voiume3 no.8 Augusti976
Nucleic Acids Research
Conformational analysis of polynucleotides. I. The favorable left-handed helical
model for the poly(8,2'-S-cycloadenylic acid) with high anti conformation
Satoshi Fujii and Ken-ichi Tomita
Faculty of Pharmaceutical Sciences, Osaka University, 133-1 Yamada-Kami,
Suita, Osaka 565, Japan.
Received 25 May 1976
ABSTRACT
rj~Energy calculations have shown that poly(8,2'-S-cycloadenylic acid) can form left-handed helices owing to the high
anti conformation. 2) Two favorable left-handed helices are
characterized by axial translation per residue (Z=4.3 and 3.6A)
and by rotations per residue (0= -40° and -25°). 3) The
proposed helical models might be stable in aqueous solution and
is well explicable of the optical property of this compound.
INTRODUCTION
The bond lengths and angles of a molecule can be adequately
approximated by constant values even in various environments.
Therefore, the conformational specificities of nucleosides,
nucleotides and polynucleotide chains can be defined by the
torsion angles.
Such torsion angles may be divided into the
following three categories (see Fig.l);
1) the glycosidic
torsion angle x (0(1')-C(1')-N(9)-C(8)) defines the geojnetry
between base and sugar moieties.
2) the torsion angle about
each bond in the sugar ring, especially ij*1 , defines the ring
puckering.
3) the five torsion angles, <t>, I|J, <t>' , u' and u> define
the configuration of the sugar-phosphate backbone.
It should be
noted that the allowed values of these torsional angles are
limited only in some restricted regions, which are significantly
influenced by other surrounding angles.
The X-ray structure
analyses of several nucleosides and nucleotides have given us
valuable informations about these angles as summarized by
Sundaralingam .
The conformational analyses by various
theoretical investigations using both semi-empirical potential
functions and quantum-mechanical calculations lead to the results
which agree well with the conformations found in the crystal
structures ' ' ' 5 . Therefore, semi-empirical energy calculations
for plausible conformations might be essential for estimation of
© Information Retrieval Limited 1 Falconberg Court London W1V5FG England
1973
Nucleic Acids Research
the rotational preferences in a molecule from the limited
experimental evidence.
It is well known from the result of CD or NMR spectra that
the poly(rA) chain may preserve its regularly repeating rightft 7
handed structure in aqueous solution ' .
This right-handed
helical conformation is similar to the arrangements observed in
0
the X-ray fiber diffraction studies of polynucleotides .
Ikehara
et al. reported that CD spectra of the dinucleoside monophosphate
A S p A S , the 8,2'-S-cycloadenosine dimer, shows a Cotton effect
a
just opposite to that of ApA . The observed drastic change of
Cotton curves supports the possibility of the left-handed base
stacking in poly(A s ), poly(8,2'-S-cycloadenylic acid).
Furthermore, poly(A s ) could not form a double helix with poly(U),
uridine
6 , 2'-anhydro-6-oxy-l-6-D-arabinofuranosyl
but
poly(A s ) could form a duplex with poly(U°),
themonophosphate
polymer of
This duplex might well retain a left-handed conformation.
other hand, poly(rA) forms a complex with poly(U).
On the
Therefore,
poly(rA) has a tendency to form the right-handed geometry and
poly(A s ) has a strong left-handed tendency.
In the case of 8,2'-
S-cycloadenosine, the glycosyl torsion angle x» is so fixed in
the high anti region that the remaining six rotation angles, $,
<f>' , tjj, i|i', co' and uj, which belong to the second and third
categories cited
above, are variable from a consideration of
molecular conformation of poly- or oligo-S-cyclonucleotides.
Recently, Sundaralingam suggested the possibility of left-handed
helical structure with helical parameters very similar to those
observed for right-handed helices
.
We have carried out the
semi-empirical potential calculation using the minimization
technique and obtained the more satisfactory conformation for
A s p A s or poly(A s ) model.
In addition, a similar calculation was
performed for the poly(rA) conformation in order to make sure
of the validity of this method.
