Geometry of Experimentally Observed RNA Residues in tRNA and Dinucleoside Monophosphates: The Effect of Small Variations in the Backbone Angles B. HINGERTY ,* M R C Laboratory of Molecular Biology, Cambridge C B 2 2QH, England Synopsis The polymerization of various experimentally observed conformers of RNA from tRNA and some dinucleoside monophosphates have been examined with a program that computes the basic helix parameters directly from the six backbone torsion angles w’, 4’, J.’,$, 4, w to give n (= 360/6’), the number of residues per turn; h , the rise per residue; and r , the radius of the phosphate atoms from the helix axis. The single-stranded regions of tRNA that have A-form residues have a notably lower value of n than the double-stranded regions. The G-U “wobble” base pair is shown to be a n energetically strained left-handed form. The A-form dinucleoside monophosphates also have a low value of n. A model of UpAl polymerized as a fourfold left-handed helix with the bases on the outside and phosphates on the inside is investigated for its sharp 90” turn angle characteristics. UpA2 cannot be polymerized due to a low values of h (1.31 A) and r (2.72 A), which cause steric hindering. An eightfold model of poly(rA) is discussed as are the nonhelical residues of tRNA. Finally, the effects of small changes in dihedral angles and bond lengths and angles on the helical parameters are investigated and discussed by way of explaining this behavior.
INTRODUCTION Much effort has been expended over the years in evaluating the helical parameters of polynucleotides from fiber-diffraction ~ t u d i e s . l - ~ However, the fiber analysis suffers from the inherent low resolution of the data compared to single crystals. Consequently, the analysis of‘single crystals of dinucleoside monophosphates forming miniature double he lice^^-^ has been of great interest. The helical parameters of some of these fragments have been calculated and compared with the fiber-diffraction results for larger polymers. With detailed conformations available now for the larger tRNA7-10 the helix parameters of the various helical stems are of considerable interest. Hingerty et al.ll have used a least-squares technique to fit the helical stems of tRNA to an 11-fold model using the method of Mackay.12 Yathindra and Sundaralingam13J4 have recently investigated possible left- and right-handed polynucleotide helical conformations. Ikehara systems15 allow left-handed polymers where cyclonucleosides are fixed in the high a n t i orientation. * Present address: Oak Ridge National Laboratory, Biology Division, P.O. Box Y, Oak Ridge, Tennessee 37830. Biopolymers, Vol. 18, 1901-1915 (1979) 0 1979 John Wiley & Sons, Inc.
0006-3525/79/0018-1901$01.00
HINGERTY
1902
TABLE I Dihedral Angle Definitionsa Angle
Atoms
w‘
05’-P-O3’-C3’ P-O3’-C3’-C4’ 03’-C3’-C4’-C5’ CY-C4’-C5’-05’ C4’-C5’-05’-P C5’-05’-P-03’ 01’-Cl’-N9-C8 (Pur) Ol’-Cl’-Nl-CG (Pyr)
*
6’
l J
6 w
X
a All angles A-B-C-D are measured by a clockwise rotation of D with respect to A, looking down the B-C bond, A eclipsing D is Oo. Note that the angle $’ is dependent on the sugar puckering.
The purpose of this report is to investigate the reason for the apparent wide variation of helical parameters for these experimentally observed quantities even though the actual values of the dihedral angles vary by relatively small amounts. The complicated geometry of the polynucleotide backbone seems to be the basis of the problem (Table I and Fig. 1). The six backbone bonds that determine the helical parameters are clearly more complicated than the simple geometry of the trans planar peptide. In the case of the peptide, we have only two torsion angles ($,#) that are variable. These produce a small number of well-defined helical structures. For a polynucleotide only p,determined by the sugar pucker, is relatively fixed a t -80’ for C3’-endo
00
N6
II
I
‘
H3
I C2
II Adenine
I
II
C6
Uracil
Fig. 1. The geometry of GpC with dihedral angles indicated. The bases A and U are also given. This defines the polynucleotide backbone necessary to define a helix (Table I).
GEOMETRY OF RNA RESIDUES
1903
and -144’ for C2’-endo with less than a flO’ variation. Such a large number of variables produces a complicated surface in six dimensions relating various combinations of these angles to a given foldedness of the backbone. A study of the number of nucleotides per turn, n versus h , the rise per residue along the helix axis, have been made by Yathindra and S ~ n d a r a l i n g a mfor l ~ the w’, w angle pair. In the present work, the helical parameters of several known experimental structures are calculated from dinucleoside monophosphate building blocks. These include the tRNA residues, the A-form [ (w’,w) = ( g - , g-); II/ = g+; C3’-endo ribose; 6’= t ; 6 = t ; x = anti] dinucleoside monophosphates and the non-A-form UpA conformers.16J7 The effect of small variations in the backbone conformational angles and bond angles on the helical parameters is discussed.
METHODS An analysis of single-stranded DNA from semiempirical potential energy calculations is presented elsewhere.18J9 The helical parameters were evaluated using the method developed by Mizushima and ShimanouchiZ0for polypeptides and later extended by Olson21,22for polynucleotides by the single virtual bond method. Table I1 gives the average values of the bond lengths and angles from the x-ray crystal structure of A ~ A P A .These ~ ~ have been averaged where appropriate, and those regions which display end effects such as the free 05’ and 03’ were omitted. The six rotation matrices for the six bonds that comprise the virtual bond employ these fixed bond lengths and angles. The quantities calculated are 8 (turn angle), n (360/8),h (the rise per residue), and r (the P atom radius from the helix axis). The ratio 0lh < 0 defines a left-handed helix, while 8/h > 0 defines a right-handed one, (0’ < 101 < 180’). This can be evaluated unambiguously by the method of Sugeta and M i y a ~ a w a . ~The ~ angles x need not be identical for dinucleoside monophosphates but are required to be so for strictly helical structures. This is a source of end-effect problems, which will be discussed below. TABLE I1 Parameters Used in Geometrical Calculationsa Bond Lengths Atoms
(A)
Atoms
P-05‘ 05‘-C5‘ C5‘-C4‘ C4’-C3‘
1.589 1.459 1.505 1.514 1.429 1.614
P-O3’-C3’ 03’-C3’-C4’ C3’-C4’-C5’
C3‘-03‘ 03‘-P a
From Ref. 23.
C4’-C5’-05’ C5’-05’-P 03’-P-05’
Bond Angles (deg) 119.0 109.8 117.5 108.8 120.3 104.6
1904
HINGERTY
For the CCA and anticodon loop of tRNA, the dihedral anglesll were averaged to find a helix. This was also done for the four helical stems of tRNA (amino acid, dihydro uracil, TGC, anticodon stems). However, the procedure was not entirely satisfactory, first due to the variability in bond lengths and angles producing a systematic effect on the structure and second because of the lower reliability of the coordinates (rms deviation of 0.3 A). The variation in dihedral angles from residue to residue was also considerable. Because of this variability in the helical parameters from seemingly small variations in conformation, a systematic investigation of this effect was made. For this purpose, residue A62 or tRNA,I1 which is an almost exact 11-fold helix, was used. Helical parameters were calculated as a function of all dihedral angles except @. The dihedral angles were varied in steps of 5" over a range of f25" from the observed value. Finally, the effect of variability in the bond lengths and bond angles on the helical parameters was investigated. The bond lengths were altered up to f0.04 A (the maximal variation possible) in steps of 0.02. The bond angles were varied in steps of 2" to f4" of the observed value.
