J. Mol. Hiol. (1989) 209, 459-474
Crystallographic
Structure of an RNA Helix: [U(UA),A],
A. C. Dock-Bregeon ‘, B. Chewier’, A. Podjarnyl, J. Johnson2, J. S. de Bear’ G. R. Gough2, P. T. Gilham and D. Morasl ‘Institut de Biologic Mole’culaire et Cellulaire de C.N.R.S. 15, rue Rent Descartes, 67084 Strasbourg, France ‘Department
of Biological West Lafayette,
Sciences, Purdue University IN 47907, U.S.A.
(Received 2 May
1989)
The crystallographic structure of the synthetic oligoribonucleotide, U(UA),A, has been solved at 2.25 A resolution. The crystallographic refinement permitted the identification of 91 solvent molecules, with a final agreement factor of 13%. The molecule is a dimer of 14 base-pairs and shows the typical features of an A-type helix. However, the presence of two kinks causes a divergence from a straight helix. The observed deformation, which is stabilized by a few hydrogen bonds in the crystal packing, could be due to the relatively The complete analysis of the structure is high (35°C) temperature of crystallization. and the presented. It includes the stacking geometries, the backbone conformation solvation.
meric chains, while the tRNA crystals diffract to only a little beyond 3 A (1 A = 6 1 nm). In the case of DNA, the development of synthesis methods have enabled the production of oligonucleotides in the quantity and the purity needed to grow single crystals, and therefore the fine details of its conformation can be studied. From these studies (for reviews, see Shakked & Kennard, 1985; Shakked & Rabinovitch, 1986; Dickerson et al., 1985; Wang & Rich, 1985) new insights are emerging regarding the effect of base sequence on structure (Calladine, 1982; Dickerson, 1983; Calladine & Drew, 1984) and the way that DNA can be recognized by proteins (Dickerson et al., 1987). Recently, the production of synthetic oligoribonucleotides in milligram quantity has also become feasible, allowing the growth of single crystals of RNA suitable for crystallographic studies. This enables us to study RNA conformation at a level similar to that attained for DNA. This paper describes the first structure of an oligoribonucieotide, the duplex form of U(UA),A, at high resolution (2.25 A). It provides new references for A-RNA helices, helical parameters and stacking description, as well as solvation. It also provides new insight into the conformational variability of A-RNA helices as the structure diverges from a straightforward A-helix by the formation of two kinks. This structure shows the surprising flexibility of RNA molecules and provides evidence of the participation of 2’-hydroxyl groups in intermolecular interactions.
1. Introduction The ability of RNA molecules to play a large variety of roles in nature, ranging from the genomic function in some viruses to their recently discovered catalytic activity (Cech, 1987) is related to the capacity of RNA to fold in specific tertiary structures, based always on the double helix. Compared to DNA, the double-stranded regions of RNA show a more restricted conformational variety, and RNA helices seem therefore more rigid (Saenger, 1984). Double-stranded RNA molecules exist principally as A-type helices; only a few examples of B-type RNA or Z-RNA have been found (Hall et al., 1984; Tinoco et al., 1987); a description of the Z-form is provided by the crystallographic structure of the modified tetramer (C-Br*G)z (Nakamura et al., 1985). The helical parameters of A-type RNA have been deduced from diffraction studies on fibers (Arnott et al., 1972, 1973), but the diffraction patterns provide only an averaged structure and give no information regarding the local effects of the base sequence. The single-crystal analysis of ApU (Seeman et al., 1976) and GpC (Rosenberg et al., 1976), followed by the refinements of tRNA structures (Hingerty et al., 1978; Holbrook et al., 1978; Westhof et al., 1985u; Westhof & Sundaralingam, 1986), have brought forth a wealth of detailed information. However, the dinucleotide structures provide limited stereochemical information for poly459 Oo~-es~6/sQ/l90459-16
$O.?.OO/O
0
1989 Academic:
Press Limited
460
A. C. Dock-Bregeon
2. Materials and Methods
mol-‘; mol-‘.
