volume 3 no.3 March 1976
Nucleic Acids Research
Analysis of the possible helical structures of nucleic acids and polynucleotides.
Application of (n-h) plots.
N. Yathindra and M. Sundaralingam
Department of Biochemistry, College of Agricultural and life Sciences,
University of Wisconsin, Madison, WI 53706, USA
Received 28 January 1976
ABSTRACT
The two helical parameters n and h where n is the number of nucleotide
residues per turn and h is the height per nucleotide residue have been evaluated for single stranded helical polynucleotide chains comprising C(3') endo
and C(2') endo class of nucleotides. The helical parameters are found to be
especially sensitive to the C(U')-C(3') (sugar pucker) and the C(l*')~C(5')
torsions. The (n-h) plots display only one important helix forming domain
for each class of nucleotides characterized by the sugar pucker and the C{U')C(5') torsion. A correlation between the (n-h) plots and the known RNA (A,A 1 )
and DHA (A,B,C) helical forms has been established. It is found that all
forms of helices except the C-DNA possess a favorable combination of P-0
torsions. The analysis of the (n-h) plots suggests that C-DNA can have a
conformation very similar to B-DNA. Although the (n-h) plots predict the
stereochemical possibility of both right-handed and left-handed helices,
nucleic acids apparently prefer right-handed conformation because of the
energetics associated with the sugar-phosphate backbone and the base.
aUTRODUCTICm
Helices represent the single most important secondary structural form
of nucleic acids. It is therefore important to examine the possible types
of helices that could be generated from the monomer nucleotide unit.
1 2
Although there have been attempts, ' no detailed analysis is reported so
far on the possible types of helical and double helical nucleic acid
conformations presumably because of the complexity arising from the presence
of six rotatable single bonds in the moncmeric unit. This has been simplified to a considerable degree by the suggestion
that nucleic acids and
polynucleotides may be regarded as being composed of nucleotide units
possessing either the preferred C(3') endo or C(2') endo type of conformations (Fig. 1) and that the primary flexibility in the polynucleotide
backbone conformation involves the torsions around the phosphodiester
bonds linking the successive nucleotide units. Using this idea we report
here the evaluation of the helical parameters, viz., the number of nucleotide residues per turn (n) and the unit translation (h) for single stranded
polynucleotides as a function of the internucleotide phosphodiester
© Information Retrieval Limited 1 Falconberg Court London W1V5FG England
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Nucleic Acids Research
torsions P-0(3') (u 1 ) and P-0(5') (u).
These results in addition to
furnishing valuable information on the possible single stranded helical
conformations of nucleic acids, such as those in certain viruses, also
provide a basis for examining the possible double helical and nmltistranded
nucleic acid and polynucleotide structures.
METHODS
flUCLEOTIDE GEOMETRY
The c a l c u l a t i o n o f h e l i c a l parameters depends o n l y on t h e backbone
t o r s i o n s , and i s independent of the g l y c o s y l t o r s i o n s although they have
important i n f l u e n c e i n deciding t h e stereochemical f e a s i b i l i t y and
3 h
We have shown ' t h a t t h e
s t a b i l i t y of t h e r e s u l t i n g h e l i c a l s t r u c t u r e s .
t o r s i o n s around t h e s i x backbone bonds of the monomer n u c l e o t i d e are
restricted.
For t h e most preferred conformation of the n u c l e o t i d e , the
t o r s i o n I|I ' around t h e backbone C(U')-C(3') bond of t h e furanose r i n g i s
c e n t e r e d around gauche
( 7 6 ° ) or t r a n s (150°) domain corresponding t o t h e
C ( 3 ' ) endo and C ( 2 ' ) endo pucker of the sugar r e s p e c t i v e l y .
backbone t o r s i o n s around C ( 5 ' ) - 0 ( 5 ' )
(*), C(3')-0(3')
The other
( + ' ) and C ( U ' ) - C ( 5 ' )
(ip) of t h e n u c l e o t i d e are centered around the values l 8 0 ° ( t r a n s ) , 210°
( t r a n s ) and (.60°)
gauche
(gauche ) r e s p e c t i v e l y ( s e e F i g . 1 ) .
Although the
i s t h e most predominant conformation around t h e C(U')-C(5') bond
in n u c l e o t i d e s as w e l l a s n u c l e o t i d e s o f double h e l i c e s ' '
energetically,
and i s favored
c a l c u l a t i o n s have been performed for the t r a n s and gauche" .
conformations a l s o t o examine the nature and types o f p o s s i b l e h e l i c a l
structures that t h e s e nucleotides generate.
distances
Standard bond a n g l e s and bond
have been used f o r the sugar-phosphate backbone and a l l t h e
c a l c u l a t i o n s a r e f o r 0 ( 3 ' ) - P - 0 ( 5 ' ) bond angle of 1 0 3 ° .
EVALUATION OF HELICAL PARAMETERS
When t h e t o r s i o n s along t h e s u c c e s s i v e n u c l e o t i d e backbone bonds and
t h e phosphodiester l i n k a g e s are kept constant, the polynucleotide backbone
chain f o l d s i n t o a h e l i c a l s t r u c t u r e .