RESULTS tRNA Yeast Phenylalanine The conformational angles for tRNA, which have been refined to a standard crystallographic R factor of 0.21, are given e1sewhere.l' Previous results have been given at R = 0.31.7 Table 111 gives the helical parameters for the dinucleoside monophosphate residues 2-75 of yeast phenylalanine tRNA. Residues 1and 76, which do not possess a complete backbone, were omitted. A negative h denotes a left-handed configuration. As can be seen from Table 111, there appeared to be much variation from one residue to the next in each A-type region. [A-type regions include the double-stranded residues: 2-6,ll-15,23-33,38-45,50-55, and 61-72 and the single-stranded A-type regions 8,20,35-36, and 73-75 (55 total residues A-form).] The low resolution of the data (2.5 A) and the variability in bond lengths and angles permitted by the energy refinement accounts in part for this. However, some systematic variation could be detected from residues that take part in unusual interactions. In addition, some variation due to base sequence was discernible. G3 has an unusual 0 of -26.2" (left-handed) or, equivalently, h = -4.2. This is the residue just before the unusual G-U base pair wobble. The left-handed helical backbone is required to permit this pairing. The low value of n (high 0) for C2 may also be related to this. C61 is also left-handed and has a low value of II/ (38"). This may be caused by the hydrogen bonding of C60 and D16 bases in the variable pocket, which results in some strain on the helix backbone at this point. The left-handed A29 with 8 = -29.2 may be correlated with the high 13 (52.9) of G30 to compensate for
63.7 26.2 39.0 27.5 28.6 138.1 53.0 101.8 117.2 24.2 49.2 35.9 35.9 38.6 174.9 176.7 136.5 71.5 61.9 138.7 80.3 27.0 35.6 40.0 51.0
C2 G3 G4 A5 U6 u7 U8 A9 m2G10 c11 U12 Cl3 A14 C15 D16 D17 G18 GI9 G20 A21 G22 A23 G24 C25 m5G26
5.7 13.7 9.2 13.1 12.6 2.6 6.8 3.5 3.1 14.9 7.3 10.0 10.0 9.3 2.1 2.0 2.6 5.0 5.8 2.6 4.5 13.4 10.1 9.0 7.1
n
3.4 -4.2 3.7 2.8 2.5 5.7 3.8 6.3 -4.6 3.6 2.3 1.4 2.7 2.1 -6.5 -5.1 -3.9 6.3 3.7 4.8 -6.1 2.3 1.9 2.5 3.7
h
4.1 10.0 7.1 11.8 11.2 1.9 4.2 0.2 2.2 12.3 6.7 11.1 7.9 8.9 0.9 1.8 2.5 2.3 3.8 2.3 2.1 11.5 9.2 8.5 5.7
r
C27 C28 A29 G30 A31 Cm32 u33 Gm34 A35 A36 Y37 A38 $39 m5C40 U4 1 G42 G43 A44 G45 m7G46 u47 C48 m5C49 U50 G51
Residue 38.0 38.8 29.2 52.9 40.9 43.3 37.7 131.5 45.3 40.7 59.8 38.2 49.9 37.1 45.6 26.3 23.0 42.9 78.6 133.2 96.6 105.2 169.2 32.9 34.2
B 9.5 9.3 12.3 6.8 8.8 8.3 9.5 2.7 8.0 8.8 6.0 9.4 7.2 9.7 7.9 13.7 15.7 8.4 4.6 2.7 3.7 3.4 2.1 11.0 10.5
n 1.5 3.5 -0.7 4.8 3.4 2.7 0.8 3.1 1.4 -0.2 2.8 2.3 3.3 1.6 3.3 0.2 4.3 3.9 3.7 5.6 2.0 -1.9 -1.6 7.4 2.8
h 8.7 6.9 13.0 4.0 7.1 7.4 8.9 2.8 7.2 9.5 5.5 9.2 5.9 9.6 6.0 12.9 11.7 6.4 3.3 1.2 4.8 4.3 2.8 8.6 9.1
r
U52 G53 T54 $55 C56 G57 m'A58 U59 C60 C61 A62 C63 A64 G65 A66 A67 U68 U69 C70 G71 C72 A73 C74 C75
Residue
n 12.8 10.8 7.2 7.2 2.8 5.1 2.2 2.1 2.6 6.0 11.1 11.7 15.8 10.8 12.8 14.3 14.9 9.5 15.9 7.6 13.7 10.1 7.3 10.5
0 28.2 33.4 50.2 49.7 130.5 70.0 165.6 168.5 138.1 59.6 32.5 30.8 22.8 33.3 28.1 25.2 24.1 37.8 22.6 47.6 26.3 35.5 49.4 34.2
r
11.1 9.2 5.0 5.8 2.3 4.4 1.7 1.8 2.1 5.5 9.5 10.6 15.2 10.0 11.2 10.6 13.8 8.0 16.0 6.9 10.8 8.4 5.3 10.4
h 3.4 3.7 3.5 2.8 -3.9 3.7 5.4 4.4 5.5 -0.3 2.4 2.4 1.3 2.0 3.0 4.0 2.3 3.0 0.4 2.8 3.8 3.2 3.1 2.6
a
From Ref. 11. For residues 2-75, 18 are non-A-form. Four are C (C48, m5C49, C56, C60); 6 are G (m2G10,G18, G19, G22, Gm34, m7G46); 3 are A (A9, A21, m'A58); and 5 are U (U7, D16, D17, U47, U59). The single-stranded regions are 8, 20, 35-36, 73-75.
I)
Residue"
TABLE 111 Helical Parameters for Individual Residues of Yeast tRNA Phenylalanine Taken as 5'-Nucleotides"
1906
HINGERTY
the negative turn angle, although this may indicate only a transfer of strain along the backbone. G45, the last residue of the anticodon arm, has an unusually high 0 (78.6) and low n (4.6). This is mostly an end effect, as the helix terminates a t m7G46. However, G45 is also involved in a base triple with m2G10 and C25, which may contribute to the high 0. Examination of other A-form residues that are not part of the base-paired stems shows that U8 and G20 have low n values of 6.8 and 5.8, respectively. These are more similar to single-stranded helices that have low n and r as compared to the d ~ p 1 e x e s . l ~ The existence of conformational strain in the backbone is consistent with a recent study by R h ~ d e on s ~the ~ initial stages of thermal unfolding of yeast tRNA phenylalanine. This study has shown that the left-handed G-U26 base pair is unstable and melts easily. The m5 C49-G65 base pair also melts early, since the phosphate of 49 is altered from the A-form c o n f ~ r m a t i o n . ~ ~ The m5C49 has an unusual skewed w‘ of looo, which is shifted from the standard g+ (60”). The stacking of U59 with C60 is the most easily disrupted part of the structure in the absence of Mg++. This may be related to the left-handed nature of C61 mentioned above. The nonstandard base pair G15-C48 melts somewhat later than U48-Al4, which may involve different strains a t m5C49 and U8. In addition, C48 has unusual values of (w’,w) of (g+,g-) = (86”, 332”). The two base triples C13-G22-m7G46 and m2G10-C25-G45open up a t about the same temperature. G45 was described previously, while m7 G46 shows strain with w’ = 235” (skewed). Because of the consistency with the thermal unfolding data,25we do not believe this is due to errors in the model. Loops and bends are produced by special configurations. A stretch is caused either by w’,w = t,g- or a C3’-endo-(3’,5’)-C2’-endo ribo~e.~ Residues 19,9, and 58 show this. They have high h values of 6.3,6.3,5.4, which roughly correspond to a double base spacing. Bends in the structure come from w’,w = g-,t or C2’-endo- (3’,5’)-C3’-endo r i b ~ s e s . Residues ~ 7,10,19,34, and 56 have one or the other of these conformational features. This translates into a very small turning radius ( r < 3 A) and high 0. All the H are over 100” except 19, which is 72’, and 7 has a high h of 5.7 A. In addition, 10 and 56 are left-handed. All left-handed conformations are in bends of the structure except for G3, C61, and A29, which are strained due to tertiary interactions. The existence of left-handed bends in tRNA has already been mentioned by Sundaralingam and Yathindra.14 Table IV gives the percentage of non-A-form residues in tRNA and the average value of n (number of residues per turn of helix). We see clearly the preference of G and U for non-A-form conformations, consistent with semiempirical energy calculations on RNA residues done previously by Broyde et a1.28 In considering the average value of n for the different bases in tRNA, we see that for double-helical regions, n is lower for (G,U) compared to (C,A). In addition the single-stranded A-forms have a markedly lower n for (G,U) compared to (C,A). The single-stranded regions have a lower nthan the double-stranded regions, which are similar to 10- to
GEOMETRY OF RNA RESIDUES
1907
TABLE IV Percent of Non-A-Form Residues in tRNA and the Average Value of na
P1
Base C A G U
nl
P2
n2
8.9 9.0 5.8 6.8
38.9 (7/18)
17.6 (3/17)
61.1 (11/18)
29.4 (5/17)
Mean
10.3
8.2
a A form: (w’,w) = (g-,g-); $ = g+; ribose = C3’-endo; 6 = t , 6’= t , and x = anti. P I , percentage of non-A-form residues for each type; the number in parentheses indicates fraction where modified bases are considered as normal for this purpose. The Y-base is omitted. Pz, the percentage of non-A-form being either C A or G U (fraction in parentheses). nl, average value of n for double-helical regions (48 residues). n2, average value of rz for singlestranded A-form regions (7 residues).
+
+
12-fold values. This is consistent with theoretical calculations on DNA done p r e v i o u ~ l y . In ~ ~addition, a sixfold model of poly(rC) by Arnott et aL29using fiber diffraction and also a 6.6-fold theoretically calculated model of 8-bromo-poly(rA) by Govil et al.30confirm a lower value of n for singlestranded structures. Arnott31 observed the same sixfold structure in an orthorhombic crystal form of poly( 2’-OMe-C) using fiber diffraction; in such a structure there can be no -OH.--OH hydrogen bonds. Table V gives the average values of the torsion angles and the corresponding helices that are generated for the amino acid, dihydro U, T$C, and anticodon stems. Hingerty et a1.l1 have used a least-squares program to fit the helical stems to an 11-fold type of RNA with h = 2.5 A,and it was not clear why the values of n in this case should vary from 9.3 to 11.9 residues per turn. When all four helices were averaged, n = 10.4 residues per turn and h = 2.80 A. The low value of h (1A) in the anticodon loop (residues 35,36) is unusual and is probably due to a low value of 4 (141O). When the anticodon is complementary base paired to the codon UUC, we would expect a small but noticeable conformational change that would most likely cause h to increase. TABLE V Average Parameters for tRNA Stems, CCA. and Anticodon Lo00 Rep.ion * 1. 2. 3. 4. 5. 6. 7.
