in part responsible for the calculated stable conformations of the Ala-Gly and Gly-Ala dipeptides when in the cis orientation as predicted in the present work. As w approaches O", the (?-methyl group of the alanyl residue encounters steric interference with the Ca hydrogens of the glycyl residue. This interference is great enough to cause the minimum in the potential surface to be shifted by 20°, resulting in a nonplanar cis conformation in these dipeptides. The large barrier to rotation about the peptide bond has been cited as a significant factor in the observation that the trans conformation is predominant in polypeptides, despite the relatively small difference in energy between the cis and trans isomers. This energy difference has been calculated for formamide and its single methylated derivatives (acetamide and N-methylformamide) to be less than 2 kcal mol, with the trans being the more stable in every c a s e i For neutral and zwitterionic Gly-Gly, the energy difference between the trans and cis forms is 1.3 and -1.4 kcal/mol, respectively (see Table 111). As in the formamide studies, neutral Gly-Gly was calculated to be most stable in the trans conformation; in the +Gly-Glyzwitterion, however, it is the cis orientation which is predicted to be the most stable. This may be due in part to the decreased distance between the positive and negative charges in the zwitterion when the dipeptide is cis. Thus, in the zwitterion the difference in energy between the trans and cis isomers is reduced by 2.7 kcal/mol. This effect was also observed for the other dipeptides studied, with the +Ala-Gly-and 'Gly-Ala- zwitterions stabilizing the energy difference between the trans and cis forms by about 3 kcal/mol. This stabilization, however, was not sufficient to lower the cis energy below the trans as was the case with Gly-Gly. Of the seven stable conformations of neutral Gly-Gly presented in the current study, the two most likely to be observed are conformations (1) and (3). Conformation (1) is the dipeptide in the extended trans form and is stabilized by the two five-membered hydrogen-bonded rings
Wright and Borkman
characteristic of the C5 structure. Although conformations (2) and (3) are of comparable energy, with (2) being slightly more stable than (3), the energy required for the transformation of the dipeptide from (1) to (2), corresponding to rotation about the peptide bond, is in excess of 20 kcal/mol (see Tables I11 and V). The barrier to rotation from (1)to (3), however, is only 1.8 kcal/mol. This significant difference would strongly favor the formation of (3) over (2). Conformation (3) is analogous to the C7 structure of the model peptides although, as previously noted, dipeptides are unable to form this structure as defined. The feature common to both (3) and C7 is the value of 4 (-90"). In previous calculations on several amino acids, it was determined that in each case the gaseous neutral species was more stable than the zwitterion, in contrast to the experimental observation that the zwitterion is predominant in solution.22 The results presented in the current work predict the same trend for the gaseous peptides, with the difference in energy between the neutral and zwitterionic species increasing by about 25 kcal/mol with each additional glycyl residue added to the peptide (see Table 11). The greater instability exhibited by zwitterionic peptides is due in part to the increased distance between the charges in the di- and tripeptides. This increased charge separation also had an effect on the calculated properties of the peptides as compared to the free amino acids. In the neutral molecules, there was a moderate increase in the dipole moments in going from the amino acids glycine and alanine (1.6 D) to the tripeptide Gly-Gly-Gly (4.3 D). This is in sharp contrast to the calculated dipole moments of the zwitterionic species, which ranged from 12.7 D for +Gly- to 42.1 D for +GlyGly-Gly-. The value for the +Gly- zwitterion is in good agreement with the 13.3 D determined by Buckingham in aqueous solution.36 To the authors' knowledge, however, there are no experimental dipole moments for the di- and tripeptides available for comparison. The neutral amino acids and peptides displayed remarkably constant ionization potentials, averaging 10.8 f 0.6 eV. In both theoretical22and experimentaP7 studies, it has been determinted that ionization of a neutral amino acid occurs at the amine group. The similar ionization potentials calculated for the neutral amino acids and peptides in the present work are indicative of ionization from the nonbonding nitrogen orbital of the N terminal of the peptide. In the amino acid zwitterions, however, Mulliken population analyses of the singly positive species showed that the ionized electron originated from the carboxylate group. As the distance between the positively charged N terminal and the negatively charged C terminal of the zwitterions increases in going from an amino acid (2.4 A) to a di- (6.1 A) and tripeptide (9.7 A), ionization is facilitated (see Table 11). A plot of ionization potential vs. number of peptide bonds in the zwitterion yields an assymptotic value of about 3.5 eV. Thus, all polypeptides of five or more residues are predicted to have a constant ionization potential of 3.5 eV. Unfortunately, experimental values have yet to be determined. (36) A. D. Buckingham, A u t . J . Chem., 6 , 323-31 (1953). (37) T. P. Debies and J. W. Rabalais, J. Electron Spectrosc. Re&. Phenom., 3, 315-22 (1974).