In such a s i t u a t i o n , each n u c l e o t i d e
r e s i d u e can be generated from the previous one by r o t a t i n g through an
a n g l e t (=36O/n, where n i s the number of residues per turn) and advancing
i t through a d i s t a n c e h, t h e unit h e i g h t along the h e l i x a x i s .
The
e v a l u a t i o n of t h e h e l i c a l parameters n and h from t h e dimensions of t h e
monomer n u c l e o t i d e u n i t reduces t o obtaining the transformation matrix
which transforms a v e c t o r from t h e coordinate system a s s o c i a t e d with t h e
( i + l ) t h u n i t or v i r t u a l bond t o the coordinate system of t h e i t h u n i t
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Nucleic Acids Research
(b)
Fig. 1: The two energetically most favored conformations for the nucleotide
building blocks (a) C(3') endo nucleotide and (b) C(2') endo nucleotide. The notations defining the bond rotations are indicated.
Note that the main difference between the two nucleotide units is
in the sugar pucker. The torsions around the C(U')—C(5') ($),
C(5')-O(5') (•) and C(3')-O(3') (<f>') bonds have values 60°, 180°
and 210° respectively in both types.
or virtual bond.
The mathematical formulation of this matrix is based on
the rigid body transformation similar to that described by Ramachandran
o
et al.
The helical parameters n and h are determined from this matrix
Q
on the same lines as detailed by Ramakrishnan
et al.
for polysaccharides.
for polpeptides and Rao
The helical parameters are computed for each
class of nucleotides as a function of internucleotide P-0(3') (o>') and
P-0(5') (">) torsions at intervals of 10°.
The possible values of n and h
i plot.
are depicted as contours of constant values of n's and h's on a u f ., <>
The dotted lines correspond to curves of constant n and the f u l l l i n e s correspond to curves of constant h.
Positive values of h represent a right-handed
helix while negative values of h denote a left-handed helix.
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Nucleic Acids Research
RESULTS
HELICAL PARAMETERS FOR THE C(3') ENDO ( 3 E) HUCLEOTIDES
The p o s s i b l e values of n and h computed as a function of the i n t e r nucleotide P-0 t o r s i o n s for a C(3') endo nucleotide unit i s shovn in F i g . 2
in the form of a (n-h) p l o t .
The points of i n t e r s e c t i o n of the h-curves
with the n-curves are interpreted in terms of s i n g l e stranded h e l i c a l
structures (n, ) characterized by s p e c i f i c values of n and h.
Thus the
(n-h) p l o t provides at a glance the p o s s i b i l i t i e s of various h e l i c a l s t r u c tures.
Values of n greater than 12 and l e s s than 3 are not shovn in F i g . 2
for c l a r i t y .
The maximum permissible value of n = 2 8 . 2 occurs at (aj',(u) =
o
(260°,310°). The maximum value of h corresponds to the length (^5.9 A) of
the nucleotide unit and values of h greater than this are obviously not
360
360
Fig. 2:
732
Curves of iso-n (
) and iso-h(} for single stranded C(3')
endo polynucl eot ide helices (i|) = g ). n .Th e t w o possible positions
of occurrence of right-handed A-RNA ( ;LL 2.8l) and A'-RHA (-^3) are
shown.
Nucleic Acids Research
possible.
It is noticed that curves of constant n from 3-12 occur in the
broad region of the (u',u)) map encompassing the ii>' torsions from -210 to +20°
and u from 190 to 360°.
This region corresponds to the g~g~ (300°,300°),
tg" (l6o°,3OO°) and upper portions of g~t (300°,l80°) conformations! domains
of the (u)',u) map.
Similarly curves of constant h ranging from -5 to +5
also occur in the same region intersecting the n-curves indicating the
possibility of a variety of helical polynucleotide structures.
Another
(l80o,60°)
region where the n and h curves intersect corresponds to the tg
conformation domain which generates helices comprising 3 and k nucleotide
residues per turn.
+
(6O°,6O°),
The n values between 2 and 3 occur in the g g
+
g t (60°,l80°), g g" (60,300°), g"g
(3OO°,l8O°) domains.
+
(-300°,60°) and lower portions of g"t
Some of these correspond to higher energy conformations
and are therefore unlikely to form stable helices.
For instance, it is
impossible to generate a stereochemically acceptable polynucleotide chain
with successive phosphodiesters in the g g
Similarly, the g~g
unfavorable.
or g t conformations. '
region has also been shown to be energetically
Both in the skewed g g~ as well as the tg
conformations,
the adjacent bases lie on opposite side of the central phosphodiester and
therefore cannot generate the energetically favored stacked helical structure.
These conformations have therefore been suggested as loop phospho-
diesters.
Thus the broad region comprising the tg" and g~g~ conformational
domains for which the adjacent bases are on the same side of the phosphodiester represent the single most important secondary structural region for
nucleic acids.
HELICAL PARAMETERS FOR THE C(2') ENDO (2E) NUCLEOTIDES
The primary difference between the C(3') endo and C(2') endo nucleotides
lies in the backbone C(U')-CC3') torsion which is nearly gauche
the former and trans (150°) in the latter.
(76°) in
It is apparent from a comparison
of the (n-h) plots given in Fig. 2 and Fig. 3 that the change in the backbone
C(U')-C(3') torsion from gauche
(C3'-endo pucker) to trans (C2'-endo pucker)
produces considerable shift towards lower P-0(3') (u1) torsions.