Aminoacid DihydroU T$C Anticodon Average for 1-4 CCA Anticodon IOOD
w‘
6‘
288 290 289 292 290 291 279
203 205 205 208 205 203 203
82 82 84 83 83 85 80
64 66 57 62 62 59 68
176 171 175 173 174 176 141
281 281 285 284 283 288 289
8
n
h
r
30.3 33.8 35.4 38.6 34.6 35.3 37.8
11.9 10.7 10.2 9.3 10.4 10.2 9.5
2.71 2.84 2.53 3.02 2.80 3.42 0.93
10.48 9.44 8.92 7.91 9.08 8.30 9.49
a 1, contains residues 2-6, 66-72; 2, residues 11-15, 23-26; 3, residues 50-55, 61-65; 4, residues 27-33,38-45; 6, residues 73-75; 7, residues 35,36.
HINGERTY
1908
One last point to be noted is the existence of two rare B-forms (U7, C60), which are the same as the A-form except that the ribose is C2'-endo and 4 = 270". Of the 57 total A- or B-forms, only 2 or 3.5% are B, indicating the overwhelming preference for the A type in RNA.
Dinucleoside Monophosphates These structures possess all the conformational angles necessary to define a helix. Although this is the case, they suffer from end effects which make model building difficult. Since the x angles are not equal in the dinucleoside monophosphates, as they must be for a regular helix, the extension of residues on either side does not actually produce a regular structure. In the crystal structures of these molecules, the x angles depend on whether the bases are purines or pyrimidines. The base-stacking parameters, which are not considered here, will clearly depend on the x angles. In particular, y,the angle the bases make with the helix axis, will be different. Rosenberg et al.32 have recently devised the helix probe method to deal with this problem. The helical parameters from the four molecules of GpC in the Ca++ salt crystal structure: the single GpC in the Na+ salt? and the two structures of ApU5 are given in Table VI. The GpC structures are all about eightfold, while ApU appears to be ninefold. The average of Ca++ GpC 1to 4* gives roughly the same result of n = 7.8 and h = 2.6. These results differ from those of Rosenberg et al.,6,32who used the helix-probe method. Their results gave GpC with n = 10.4 and pitch 26.9 (h = 2.6), while ApU had n = 11.9 and pitch 28.1 ( h = 2.4). The reason for the difference is in the sensitivity of the calculation to small variations in dihedral and bond angles (discussed below). Fiber diffraction on poly(dGdC) by Arnott et al.33is eightfold, as are the computed helices from the rib0 GpC crystal structures. TABLE VI Parameters for Dinucleoside Monophosphates Molecule
Ref.
4 GpCl 4 GpC2 4 GpC3 4 GpC4 4 GpCl-4 6 GpC (Na+) GpC (all 5) 5 ApU2 5 ApU 1 ApA+ 23 UpAl 16,17 UpA2 16,17
w' 6' -
294 29 1 290 288 291 292 291 284 29 1 283 163 84
222 217 224 216 220 211 218 22 1 213 223 224 202
P
#
6
w
6
n
h
r
77 76 72 85 78 83 79 78 78 82 92 85
47 57 63 52 55 50 54 58 57 53 52 56
181 172 167 181 175 184 177 168 177 161 192 202
291 293 286 283 288 285 288 295 288 298 272 84
51.7 41.1 43.2 45.7 46.1 43.7 45.1 39.0 41.1 44.3 88.3 178.9
6.97 8.77 8.34 7.87 7.82 8.24 8.04 9.22 8.76 8.13 4.07 2.01
2.26 2.96 2.32 2.43 2.56 2.42 2.48 3.10 2.89 2.65 -3.35 -1.31
5.44 6.89 6.99 6.56 6.32 6.79 6.53 7.16 7.01 6.17 3.13 2.72
GEOMETRY OF RNA RESIDUES
1909
Models of UpA Helical parameters were calculated for the unusual bent conformers of the crystal structure of UpA.16J7 Results are given in Table VI. UpAl with w',w = t,g- produces a fourfold left-handed helix (90' turn angle 0) with the base planes nearly perpendicular to the helix axis and h = 3.35. No stacking takes place because of the 90" turn angle. The phosphates are on the inside of the structure with r = 3.1 A. UpA2 with w',w = g+,g+ produces a left-handed, twofold helix with h = 1.3 A. The value of h is too low for the structure to be polymerized. The phosphates are also on the inside a t r = 2.7 A. Recently a fiber-diffraction study of poly(rA) in the denaturing solvent formamide showed the structure to be twofold with h = 2.9 and w',w = gf,gi.34 As pointed out earlier, the t,g- conformer is important in the tRNA molecule. It is found a t G19, G22, and U47, although G19 is C2'-endo. These conformers take part in important bends of the structure in the dihydro U loop and extra arm extension from 45 to 49 (Fig. 2).
Model of Poly(rA) The helical parameters for poly(rA) were calculated using the coordinates of ApA+ from the crystal structure of A P A ~ A . We ~ ~ were surprised to obtain an eightfold model, since a ninefold has already been presented. We used the actual bond lengths and angles from the ApApA crystal structure. Although the difference between 40' and 44' may not
'
'
2
I D-stem 1
'
vr"
TVC loop plus G , E G , ~
Fig. 2. Schematic diagram of the chain-folding and tertiary interactions between bases in yeast tRNAPhe. Long lines indicate base pairs in double-helical stems. Shorter lines represent unpaired bases. Dotted lines represent base pairs outside the helices. From Ladner e t al. (Ref. 8).
HINGERTY
1910
be significant, the eightfold model allows a symmetrical bonding system as in poly(rAH+) poly(rAH+) by Rich et al.36 This agrees with the fiber work, although in our case we have a screw of 2.7 8, compared to the 3.8 A in the fiber analysis. As pointed out by one of the referees, this difference in h corresponds to the difference between a large negative base tilt and the large positive tilt of the usual A-form.
Variation from Small Changes in Dihedral Angles The effect of a small variation in parameters about the A-form conformation was examined. The dihedral angles of A62 of tRNAll were used as starting parameters. This residue is almost exactly 11-fold. The torsion = 84', w = 52', 4 = 172', and w = 293'. angles are w' = 280°, 4 = 211', Bond lengths and angles given in Table I1 were fixed. The dihedral angles were varied f25" in 5' steps. Results given in Fig. 3 show the variation of 8, n, h, r with w', w , 4', 4, and $. For w' and 4', the parameter most affected is 8 or n with a near linear
n
t
11.0
44.0 5.0
10.0
42.0 4.0 100 40.0 3.0
9.0
90
8.0
38.0 2.0
7.0
36.0 1.0
6.0
34.0 0.0 8.0 32.0 -1.0
5.0 4.0-
--W
0 5 !
!
3.0
26.0 52.0 18.0 47.0 16.0 42.0
17.5
14.0 37.0
1.0 15.0
12.0 32.0
12.5
10.0 27.0
0 0 10.0 7.5
8.0 22.0 6.0 17.0
~~
255
265
275
285
295
305
i
2 . 0 20.0
-1.0
5.0,
W'-+
Fig. 3. Variation of 0 ( - - -), n (-), h (-@-), and r (-O-) with (A) a',(B) w , (C)b', (D) @, and (E) IC. dihedral angles from A62 of tRNA (Ref. l l ) , with w' = 280', 4' = 211', w' = 84', $ = 52', 4 = 172', and w = 293'.
GEOMETRY OF RNA RESIDUES C
0 54 0 3 0
o/.-.-,.20
1911 r
En0 4 1 0;2 16 0 44 0 2 0 18 0
-.. 186
, , , 196
/
,
1 4 0 3 9 0 1 5 15 0 12 0 3 4 0 1 0 12 0
/
206
216
10 0 29 00 5 9 0 8024000 6 0 6019 0-05I 3 0 23,6
226
-0
-
n e h r
.-,
11.5 44 0 110420
100
1054004 09 0
1
1003803080 9 53802 0 7 0
-147
157
167
903401060 177
187
853200050 197_
-@
n e h r
t
\\
k,
0’
27
37
1
47
a(
0,
Fig. 3. (continued from the previous p a g e )
variation, while h increases with a much more level distribution, especially about the helical values w’ (280’) and 6’(211’). T h e radius is, as noted before,lg correlated with n , which has also been pointed out by Zimmerman.:’7 The variation due to w , 6,and Ic/ expresses itself in a different way as a pronounced centroid of the distribution in 0 or n , while h shows the greatest variation. If h varies too much, either stacking is lost or nonbonded contacts become important in inhibiting the conformation. T h e stability of these angles to small variations is reminiscent of a potential well from perturbation theory in quantum mechanics. It is clear that a large variation in helical parameters can be observed from a small perturbation of the angles. Only certain complex combinations of angles can preserve a similar structure.
Variations from Small Changes in Bond Lengths and Angles Because of the wide variations found in the helical parameters from seemingly small variations in conformation, it was decided to investigate the effect of variable bond lengths and angles on these quantities. Results
HINGERTY
1912
are given in Fig. 4. Variations of f 4 ’ in steps of 2O were taken for bond angles. Variations of f0.04 A in steps of 0.02 A were taken for bond lengths. Standard values of bond lengths and angles are given in Table 11. The bond lengths had little effect on the results. There is no variation in H or n , since by geometrical considerations only h and r can vary. Only bond angles and dihedral angles can affect 0 or n , since the single virtual bond-rotation matrix, T , is only a function of the bond angles and dihedral angles in the backbone. The maximum variation in h was 0.07 A for P-05’ bond length and the maximum variation in r was 0.14 A for the C4’-C3’ bond length. These results are not tabulated, since the changes were insignificant. The bond angles, on the other hand, had a dramatic effect on the parameters. Figure 4(A)-(C) shows the variability due to P-O3’-C3’, C4’C5’-05’, and C5’-05’-P. These angles affect h, r, and H or n by the largest amounts, respectively. Maximal change was h by 1.3 A, r by 2.8 A, and n by 2.7 residueshurn (0 by 7.9’). It was possible by just varying C5’-05’-P to change n from 9.9- to 12.6-fold. The other angles 03’-C3’-C4’, C3’-C4’C5’, and 03’-P-05’ show less effect and are given in Figs. 4(D)-(F). This
30g51
I
enhrl
35 012 0 3 5
/e
340 33011 0 2 5 9 4 320
- --.