METHOD
Model building
The requisite structural parameters of
8,2'-S-cycloadenosine
molecule were obtained from the X-ray analysis of 8 ,2'-S-cycloadenosine-3', 5 '-cyclic monophosphate
1974
.
In this case, the torsion
Nucleic Acids Research
Fig.l The notation of
the torsion angles.
angle x is 126°, and the sugar puckering is C(4')-exo.
Although
3' ,5'-cyclization may significantly affect the conformation of
the sugar moiety, a C(4')-exo conformation is also found in the
6,2'-O-cyclocytidine molecule
.
It seems likely that the
cyclization between atom 0(2') of arabinose and the respective
atom of the base may also restrict the puckering form of the
sugar ring to a C(4')-endo or C(4')-exo conformation.
In fact,
a C(4')-endo conformation was observed in the crystals of 2,2'O-cyclocytidine and 2,2'-0-cyclouridine
'
s
.
From the observed
s
NMR spectra of 8,2'-S-cycloadenosine and A pA , a C(4')-endo
conformation as a possible sugar puckering cannot be excluded 16
Only a C(4')-exo conformation was considered in this study,
because this conformation seems a feasible modification of the
C(3')-endo conformation usually observed in many nucleosides.
The remaining bond lengths and valence bond angles were
provided by the similar method as described by Sasisekharan et
1975
Nucleic Acids Research
al.
and Sundaralingam ,
The structure parameters for adenosine
itself are referred to the atomic parameters cited by
Sasisekharan et al..
The hydrogen atoms in hydroxy groups were
eliminated from the calculation, because of little contribution
to total energy even if the hydroxy groups rotate freely.
The definition or notation of torsion angle in this study follows
that given by Sundaralingam
(see Fig.l).
Energy calculation
The total energy E of a molecule is defined by the following
equation ;
E
" E nb + E el +
where E , , E ., and E
E
t
are the nonbonded, electrostatic, and
torsional energies, respectively.
Parameters used in the
Lennard-Jones potential function for the first term E , , were
taken from that cited in ref. 18.
The Coulomb charges used in
the second term E ,, were taken partly from those cited in ref.
19 and also from those calculated by CNDO/2 method for
8,2'-S-cycloadenosine and extrapolated for the polynucleotide.
value of 4.0 was used for the dielectric constant.
A
The energy
barrier heights by rotation around the respective bonds were taken
from those given in ref. 2 and 3.
In the case of A s p A s , energy calculations were performed for
all the possible interactions in this molecule.
On the other
hand, a total energy for the polynucleotide, poly(rA) or poly(A s ),
was calculated as the sum of three kinds of the interaction
energy, (1) between individual two atoms in a unit (nucleotide),
(2) between atoms in the original unit and atoms in the adjacent
unit, (3) between atoms in the original nucleoside and atoms in
the phosphate group of the next nearest unit on the 3'-linkage side.
Minimization of the energy
Various parameters such as the dihedral angle are optimized
by the Powell algorithm
.
The energy minimization was carried
out by the parabola approximation with 4° intervals (bracketed
in 8 ° ) , and no angle was permitted to vary by more than 12° at
each step.
This minimization by parabola approximation which
has a great advantage in saving computer time, gave a similar
1976
Nucleic Acids Research
result as the trial and error routine with an accuracy of 1°.
The most reasonable values for each torsion angle, <t> ; 180°,
I|I ; 60°, 180°, 300°, <f>' ; 180°, w1 ; 60°, 180°, 300°, u ; 80°,
180°,
300°, x ; 30° for poly(rA), were postulated from various
investigations and were used by many investigators
27 different sets ( 1 x 3 x 1 x 3 x 3 x 1 ) ,
'
.
Among
some were excluded
because of abnormal steric short contacts.
In order to distinguish their individual sets, nine possible
(w',u>) combinations are represented by numbers ; 1 for (60°, 80°),
2 for (60°, 180°) and so on up to 9 for (300°, 300°).
The second
letter, gg, gt or tg, corresponding to 60°, 180° or 300°,
respectively, represents <J/, the rotational angle about the C(5')C(4") bond.