The contours
which occur at (U'.UJ) = (270°,310°) (g~g~) for the C(3') endo nucleotide now
occur at (u',u) = (200°,280°) (tg~) for the C(2') endo nucleotide causing a
shift of nearly 70° along u 1 and 30° along u.
Nevertheless the other
general features in the (n-h) plot are very similar to those obtained for
the C(3') endo nucleotide (Fig. 2 ) . The maximum permissible value of n =
U8.9 occurs at (w'.io) = (200°,270°) and is much higher than the value
(28.2) obtained for C(3') endo nucleotides indicating that C(2') endo
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Nucleic Acids Research
nucleotides can generate wider h e l i c e s than the C(3') endo nucleotides.
As
previously n-values greater than 12 are not shown in Fig. 3 for c l a r i t y .
The broad tg~ domain represents the single most important h e l i x forming
domain in the e n t i r e (<D',O)) surface.
Other features in the (n-h) plot are
similar t o Fig. 2 .
360
300
300
F i g . 3:
360
(n-h) p l o t for C(2') endo polynucleot ide h e l i c e s with C(U')-C(5')
in the preferred gauche conformation. The two possible positions
of occurrence of B-DNA and C-DNA are shown (see also t e x t ) .
(n-h) PLOT FOR C(3') EXO NUCLEOTIDES
Since C(3') exo, a form of C(2') endo pucker, i s frequently observed
U 12
13
for 2'-deoxyribose sugars '
and i s also favored in B-DNA,
i t i s of
i n t e r e s t t o compute the (n-h) p l o t with the C(3') exo nucleotide dimensions.
F i g . h shows the (n-h) p l o t obtained using C(3') exo nucleotide t o r s i o n s ,
* = 211*°, <t>' = 155°, * = 36°, i(«' = 156° as found in the B-DNA model. 1 3
These t o r s i o n s d i f f e r from t h e i r preferred values and are used in t h i s
c a l c u l a t i o n for the purpose of correlating the current B-DHA model with
the (n-h) p l o t .
734
Noticeable s h i f t s towards higher values of <u and a)1 are
Nucleic Acids Research
360
300
300
F i g . h:
360
( n - h ) p l o t f o r c ( 3 ' ) exc; p o l y n u c l e o t i d e h e l i c e s with C ( U ' ) - C ( 5 ' )
in t h e p r e f e r r e d gauche domain. The two p o s s i b l e p o s i t i o n s o f
o c c u r r e n c e of B-DNA and C-DNA a r e shown.
observed in t h e ( n - h ) p l o t s compared t o F i g . 3 .
These s h i f t s a r e due t o
t h e changes i n t h e n u c l e o t i d e backbone t o r s i o n s (i)> and $ ' ) r a t h e r t h a n t h e
change i n t h e sugar pucker from C ( 2 ' ) endo t o C ( 3 ' ) e x o . C a l c u l a t i o n shows
t h a t t h e ( n - h ) p l o t s f o r C ( 3 ' ) exo n u c l e o t i d e w i t h u s u a l backbone t o r s i o n s
(I|I = 6 0 ° , $ ' = 210°) i s v i r t u a l l y i d e n t i c a l t o t h a t obtained f o r C ( 2 ' ) endo
nucleotide ( F i g . 3 ) .
NUCLEOTIPES WITH ALTERNATIVE BACKBONE CONFORMATIONS
Although t h e gauche ( g ) t o r s i o n around t h e C(k')-C(5')
bond of a
nucleotide is energetically the most favored conformation, i t can also
adopt the other two staggered but less favored trans (t) and gauche (g )
orientations.
Such conformations may be important in the single stranded
loop structures and also in helical nucleic acids such as in viruses and
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Nucleic Acids Research
chromatin which axe involved in complicated t e r t i a r y structures. Hence,
i t i s important t o examine the nature of helical structures that the
alternative nucleotide conformations generate. These results furnish
information on the effect of C(U')-C(5') torsions on the helical parameters.
We have considered both the C(3') endo and C(2') endo sugar puckers as
before.
(n-h) PLOT FOR C(3') ENDO NUCLEOTIDE WITH THE TRANS (t) C(U')-C(5') TORSION
Fig. 5 shovs that when the C(U')-C(5') torsion is changed from the
preferred gauche (g ) to the trans (t) orientation, the (n-h) curves are
shifted along <o to the g~t domain (u',u) = (300°,l80°). The maximum value
of n = 60.3 occurs at (<»• ,u) = (28O°,l8O°) suggesting that the trans
nucleotide conformation permits wider nucleic acid helices than the preferred
standard C(3') endo or C(2') endo nucleotide conformations (see above). The
n-values greater than 12 occur in the g t domain and are not shown in Fig. 5
for c l a r i t y . The g~t represents the single most important helix forming
domain for t h i s class of nucleotide monomer. Furthermore potential energy
360
300
360
Fig. 5:
736
(n-h) plot for C(3')-endo polynucleotide helices with C(U')-C(5')
in the trans conformation.
Nucleic Acids Research
calculations have shown
that this conformation is energetically favored
and model building studies show that it is the only phosphodiester domain
that would provide possible stacking between the adjacent bases.
Interest-
ingly, the original Watson-Crick structure had this stereochemistry.