2093
31010015 9 3
1-
115
117
119
121
p-03’-c3’
123
B
33011525100 31 0 11 0 24 29010523 9 0
27 0100 2 2
:n
h r
-
7
1
380130
320100 24100 30090
90
Fig. 4. Variation of 0 ( - - - ) , n (-), h (-0-1, and r ( - O ) with (A) P-O3’-C3’, (B) C4‘-C5’-05’, (C) C5’-05’-P, (D) 03’-C3’-C4’, (E) C3’-C4’-C5’, and (F)03’-P-05’ from A62 as in Fig. 3.
GEOMETRY OF RNA RESIDUES
1913
D
e n h r
35 0 34 012025 330 96 3201102094 310
92
3001001 5 9 0
03'-C3'-C4' 105 8 1078 109 8
1118
1138
E
e n h r
32011 0 2 2 9 0 310 21 3001002 0 8 0
1135 1155
1175
1195 121 5
C3'-C4'-C5'
35.0 12.0 2.6100 34.0 2.5 33.0 11.02.49 0 32.0 2.3 31.0 1002.28.0
1006
102.6 104.6 106.6 1086 03'-'-05'
Fig. 4. (continued from t h e previous p a g e )
clearly has implications for fiber diffraction analyses, since bond angles are normally held fixed in these cases. It is also pertinent to the end-effect problem encountered in extending small molecules to polymers, since such variations can cause drastic changes in the'helical parameters.
CONCLUSION The helical parameters of the individual residues of yeast tRNA phenylalanine and some dinucleoside monophosphates have been examined by a program that computes these parameters directly from the six backbone torsion angles. Wide variations were found that disagreed with other calculation^.^,^^ Some of the variation is explained by backbone strain in the molecule consistent with a thermal-unfolding experiment of tRNA.25 The best example is the conformationally strained G-U "wobble" base pair26that melts easily, possibly due to its left-handed backbone. However, not all of these results can be accounted for in this way. A systematic study of the effect on the helical parameters of small perturbations in the dihedral angles and bond lengths and bond angles was made. Although bond lengths had negligible effect, dihedral and bond angles produced large
HINGERTY
1914
changes. The angles w' and $' caused n to linearly decrease in value as they were increased. w , $, and affected h more dramatically, with a well-like surface in the 8-h curve similar to that of a potential well in perturbation theory. The variations due to bond angles are to be viewed seriously, since these are normally held fixed in fiber computations. It might be worthwhile to include bond angle bending terms of the form w ( 8 - 1 9 0 ) as ~ done by L e ~ i tand t ~ also ~ suggested by Sundaralingam et al.39 as an extra term in fiber refinement because of the sensitivity of the helical parameters to bond angle strain. In the helix-probe method of R o ~ e n b e r g ,the ~ , ~generated ~ helix is assumed to be 10- to 12-fold, so that only a small change in this parameter is permitted. By using this procedure you can force the structure into a given foldedness by bending the backbone. For these reasons we must be careful in making conclusions regarding helical parameters from monomer geometries. Therefore, those who calculate helical parameters need to be very sure of their bond lengths and angles and dihedral angles if valid information is to be obtained. It can be speculated here that the wide variability in helical parameters with small changes in molecular geometry could relate to protein-nucleic acid interactions. In such a case the sequence dependence and flexibility of the nucleic acid would play an important role in the complexes that are formed and the interactions that take place.
+
B. H. would like to thank the National Institutes of Health, National Cancer Institute for postdoctoral fellowships 1F22 CA02210-01 and 1F32 CA06223-01. B.H. would also like to thank J. R. Rubin for help with the UpA and poly(rA) structures, S. Broyde for detailed comments on the manuscript, and D. Rhodes for the thermal-unfolding data for tRNA.
References 1. Watson, J. D. & Crick, F. H. C. (1953) Nature 171,737-738. 2. Langridge, R., Marvin, D. A., Seeds, W. E., Wilson, H. R., Hooper, C. W., Wilkins, M. H. F. & Hamilton, L. D. (1969) J . Mol. Biol. 2, 38-64. 3. Arnott, S., Chardrasekaran, R. & Selsing, E. (1975) in Structure and Conformation of Nucleic Acids and Protein-Nuclezc Acid Interactions, Sundaralingam, M. & Rao, S. T., Eds., University Park Press, Baltimore, Maryland, pp. 577-596. 4. Hingerty, B., Subramanian, E., Stellman, S. D., Sato, T., Broyde, S. B. & Langridge, R. (1976) Acta Crystallogr., Sect. B 32,2998-3013. 5. Seeman, N. C., Rosenberg, J. M., Suddath, F. L., Kim, J. J. P. &Rich, A. (1976) J . Mol. Biol. 104,109-144. 6. Rosenberg, J. M., Seeman, N. C., Day, R. 0. & Rich, A. (1976) J . Mol. Biol. 104,145167. 7. Jack, A., Ladner, J. E. & Klug, A. (1976) J . Mol. Biol. 108,619-649. 8. Ladner, J. E., Jack, A,, Rohertus, J. D., Brown, R. S., Rhodes, D., Clark, B. F. C. & Klug, A. (1975) Proc. Natl. Acad. Sci.USA 72,4414-4418. 9. Quigley, G. J., Seeman, N. C., Wang, A. H.-J., Suddath, F. L. & Rich, A. (1975) Nuclezc Acids Res. 2, 2329-2341. 10. Stout, C. D., Mizuno, H., Rubin, J., Brennan, T., Rao, S. T. & Sundaralingam, M. (1976) Nucleic Acids Res. 3, 1111-1124. 11. Hingerty, B., Brown, R. S. &Jack, A. (1978) J . Mol. Biol. 124,523-534. 12. Mackay, A. L. (1977) Acta Crystallogr., Sect. A 33,212-215. 13. Yathindra, N. & Sundaralingam,M. (1976) Nucleic Acids Res. 3, 729-747.
GEOMETRY OF RNA RESIDUES
1915
14. Sundaralingam, M. & Yathindra, N. (1977) Quant. Biol. S y m p . 4, 285-303. 15. Ikehara, M., Uesugi, S. & Yana, J. (1972) Nature [NewBiol.] 240, 16-17. 16. Rubin, J., Brennan, T. & Sundaralingam, M. (1972) Biochemistry 11,3112-3128. 17. Sussman, J. L., Seeman, N. C., Kim, S. H. & Berman, H. M. (1972) J. Mol. Biol. 66, 403-422. 18. Broyde, S. B., Wartell, R. M., Stellman, S. D. & Hingerty, B. (1978) Biopolymers 17, 1485- 1506. 19. Hingerty, B. & Broyde, S. (1978) Nucleic Acids Res. 5, 127-137. 20. Mizushima, S. & Shimanouchi, T. (1961) Adu. Enzymol. 23,l-27. 21. Olson, W. K. (1976) Biopolymers 15,859-878. 22. Olson, W. K. (1975) Macromolecules 8,272-275. 23. Suck, D., Manor, P. C. & Saenger, W. (1976) Acta Crystallogr., Sect. B 32, 17271737. 24. Sugeta, H. & Miyazawa, T. (1967) Biopolymers 5,673-679. 25. Rhodes, D. (1977) Eur. J . Biochem. 81,91-101. 26. Crick, F. H. C. (1966) J . Mol. Biol. 19,548-555. 27. Robertus, J. D., Ladner, J. E., Finch, J. T., Rhodes, D., Brown, R. S., Clark, B. F. C. & Klug, A. (1974) Nature 250,546-551. 28. Broyde, S. B., Wartell, R. M., Stellman, S. D., Hingerty, B. & Langridge, R. (1975) Riopolymers 14,1597-1613. 29. Arnott, S., Chandrasekaran, R. & Leslie, A. (1976) J . Mol. Biol. 106,735-748. 30. Govil, G., Fisk, C., Howard, F. B. & Miles, H. T. (1977) Nucleic Acids Res. 4, 25732592. 31. Arnott, S. (1977) First Cleveland Symposium on Macromolecules, Elsevier, Amsterdam, pp. 87-104. 32. Rosenberg, J. M., Seeman, N. C., Day, R. 0. & Rich, A. (1976) Biochem. Biophys. Res. Commun. 69,979-987. 33. Arnott, S., Chandrasekaran, R., Hukins, D., Smith, P. & Watts. L. (1974) J . Mol. Biol. 88,523-533. 34. Zimmerman, S. B., Davies, D. R. & Navia, M. A. (1977) J . Mol. Biol. 116,317-330. 35. Saenger, W., Riecke, J. & Suck, D. (1975) J . Mol. Biol. 93,529-534. 36. Rich, A,, Davies, D. R., Crick, F. H. C. &Watson, J. D. (1961) J . Mol. Biol. 3,71-86. 37. Zimmerman, S. B. (1976) Biopolymers 15,1015-1018. 38. Levitt, M. (1974) J . Mol. Biol. 82,393-420. 39. Sundaralingam, M., Liebman, M., Rubin, J., Stout, D. C., Alper, J. C. & Satyshur, K. (1978) International Symposium on Biomolecular Structure, Conformation, Function and Euolution, Madras, India, Abstract D1, p. 34.