The helical parameters
Each helix is described by the step height Z, the radius R
(the perpendicular distance from phosphorous atom to the helix
axis), and the cylindrical rotation angle 0 (relating the angular
displacement of neighbouring residues).
A helix is characterized
as right-handed or left-handed depending upon whether 0 is
positive or negative, respectively.
These helical parameters
were calculated following the method reported by Miyazawa
It is necessary to determine the allowed region of each
parameter to form a reasonable helical structure.
Polynucleotide
chains can interact with each other via base pairing to form a
multistranded helix.
The radius seems to be large enough to form
a loosely wound helix.
The most typical polynucleotide helix is
o
o
a rigid rod with an approximate repeating distance of 3A to 4A
per a residue.
According to the observed parameters, we
estimated the following criteria ;
1.5 < Z < 4.5 A
5.0
A
< R
-60° < 0 < 60°
The base geometry
X-ray fiber diffraction, ORD, NMR and hypochromism studies
of polynucleotide helices indicate that the bases are stacked
nearly parallel to one another with the base-base distance of
1977
Nucleic Acids Research
3-4 A , and the base planes are nearly perpendicular to the helix
axis.
Therefore, the parameters specifying the base geometry are
represented by the two angles, n and A, in which the former
defines the complementary angle between the base plane and the
helix axis and the latter is the dihedral angle between neighbouring bases.
When n is equal to zero, the base plane is exactly
perpendicular to the helix axis.
If A is equal to zero, the
neighbouring bases are parallel to each other.
RESULTS AND DISCUSSION
Poly(rA)
For the poly(rA) helical molecule with the sugar puckering
either C(2')-endo or C(3')-endo, seventeen different sets, all of
which satisfy the energy minimization are listed in Tables I and
II.
It is noteworthy that some sets with 300° as the starting
Table I. The starting and final torsional angles of poly(rA) with C(2')-endo
conformation
set N o .
1-gt
2-gt
4-gt
5-gt
6-gt
8-gt
9-gt
2-tg
4-tg
6-tg
1-gg
2-gg
4-gg
5-gg
6-gg
8-gg
9-gg
starting angles(°)
V
*' co' CO
180 60 80 180 180
180 6Q 180 180 180
180 180 80 180 180
180 180 180 180 180
180 180 300 180 180
180 300 180 180 180
180 300 300 180 180
180 60 180 180 300
180 180 80 180 300
180 180 300 180 300
180 60 80 180 60
180 60 180 180 60
180 180 80 180 60
180 180 180 180 60
180 180 300 180 60
180 300 180 180 60
180 300 300 180 60
X
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
final angles(° )
f
us' us *
X
84 26 2 82 99 197 171
64 284 96 185 223 162
80 211 137 67 216 175
41 208 200 176 205 147
52 216 194 289 191 168
47 182 253 185 181 160
39 204 263 295 194 185
74 214 200 187 227 171
91 257 223 53 220 214
80 222 103 296 192 295
58 234 75 51 126 73
28 207 46 165 173 63
63 284 201 57 146 58
37 276 14S 176 149 46
66 228 185 294 145 57
-- • abnormal values -72 206 268 302 184 59
Energy
(kcal/unit) ordeT
3.8
"2
9.1
11
5.8
5
6.9
6
14
11.4
3
4.1
13
9.9
15
11.9
4
4.7
16
12.6
12
9.4
9
8.8
8
8.1
7
7.8
1
2.2
8.7
9
angle of IJJ show the energy minima with considerable change of
ijj but the set No. 8-gg with a C(2')-endo conformation does not
converge to a structure having reasonable spacial geometry.
The helical parameters and base geometries of the five possible
poly(rA) helices which have relatively low energy and satisfy the
helical criteria described previously are tabulated in Table III.