Other
details are similar to those found in Fig. 2 and are self explanatory.
(n-h) PLOT FOR C(3') ENDO NUCLEOTIDE WITH THE GAUCHE (g~) C(4')-C(5') TORSION
Fig. 6 shows the (n-h) plot obtained with the gauche (g~) torsion for
the nucleotide.
Compared to Fig. 2, Fig. 6 shows a shift in the (n-h) plot
along P-0(5') (a)) from the g~g~ domain to the g g
domain (IO'.CO) (300°,60°)
while the general features of the (n-h) curves are very similar, as was also
noticed in Fig. 5-
The maximum permissible value of n is only 13.6 and it
occurs at (u'.w) = (270°,60°) indicating that this nucleotide conformation
would generate narrow helices compared to the gauche and trans nucleotide
- +
conformations. The g g is the only important helix forming phosphodiester
domain.
The skewed g g
is one of the sterically accessible domain (although
energetically not highly favored) for the phosphodiester and is the only
Ik
conformation which leads to the overlap of the adjacent bases.
360
180
Fig. 6:
240
300
360
(n-h) plot for C(3')-endo polynudeotide helices with C(l+')-C(5')
in the gauche" conformation.
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Nucleic Acids Research
(n-h) PLOT FOR C(2') ENDO NUCLEOTIDES WITH THE TRANS (t) AMD GAUCHE (g~)
C(U')-C(5') TORSION
The (n-h) plots computed for the C(2') endo nucleotide with the trams
and gauche" orientations around the C(U')-C(5') bond showed shifts of 120°
along P-0(5') (u) very similar to those observed for C(3') endo nucleotides
(Figs. 5 and 6) and hence are not described.
The important helix forming
domains occur at the tt and tg phosphodiester (Table 1 ) .
These analyses
however demonstrated that the position of occurrence of the helix forming
domain on the (<i)'t(i>) surface is intimately correlated to the adjacent C d ' ) C(3') torsion associated with the sugar pucker.
While the changes in the
C(U')-C(5') torsion produce shifts mainly along P-0(5') (ID), changes in the
sugar pucker (Clt'-C3' torsion) produce shifts along P-0(3') (ui1).
Hence it
would be expected that lower values of CC*')-C(5') torsion (<60°) would
shift the helical domain towards higher P-0(5') torsions (eg. Fig. k). The
(n-h) plots obtained with nucleotides having values other than these would
be expected to exhibit properties intermediate to those discussed above.
DISCUSSION
CYCLIC STRUCTURES
It is seen from Figs. 2-6 that the value of h = 0 occur in the important
helix forming domain separating the curves of positive and negative h-values.
The intersection of the h = 0 curve with an n-curve is interpreted as a helix
with residue height eqjial to zero, in other words a flat helix.
Thus the
points of intersections of h = 0 and different n-curves generate ring
Table 1
Correlation between the nucleotide
geometry and the helix phosphodiester
Important Helix Forming Phosphodiester
Domain (OJ'.UJ)
C(U')-C(5')
t o r s i o n (i|i)*
C(3') endo
+
C(2') endo
tg"
1
g
2
t
g~t
tt
3
g~
- +
g g
tg+
g~g~
•The C(5')-O(5') (<t>) and C(3')-0(3') (*') torsions are
assigned 180° and 210° respectively.
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Nucleic Acids Research
s t r u c t u r e s comprising d i f f e r e n t number of n u c l e o t i d e residues ( n ) .
It
would be i n t e r e s t i n g t o examine whether t h e s e macro-cyclic r i n g s t r u c t u r e s
comprising i n t e g r a l number of r e s i d u e s a r e in fact
feasible.
The r i n g s t r u c t u r e s develop i n t o
stereochemicaily
right-handed h e l i c e s as t h e
value of m t o r s i o n i n c r e a s e s .
RIGHT-HANDED HELICES .
.
.
.
.
HELICES COMPRISING C ( 3 ' ) EKDO NUCLEOTIDES - A,A' FORMS OF RNA •
The p o i n t s of i n t e r s e c t i o n of h-curves (h>0) with the n-curves in t h e
(n-h) p l o t r e p r e s e n t right-handed h e l i c e s .
I t i s c l e a r from F i g . 2 t h a t
the g~g~ region r e p r e s e n t s the most important h e l i x forming domain and t h e
h-curves intersect the n-curves in this region at two different points
suggesting two different types of helical conformations for a given n and h.
For instance h = +3 curve intersects n = 11 curve at (tu'.u) = (290°,290°) and
also at (21*0°,320°).
To distinguish the two models, we refer to the region
near the phosphodiester (290°,290°) as the type 1 and the region near the
phosphodiester (2U0°,32O°) as type 2.
The preference for either of these
conformations is decided by energy and other geometric and structural
considerations like hydrogen bonding and stacking.
Although both of these
phosphodiester conformations are stereochemicaily accessible, type 1, with
the phosphodiester near (w'.w) = (290°,290°), has been shown to be energetically most favored for a dinucleoside triphosphate and a polynucleotide
backbone. '
Furthermore, i t is readily apparent from model studies that
type 1 provides better stacking interactions between the adjacent bases,
satisfying at the same time the requirements of base-pairing geometry.