Received January 10,1978 Returned for Revision March 16,1978 Accepted January 3,1979
INTRODUCTION Much effort has been expended over the years in evaluating the helical parameters of polynucleotides from fiber-diffraction ~ t u d i e s . l - ~ However, the fiber analysis suffers from the inherent low resolution of the data compared to single crystals. Consequently, the analysis of‘single crystals of dinucleoside monophosphates forming miniature double he lice^^-^ has been of great interest. The helical parameters of some of these fragments have been calculated and compared with the fiber-diffraction results for larger polymers. With detailed conformations available now for the larger tRNA7-10 the helix parameters of the various helical stems are of considerable interest. Hingerty et al.ll have used a least-squares technique to fit the helical stems of tRNA to an 11-fold model using the method of Mackay.12 Yathindra and Sundaralingam13J4 have recently investigated possible left- and right-handed polynucleotide helical conformations. Ikehara systems15 allow left-handed polymers where cyclonucleosides are fixed in the high a n t i orientation. * Present address: Oak Ridge National Laboratory, Biology Division, P.O. Box Y, Oak Ridge, Tennessee 37830. Biopolymers, Vol. 18, 1901-1915 (1979) 0 1979 John Wiley & Sons, Inc.
0006-3525/79/0018-1901$01.00
HINGERTY
1902
TABLE I Dihedral Angle Definitionsa Angle
Atoms
w‘
05’-P-O3’-C3’ P-O3’-C3’-C4’ 03’-C3’-C4’-C5’ CY-C4’-C5’-05’ C4’-C5’-05’-P C5’-05’-P-03’ 01’-Cl’-N9-C8 (Pur) Ol’-Cl’-Nl-CG (Pyr)
*
6’
l J
6 w
X
a All angles A-B-C-D are measured by a clockwise rotation of D with respect to A, looking down the B-C bond, A eclipsing D is Oo. Note that the angle $’ is dependent on the sugar puckering.
The purpose of this report is to investigate the reason for the apparent wide variation of helical parameters for these experimentally observed quantities even though the actual values of the dihedral angles vary by relatively small amounts. The complicated geometry of the polynucleotide backbone seems to be the basis of the problem (Table I and Fig. 1). The six backbone bonds that determine the helical parameters are clearly more complicated than the simple geometry of the trans planar peptide. In the case of the peptide, we have only two torsion angles ($,#) that are variable. These produce a small number of well-defined helical structures. For a polynucleotide only p,determined by the sugar pucker, is relatively fixed a t -80’ for C3’-endo
00
N6
II
I
‘
H3
I C2
II Adenine
I
II
C6
Uracil
Fig. 1. The geometry of GpC with dihedral angles indicated. The bases A and U are also given. This defines the polynucleotide backbone necessary to define a helix (Table I).
GEOMETRY OF RNA RESIDUES
1903
and -144’ for C2’-endo with less than a flO’ variation. Such a large number of variables produces a complicated surface in six dimensions relating various combinations of these angles to a given foldedness of the backbone. A study of the number of nucleotides per turn, n versus h , the rise per residue along the helix axis, have been made by Yathindra and S ~ n d a r a l i n g a mfor l ~ the w’, w angle pair. In the present work, the helical parameters of several known experimental structures are calculated from dinucleoside monophosphate building blocks. These include the tRNA residues, the A-form [ (w’,w) = ( g - , g-); II/ = g+; C3’-endo ribose; 6’= t ; 6 = t ; x = anti] dinucleoside monophosphates and the non-A-form UpA conformers.16J7 The effect of small variations in the backbone conformational angles and bond angles on the helical parameters is discussed.
METHODS An analysis of single-stranded DNA from semiempirical potential energy calculations is presented elsewhere.18J9 The helical parameters were evaluated using the method developed by Mizushima and ShimanouchiZ0for polypeptides and later extended by Olson21,22for polynucleotides by the single virtual bond method. Table I1 gives the average values of the bond lengths and angles from the x-ray crystal structure of A ~ A P A .These ~ ~ have been averaged where appropriate, and those regions which display end effects such as the free 05’ and 03’ were omitted. The six rotation matrices for the six bonds that comprise the virtual bond employ these fixed bond lengths and angles. The quantities calculated are 8 (turn angle), n (360/8),h (the rise per residue), and r (the P atom radius from the helix axis). The ratio 0lh < 0 defines a left-handed helix, while 8/h > 0 defines a right-handed one, (0’ < 101 < 180’). This can be evaluated unambiguously by the method of Sugeta and M i y a ~ a w a . ~The ~ angles x need not be identical for dinucleoside monophosphates but are required to be so for strictly helical structures. This is a source of end-effect problems, which will be discussed below. TABLE I1 Parameters Used in Geometrical Calculationsa Bond Lengths Atoms
(A)
Atoms
P-05‘ 05‘-C5‘ C5‘-C4‘ C4’-C3‘
1.589 1.459 1.505 1.514 1.429 1.614
P-O3’-C3’ 03’-C3’-C4’ C3’-C4’-C5’
C3‘-03‘ 03‘-P a
From Ref. 23.
C4’-C5’-05’ C5’-05’-P 03’-P-05’
Bond Angles (deg) 119.0 109.8 117.5 108.8 120.3 104.6
1904
HINGERTY
For the CCA and anticodon loop of tRNA, the dihedral anglesll were averaged to find a helix. This was also done for the four helical stems of tRNA (amino acid, dihydro uracil, TGC, anticodon stems). However, the procedure was not entirely satisfactory, first due to the variability in bond lengths and angles producing a systematic effect on the structure and second because of the lower reliability of the coordinates (rms deviation of 0.3 A). The variation in dihedral angles from residue to residue was also considerable. Because of this variability in the helical parameters from seemingly small variations in conformation, a systematic investigation of this effect was made. For this purpose, residue A62 or tRNA,I1 which is an almost exact 11-fold helix, was used. Helical parameters were calculated as a function of all dihedral angles except @. The dihedral angles were varied in steps of 5" over a range of f25" from the observed value. Finally, the effect of variability in the bond lengths and bond angles on the helical parameters was investigated. The bond lengths were altered up to f0.04 A (the maximal variation possible) in steps of 0.02. The bond angles were varied in steps of 2" to f4" of the observed value.
