3033
Helical Conformations of a Tetrapeptide of Poly-L-alanine with a symmetric kernel. J. A. R. Coope, R. F. Snider, and F. R. McCourt, J. Chem. Phys., 43,2269 (1965). D. K. Hoffman, J. Chem. Phys., 50, 4823 (1969). E. Boyd and W. D. Harkins, J. Amer. Chem. Soc., 61, 1186 (1939). M. J. Povich, Thesis, Universityof Hawaii, 1972. R. J. Mannheimer and R. S. Schechter, J. Colloid lnterface Sci., 27,342 (1968); 32, 195 (1970); 32, 212 (1970). F. C. Goodrich and L. H. Allen, J. Colloid lnterface Sci.. 37, 68 11971) \ . _ . .,.
N. Lifschutz, M. G. Hegde, and J. C. Slattery. J. Colloid lnterface So., 37,73 (1971). J. A. Mann in "Techniques of Surface Chemistry and Physics," R. J. Good, et ai.. Ed., Marcel Dekker, New York, N. Y., 1972.
(20) R. S. Hansen and J. Ahmad, Progr. Surface Membrane Sci., 4, 1 (1971). (21) . . E. H. Lucassen-Reynders and J. Lucassen, Advan. Colloid lnterface Sci., 2, 347 (1969). (22) M. G. Hegde and J. C. Slattery, J . Colloid lnterface Sci., 35, 183 (23) (24) (25) (26)
11971) \ ' - . ','
C. Huh and L. E. Scriven, J. Colioid lnterface Sci., 35,85 (1971). J. A. Mann and J. Ahmad, J. Colloid lnterface Sci., 29, 158 (1969). J. Ahmad and R. S. Hansen, J. Colloid lnterface Sci., in press. R. J. Bearman and J. G. Kirkwood, J. Chem. Phys., 28, 136 (1958). (27) E. K. Sakata and J. C. Berg, Ind. Eng. Chem., Fundam.. 8, 570 (1969) (28) D. Montgomery, Phys. Fluids, 14, 2088 (1971).
A CNDO/2 Calculation on the Helical Conformations of a Tetrapeptide of Poly-L-alanine. V. The $-$ Energy Surface' Hans Stymne, Gunnar Wettermark, Division of Physical Chemistry, The Royal Institute of Technology, Stockholm 70, Sweden
Robert Schor," Department of Physics and lnstitute of Materials Science, The University of Connecticut, Storrs, Connecticut 06268
and Carl W. David Department of Chemistry, The University of Connecticut, Storrs, Conneciicut 06268 (Received July 79, 1973) Publication costs assisted by The University of Connecticut Research Foundation
The ground-state potential energy surface for the helical conformations of a tetrapeptide of poly-L-alanine has been calculated using the CNDO/2 method. The potential energy surface contains four nonequivalent minima. The absolute minimum is found in a region close to both the right-handed a helix and the right-handed 310 helix. A second local minimum of about 2 kcal/mol of residue higher is found near the corresponding left-handed helices. The 2, helix may be represented by the third minimum of about 3 kcal/mol of residue. The last local minimum of about 5 kcal/mol of residue is near the fully extended chain conformation. The results are compared to our previous calculations on the same system as well as to our calculations on the tetrapeptide of polyglycine.
Introduction Theoretical studies of the conformations of isolated helices (under vacxum) of polypeptide chains with intramolecular interactions have been carried out by many workers2x3 using semiempirical potential functions for rotation around single bonds, nonbonded interactions, dipole-dipole interactions between amide groups, and hydrogen bonding potential energy functions. More recently semiempirical quantum mechanical techniques have been used to study glycyl and alanyl r e ~ i d u e s ,polypeptide ~ chains,5 and model peptide molecules.6 A detailed study by extended Hiickel theory of a polypeptide chain of polyL-alanine long enough to incorporate an intramolecular hydrogen bond (see Figure 1) has been presented.? In the present work, vve present the corresponding results using the CNDO/Z method. It should now be possible to make a preliminary but more detailed comparison of the two methods on these systems and of the differences between the tetrapeptide of glycine and poly-L-alanine.