It is interesting to note that all the calculated stable polynucleotide helices have the preferred helical parameters corre-
1978
Nucleic Acids Research
Table II. The starting and final torsional angles of poly(rA) with C(3')-endo
conformation
set No.
starting angles(°)
*
y
U)
*'
1-gt
2-gt
4-gt
5-gt
6-gt
8-gt
9-gt
X
30
30
30
30
30
30
30
2-tg
4-tg
6-tg
30 180 60 180 180 300
80 180 300
30 180 180
30 180 180 300 180 300
1-gg
2-gg
4-gg
5-gg
30
30
30
30
30
30
30
8-gg
9-gg
180
180
180
180
180
180
180
180
180
180
180
180
180
180
60
60
180
180
180
300
300
60
60
180
180
180
300
300
80
180
80
180
300
180
300
80
180
80
180
300
180
300
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
1-80
180
180
180
180
180
60
60
60
60
60
60
60
final
angles(
Energy
•
¥
;kcal/unit)
order
185
175
198
191
191
186
180
176
172
176
176
175
169
162
0.9
9.4
9.3
8.6
8.9
-2.2
8.4
39 1 7 3 62 195 191 283
49 202 224
60 213 194
49 188 157 302 180 307
71
58 88 177
32 170
- 1 0 169 68 178 180
53
42 184 1 8 3 60 154
71
69
49 182 149 182 144
47 1 9 1 196 292 1 1 3 70
60
42 215 291 170 162
65
21 199 297 288 178
12.6
10.0
11.4
3
14
13
10
11
1
9
17
15
16
5
4
11
8
7
6
2
X
44
41
41
42
42
18
42
*'
w'
167
183
188
187
184
190
182
48
52
181
181
180
301
282
70
179
68
180
292
176
288
4.9
4.0
8.9
7.4
7.0
6.0
-2.0
Table III. The helical and base geometrical parameters
for the calculated poly(rA) conformations
satisfird the helical criteria.
Helical parameters
2n/e
Z(A)
R(A)
©
poly CrA)
[C(2')-endo]
15.0
2.64 1 7 . 2 1 24°
5-gt
8-gt
3.77
7.81 51°
7.1
1.69 10.60 38°
9.5
9-gg
poly(rA)
[C(3')-endo]
11.3
8-gt
2.74 12.15 32°
2.73 10.04 31°
11.6
9-gg
s e t No.
Base geometries
n
18 O
A
J O
15
13°
43
25°
50 o
19
2 4
o
10°
sponding to the observed conformations of RNA and DNA. The
energetically stable conformations, 8-gt (with C(3')-endo), 9-gg
(C(3')-endo), and 6-gg (C(2')-endo), have the final angles similar
to that of observed helical RNA's and DNA's, i.e., Watson-Crick
type DNA-10 2 4 , doublestranded RNA's 2 5 and C-DNA 26 , respectively.
The stacking schemes viewed along the helical axis of 8-gt(C(3')endo) and 9-gg (C(3')-endo) are shown in Fig- 2 and Fig. 3,
respectively. The 8-gt helical conformation has less favored
base stacking, with the base-base distance of 3.5 A to 4.5 A.
On the other hand, the corresponding distance in 9-gg conformation
1979
Nucleic Acids Research
Fig.3 The calculated poly(rA) helix
having the energetically stable
conformation with the C(3')-endo
conformation (set No. 9-gg) viewed
along the helycal axis MM -
Fig.2 The calculated poly(rA) helix
having the energetically stable
conformation with the C(3')-endo
conformation (set No. 8-gt) viewed
along the helical axis [0J .
is 3.4 A to 3.6 A
and a broad overlapping is maintained.
In both
conformations, the base planes are perpendicular to the helical
axis and form a right-handed helix.
The 1-gt conformation which
has a relatively low energy but a poor helical array, could
correspond to a tightly wound helix.
Saenger et al.
proposed
a detailed model for the poly(rA) single helix which is 9-fold
with a helix pitch of 25.4 A and the step height of 2.82 A .
The
adenine planes form an angle of 24° with a plane perpendicular
to the helix axis.
On the other hand, the 9-gg helix with the
C(3')-endo conformation in this work is 11- or 12-fold and the
adenine planes form an angle of 19° with a plane perpendicular
to helix axis.