RESULTS tRNA Yeast Phenylalanine The conformational angles for tRNA, which have been refined to a standard crystallographic R factor of 0.21, are given e1sewhere.l' Previous results have been given at R = 0.31.7 Table 111 gives the helical parameters for the dinucleoside monophosphate residues 2-75 of yeast phenylalanine tRNA. Residues 1and 76, which do not possess a complete backbone, were omitted. A negative h denotes a left-handed configuration. As can be seen from Table 111, there appeared to be much variation from one residue to the next in each A-type region. [A-type regions include the double-stranded residues: 2-6,ll-15,23-33,38-45,50-55, and 61-72 and the single-stranded A-type regions 8,20,35-36, and 73-75 (55 total residues A-form).] The low resolution of the data (2.5 A) and the variability in bond lengths and angles permitted by the energy refinement accounts in part for this. However, some systematic variation could be detected from residues that take part in unusual interactions. In addition, some variation due to base sequence was discernible. G3 has an unusual 0 of -26.2" (left-handed) or, equivalently, h = -4.2. This is the residue just before the unusual G-U base pair wobble. The left-handed helical backbone is required to permit this pairing. The low value of n (high 0) for C2 may also be related to this. C61 is also left-handed and has a low value of II/ (38"). This may be caused by the hydrogen bonding of C60 and D16 bases in the variable pocket, which results in some strain on the helix backbone at this point. The left-handed A29 with 8 = -29.2 may be correlated with the high 13 (52.9) of G30 to compensate for
63.7 26.2 39.0 27.5 28.6 138.1 53.0 101.8 117.2 24.2 49.2 35.9 35.9 38.6 174.9 176.7 136.5 71.5 61.9 138.7 80.3 27.0 35.6 40.0 51.0
C2 G3 G4 A5 U6 u7 U8 A9 m2G10 c11 U12 Cl3 A14 C15 D16 D17 G18 GI9 G20 A21 G22 A23 G24 C25 m5G26
5.7 13.7 9.2 13.1 12.6 2.6 6.8 3.5 3.1 14.9 7.3 10.0 10.0 9.3 2.1 2.0 2.6 5.0 5.8 2.6 4.5 13.4 10.1 9.0 7.1
n
3.4 -4.2 3.7 2.8 2.5 5.7 3.8 6.3 -4.6 3.6 2.3 1.4 2.7 2.1 -6.5 -5.1 -3.9 6.3 3.7 4.8 -6.1 2.3 1.9 2.5 3.7
h
4.1 10.0 7.1 11.8 11.2 1.9 4.2 0.2 2.2 12.3 6.7 11.1 7.9 8.9 0.9 1.8 2.5 2.3 3.8 2.3 2.1 11.5 9.2 8.5 5.7
r
C27 C28 A29 G30 A31 Cm32 u33 Gm34 A35 A36 Y37 A38 $39 m5C40 U4 1 G42 G43 A44 G45 m7G46 u47 C48 m5C49 U50 G51
Residue 38.0 38.8 29.2 52.9 40.9 43.3 37.7 131.5 45.3 40.7 59.8 38.2 49.9 37.1 45.6 26.3 23.0 42.9 78.6 133.2 96.6 105.2 169.2 32.9 34.2
B 9.5 9.3 12.3 6.8 8.8 8.3 9.5 2.7 8.0 8.8 6.0 9.4 7.2 9.7 7.9 13.7 15.7 8.4 4.6 2.7 3.7 3.4 2.1 11.0 10.5
n 1.5 3.5 -0.7 4.8 3.4 2.7 0.8 3.1 1.4 -0.2 2.8 2.3 3.3 1.6 3.3 0.2 4.3 3.9 3.7 5.6 2.0 -1.9 -1.6 7.4 2.8
h 8.7 6.9 13.0 4.0 7.1 7.4 8.9 2.8 7.2 9.5 5.5 9.2 5.9 9.6 6.0 12.9 11.7 6.4 3.3 1.2 4.8 4.3 2.8 8.6 9.1
r
U52 G53 T54 $55 C56 G57 m'A58 U59 C60 C61 A62 C63 A64 G65 A66 A67 U68 U69 C70 G71 C72 A73 C74 C75
Residue
n 12.8 10.8 7.2 7.2 2.8 5.1 2.2 2.1 2.6 6.0 11.1 11.7 15.8 10.8 12.8 14.3 14.9 9.5 15.9 7.6 13.7 10.1 7.3 10.5
0 28.2 33.4 50.2 49.7 130.5 70.0 165.6 168.5 138.1 59.6 32.5 30.8 22.8 33.3 28.1 25.2 24.1 37.8 22.6 47.6 26.3 35.5 49.4 34.2
r
11.1 9.2 5.0 5.8 2.3 4.4 1.7 1.8 2.1 5.5 9.5 10.6 15.2 10.0 11.2 10.6 13.8 8.0 16.0 6.9 10.8 8.4 5.3 10.4
h 3.4 3.7 3.5 2.8 -3.9 3.7 5.4 4.4 5.5 -0.3 2.4 2.4 1.3 2.0 3.0 4.0 2.3 3.0 0.4 2.8 3.8 3.2 3.1 2.6
a
From Ref. 11. For residues 2-75, 18 are non-A-form. Four are C (C48, m5C49, C56, C60); 6 are G (m2G10,G18, G19, G22, Gm34, m7G46); 3 are A (A9, A21, m'A58); and 5 are U (U7, D16, D17, U47, U59). The single-stranded regions are 8, 20, 35-36, 73-75.
I)
Residue"
TABLE 111 Helical Parameters for Individual Residues of Yeast tRNA Phenylalanine Taken as 5'-Nucleotides"
1906
HINGERTY
the negative turn angle, although this may indicate only a transfer of strain along the backbone. G45, the last residue of the anticodon arm, has an unusually high 0 (78.6) and low n (4.6). This is mostly an end effect, as the helix terminates a t m7G46. However, G45 is also involved in a base triple with m2G10 and C25, which may contribute to the high 0. Examination of other A-form residues that are not part of the base-paired stems shows that U8 and G20 have low n values of 6.8 and 5.8, respectively. These are more similar to single-stranded helices that have low n and r as compared to the d ~ p 1 e x e s . l ~ The existence of conformational strain in the backbone is consistent with a recent study by R h ~ d e on s ~the ~ initial stages of thermal unfolding of yeast tRNA phenylalanine. This study has shown that the left-handed G-U26 base pair is unstable and melts easily. The m5 C49-G65 base pair also melts early, since the phosphate of 49 is altered from the A-form c o n f ~ r m a t i o n . ~ ~ The m5C49 has an unusual skewed w‘ of looo, which is shifted from the standard g+ (60”). The stacking of U59 with C60 is the most easily disrupted part of the structure in the absence of Mg++. This may be related to the left-handed nature of C61 mentioned above. The nonstandard base pair G15-C48 melts somewhat later than U48-Al4, which may involve different strains a t m5C49 and U8. In addition, C48 has unusual values of (w’,w) of (g+,g-) = (86”, 332”). The two base triples C13-G22-m7G46 and m2G10-C25-G45open up a t about the same temperature. G45 was described previously, while m7 G46 shows strain with w’ = 235” (skewed). Because of the consistency with the thermal unfolding data,25we do not believe this is due to errors in the model. Loops and bends are produced by special configurations. A stretch is caused either by w’,w = t,g- or a C3’-endo-(3’,5’)-C2’-endo ribo~e.~ Residues 19,9, and 58 show this. They have high h values of 6.3,6.3,5.4, which roughly correspond to a double base spacing. Bends in the structure come from w’,w = g-,t or C2’-endo- (3’,5’)-C3’-endo r i b ~ s e s . Residues ~ 7,10,19,34, and 56 have one or the other of these conformational features. This translates into a very small turning radius ( r < 3 A) and high 0. All the H are over 100” except 19, which is 72’, and 7 has a high h of 5.7 A. In addition, 10 and 56 are left-handed. All left-handed conformations are in bends of the structure except for G3, C61, and A29, which are strained due to tertiary interactions. The existence of left-handed bends in tRNA has already been mentioned by Sundaralingam and Yathindra.14 Table IV gives the percentage of non-A-form residues in tRNA and the average value of n (number of residues per turn of helix). We see clearly the preference of G and U for non-A-form conformations, consistent with semiempirical energy calculations on RNA residues done previously by Broyde et a1.28 In considering the average value of n for the different bases in tRNA, we see that for double-helical regions, n is lower for (G,U) compared to (C,A). In addition the single-stranded A-forms have a markedly lower n for (G,U) compared to (C,A). The single-stranded regions have a lower nthan the double-stranded regions, which are similar to 10- to
GEOMETRY OF RNA RESIDUES
1907
TABLE IV Percent of Non-A-Form Residues in tRNA and the Average Value of na
P1
Base C A G U
nl
P2
n2
8.9 9.0 5.8 6.8
38.9 (7/18)
17.6 (3/17)
61.1 (11/18)
29.4 (5/17)
Mean
10.3
8.2
a A form: (w’,w) = (g-,g-); $ = g+; ribose = C3’-endo; 6 = t , 6’= t , and x = anti. P I , percentage of non-A-form residues for each type; the number in parentheses indicates fraction where modified bases are considered as normal for this purpose. The Y-base is omitted. Pz, the percentage of non-A-form being either C A or G U (fraction in parentheses). nl, average value of n for double-helical regions (48 residues). n2, average value of rz for singlestranded A-form regions (7 residues).
+
+
12-fold values. This is consistent with theoretical calculations on DNA done p r e v i o u ~ l y . In ~ ~addition, a sixfold model of poly(rC) by Arnott et aL29using fiber diffraction and also a 6.6-fold theoretically calculated model of 8-bromo-poly(rA) by Govil et al.30confirm a lower value of n for singlestranded structures. Arnott31 observed the same sixfold structure in an orthorhombic crystal form of poly( 2’-OMe-C) using fiber diffraction; in such a structure there can be no -OH.--OH hydrogen bonds. Table V gives the average values of the torsion angles and the corresponding helices that are generated for the amino acid, dihydro U, T$C, and anticodon stems. Hingerty et a1.l1 have used a least-squares program to fit the helical stems to an 11-fold type of RNA with h = 2.5 A,and it was not clear why the values of n in this case should vary from 9.3 to 11.9 residues per turn. When all four helices were averaged, n = 10.4 residues per turn and h = 2.80 A. The low value of h (1A) in the anticodon loop (residues 35,36) is unusual and is probably due to a low value of 4 (141O). When the anticodon is complementary base paired to the codon UUC, we would expect a small but noticeable conformational change that would most likely cause h to increase. TABLE V Average Parameters for tRNA Stems, CCA. and Anticodon Lo00 Rep.ion * 1. 2. 3. 4. 5. 6. 7.
Aminoacid DihydroU T$C Anticodon Average for 1-4 CCA Anticodon IOOD
w‘
6‘
288 290 289 292 290 291 279
203 205 205 208 205 203 203
82 82 84 83 83 85 80
64 66 57 62 62 59 68
176 171 175 173 174 176 141
281 281 285 284 283 288 289
8
n
h
r
30.3 33.8 35.4 38.6 34.6 35.3 37.8
11.9 10.7 10.2 9.3 10.4 10.2 9.5
2.71 2.84 2.53 3.02 2.80 3.42 0.93
10.48 9.44 8.92 7.91 9.08 8.30 9.49
a 1, contains residues 2-6, 66-72; 2, residues 11-15, 23-26; 3, residues 50-55, 61-65; 4, residues 27-33,38-45; 6, residues 73-75; 7, residues 35,36.
HINGERTY
1908
One last point to be noted is the existence of two rare B-forms (U7, C60), which are the same as the A-form except that the ribose is C2'-endo and 4 = 270". Of the 57 total A- or B-forms, only 2 or 3.5% are B, indicating the overwhelming preference for the A type in RNA.