(a) Chemical synthesis of the duplex The sequence U(UA),A was chosen for its simplicity, in that it could be easily constructed by multiple use of a tetramer block UAUA, formed in turn from the dinucleotide UA; the strategy of chemical block synthesis in solution permits the preparation of large quantities of oligomers, and also facilitates the generation of sets of molecules with closely related sequences for comparative structural studies. The UU and AA terminals were designed to favor the formation of a unique duplex by preventing slippage of the self-complementary strands. Synthesis of the oligomer was carried out using a modified version (Gough et al., 1979) of the phosphotriester method (Catlin & Cramer, 1973; Itakura et al, 1973) adapted for construction of oligoribonucleotides (Gough et al., 1980; Hayes et aE., 1985). The 5’-0-dimethoxytrityl 2’-0-(o-nitrobenzyl) derivatives of uridine (Ohtsuka et al., 1974) and N6-benzoyladenosine (Ohtsuka et al., 1977) were converted to their 3’-p-chlorophenyl phosphates (Sung & Narang, 1982), which were isolated as the barium salts (Gough et al., 1979). At this point the anisoylation step was added in order to protect the uracil from unwanted side-reactions (Gough et al., 1983). The barium salt of the protected uridine nucleotide was treated for 18 h with anisoyl chloride (4 equiv.) and triethylamine (5 equiv.) in pyridine (10 ml/mmol of nucleotide). anhydrous Following removal of excess triethylamine by co-evaporation with pyridine, water was added and, after standing for 24 h, the mixture was poured into cold 1 y. barium chloride solution, with stirring. The resulting precipitated barium salt of the 3-anisoyl-uridine nucleotide was collected by filtration, washed with 0.5% aqueous lutidine, and stored in anhydrous pyridine solution at - 20 “C. The barium salts of the A and U derivatives were then used to construct the dimer [(MeO)Tr]IY (NBzl)p(CIPh)Ab’ (NBzl)p(ClPh)(CNEt) which, after removal of appropriate groups and subsequent condensation, gave the protected tetramer UAUA. One-third of this material was extended at its 5’ end by condensation with the uridine monomer above, while N6,N6,02’,03’-tetrabenzoyladenosine (Lohrmann & Khorana, 1964) was added to the 3’ end of another third. The resulting blocks UUAUA, UAUA and UAUAA were then assembled on a 38 pmol scale to yield 180 mg of the protected tetradecanucleotide. Successive treatments with tetramethylguanidinium pyridinealdoximate, ammonia and longwave ultraviolet light at pH 3.5 (Hayes el al., 1985) were used to remove the protecting groups. A portion of the product was purified by preparative h.p.1.c.t (Lawson et al., 1983), converted to its sodium salt, and lyophilized. The molecule was characterized using described methods (Nadeau & Gilham, 1985): its base composition and molar absorptivity were determined by exonuclease digestion; its sequence was confirmed by ribonuclease A degradation; its thermodynamic values were obtained from a least squares analysis of its melting curve. The values for the duplex, dissolved in I.0 M-NaCl, 0.01 M-sodium phosphate, 61 mM-EDTA (pH 7) are molar absorptivity (at 260 mM and 25°C) = 99,090; t, (at 3.8 PM strand concentration) = 43°C; AH” = -895 kcal mol-‘; AS” = -258 cal mol-’ K-l; AGO,, = -9.4 kcal mol-’ (1 cal=4.184 J). Values calculated from nearest neighbor parameters (Freier et al., 1986): AH” = -90 kcal t Abbreviations used: h.p.l.c., high-pressure chromatography; r.m.s., root-mean-square.