The more detailed discussion on the torsion
angles in poly(rA) will be noted elsewhere.
These preliminary results for the poly(rA) helix reveal that
this method is also suitable for conformational analysis of other
polynucleotides.
None of many calculations thus far investigated,
in which the energy minimum was obtained with varying torsion
angles between merely two adjacent bonds, shows such reasonable
values as obtained in this work.
This is due to the fact that
the change in one angle significantly influences the other
1980
Nucleic Acids Research
torsion angles not only of the adjacent bond but also of the
bonds far apart and many investigations thus far reported have
disregarded the influence of the base portion from calculation.
A s pA s and poly(A s )
Twenty-seven possible sets for A S pA S conformations are
listed in Table IV. Of these, the considerable change between
Table IV.
The starting and final torsional angles of A pA
molecule used
with C(4')-exo conformation
final anglesC )
starting anglesf)
set No .
1-gt
2-gt
3-gt
4-gt
5-gt
6-gt •
7-gt
8-gt
9-gt
1-tg
2-tg
3-tg
4-tg
5-tg
6-tg
7-tg
8-tg
9-tg
1-gg
2-gg
3-gg
4-gg
5-gg
6-gg
7-gg
8-gg
9-gg
fi
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
54
*'i
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
60
60
60
180
180
180
300
300
300
60
60
60
180
180
180
300
300
300
60
60
60
180
180
180
300
300
300
80
180
300
80
180
300
80
180
300
80
180
300
80
180
300
80
180
300
80
180
300
80
180
300
80
180
300
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
180
Y2
180
180
180
180
180
180
180
180
180
300
300
300
300
300
300
300
300
300
60
60
60
60
60
60
60
60
60
fi
62
63
48
63
66
66
83
69
67
68
61
52
59
67
66
76
68
64
64
63
42
66
66
66
84
64
63
*'.
179
174
186
174
173
174
221
171
180
179
175
179
177
174
173
221
182
165
169
181
191
173
173
173
219
171
172
49
48
54
154
164
164
324
281
276
42
49
68
151
164
164
310
279
280
44
61
64
162
164
164
327
281
286
"i
*2
73
198
226
78
181
283
120
169
295
179
185
254
180
188
266
154
193
297
88
155
250
78
180
274
86
183
279
192
174
154
217
183
181
153
189
177
179
175
165
178
178
138
157
194
189
181
179
175
191
176
176
125
173
175
Energy
182
182
187
169
176
179
151
160
182
301
295
299
298
295
291
306
296
293
67
64
63
64
67
67
289
65
53
(kcal/mol.)
order
-60.4
-54.7
-52.9
-56.2
-56.6
-55.4
-55.3
-64.6
-52.5
5
19
21
12
9
15
17
2
22
7
6
25
14
12
19
26
18
24
4
3
23
10
8
15
27
10
1
-58.2
-58.6
-49.2
-55.6
-56.2
-54.7
-48.9
-54.8
-51.3
-61.2
-63.5
-52.1
-56.3
-57.1
-55.4
-29.1
-56.3
-66.3
starting and final angles was found in five sets, 3-gt, 1-tg,
4-tg, 7-tg, and 7-gg. The helical parameters and base geometries
for the four sets with lowest energy, 9-gg. 8-gt, 2-gg, and 1-gg, are
listed in Table VI, of which 9-gg and 8-gt gave reasonable
o
o
parameters, i.e., Z as 3.62 A and 3.91 A and e as -28° and -39°,
respectively. The adjacent bases' are nearly parallel to each
other (the dihedral angles for 9-gg and 8-gt are 12° and 30°,
respectively). The base-base stacking distance for 9-gg is
o
o
oo
3.0 A to 3.6 A and that for 8-gt is 3.2 A to 4.2 A. Because of
the observed strong CD splitting, 9-gg is a more plausible model
than 8-gt. It is important to note that these models with the
1981
Nucleic Acids Research
high anti conformation around the glycosyl bond have the lefthanded helical array and the stacking bases are nearly perpendicular to the helical axis.