Dinucleoside Monophosphates These structures possess all the conformational angles necessary to define a helix. Although this is the case, they suffer from end effects which make model building difficult. Since the x angles are not equal in the dinucleoside monophosphates, as they must be for a regular helix, the extension of residues on either side does not actually produce a regular structure. In the crystal structures of these molecules, the x angles depend on whether the bases are purines or pyrimidines. The base-stacking parameters, which are not considered here, will clearly depend on the x angles. In particular, y,the angle the bases make with the helix axis, will be different. Rosenberg et al.32 have recently devised the helix probe method to deal with this problem. The helical parameters from the four molecules of GpC in the Ca++ salt crystal structure: the single GpC in the Na+ salt? and the two structures of ApU5 are given in Table VI. The GpC structures are all about eightfold, while ApU appears to be ninefold. The average of Ca++ GpC 1to 4* gives roughly the same result of n = 7.8 and h = 2.6. These results differ from those of Rosenberg et al.,6,32who used the helix-probe method. Their results gave GpC with n = 10.4 and pitch 26.9 (h = 2.6), while ApU had n = 11.9 and pitch 28.1 ( h = 2.4). The reason for the difference is in the sensitivity of the calculation to small variations in dihedral and bond angles (discussed below). Fiber diffraction on poly(dGdC) by Arnott et al.33is eightfold, as are the computed helices from the rib0 GpC crystal structures. TABLE VI Parameters for Dinucleoside Monophosphates Molecule
Ref.
4 GpCl 4 GpC2 4 GpC3 4 GpC4 4 GpCl-4 6 GpC (Na+) GpC (all 5) 5 ApU2 5 ApU 1 ApA+ 23 UpAl 16,17 UpA2 16,17
w' 6' -
294 29 1 290 288 291 292 291 284 29 1 283 163 84
222 217 224 216 220 211 218 22 1 213 223 224 202
P
#
6
w
6
n
h
r
77 76 72 85 78 83 79 78 78 82 92 85
47 57 63 52 55 50 54 58 57 53 52 56
181 172 167 181 175 184 177 168 177 161 192 202
291 293 286 283 288 285 288 295 288 298 272 84
51.7 41.1 43.2 45.7 46.1 43.7 45.1 39.0 41.1 44.3 88.3 178.9
6.97 8.77 8.34 7.87 7.82 8.24 8.04 9.22 8.76 8.13 4.07 2.01
2.26 2.96 2.32 2.43 2.56 2.42 2.48 3.10 2.89 2.65 -3.35 -1.31
5.44 6.89 6.99 6.56 6.32 6.79 6.53 7.16 7.01 6.17 3.13 2.72
GEOMETRY OF RNA RESIDUES
1909
Models of UpA Helical parameters were calculated for the unusual bent conformers of the crystal structure of UpA.16J7 Results are given in Table VI. UpAl with w',w = t,g- produces a fourfold left-handed helix (90' turn angle 0) with the base planes nearly perpendicular to the helix axis and h = 3.35. No stacking takes place because of the 90" turn angle. The phosphates are on the inside of the structure with r = 3.1 A. UpA2 with w',w = g+,g+ produces a left-handed, twofold helix with h = 1.3 A. The value of h is too low for the structure to be polymerized. The phosphates are also on the inside a t r = 2.7 A. Recently a fiber-diffraction study of poly(rA) in the denaturing solvent formamide showed the structure to be twofold with h = 2.9 and w',w = gf,gi.34 As pointed out earlier, the t,g- conformer is important in the tRNA molecule. It is found a t G19, G22, and U47, although G19 is C2'-endo. These conformers take part in important bends of the structure in the dihydro U loop and extra arm extension from 45 to 49 (Fig. 2).
Model of Poly(rA) The helical parameters for poly(rA) were calculated using the coordinates of ApA+ from the crystal structure of A P A ~ A . We ~ ~ were surprised to obtain an eightfold model, since a ninefold has already been presented. We used the actual bond lengths and angles from the ApApA crystal structure. Although the difference between 40' and 44' may not
'
'
2
I D-stem 1
'
vr"
TVC loop plus G , E G , ~
Fig. 2. Schematic diagram of the chain-folding and tertiary interactions between bases in yeast tRNAPhe. Long lines indicate base pairs in double-helical stems. Shorter lines represent unpaired bases. Dotted lines represent base pairs outside the helices. From Ladner e t al. (Ref. 8).
HINGERTY
1910
be significant, the eightfold model allows a symmetrical bonding system as in poly(rAH+) poly(rAH+) by Rich et al.36 This agrees with the fiber work, although in our case we have a screw of 2.7 8, compared to the 3.8 A in the fiber analysis. As pointed out by one of the referees, this difference in h corresponds to the difference between a large negative base tilt and the large positive tilt of the usual A-form.
Variation from Small Changes in Dihedral Angles The effect of a small variation in parameters about the A-form conformation was examined. The dihedral angles of A62 of tRNAll were used as starting parameters. This residue is almost exactly 11-fold. The torsion = 84', w = 52', 4 = 172', and w = 293'. angles are w' = 280°, 4 = 211', Bond lengths and angles given in Table I1 were fixed. The dihedral angles were varied f25" in 5' steps. Results given in Fig. 3 show the variation of 8, n, h, r with w', w , 4', 4, and $. For w' and 4', the parameter most affected is 8 or n with a near linear
n
t
11.0
44.0 5.0
10.0
42.0 4.0 100 40.0 3.0
9.0
90
8.0
38.0 2.0
7.0
36.0 1.0
6.0
34.0 0.0 8.0 32.0 -1.0
5.0 4.0-
--W
0 5 !
!
3.0
26.0 52.0 18.0 47.0 16.0 42.0
17.5
14.0 37.0
1.0 15.0
12.0 32.0
12.5
10.0 27.0
0 0 10.0 7.5
8.0 22.0 6.0 17.0
~~
255
265
275
285
295
305
i
2 . 0 20.0
-1.0
5.0,
W'-+
Fig. 3. Variation of 0 ( - - -), n (-), h (-@-), and r (-O-) with (A) a',(B) w , (C)b', (D) @, and (E) IC. dihedral angles from A62 of tRNA (Ref. l l ) , with w' = 280', 4' = 211', w' = 84', $ = 52', 4 = 172', and w = 293'.
GEOMETRY OF RNA RESIDUES C
0 54 0 3 0
o/.-.-,.20
1911 r
En0 4 1 0;2 16 0 44 0 2 0 18 0
-.. 186
, , , 196
/
,
1 4 0 3 9 0 1 5 15 0 12 0 3 4 0 1 0 12 0
/
206
216
10 0 29 00 5 9 0 8024000 6 0 6019 0-05I 3 0 23,6
226
-0
-
n e h r
.-,
11.5 44 0 110420
100
1054004 09 0
1
1003803080 9 53802 0 7 0
-147
157
167
903401060 177
187
853200050 197_
-@
n e h r
t
\\
k,
0’
27
37
1
47
a(
0,
Fig. 3. (continued from the previous p a g e )
variation, while h increases with a much more level distribution, especially about the helical values w’ (280’) and 6’(211’). T h e radius is, as noted before,lg correlated with n , which has also been pointed out by Zimmerman.:’7 The variation due to w , 6,and Ic/ expresses itself in a different way as a pronounced centroid of the distribution in 0 or n , while h shows the greatest variation. If h varies too much, either stacking is lost or nonbonded contacts become important in inhibiting the conformation. T h e stability of these angles to small variations is reminiscent of a potential well from perturbation theory in quantum mechanics. It is clear that a large variation in helical parameters can be observed from a small perturbation of the angles. Only certain complex combinations of angles can preserve a similar structure.
Variations from Small Changes in Bond Lengths and Angles Because of the wide variations found in the helical parameters from seemingly small variations in conformation, it was decided to investigate the effect of variable bond lengths and angles on these quantities. Results
HINGERTY
1912
are given in Fig. 4. Variations of f 4 ’ in steps of 2O were taken for bond angles. Variations of f0.04 A in steps of 0.02 A were taken for bond lengths. Standard values of bond lengths and angles are given in Table 11. The bond lengths had little effect on the results. There is no variation in H or n , since by geometrical considerations only h and r can vary. Only bond angles and dihedral angles can affect 0 or n , since the single virtual bond-rotation matrix, T , is only a function of the bond angles and dihedral angles in the backbone. The maximum variation in h was 0.07 A for P-05’ bond length and the maximum variation in r was 0.14 A for the C4’-C3’ bond length. These results are not tabulated, since the changes were insignificant. The bond angles, on the other hand, had a dramatic effect on the parameters. Figure 4(A)-(C) shows the variability due to P-O3’-C3’, C4’C5’-05’, and C5’-05’-P. These angles affect h, r, and H or n by the largest amounts, respectively. Maximal change was h by 1.3 A, r by 2.8 A, and n by 2.7 residueshurn (0 by 7.9’). It was possible by just varying C5’-05’-P to change n from 9.9- to 12.6-fold. The other angles 03’-C3’-C4’, C3’-C4’C5’, and 03’-P-05’ show less effect and are given in Figs. 4(D)-(F). This
30g51
I
enhrl
35 012 0 3 5
/e
340 33011 0 2 5 9 4 320
- --.
