E X T E ~ DHWCKEL E~ CALCULATION^
ON POLYPEPTIDE CHAINS
same ratio as OUPB at 12 ’. These authors, however, measured the reacthi iti toward peroxy radicals of d ~ ~ estnxc r ~I;laso. ~ t peroxy ~ ~ d as~thec chain ~ ~carriers, s the main tioir reactkm should be reaction 15, and thus from eq 30 the OXidiB bility of ethylbenzene, that is, the rakio BGI/FCI~”’~, can b~ cdculated as (33) ~ ~ o ~ e s p o n dvalues i n g are given in column 5 of Table 111. As can be seen, they are constant up to 13 hr
2793
within the limits of error. Later on, 1iosvever, a marked decrease can be observed. ‘This is due, likely, to the appearancc of new chain c ~ a ~ ~~ lt o~ the /r ~ r ~ ~ participation of the reaction products in the propagation reaction, as suggested earlier by others in the oxidation of ~ u m e n and e ~ ~of n-decane (see ref 53, p 168). Our experiments to be published in the next parts summarize results obtained by irslag labeled hydroperoxide molecules and by studying Ihe ~ ~ ~ ~of c h a ~ the alcohol-ketone transition, (64) V. I;. Antonovski, E. T. Deniaov, J. A. ‘Kuznyclzov, Ju. Ja, Mekhrynshev, arid 1,. V. Bolntzeva, Kinet. Islatal., 6, 607 jl965).
iickel Calculations on Polypeptide Chains. IV. he +-IC. Energy Surface for a Tetrapeptide of Poly-L-alanine by Angelo R. Rossi, Carl W. David, and Robert Schor” Departments of Chemistry and Physics and Institute of Materials Science, The University of Connecticut, Stows, Connecticut 06‘268 (Eeceived December ld, 1971) Publication costs asaisted by the University o/ Connecticut Research Foundation
The potential energy surface of a tetrapeptide of L-alanine obtained by extended Niickel calculations contains three nonequivalent minima of comparable energy which can be assigned to well-known conformations. Two {of these minima are relatively well defined and are near the conformations assigned to the left-handed and the right-handed a helices, respectively. A third broad minimum occurs in the region of the fully extended chain conformations. Other minima occurring in the map cannot be assigned to conformations occurring In nature but are consistent with those obtained in other recent calculations on the same system.
Introduction Theoretical studies of the conformations of isolated helices (under vacuum) of polypeptide chains with intramolecular interactions have been carried out by many r n ~ r k e r s ~ -using - - ~ semiempirical potential functions for barriers; t o rot,ation around single bonds, nonbonded interactions, dipole-dipole interactions between amide groups, and hydrogen-bonding potential energy functions. More recently, semiempirical quantum mechanical teehniyues have been used to study glycyl and alanyl residues,4 polypeptide chain^,^ and model peptide molecules.6 We have presented the resuits OF a detailed study by extended Huckel theory (EHT) of the helical conformations of a tetrapeptide of glycine which is long enough to incorporate an inIxamolecular hydrogen bond. We havc also presented the corresponding resuits using the CNDO/2 method on this system.’ The present work which presents the results (9f an FI-TT cdouiation on the tetrapeptide of
poly-L-alanine was undertaken to investigate the effects of varying the side chain. It was anticipated that the primary differences in the results of the EHT calculations on the tetrapeptide of glycine and on the tetr* peptide of poly-L-alanine would be an exchxsion, due to steric factors, of a large portion of the +-IC. map which was previously allowed and a differerice of the energy between the right-hand and the left-handed a-helix conformations. (1) D. A. Brant and P. J. Flory, J . Amer. Chem. Soc., 87, 663, 2791 (1965). (2) G. N. Ramachandran, C . M. Venkatachalm, and S. ICrimm, Biophys. J., 6, 849 (1966). (3) R. A. Scott and I-I. A. Soheraga, J . Chcm. Phys., 45,2091 (1966). (4) R. Hoffmann and A. Imamura, Biopolymers, 7, 207 (1989). (5) A. Rossi, C. W. David, and R. Schor, Theoret. Chhim. Acta, 14, 429 (1969). (6) J, F. Yan, F, A. Momany, R. Roffmann, and H. A. Soheraga, J. Phys. Chem., 74, 420 (1970). (7) R. Schor, H. Stymne, G. Wettermarlr, and C. W. David, in press. The Journal of Physical Chemistry, VoL 76, N o . 19, 1972
A. R. ROSSI, C. w.DAVID, A N D R. S C H ~ R
2794
Method The EIITEprovides an approximate solution to the biCALOmolecular Harlree-Fock equations in which all valence electrons are explicitly treated, all overlap integrals are calculated, but electron repulsion is not explicitly included. We have used the same paras;ietrizatkon for the overlap and Coulomb integrals as well as the Slatea: exponents as we did in our previous
0
R
H
H
0
R
H
H
Figure 1. Diagrammatic representation of a tetrapeptide of L-alanine with R = CHI including the rotation angles +(N-c*) and $(Ca-C') around the single bonds.