The base geometries in these two
conformations are suitable for interpretation of the observed
unusual CD spectra.
The large overlapping patterns along the
helical axis are shown in Fig. 4 for 9-gg and in Fig. 5 for 8-gt
Fig.4 The calculated poly(A s ) helix
having the energetically stable
conformation (set No. 9-gg) viewed
along the helical axis 10].
Fig.5 The calculated poly(A s ) helix
having the energetically stable
conformation (set No. 8-gt) viewed
along the helical axis [0] .
This calculation can easily be extended to the case of the
polynucleotide, poly(A s ), in which the torsion angle x is fixed
at 126°.
The possible sets with the minimized energy for
s
poly(A ) are listed in Table V and the helical parameters are in
the lower part of Table VI.
The 9-gg and the 8-gt conformations
in poly(A s ) which are both the lower energy ones, have also the
preferred helical parameters as expected from the calculated
A s p A s conformation.
In these cases, the base planes are almost
perpendicular to the helical axis and the left-handed fashion is
retained in the sugar-phosphate backbone as well as base-base
stacking.
These left-handed helical conformations of poly(A s )
may be affected not only by the geometry between base and sugar
moieties fixed at high anti region, but also by the C(4')-exo
conformation and/or the nature of the arabinose moiety.
A detailed comparison of values in the torsion angle of the
1982
Nucleic Acids Research
Table V.
The starting and final torsional angles of poly(A s ) with C(4')-exo
conformation
final angles(° )
starting angles(°
set No.
4-gt
8-gt
4-tg
5-tg
6-tg
1-gg
2-gg
5-gg
6-gg
9-gg
Table VI.
X
*'
174
,-, 171
„
180
•o
174
2
„
173
169
181
173
173
172
^
*
169
160
300
295
291
67
64
67
67
53
4*
">'• w
154 78 217
281 169 189
180 80 180
164 188 178
164 266 138
44 88 181
61 155 179
164 180 176
164 274 176
286 279 175
Z(A)
R(A)
e
3.91
8.96
3.62
9-gg
poly(A s )
4.34
8-gt
9.45
8.02
-40°
3.61 10.81
-25°
A s pA :>
8-gt
9-gg
*'
0)'
165 153
279
157
135
179
43
67
176 179
*-" 167 158
179 281
,-,
„
>o
~
„
181
168
173
179
168
L 177
(1)
67
168
69
181
262
86
148
163
290
278
223
188
201
188
162
175
170
173
121
173
Energy
*
167
152
286
298
304
75
75
61
57
59
(kcal/unit)
order
-55.1
-55.6
-50.1
-48.5
-56.2
-55.0
-60.1
-50.8
-52.6
-55.6
5
3
9
10
2
6
1
8
7
3
The helical and base geometrical parameters
for the calculated A s p A s and poly(A s )
conformations.
Helical parameters
set No.
X
Base geometries
2Tt/6
n
A
-39"
-9.3
-28°
- 12.7
51°
26°
30°
12°
30"
22°
20°
9°
-9.0°
- 14.3
left-handed helix with that of a right-handed one is most fundamental in elucidation of the helical nature of polynucleotides.
The following valuable information is deduced from Table II and
Table V.
1. The difference in each torsion angle between the left- and the
right-handed helix does not exceed 25 degrees.
2. In the 9-gg conformation, the torsion angles, <j>' and w', may
affect the change in the sense of the helical turn.
On the
other hand, the corresponding angles in the 8-gt conformation
are w' and \p.
It is remarkable that poly(A ) can form a helical duplex or
triplex with other polynucleotide chains such as poly(U ) or
28
poly(laurusin phosphate) . In this case, base pairs of the
Watson-Crick or Hoogsteen type may form and the complementary
polynucleotide chains should be the left-handed as well as in
poly(A s ).
ACKNOWLEDGEMENTS
We thank Professor Morio Ikehara and his collaborators, in
1983
Nucleic Acids Research
particular Dr. Seiichi Uesugi for encouragement and helpful
discussions.
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