The
o
type 2 model corresponding to the phosphodiester conformation (2U0 ,320°)
on the other hand results in poor stacking.
Consequently, the type 1
model (u',w) = (290°,290°) is expected to prevail in single as well as
double stranded nucleic acid and polynucleotide helices.
It is noteworthy
that a l l the observed helical nucleic acid and polynucleotide structures
comprising C(3') endo nucleotides such as RNA-11, RNA-12, A-DNA, poly A and
other synthetic polynucleotides indeed possess the phosphodiester in this
narrow g~g~ domain corresponding to the type 1 model (Table 2 ) .
It is striking that values of n > 6 and h = 1 to 5 occur in a narrow
region around (u>',u>) = (300 ± 20°, 300 ± 20°) indicating that relatively
small variations in the internucleotide P-0(3') and P-0(5') torsions would
result in a variety of helical conformations for nucleic acids.
This
also suggests that the possible transitions among these different but very
similar structures are expected to be smooth and noncooperative in nature.
The close proximity of the positions of occurrence of A-RNA (n = 11, h =
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Nucleic Acids Research
Table 2
Correlation between the helical parameters, the nucleotide geometry and
the phosphodiester conformation. Comparison of experimental and theoretically
predicted values
Polynucleot ide
Helices
n
h
observed
Internucleotide phosphodiester (ID',u)
Bef.
predicted
Type 2
Type 1
8
9
3.8
2.82
2.9
2.81
3.0
2.56
(295,285)
(290,286)
(285,257)
(286,298)
(300,295)
(313,275)
(305,305)
(300,295)
(295,300)
(295,295)
(290,300)
(290,290)
(2U0.335)
(21*5,330)
(21*5,328)
(250,325)
(21*5,325)
23
23
13
3-03
3.32
3.32
(259,298)
(212,315)
(21*1*, 326)
(25U,321)
(261*,311*)
(273,308)
(275,315)
(275,315)
(215,360)
(215,360)
21*
16
19
(265,310)
(265,310)
(220,355)
(220,355)
13
19
c(3')-endo
Helices
poly AH+, poly AH+
poly A
RNA-10
A-RtfA
A'-RNA
A-DNA
10
11
12
11
(2U0,3l+0)
20
21
22
C(2')-endo (C,,-exo)
J
Helices
p o l y (dA-dT).poly
(dA-dT)
C-DNA
C-DNA
B-DNA
B-DNA
8
9.3
9.3
10
10
3.38
3.38
2.81) and A'-RNA (n = 1 2 , h = 3) in the (n-h) plot (Fig. 2) indicate that
the p o s s i b l e A-*-A' t r a n s i t i o n in polynucleotide structures i s noncooperative,
in agreement with the conclusions from circular dichroism s t u d i e s .
CONFORMATIONS OF DHA HELICES - A, B, C FORMS
DNA i s know t o e x i s t in several polymorphic modifications.
In addition
t o A- and B- forms, DNA has been found t o exhibit the C- form in the presence
IT
16
of l i t h i u m
a s well a s sodium
s a l t s . A- form i s well characterized and
has e s s e n t i a l l y the same structure as RNA-11.
The position of occurrence
of A-DNA in the (n-h) plot l i e s therefore very c l o s e t o A-RNA ( F i g . 2 ) .
Both B-DNA and C-DNA have been implicated t o possess the C(2') endo c l a s s
of n u c l e o t i d e s .
'
I t i s of considerable importance to examine t h e i r
p o s i t i o n s of occurrence in the (n-h) plot since t h i s would reveal information
on t h e p o s s i b l e s i m i l a r i t y or d i s s i m i l a r i t y in the conformational structures
of t h e two forms.
and C-DNA,
740
B-DNA13*
has the h e l i c a l parameters n = 10 and h = 3.37
n = 9 and h = 3 . 3 2 . I t i s clear from F i g . 3 that the phospho-
Nucteic Acids Research
diesters corresponding to these structures l i e in the broad tg~ domain.
Interestingly, there are two possible phosphodiester conformations for a
single set of helical parameters since the h-curves intersect the n-curves
at two points, a feature also noticed in Fig. 2.
To distinguish the two
regions which generate two different structures we refer to the phosphodiester (u'.io) = (2U0°,270°) as type 1 and the phosphodiester (U'.OJ) =
(l80°,300°) as type 2.
It is striking that the points corresponding
to B-DNA and C-DNA in both type 1 and type 2 regions occur very close to
each other in the (n-h) plot (Figs. 3 and h).
This strongly suggests that
the conformational structures of B-DNA and C-DNA should be very similar.
However, in previous models the type 1 model was favored for B-DNA and
type 2 for C-DNA.
I t has therefore been regarded that the conformation of
C-DNA is considerably different from B-DNA.
is favored for B-DNA '
We agree that the type 1 model
probably because of favorable stacking inter-
actions and the base pairing geometry, and i t is now clear from the (n-h)
plot that the type 1 model for C-DHA is also possible.
We argue that C-DNA
would also favor the type 1 model (skewed g~g~ phosphodiester) rather than
the type 2 model (extended tg~ phosphodiester) and that the conformational
difference between the B-DNA and C-DNA structures is one of degree rather
than of kind.