liquid
et al. AS”=
-262
cal mol-’
Km’: AGO,,=
-9.1 kcal
(b) The crystals U(UA),A was crystallized in hanging drops by the vapor diffusion method. Methyl-2,2-pentanediol was used as the precipitating agent in a sodium cacodylate buffer (40 mM, pH 65). The oligomer crystallizes readily for a large range of spermine and magnesium concentrations. These crystals are highly polymorphic and show very poor diffraction. Crystals diffracting to high resolution were obtained at high magnesium concentration (400 mM) and rather high temperature (35”C), at a concentration of oligonucleotide of 4 mM and methyl-2.2-pentanediol of 35%, without the presence of spermine. The crystals belong to space group P2,2,2, with unit cell dimensions of a = 3411 A, b = 4461 A and c = 4911 A. Three-dimensional X-ray diffraction data were collected at 18°C on an Enraf-Nonius CAD4 diffractometer using the Q/20 scan mode and a crystal of approximate dimensions: 640 mm x 930 mm x 025 mm. A set of standard reflections was monitored during data collection. A total loss in intensity of 17% was observed during the exposure time of 85 h. The data were reduced by standard procedures and included an empirical absorption correction (North et al., 1968). A total of 4924 independant reflections were measured and of those 2492 were above the 2 sigma level for F,,,values in the 25 A to 2.25 A resolution range. In the shell between 25 and 2.25 A resolution 30$4 of the reflections were still significant (F > 24 F)). (c) Structure determination
and rejinement
The structure was solved by molecular replacement, using the g-dimensional search program ULTIMA (Rabinovitch & Shakked, 1984). The starting model was a canonical RNA helix (Arnott et al., 1973) with the weight of the phosphate group increased by a factor 1.6. The observed and calculated values of 52 structure factors between 25 and 10 A resolution were compared for all positions, with steps in translation of 5 A and orientation 30”. Positions that led to overlaps between symmetryrelated molecules were eliminated from the search. The 20 positions and orientations with best R-factors were then refined by least squares, and the 2 best solutions with R-factors of 26% and 25% were considered (the third best value was 38%). The model with unweighted phosphate groups was then introduced, leading to R-values of 42% and 30%. This last solution was then kept and refined in increasing resolution ranges by rigid-body least squares, arriving to a final R-factor of 46% for 371 reflections between 25 and 5 A resolution. This position was the starting point of a least-squares procedure, which proceeded in 2 steps. First, the program CORELS (Sussman, 1985) was used to position the bases, ribose units and phosphate groups as rigid bodies. The positions and orientations of the separate groups were refined against 1568 reflections between 8 and 3 A resolution, leading to a drop in R-factor from 53 To to 37 y. with fixed group temperature factors. Further refinement of the group temperature factors led to an R-factor of 32%. Analysis of this solution using 2F,,, - Feale maps showed that the positioning of the ribose and base moieties was correct, even when it involved some large displacements. The stereochemistry, however? was distorted at the connection of the phosphate groups to the rest of the molecule.
461
Structure of U ( U A) 6A
2
Figure 1. Group temperature (-m-m-)
4
6 8 IO First strand
12
14
16
I8
factors at the end of the refinement.
20
22 24 26 Second strand
(-
28
l - l - ) Phosphates; ( - 0 - 0 - ) riboses;
bases.
In the second step, the refinement was followed by stereochemically restrained least squares using the nucleic acids version NUCLSQ (Westhof et al., 1985a) of the Hendrickson-Konnert program (Hendrickson & Konnert, 1980; Hendrickson, 1985). Restraints were placed on bond length and angles, base planes, ribose chiral centers, nonbonded contacts and thermal factors of linked atoms after these had been allowed to vary. The resolution was extended from 3 A to the limit of 2.25 A. All atoms were refined isotropically up to an R-factor of 0191. Finally, the solvent peaks, located from 2F,b,-F,,,, and Foba- Fca,c electron density maps in conjunction with FRODO (Jones, 1978) model building on a vector graphics system, were introduced in the refinement as water molecules with individual isotropic temperature
factors. The water molecules were first refined at fixed occupancy, then the occupancy was varied. A total of 91 water molecules were introduced leading to a final R-factor of @131. Only water molecules with a B-factor less than 40 ir2 and an occupancy larger than 70% were kept. The r.m.s. positional shift in the last cycle was 0016 A and the r.m.s. temperature factor shift was @40 A2. Table 1 gives a summary of the refinement parameters and the agreement statistics for geometrical parameters at the end of the refinement. Fig. 1 shows the mean group temperature factors. While Ul is stabilized by packing contacts, the high mobility of U15 is typical of the end-helix effect. Atomic co-ordinates will be deposited in the Brookhaven Protein Data Bank.