Method Santry's modifications of the CNDO/2 method*-i2 was applied. The CNDO/2 method provides an approximate SCF solution to the LCAO molecular Hartree-Fock equations, in which all valence electrons are included and in which electronic repulsion is explicitly introduced. The methods of determining the coordinates of the atoms in the helical conformations of the polypeptide chain as shown in Figure 1 is due to NBmethy and Scheraga.i3 The peptide unit is considered to have a rigid planar structure with fixed bond angles and bond lengths. The coordinates of the atoms in a peptide unit for the bond angles and distances taken from Leach, NBmethy, and Scheragai4 are given in Table I. Figure 2 shows a representation of a dipeptide segment of poly-L-alanine. The new conventionsi5 for the rotation angles (b and fi are used in the present work. (The rotation angles (b and $ as given by the former conventioni6 are related to the new rotation angles '$ and # by @new = '$old - r, $new = $old - r.1 The Journal of Physical Chemistry, Vol, 77, No. 25, 1973
Stymne, Wettermark, Schor, and David
3034 R
0
/\
H
H
H
I
H
II
H
0
R
0
/ \H
H
180
/ \H
Ii
I
H
R
H
120
H
0
Figure 1. Diagrammatic representation of a tetrapeptide of polyL-alanine with R = CH3 including the rotation angles #(N-Ca) and $ (Ca-C') around the single bonds.
60
TABLE I: Coordinates for the Atoms in a Planar Peptide Unit
i
Atom
Xj,
A
yj,
A
zj,
GQ C'
1 2
0.00
0.00
1.42
8
3
1.61
N
4 5
2.37 2.18 3.80
0.58 1.80 -0.34 -1.32
H (amide) CQ
6
A
0.00 0.00 0.00 0.00 0.00 0.00
0.00
-50
-120
-180
-120
-60
0
60
120
I80
@
Figure 3. Ground-state potential energy surface tor a tetrapeptide of L-alanine calculated by C N D 0 / 2 method. The contours of constant energy are chosen relative to the most stable conformation which I S chosen as zero energy and are in units of kcal/mole of residue.
0
I/ Ca / c :
Figure 2. Diagrammatic representation of a dipeptide segment of poly-L-alanine. A residue is enclosed within brackets. x = GO", Le., all methyl groups are staggered with respect to the polypeptide backbone; w = 180", ;.e., all peptide units are in
the planar trans conformation.
The calculations were performed on an IBM 360/75 computer. (The execution time for a tetrapeptide of poly-Lalanine was approximately 3 min for each point on the potential energy surface.) The largest grid size was taken to be 30", but a width as small as 5" was used for studying certain energy contours which varied more rapidly with 4 and .)I Since R = CH3, the potential energy surface is no longer centrosymmetric, and the whole range of # and was used.