It is also clear from the (n-h) plot obtained for C(3') exo
nucleotide (Fig. It) that the type 2 model is also energetically unfavorable
because of eclipsed torsion around the P-0(5') bond further indicating the
preference of the B- and C-DNA forms for the type 1 model near the g~g~
domain.
The phosphodiester in the g~g~ domain tends to provide a better
overlap between the adjacent bases while the tg~ domain results in an
extended phosphodiester conformations causing the adjacent bases to drift
apart.
COHFORMATIONAL TRANSITIONS IM NUCLEIC ACID HELICES
The apparent s i m i l a r i t y in t h e conformational s t r u c t u r e s of B-DNA and
C-DNA described above also gains support from t h e experimental observation
'
of noncooperative B-DNA+ C-DNA t r a n s i t i o n .
I t i s clear that this
t r a n s i t i o n would be expected t o be n e c e s s a r i l y noncooperative only i f both
t h e B-DNA and C-DNA s t r u c t u r e s occur in t h e type 1 o r type 2 conformations
( F i g s . 3 and h).
In such a s i t u a t i o n t h e B-DNA-»• C-DNA t r a n s i t i o n involve
only minor l o c a l modifications in t h e phosphodiesters.
in type 1
But i f B-DNA occurs
conformation and C-DNA in type 2 conformation, B-DNA •*• C-DNA
t r a n s i t i o n would then involve r e l a t i v e l y l a r g e r o t a t i o n s around t h e P-0
bonds.
Such a t r a n s i t i o n i s expected t o be cooperative in n a t u r e .
It is
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Nucleic Acids Research
extremely i n t e r e s t i n g t o note that the recent C-DNA model
has the phos-
phodiester in the region suggested by the (n-h) p l o t s thus providing
further confirmation t o the above deductions from the (n-h) p l o t s .
The
B-DNA-»-A-DNA t r a n s i t i o n i s necessarily cooperative since the C(U')-C(3')
t o r s i o n (sugar pucker) has t o change from the gauche
(C3'-endo pucker) t o
the trans (C2'-endo pucker) conformation domain involving a rotational
change of nearly 8 0 ° .
On the other hand the A^RHA + A'-KHA t r a n s i t i o n i s
expected t o be noncooperative since i t involves small adjustments in the
i n t e r n u c l e o t i d e P-0 torsions (Fig. 2 ) .
LEFT-HANDED HELICES
One of the most i n t e r e s t i n g observations in the (n-h) plot i s that
the negative values of h, for instance h = - 2 , - 3 , -U also i n t e r s e c t curves
of n = 3 t o 12 in the g"*g~ domain suggesting the p o s s i b i l i t y of left-handed
h e l i c a l structures with h e l i c a l parameters very similar to those observed
for right-handed h e l i c e s .
For instance according t o Fig. 2 , phosphodiester
t o r s i o n s (U'.UJ) = (290°,300°) generate a right-handed h e l i c a l backbone with
n =-12 and h = 3 whereas (io ' ,u ) = (265°,275°) lead t o a left-handed h e l i c a l
backbone with (n = 12 and h = - 3 ) .
Thus r e l a t i v e l y small changes in the
i n t e r n u c l e o t i d e phosphodiester separate right-handed and left-handed h e l i c a l
polynucleotide backbones.
It i s therefore important to examine why only
right-handed h e l i c e s are found in naturally occurring nucleic a c i d s .
F i g . T and F i g . 8 show a t y p i c a l right-handed and a left-handed polynucleotide backbone having identical torsions along the backbone except for
i n t e r n u c l e o t i d e phosphodiester.
The right-handed h e l i x has the internucleo-
t i d e phosphodiester (u ' ,u) = (290°,300°) with the h e l i c a l parameters n =
10.5 and h = 3.2 ( t = 3 ^ . 2 ) .
The left-handed h e l i x has the phosphodiester
(265°,275°) and has the h e l i c a l parameters n = l l . l t and h= - 3 . 2 (t = - 3 1 . 6 ) .
The g l y c o s y l conformation i s set at anti (x = 10°) in right-handed h e l i x
while i t i s s e t at high-anti (x = 120°) in the left-handed h e l i x .
The high-
ant i range i s d e l i b e r a t e l y chosen in the l a t t e r t o demonstrate that the base
plane i s nearly perpendicular only for t h i s range of glycosyl torsion whereas
the normal a n t i glycosyl conformation renders the base plane nearly p a r a l l e l
t o the h e l i x a x i s .
Comparison of Fig. 8 with Fig. 7 shows that e x a c t l y the
opposite i s t r u e for a rigit-handed h e l i x .
I t should be noted that the high-
a n t i g l y c o s y l conformation shown in Fig. 8 i s not meant to imply that i t w i l l
a u t o n a t i c a l l y l e a d t o left-handed h e l i x .
Complementary Watson-Crick hydrogen
bonding with the bases of the opposing strand r e s u l t s in a left-handed
ribbon or sheet l i k e structure.
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It i s clear that there is hardly any overlap
Nucleic Acids Research
Fig. 7:
I l l u s t r a t i o n of a right-handed helical polynucleot ide cnain
comprising the preferred C(3') endo nucleotides with successive
phosphodiesters having (u',(•>) = (290°,300°). The backbone has
the h e l i c a l parameters n = 10.5 and h = 3.2 (t = 3^.2°).