WOH'k. 9
The method for determining the coordinates of the atoms in the trelical conformations of the polypeptide chain as shown in Figure I is due to Leach, NBmethy, and flcheraga. 'The peptide unit is considered to have a rigid planar structure with fixed bond angles and bond lengths. 'The values of these parameters used are shown in Table 1. Figure 2 shows a diagrammatic of 1,-alanine. r e p ~ e ~ e of~ 3~ dipeptide a ~ ~ o segment ~
7
C'
!I
0
N H (amide) C*
2 3 4 5
Xj,
tlj,
zjv
b
A
A
1.42 1.61 2.37 2.18 3.80
0.58 1.80 -0.34 -1.32 0.00
0.00 0.00 0.00 0.00 0.00
Bond length, Bond
if
C*-.C8
1.53 1.53 1.09 1.09 1.00 1.47 1.24 1.32
C"-C' C*-H
CP-H N--I3 N-C" C'-0 c '-N Bond
angle
a [C*C'01 a [ C T "1
a[C'NC*] T[C"Nj 7 [C@@TP]
a[NCaC']
0
1
Figure 2. Diagrammatic representation of a dipeptide segment of L-alanine. A residue is enclosed within brackets. x = 60", ie., all methyl groups are staggered with respect to the polypeptide backbone; w = 180°, ie., all peptide units are in the planar trans conformation.
Table E : Coordinates for the Atoms in a Planar Peptide Unit of iL-Alanine
Atom
IN
Value, deg
121 114 123 123 109.5 109.5
The conventions for the rotation angles 4 and II. are those recently adopted by an IUPAC-IUB Commission.ll The cstleulatjons were performed on an IBM 360/65 computer. The largest grid width was taken to be 30", but a width as s-ma,llas 5" was used for studying certain energy contours wkich varied more rapidly with 4 and $. Since R = CH,, the potential energy surface is no longer centrosymmatric, and the whole range of 4 and $ was used. The Journal of F'hytiieal Chemistrg, Vol. 76,No. 19, 10'7%
Results A. Conformational Analysis. As it is not possible using EHT or other molecular orbital techniques to decompose the total energy into physically identifiable components such as nonbonded interactions, hydrogenbonding potential energy functions, dipole-dipole interactions, and barriers to rotation around single bonds the following discussion refers to the total orbital energy. The ground-state potential energy surface for a tetrapeptide of poly-L-alanine is shown in Figure 3. The most stable conformation has been assigned zero energy. The results of the present calculation are comparable in the regions of high steric repulsion to those of Hoff mann and Imamura4 while significant differences occur in the sterically allowed regions. It is interesting to note that the 310 helix (4 = -4Yo, II, = --260)12 and the 2.27and 27 helices ( 4 = -75", $ =; +%Oo and 4 = -75") II. = +60°, respectively),"V1'O which Maigret and coworkers found to be the most stable coniormation in their calculations on Ai-acetyl-N..methylglycylamide, occur in a relatively high energy region of our (8) R. Hoffmann and W. N. Lipscomb, J . Chem. P h p . , 36, 2179, 3489 (1962); 37, 2872 (1962). (9) A. Rossi, C. W. David, and R , Schor, J . Phys. Chem., '94, 4551 (1970). (10) 9. J. Leach, G. N. NBmethy, and N. A. Scheraga, Biopolymers, 6, 369 (1906). (11) IUPAC-IUB Commission on Biochemical Nomenciature, Biochemistry, 9, 3471 (1970). (12) G. N. Ramachandran and V. Sasisekharan, Advan. Protein Chem., 23, 323 (1968). (13) R. E. Dickerson and I. Geis, "Structure and Action of Proteins," Harper and Row, New York, N. Y . , 1969.