+
Results The ground-state potential energy surface for four peptide units (three residues) is shown in Figure 3. Since R = CH3, the map is not centrosymmetric about the point # = O", $ = 0". There are four nonequivalent minima in the contour -35" map; (1) the absolute minimum # = -40", whose energy has been set equal to zero. It should be noted that the minimum is quite shallow in this region and the interpolation is uncertain. Hence the estimated
+
error bars in the position of the minimum is about *15" in both # and $; (2) a local minimum a t $J 31 35", 4, = 40" whose energy is approximately 2 kcal/mol of residue; (3) a local minimum 4 N 75", = -40" of about 4 kcal/mol of 165" of residue; and (4) a local minimum # = -180", approximately 5 kcal/mol of residue near the fully extended chain conformation. The absolute minimum a t # = -40", $ = -35" has shifted substantially from the calculated absolute minimum for the tetrapeptide of glycine at # = -20", IC, = -60".17 The present absolute minimum is closer to the -48", $ = -57" and significantright-handed a helix # ly closer to the right-handed 310 helix at # = -49", = -26". It is interesting to note, however, the suggestion of a faint minimum near the right-handed a-helix conformation. A local minimum of about 2 kcal/mol of residue at # = 35", rF, 40" is very close to the left-handed 310 helix at # = 49", $ = 26". Additionally, one notes the suggestion of a valley which runs straight through the left-handed a helix conformation, The difference in stability between the right-handed a helix and the left-handed a helix (and between the right-handed 310 helix and the left-handed 310 helix) is approximately 2 kcal/mol of residue with the right-handed conformations being the most stable. This result agrees with our extended Huckel calculations on the tetrapeptide of poly-L-alanine.18 The local minimum a t 4 = 75", IC, = -40" of approximately 3 kcal/mol of residue is broad and it is particular-
+
+
+
TABLE II: Gross Charges on the Atoms in a Planar Peptide Unit for Various Helical Conformations of the Tetrapeptide of Poly-L-alanine Conformation
Fully extended chain Antiparallel-chain pleated sheet Right-handed a helix
-0.19
+0.12
-0.38
0.36
-0.09
f0.01
+0.03
-0.18 -0.20
+0.11 0.15
-0.37 -0.38
0.36 0.37
-0.09 -0.10
+0.01
4-0.03 4-0.03
a Atomic charge taken from the fourth peptide unit.
Atomic charge taken from the first peptide unit,
The Journal of Physical Chemistry, Vol. 77, No. 25, 7973
+0.02
Communications to
3035
the Editor
ly difficult to determine the angle $ with precision. This minimum may therefore "correspond" to the 27 and the 2.Z7 helices a t 4 II E " ,$ N -70" for polyglycine.lg Maigret, e t al.,zOfound the conformation d~ -80°, il/ = -40" to be the most stable conformation in their calculation on N-acetyl-N'-msthylalanylamide.The local minimum 4 -60", $ 60" of approximately 4 kcal/mol of residue obtained for the tetrapeptide of glycinel7 has disappeared in the present calculation and this +, $ pair is now on a 6 kcal/mol of residue contour. There is a suggestion, however, of the formation of a new local minimum at about 4 = -70", $ 50", of slightly less than 4 kcal/mol of residue. The local mnnimum near the fully extended chain conformation of about 5 kcal/mol of residue has shifted from 4 = - 180", $ N - 180" for the tetrapeptide of glycine1? to 4 = - B O " , $ 1: -165" in the present case. Hence, there is a faint suggestion of pleatingz1 on substituting the bulkier CH3 group for H in the side chains. The partial charges which are sensibly independent of the rotation angles 4 and $ are substantially the same as for the tetrapeptide of glycine1? and are given in Table I1 for some selected conformations. Conclusions The CNDO/2 calculations on the helical conformations of the tetrapeptide of poly-L-alanine, in agreement with all our previous calculations, show that the difference in the computed energy between the absolute minimum (near a contracted form of the polypeptide chain) and the extended forms of the polypeptide chain is about 5 kcal/ mol of residue. In addition, there is essentially only one easy direction on the 4-1)map for the chain to unwind in going from the contracted to the extended form. The right-handed a-helical conformation for poly-L-alanine is predicted to be about 2 kcal/mol of residue lower in energy than the left-handed a-helical conformation. This difference appears to be a real one and not an artifact of the calculations.
The present calculations indicate, however, a new feature which is perhaps somewhat unexpected. The absolute minimum is now significantly closer to the 310 helix than to the a helix. Further theoretical work is in progress which may help to make a more definite assignment.