Note
that the base i s anti and i t s plane i s perpendicular t o the h e l i x
axis.
of the adjacent bases in the left-handed helix and furthermore the favorable
short-range van der Waals interactions between the adjacent sugar residues
are reduced.
These factors at l e a s t in part, may be responsible for the
preference of a right-handed rather than a left-handed double h e l i x for
nucleic acids in nature.
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Nucleic Acids Research
Fig.
8:
I l l u s t r a t i o n of a t y p i c a l left-handed h e l i c a l polynucleotide chain
comprising the preferred C(3') endo n u c l e o t i d e s with s u c c e s s i v e
p h o s p h o d i e s t e r s having (<D',U>) = ( 2 6 5 ° , 2 7 5 ° ) . The backbone has the
h e l i c a l parameters n = 1 1 . h and h = - 3 . 2 ( t = - 3 1 . 6 ° ) . Note t h a t
t h e base i s h i g h - a n t i and i t s plane i s perpendicular t o the h e l i x
axis.
The base plane would be p a r a l l e l t o h e l i x a x i s for the
normal a n t i conformation.
CONCLUSIONS
Although the r e s u l t s reported here provide d i r e c t information only on
the h e l i c a l s t r u c t u r e s of s i n g l e stranded p o l y n u c l e o t i d e c h a i n s , they a l s o
serve a s a f i r s t
s t e p toward understanding the p o s s i b l e double, t r i p l e
and multistranded h e l i c a l s t r u c t u r e s of polynucl eot i d e s .
A knowledge
of t h e s e would be p a r t i c u l a r l y helpful i n p r e d i c t i n g the h e l i c a l
structures
of n u c l e i c a c i d s i n such g i a n t molecules as v i r u s e s , chromatin, c e r t a i n
RNA-DNA hybrid complexes and c i r c u l a r DNA.
The r e s u l t s a l s o provide u s e f u l
d e t a i l s concerning t h e h e l i c a l conformations of n u c l e i c acids a f t e r
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Nucleic Acids Research
unwinding due to intercalations.
In double helical nucleic acids, at
least in the naturally occurring ones, the two backbone strands are
necessarily related by a diad symmetry.
In such cases, the tvo strands
have the same helical parameters, but instead of having separate helical
axes, the two strands share the common helix axis.
Therefore the helical
parameters determined for single stranded polynucleotide chain are
especially relevant for the understanding of the double helical nucLeic
acid conformations.
Model building studies clearly indicate that the
necessity of complementary base-pairing between the opposing strands
places stringent restrictions on the number of possible double helical
conformations.
Studies are currently in progress to examine in detail
the possible double helical conformations in nucleic acids.
The present analysis shows that there is a striking correlation between
the helical parameters and the geometry of the nucleotide "building block,
especially the nature of the sugar pucker (cU'-C3* torsion) and the exocyclic C(l*')-C(5') torsion.
There is only one broad, principal helix
forming domain in the (cu'.w) surface regardless of the sugar pucker and the
C(l+')-C(5') torsion.
and g~g
For C(3') endo nucleotides it occurs at the g~g~, g~t
phosphodiester domains when the C(l+')-C(5') torsion assumes the
gauche , trans and gauche" conformations respectively (Table 1 ) .
It is most
interesting that the adjacent nucleotide bases tend to overlap only for
these phosphodiesters which also represent the important helix forming
domains.
This suggests that the 'stacking' interactions between the
adjacent bases appears to be the fundamental property of nucleic acid
helices.
For C(2'0 endo (C3'-exo) nucleotides, the helix forming domain
occurs at the tg~, tt and tg
phosphodiesters for g , t and g~ orientations
of C(l*')-C(5') bond respectively.
Although the adjacent bases lis
on the
same side of the phosphodiester, there is hardly any base overlap in the tt
and tg
phosphodiester due to the extended nature of the nucleotide as well
as phosphodiester conformations.
Some of these helical domains seem less
likely because the mononucleotide as well as the internucleotide phosphodiester conformations corresponding to them are energetically unfavorable.
The C(3') endo and C(2') endo nucleotides with the gauche
conformation
around the C(l»')-C(5') bond are energetically the most favored, and are
the only conformations that have so far been observed in single, double
and multistranded helices. ? >
Short segments of helices comprising the
less favored nucleotide conformations may become important in certain
nucleic acids possessing complex tertiary structures.
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Nucleic Acids Research
For each class of, nucleotides, three broad types of helical structures
could be defined depending on the C(U')-C(5') torsion.
Within each type,
of course, several families of helical structures differing in the n and h
values could be generated by small variation in the internucleotide P-0
torsions.
Even though the phosphodiesters generating these helices are
energetically favored, relative stabilities of these helical structures are
determined by the helix energy (energy per nucleotide residue) which takes
ii»to account a l l the interactions of neighboring residues in one turn of the
helix.
The rapid variation of n and h in the helical domains (see for eg.
Figs. 2 and 3) and consequent close proximity of occurrence of the possible
helices i s suggestive of noncooperative transition between the different but
closely related helical structures.
As already pointed out only relatively
small changes in P-0 torsion ar necessary (Fig. 2) for A-RNA -t-A'-RNA
transition which i s therefore expected to be noncooperative.
There are two possible- phosphodiester conformations for the same nand h- values leading to two different helical structures having identical
n and h.