2093
31010015 9 3
1-
115
117
119
121
p-03’-c3’
123
B
33011525100 31 0 11 0 24 29010523 9 0
27 0100 2 2
:n
h r
-
7
1
380130
320100 24100 30090
90
Fig. 4. Variation of 0 ( - - - ) , n (-), h (-0-1, and r ( - O ) with (A) P-O3’-C3’, (B) C4‘-C5’-05’, (C) C5’-05’-P, (D) 03’-C3’-C4’, (E) C3’-C4’-C5’, and (F)03’-P-05’ from A62 as in Fig. 3.
GEOMETRY OF RNA RESIDUES
1913
D
e n h r
35 0 34 012025 330 96 3201102094 310
92
3001001 5 9 0
03'-C3'-C4' 105 8 1078 109 8
1118
1138
E
e n h r
32011 0 2 2 9 0 310 21 3001002 0 8 0
1135 1155
1175
1195 121 5
C3'-C4'-C5'
35.0 12.0 2.6100 34.0 2.5 33.0 11.02.49 0 32.0 2.3 31.0 1002.28.0
1006
102.6 104.6 106.6 1086 03'-'-05'
Fig. 4. (continued from t h e previous p a g e )
clearly has implications for fiber diffraction analyses, since bond angles are normally held fixed in these cases. It is also pertinent to the end-effect problem encountered in extending small molecules to polymers, since such variations can cause drastic changes in the'helical parameters.
CONCLUSION The helical parameters of the individual residues of yeast tRNA phenylalanine and some dinucleoside monophosphates have been examined by a program that computes these parameters directly from the six backbone torsion angles. Wide variations were found that disagreed with other calculation^.^,^^ Some of the variation is explained by backbone strain in the molecule consistent with a thermal-unfolding experiment of tRNA.25 The best example is the conformationally strained G-U "wobble" base pair26that melts easily, possibly due to its left-handed backbone. However, not all of these results can be accounted for in this way. A systematic study of the effect on the helical parameters of small perturbations in the dihedral angles and bond lengths and bond angles was made. Although bond lengths had negligible effect, dihedral and bond angles produced large
HINGERTY
1914
changes. The angles w' and $' caused n to linearly decrease in value as they were increased. w , $, and affected h more dramatically, with a well-like surface in the 8-h curve similar to that of a potential well in perturbation theory. The variations due to bond angles are to be viewed seriously, since these are normally held fixed in fiber computations. It might be worthwhile to include bond angle bending terms of the form w ( 8 - 1 9 0 ) as ~ done by L e ~ i tand t ~ also ~ suggested by Sundaralingam et al.39 as an extra term in fiber refinement because of the sensitivity of the helical parameters to bond angle strain. In the helix-probe method of R o ~ e n b e r g ,the ~ , ~generated ~ helix is assumed to be 10- to 12-fold, so that only a small change in this parameter is permitted. By using this procedure you can force the structure into a given foldedness by bending the backbone. For these reasons we must be careful in making conclusions regarding helical parameters from monomer geometries. Therefore, those who calculate helical parameters need to be very sure of their bond lengths and angles and dihedral angles if valid information is to be obtained. It can be speculated here that the wide variability in helical parameters with small changes in molecular geometry could relate to protein-nucleic acid interactions. In such a case the sequence dependence and flexibility of the nucleic acid would play an important role in the complexes that are formed and the interactions that take place.
+
B. H. would like to thank the National Institutes of Health, National Cancer Institute for postdoctoral fellowships 1F22 CA02210-01 and 1F32 CA06223-01. B.H. would also like to thank J. R. Rubin for help with the UpA and poly(rA) structures, S. Broyde for detailed comments on the manuscript, and D. Rhodes for the thermal-unfolding data for tRNA.
References 1. Watson, J. D. & Crick, F. H. C. (1953) Nature 171,737-738. 2. Langridge, R., Marvin, D. A., Seeds, W. E., Wilson, H. R., Hooper, C. W., Wilkins, M. H. F. & Hamilton, L. D. (1969) J . Mol. Biol. 2, 38-64. 3. Arnott, S., Chardrasekaran, R. & Selsing, E. (1975) in Structure and Conformation of Nucleic Acids and Protein-Nuclezc Acid Interactions, Sundaralingam, M. & Rao, S. T., Eds., University Park Press, Baltimore, Maryland, pp. 577-596. 4. Hingerty, B., Subramanian, E., Stellman, S. D., Sato, T., Broyde, S. B. & Langridge, R. (1976) Acta Crystallogr., Sect. B 32,2998-3013. 5. Seeman, N. C., Rosenberg, J. M., Suddath, F. L., Kim, J. J. P. &Rich, A. (1976) J . Mol. Biol. 104,109-144. 6. Rosenberg, J. M., Seeman, N. C., Day, R. 0. & Rich, A. (1976) J . Mol. Biol. 104,145167. 7. Jack, A., Ladner, J. E. & Klug, A. (1976) J . Mol. Biol. 108,619-649. 8. Ladner, J. E., Jack, A,, Rohertus, J. D., Brown, R. S., Rhodes, D., Clark, B. F. C. & Klug, A. (1975) Proc. Natl. Acad. Sci.USA 72,4414-4418. 9. Quigley, G. J., Seeman, N. C., Wang, A. H.-J., Suddath, F. L. & Rich, A. (1975) Nuclezc Acids Res. 2, 2329-2341. 10. Stout, C. D., Mizuno, H., Rubin, J., Brennan, T., Rao, S. T. & Sundaralingam, M. (1976) Nucleic Acids Res. 3, 1111-1124. 11. Hingerty, B., Brown, R. S. &Jack, A. (1978) J . Mol. Biol. 124,523-534. 12. Mackay, A. L. (1977) Acta Crystallogr., Sect. A 33,212-215. 13. Yathindra, N. & Sundaralingam,M. (1976) Nucleic Acids Res. 3, 729-747.
GEOMETRY OF RNA RESIDUES
1915
14. Sundaralingam, M. & Yathindra, N. (1977) Quant. Biol. S y m p . 4, 285-303. 15. Ikehara, M., Uesugi, S. & Yana, J. (1972) Nature [NewBiol.] 240, 16-17. 16. Rubin, J., Brennan, T. & Sundaralingam, M. (1972) Biochemistry 11,3112-3128. 17. Sussman, J. L., Seeman, N. C., Kim, S. H. & Berman, H. M. (1972) J. Mol. Biol. 66, 403-422. 18. Broyde, S. B., Wartell, R. M., Stellman, S. D. & Hingerty, B. (1978) Biopolymers 17, 1485- 1506. 19. Hingerty, B. & Broyde, S. (1978) Nucleic Acids Res. 5, 127-137. 20. Mizushima, S. & Shimanouchi, T. (1961) Adu. Enzymol. 23,l-27. 21. Olson, W. K. (1976) Biopolymers 15,859-878. 22. Olson, W. K. (1975) Macromolecules 8,272-275. 23. Suck, D., Manor, P. C. & Saenger, W. (1976) Acta Crystallogr., Sect. B 32, 17271737. 24. Sugeta, H. & Miyazawa, T. (1967) Biopolymers 5,673-679. 25. Rhodes, D. (1977) Eur. J . Biochem. 81,91-101. 26. Crick, F. H. C. (1966) J . Mol. Biol. 19,548-555. 27. Robertus, J. D., Ladner, J. E., Finch, J. T., Rhodes, D., Brown, R. S., Clark, B. F. C. & Klug, A. (1974) Nature 250,546-551. 28. Broyde, S. B., Wartell, R. M., Stellman, S. D., Hingerty, B. & Langridge, R. (1975) Riopolymers 14,1597-1613. 29. Arnott, S., Chandrasekaran, R. & Leslie, A. (1976) J . Mol. Biol. 106,735-748. 30. Govil, G., Fisk, C., Howard, F. B. & Miles, H. T. (1977) Nucleic Acids Res. 4, 25732592. 31. Arnott, S. (1977) First Cleveland Symposium on Macromolecules, Elsevier, Amsterdam, pp. 87-104. 32. Rosenberg, J. M., Seeman, N. C., Day, R. 0. & Rich, A. (1976) Biochem. Biophys. Res. Commun. 69,979-987. 33. Arnott, S., Chandrasekaran, R., Hukins, D., Smith, P. & Watts. L. (1974) J . Mol. Biol. 88,523-533. 34. Zimmerman, S. B., Davies, D. R. & Navia, M. A. (1977) J . Mol. Biol. 116,317-330. 35. Saenger, W., Riecke, J. & Suck, D. (1975) J . Mol. Biol. 93,529-534. 36. Rich, A,, Davies, D. R., Crick, F. H. C. &Watson, J. D. (1961) J . Mol. Biol. 3,71-86. 37. Zimmerman, S. B. (1976) Biopolymers 15,1015-1018. 38. Levitt, M. (1974) J . Mol. Biol. 82,393-420. 39. Sundaralingam, M., Liebman, M., Rubin, J., Stout, D. C., Alper, J. C. & Satyshur, K. (1978) International Symposium on Biomolecular Structure, Conformation, Function and Euolution, Madras, India, Abstract D1, p. 34.
Received January 10,1978 Returned for Revision March 16,1978 Accepted January 3,1979