EXTEXDED IIUCKEI,CALCULATIONS ON POLYPEPTIDE CHAINS I80 I20
60
9 0
-60 - 120 -120
-60
0
60
120
180
Figure 3 . Ground-state potential energy surface for a tetrapeptide of L-alanine calculated by extended IIuckel theory. The contours of constant energy are chosen relative to the most stable conformation which is chosen as zero energy and are in units of kilocalories per mole of residue.
map.14 The large diguse sterically allowed region of the Hoffman-Imamurti map (+ i 2- 180" t o Si - 60" and # - 180" to 1F. ;Z 180") is very close t o the ahelical (+ = -48", $ = -57") right-handed a helix and (+ = 48", 1F. = 5.7") left-handed a helix and contains the extended chain conformations (+ = - N O " , = -~1S0°).12There arc now local minima near the lest-handed and right-handed a-helical conformations as well as in the region of the extended chain conformations. The similarities between our rcsults and those of Hoffmann and Imamurn on thc dipeptide are again attributed to the dominant role of the hard-sphere contacts in the sterically disallowed regions while the differences in thr sterically allowed region are clearly due t o the increased chain length. Comparison of the results of the present work t o those obtained in our previous EHT calculations on the tetrapeptide of glycine5)$shows, as expected, that the substitution of L: methyl group for a hydrogen on the side chain eliminates it substantial region of the configuration space which was previously allowed. The minimum corresponding t o the left-handed a helix is approximately 2-kcal/mol residue higher in energy than that for th(. right-handed a helix. This difference is significantly 1nrgc.r but gives the same ordering as
+
+
+
2795
the value for this energy difference of about a few tenths of a kilocalorie per mole residue reported by Scott and Schcraga3 in their semiempirical force calculations on a similar system. The fact that the 2.2, and 21 helices occur in a relatively high encrgy region and that the absolute minimum is not predicted a t the right-handed a-helix conformation in our calculations but is predicted t o be near that conformation by Scott and Scheraga may be due to the suspectcd inability of EHT calculations to provide an adcquatc reprcsentation of the hydrogen bond.I6 I n this connection it should be noted that the energy differencc betwxn the predicted right-handed a-helix conformtltion and the absolute minimum in the present calculation is less than 2 kcal/mol residue. The first excited-state potential energy surface is similar to our ground-state map for both the regions of high steric repulsion and the allowed regions arid is consequently not shown. R. Churges and Population Analvsis. The charges and overlap populations in the peptide unit show no significant differences from our previous work6h9 on the tetrapeptide of glycine. The present E H T calculations on the helical conformations of a tetrapeptide of poly-L-alanine arc consistent with recent calculations on protein stweochemistry. On the basis of the corresponding work on polyglycine it may be possible t o draw more definite conclusions by performing the more time-consuming CNDO/:! calculations.
Aclcnowledgments. The authors wish t o t,hank Professor Roald Hoffmann for a fruitful discussion and for giving us a faster executing version of his program. This work was supported by Grant No. GR-6852 of the National Science Foundation. Tho computational part of tjhis work was carried out at. the Computer Center of the University of Connecticut which is supported in pa.rt by Grant No. GJ-9 of thc National Science Foundation. One of us, Angclo R. Rossi, is grateful to the University of Connecticut, Research Foundation for financial support during thc summer of 1970. (14) B. Msigret, B. Pullman, and
M.Dreyfus, J . Theoret. Bbl.,
26,
321 (1970).
(15) E'. A. Momany, It. F. McGuire, J. IC. Yan, and H. A. Scheraga, J . Phye. Chem., 74, 2424 (1970).
The Journal of Physical Chemistry, Vol. 76,No. 1.9, 1972
