Jaworski, Ekiel, Shugar
/ Coupling Constants in Pentose Nucleosides
4357
Coupling Constants between Cisoidal Protons in Pentose Nucleosides. Limitations of Range of Application of Karplus Relation, and Solution Conformations of P- Arabinofuranosyl and 6-Xylofuranosyl Nucleosides Andrzej Jaworski,la Irena Ekiel,*Iband David ShugarIb Contribution f r o m the Department of Molecular Spectroscopy, Institute of Physics, Warsaw Technical Uniuersity, 00-662 Warsaw, Poland, and Department of Biophysics, Institute of Experimental Physics, Unicersity of Warsaw, 02-089 Warsaw, Poland. Receiced December 1.5, 1977
Abstract: The finite perturbation theory INDO SCF MO method has been employed to demonstrate that the Karplus relation is not unique for cisoidal proton-proton vicinal coupling constants in the pentose rings of nucleosides. The factors responsible for this were elucidated with the aid of t h e procedure of Barfield et al. as applied by Marshall et al. to norboranes. Two model ring systems, cyclopentane and oxolane, were utilized for this purpose. Calculations for /3-arabinofuranosql nucleosides provided an interpretation for the large differences in the values of the experimental cisoidal coupling constants for the states N and S. For P-xylofuranosyl nucleosides t h e theoretical results led to formulation of the conformational state of these compounds as C(3’)endo-C(4’)exo.
Considerable effort, both experimental and theoretical, is currently being devoted to elucidation of the solution conformation of nucleosides and nucleotides, as well as nucleotide coenzymes, and a variety of their analogues, many of which are of considerable biological significance, frequently as antimetabolites. An important element in the determination of the conformational parameters of such compounds is the sugar pentose ring, for which the appropriate parameters may be deduced with the aid of ’ H N M R spectroscopy, using the Karplus relation2s3 which links proton-proton vicinal coupling constants to the dihedral angles between these protons. It is also now generally accepted that, in solution, there is an equilibrium between two extreme conformational states of the pentose ring, viz., N (C(2’)endo) and S (C(3’)endo), the experimentally determined coupling constants being regarded as the timeaverage weighted means of the coupling constants for these two states. Application to the conformation of the pentose ring of the concept of p s e u d o r o t a t i ~ nhas ~ ~ considerably ~ simplified the description of the ring conformation. However, the procedure of Altona and S ~ n d a r a l i n g a mfor ~ establishment of the pseudorotational parameters, and the conformer populations, is based on several assumptions of questionable validity, as formulated elsewhere.6 The uniqueness of the Karplus relation, which is of key importance in conformational studies, is considered in the present investigation. This relation was originally derived theoretically for the ethane molecule,* and its application to the conformation of sugar rings (including those of nucleosides) requires partition of the ring into several ethane-like fragments (see Scheme I), involving the inherent assumption that the influence of the remaining portions of the ring system is independent of the conformation. Attention has already been directed to the absence of an accurate correlation between the dihedral angle and the corresponding vicinal coupling constant,’ particularly marked for cisoidal couplings in nucleosides other than most frequently investigated ribosides (Le., arabino, xylo, lyxo, and deoxy nucleosides). The purpose of the present study was to examine the uniqueness of the Karplus relation in such nucleosides, limiting ourselves to couplings between protons cis to each other. It will now be shown that available experimental data, and theoretical calculations, for the pentose rings of nucleosides 0002-7863/78/1500-4357$01 .OO/O
Scheme I
I
OH
I
OH
I
OH
demonstrate the absence of a simple relationship between dihedral angles and cisoidal coupling constants. Furthermore, the effects of the errors, resulting from the poorly known orientation of the protons, are smaller for cis, relative to trans, protons. As regards couplings between transoidal protons, our theoretical calculations contribute nothing new, in that in such instances they merely confirm the uniqueness of the Karplus relation, while the selection of experimental values for the parameters in the Karplus relation was found to furnish better results than the direct application of numerically calculated values.