Acknowledgments. The authors wish to thank Professors Roald Hoffmann and Angelo Rossi for fruitful discussions. Valuable computational assistance was provided by Miss Brigitta Bystrom. References and Notes (1) This work was supported by Grant No. 2741 from the Swedish Natural Science Research Council. (2) (a) D. A. Brant and P. J. Flory, J. Amer. Chem. SOC., 87, 633, 2791 (1965); (b) G. N. Ramachandran, C. M. Venkatachalrn, and S. Krimrn, Biophys. J., 6, 849 (1966). (3) R. A..Scott and H. A. Scheraga, J. Chem. Phys., 45,2091 (1966). (4) R. Hoffrnann and A. Irnarnura, Biopolymers, 7, 207 (1969). (5) A. Rossi. C. W. David. and R. Schor. Theor. Chim. Acta, 14, 429 (1969). (6) J. F. Yan, F. A. Momany, R. Hoffrnann, and H. A. Scheraga. J. Phys. Chem., 74, 420 (1970). (7) A. Rossi, C. W. David. and R. Schor, J. Phys. Chem., 74, 4551 11970). (8) D.-P. Santry, J. Amer. Chem. Soc., 90, 3309 (1968). (9) J. A. Pople, D. P. Santry, and G. A. Segal, J. Chem. Phys., 43, 129 (1965). (10) J. A. Pople and G. A. Segal, J. Chem. Phys.. 43, 136 (1965). (11) J. A. Pople and G. A. Segal, J. Chern. Phys., 44,3289 (1966). (12) D. P. Santryand G. A. Segal, J. Chern. Phys., 47, 158 (1967). (13) G. N. Nemethy and H. A. Scheraga, Biopoiymers, 4, 369 (1966). (14) S. J. Leach, G. Nemethy, and H. A. Scheraga, Biopoiymers, 3, 155 (1965). (15) IUPAC-IUB Commission on Biochemical Nomenclature, Biochemistry, 9, 3471 (1970). (16) J. T. Edsall. P. J. Flory, J. C. Kendrew, A. M. Liquori, G. Nemethy, G. N. Ramachandran, and H. A. Scheraga, Biopolymers, 4, 121 (1966); J. Bioi. Chem., 241, 1004 (1966); J. Moi. Biol., 15, 399 119661. ._.,. (17) R. Schor, H. Styrnne. G. Wetterrnark, and C. W. David, J. Phys. Chem., 76,670 (1972): (18) A. R. Rossi, C. W. David, and R. Schor, J. Phys. Chem.. 76, 2793 (19721. (19) G . N. 'Ramachandran and V. Sasisekharan, Advan. Protein Chern., 23, 323 (1968). (20) B. Maigret, 6. Pullman, and M. Dreyfus, J. Theor, @io/., 26, 321 (1970). (21) L. Pauling and R. 6. Corey, Proc. Naf. Acad. Sci. U. S., 37, 251 (1 951 ) . ~
COMMUNICATIONS TO THE EDITOR
Effect of Photoionization Energy on the Distance Distribution between Trapped Electrons and
N,N,N',N'-Tetramethyl-p-phenylenediamine Cations in Organic Glasses Pubiication costs assisted by fhe
U.S. Atomic Energy Commission
Sir: Trapped electrons are produced in a variety of organic glasses by radiolysis or by photoionization of a suitable so1ute.l In both cases an ion pair is initially formed from which the charged species must separate. The electron
can move in a conduction state, as indicated by photoconductivity ~ t u d i e s , ~ before , ~ it is trapped. However, the distance distribution of trapped electrons, et -, from a positive hole is not definitely known in organic g1asses.l Here we demonstrate an effect of photoionization energy on the distance distribution between trapped electrons and N,N,N',N'-tetramethyl-p-phenylenediaminecations (TMPD+) in 2-methyltetrahydrofuran and 3-methylpentane glasses at 77 K. We demonstrate that the electrons travel further before trapping when photoionized by higher energy light. The Journal of Physical Chemistry, Voi. 77, No. 25, 1973