The phosphodiester closer to the g~g~ domain is preferred and is
favored in all double helical polynucleotides except C-DNA.
It i s argued
from the (n-h) plots that C-DNA can also display the favored phosphodiester
in the g~g~ domain thus possessing conformational structure very similar to
B-DNA.
Another interesting observation of this analysis is that small variations in the internucleotide phosphodiester in the helical domains can also
lead to left-handed helical polynucleotide backbone with helical parameters
similar to those observed in right-handed nucleic acid structures.
Model
building studies suggest that the decreased short-range van der Waals
attractive interactions between the adjacent residues of the sugar-phosphate
backbone and the concommitant loss of stacking interactions do not apparently
favor left-handed helical conformations in nucleic acids.
ACKHOWLEDGEMENTS
We gratefully acknowledge support of this research by a grant GM-17373
from the National Institutes of Health of the United States Public Health
Service.
References
1.
Sakurai, T. and Sundaralingam, M. (1971). Amer. Cryst. Assocn.,
2.
Aug. 15-20, pp. 91Sasisekharan, V . , Sato, T. and Langridge, R. (1971). Fed.. Proc.
Abs. 30, 1219.
746
Nucleic Acids Research
3.
h.
14.
15.
Sundaralingam, M. (I969). Biopolymers 7, 821-860.
Sundaralingam, M. (1973). In 'Conformation of Biological Molecules
and Polymers', The Jerusalem Symp. on Quant. Chem. Biochem., Eds.
E. D. Bergmann and B. Pullman, 5, Ul7-1*56, Academic Press, New York.
Yathindra, N. and Sundaralingam, M. (1973). Biopolymers 12, 297-31>».
Arnott, S. (1970). Progr. Biophys. Mbl. B i o l . 21, 265-319.
Yathindra, N. and Sundaralingam, M. (1974). In 'Structure and
Conformations of Nucleic Acids and Protein-Nucleic Acid Interactions ' . Fourth Harry Steenbock Symp. Eds.M. Sundaralingam and
S. T. Rao, pp. 6U9-676, University Park Press, Maryland.
Ramachandran, G. N., Venkatachalam, C. M. and Krimm, S. (1966).
Biophys. Jour. 6, 81*9-872.
Ramakrishnan, C. (I96U). Proc. Indian Acad. Sci. LIX, 327-3U3.
Rao, V. S. R., Sundararajan, P. R., Ramakrishnan, C. and Ramachandran,
G. N. (1967). In 'Conformation of Biopolymers'. Ed. G. N. Ramachandran,
pp. 721-737, Academic Press, New York.
Yathindra, N. and Sundaralingam, M. (1974). Proc. Nat. Acad. S c i . 7 1 ,
3325-3328.
Wilson, H. R. (1973). In 'Conformation of Biological Molecules and
Polymers', The Jerusalem Symp. on Quant. Chem. Biochem., Eds. E. D.
Bergmann and B. Pullman, 5, 261-267, Academic Press, New York.
Arnott, S. and Hukins, D. W. L. (1972). Biochem. Biophys. Res. Co""""
hi, 1505-1509.
Yathindra, N. and Sundaralingam, M. (1975). Biophy. J. 15, 87.
Ivanov, V. I . , Minchenkova, L. E . , Schyolkina, A. K. and Poletayen,
16.
A. I. (1973). Biopolymers 12, 89-110.
Marvin, D. A., Spencer, M., Wilkins, M. H. F. and Hamilton, L. D.
5.
6.
7.
8.
9.
10.
11.
12.
13.
17.
18.
19.
20.
21.
22.
23.
2U.
25.
26.
(1961). J. Mo^. B i o l . 3 , 5^7-565.
Brahms, J . , P i l e t , J . , Lan, T. T. P. and H i l l , L. R. (1973). Proc.
Nat. Acad. Sci. 70, 3352-3355.
Langridge, R., Marvin, D. A., Seeds, W. E . , Wilson, H. R., Hooper,
C. W., Wilkins, M. H. F. and Hamilton, L. D. ( i 9 6 0 ) . £ . Mo^. B i o l .
2, 38Arnott, S. and Seising, E. (1975). J. Mol. B i o l . 98, 265-269.
Rich, A., Davies, D. R., Crick, F. H. C. and Watson, J. D. (1961).
£ . Moj^. B i o l . 3 , 71-86.
Saenger, W., Riecke, J. and Suck, D. (1975). J. Mol.. B i o l . 9 3 , 529-531*.
F u l l e r , W., Hutchinson, F . , Spencer, M. and Wilkins, M. H. F. (1967).
£ . Mol.. Biol. 27, 5O7-52U.
Arnott, S., Hukins, D. W. L. and Dover, S. D. (1972). Biochem. Biophys.
Res. Communs. 1+8, 1392-1399.
Arnott, S., Chandrasekaran, R., Hukins, D. W. L., Smith, P. J. C. and
Watts, L. (197M. J. Mol.. Biol. 88, 523-533.
Arnott, S . , Chandrasekaran, R. and Martilla, C. M. (1971*). Biochem. £.
lfcl, 537-5U3.
Zimmerman, S. B., Cohen, G. H. and Davies, D. R. (1975). £• Mol. Biol.
92. 181-192.
747
Nucleic Acids Research
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