Methods Calculations of coupling constants were based on the formulation of finite perturbation theory (FPT)8 in the intermediate neglect of differential overlap ( INDO)9 approximation of self-consistent field (SCF) molecular orbital (MO) theory. Because of the difficulties involved in the delineation of the individual factors which influence the values of the coupling constants, the approach adopted was that of Barfield et a1.,I0 which should be consulted for details. This procedure has proven quite successful in studies on long-range H-’H and I H-I9F coupling constants.I0s1I Its application to norbornanes12 led to elucidation of the factors responsible for the nonequivalence of the exo-exo and endo-endo vicinal coupling constants and, in addition, gave results for cisoidal coupling constants in fairly good agreement with experimentally mea-
’
0 1978 American Chemical Society
/
Journal of the American Chemical Society
4358
100:14
/ J u l y 5, 1978
Table 1. Calculated Cisoidal Coupling Constants 3 J ( l,2) for the Exo Protons of Oxolane and Cyclopentane Conformation and phase angle of O,' pseudorotation deg
Type of q5,b calculdeg ationC
Conformation and Coupling constants, H z phase angle of 8,a Oxolane Cyclopentane pseudorotation deg
u C(3)endo
95 -24
18'
C(4)exo 54' O(l)endo 90'
118
141
9.02 2%
M
9.20
U
10.53
-1
4%
11.01
u
8.16
23
M I55
37
126' C(2)endo 162'
155
t
M 2%
:
8.31
U
C(l)exo
t
5.26
M
t 5.21
U
4.67
-1%
36
t 5.16
Coupling constants, Hz Oxolane Cyclopentane
9%
f
6.45
U
9.92 2%
10.10
142
C ( 3)exo 198
f
22%
22
18%
18%
23% 24%
12.31
t
4%
12.77
120
C(4)endo 234'
8.32
U
8.58
0
9.92
t
2%
10.10
97
O(1)exo 270'
t I%
6.86
289b
10%
7.18
11.60
U
8.03
C(2)exo 342'
81
10.26
u
6.53 7.27
U
6.75
M
10.89
-I%
t
10%
7.18
-
6.81
t
1%
6.78
19%
6.48
I%
t
0%
t
f-
-1%
M
22%
8.77
6%
--
t
10%
-38
t
13.68
8%
t
M 82 -37
C ( 1)endo 306'
6.48
t
M
19%
10.61
15%
22%
6.81
t
10.89
19%
26%
-22
8.77
24%
M
I4C
14%
--26%
9%
28%
9% M
------
Type of @ , b calculdeg ation'
I%
6.86
0 is the dihedral angle O( 1)-C( I)-C(2)-H(2) for oxolane. q5 is the meanvalue of the dihedral angle H( l)-C(l)-C(2)-H(2) between the coupled protons inoxolane and cyclopentane: the difference between them isusuallyabout Io."U. unmodified: M.modifiedcalculations.See text.
sured values. The five-membered rings were constructed according to the pseudorotational concept of Altona and S ~ n d a r a l i n g a mAll . ~ calculations have been performed for 7, equal to 39". Since the procedure of Saran et aI.l3 frequently leads to incorrect results, a new method has been employed using the pseudorotational model for bond angles in fivemembered rings and minimization of the differences between computed and crystallographic bond lengths, bond angles, and dihedral angles by means of the Simplex p r 0 ~ e d u r e . For l ~ the exocyclic hydroxyl group, the average values of C - 0 bond lengths and C - C - 0 bond angles are from crystallographic data, while for 0 - H and C-H bonds, standard lengths were employed.I5 The value for C-0-H angles was also taken from the standard model of Pople and Gordon.I5There are several criteria for the choice of the angles C-C-H and H-C-H, e.g., Altona and S ~ n d a r a l i n g a m ,Cremer ~ and Pople.I6 The one adopted in this study is similar to that of Cremer and Pople.16 As in their study, local CILsymmetry is retained, but with the additional condition of equality of the angles C-C-H and H-C-H, the validity of which is supported by and a b initio calculation^.^^ The results obtained with the aid of the criterion of Cremer and Pople are almost identical.
Results and Discussion One of the starting points of the present investigation was the known nonequivalence of the exo-exo and endo-endo vicinal H-H coupling constants in norbornanes. With the aid of a series of model compounds, for which theoretical calculations of coupling constants were carried out and compared with experimentally measured values, Marshall et al.12 demonstrated that the foregoing nonequivalence is due to interaction of the C(7) methylene bridge with the bonds of the C(2)-C(3) ethane bridge. On the basis of the foregoing study, it was inferred that interaction of a C-C bond with a diametrically opposed methylene group could be one of the factors responsible for the differences in coupling constants of the "mirror image" conformations endo and exo of the pentose ringZo(conformations for which there is a difference in pseudorotational parameters, P , of 1 80'). Two series of calculations were therefore carried out for the model compounds oxolane (tetrahydrofuran) and
Scheme It H
I
I
I
H
H
H
H Ea0
0X 0LANE
CYCLOPENTANE
/
OH
R
H
- 0-ARABINONUCLEOSIOE cyclopentane (see Scheme 11). The results are displayed in Table 1. For each value of the pseudorotational parameter in the table, the upper value is the cisoidal vicinal coupling constant calculated without modifications, while the lower value is that obtained when the interaction with the methylene group was set to zero. The figures set against the vertical arroNs represent the percentage decrease in coupling constant 3s a result of interaction with the methylene group. It will be noted that these values are strikingly similar for both model compounds. A second factor which influences the coupling constants in the pentose ring is the ring oxygen, testified to by the results of a number of It seems that the method of calculation herein employed quite accurately reflects the influence of the ring oxygen on the cisoidal coupling constants in six-membered rings (Table 11). Comparison of the values of the coupling constants for cyclopentane and oxolane (Scheme 11) makes possible an evaluation of the effect of the ring oxygen on the coupling constants for various conformations of the latter, as shown in Table I by the figures beside the horizontal arrows, which denote the
Jaworski, Ekiel, Shugar
/
Coupling Constants in Pentose Nucleosides
4359
Table 11. Experimental and Calculated Values of Vicinal Cis Coupling Constants in Some Six-Membered Rings
Compd tert-Butylcyclohexane trans-4-tert- Butylcyclohexanol cis-4-tert- Butylcyclohexanol I ,2-cis-Dihydroxycyclohexane 1,2-trans-Dihydroxycyclohexane I ,4-Dioxane
Assignment 3e4a 1a2e
3.1Ib 4.3'
4.56d
1 e2a
3.OC
2.1Id
3.8f
3.8g
4.5f
4.8g
2.ah
2.96
-
,Meane (2e3a 2a3e) 2a3e
-
Meane (2a3e 2e3a)
B
Coupling constants, H z Exptl Calcda 4.22
a Geometrical parameters for the rings from M. Davis and 0. Hassel, Acta Chem. Scand., 17, 1181 (1963). Standard values for bond lengths with substituents from ref 15; bond angles are as described in text. b J. D. Remijnse, H. van Bekkum, and B. M. Wepster, Recl. Trac. Chim. Pays-Bas, 90,119 (1971). F. A. L. Anet, J . Am. Chem. Soc., 84, 1053 (1962). Mean value for the two low-energy conformations of the hydroxyl group. The conformation with the hydroxyl above the ring possesses an energy about 2.5 kcal higher, so that its contribution to the mean value of the coupling constant is negligible. e Average for couplings of two equivalent conformers i n rapid equilibrium with each other, with equal populations. f R. V. Lemieux and J . W. Lown, Tetrahedron Lett., I229 (1963). g Average weighted value for the four possible orientations of the two hydroxyls. As in footnote d , the high-energy conformations were excluded. The differences between these results and those of Maciel et al. (Table V in ref 24) are due to the use of different geometrical parameters for the rings. J . B. Lambert, J . Am. Chem. Soc., 89, 1836 (1967).
decreases in coupling constants resulting from the presence of the ring oxygen. I n particular, it should be noted that these values are similar for both the modified and unmodified calculations. Puckered rings for which the difference in the pseudorotational parameter is 180' exhibit closely similar absolute values of dihedral angles. The small differences existing,