Table 1 A. Summary of rejinement parameters 10.0-2.25 A 2437 582 91
Resolution range Number of reflections
with F > 2o(F)
Number of atoms Number of solvent atoms Final R-factor Fobs/F& correlation K = =‘o&Fc,,c Mean Fobs
131% 0.963 1.002
coefficient
1876 2.45
Mean IFobs- F,,,,I The R-factor 1s defined as ZIF,,,- Fca,sll=‘ob.. The correlation coefficient is given by:
ZIP’,,,-
< Fobs> P’c,,,-
< Fca,, > )l/[VF,,-
< F,, > ?.VF,,,,-
< Fca,c’ )211’Z.
B. Agreement statistics for geometrical parameters @004/~010 @035/@050 @063/@075 0~017/0~030 0~077/0~100 0.139/0.250 @168/@250
Bond distances Bond angles Hydrogen bonds Base planarity Chiral volumes Single torsion contacts Multiple torsion contacts Isotropic thermal factors For atoms connected by a bond length For atoms connected by a bond angle For atoms involved in phosphate bonds For atoms involved in hydrogen-bonds or phosphate angles The left-hand number gives the r.m.s. deviation sigma value used in the refinement.
from ideality
3.4917.50 b30/7.50 502/7.50 k55/750 and the right-hand
number is the
462
A. C. Dock-Bregecm
et al
(b:
d
PI4
Figure 2. Two stereo views of the whole molecule. Three axes were determined separately for domain Ul A5.U24, domain A5.U24 to UlO.Al9 and domain UlO.A19 to Al4.Ul5 with the program HELIX (Fratini 1982). (a) The flat ribbon-like minor groove. (b) Looking into the deep and narrow major groove.
A28 to et al.,
Structure
3. Description of the Structure (a) Global features of the U(UA),A
helix
The self-complementary tetradecamer U(UA),A crystallizes in the duplex form as a double-helical structure of about one and a third turns, which shows the typical features of an A-type helix. Two stereo views of the molecule are displayed in Figure 2. The grooves are clearly defined: the minor groove is flat and hollow and the major groove is very deep and narrow. The sugar rings wrap around the surface of the helix cylinder, and the base-pairs are strongly tilted with respect to a plane perpendicular to the helix axis. The base-pairs do not sit on the helix axis but are displaced towards the surface of the cylinder. Helical parameters were calculated with the program written by J. Rosenberg and R.E. Dickerson and described by Fratini et al. (1982). Their average values are reported in Table 2 and compared with those of related structures. The comparison shows that the double strands of U(UA),A follow a typical A-type structure, characterized by a high tilt and a very different width for each groove, and resembling the RNA-DNA hybrid structure (Wang et al., 1982). However, large differences between the structure of U(UA),A and the canonical A-RNA helix become evident when the two helices are superimposed en bloc, the r.m.s. distance between the refined and canonical helices being 1.75 A. The superposition of onlv the central five base-pairs shows an r.m.s. dexiiation of 0.97 A. In this case the distance between the complete helices exceeds 3 A at the terminal base-pairs. This superposition, displayed in Figure 3. shows that the U(UA),A helix is kinked at
qf U(UA)
463
6A
two points, dividing the molecule into three blocks of five, five and four base-pairs. Each block is a fragment of A-helix. For clarity, the locations of the kinks are shown in the sequence in Figure 4. A comparison of the structure with a canonical A-type helix of the same sequence underlines a large variability in the major groove width (2.1 A to 6.3 A) that is probably linked with the presence of the kinks. The narrower part of the major groove is between P5 and P18 (on the left in the orientation of Fig. 3). This reflects a pinching effect resulting from the kink between the tenth and the eleventh bases-pairs (indicated in Figs 2 and 3 by the two lowermost helical axes). The kink angles are 8.5” for the uppermost kink of Figure 2 and 13%” for the other, the two distal axes making an angle of 21.7” about the middle axis. The two kinks are not coplanar. (b) The backbone The values of the torsion angles about the main chain and the glycosyl bonds are given in Table 3. The torsion angles showing the highest variability (as indicated by the standard deviations values) are c(, around P-O-5’, and y, around C-5’-C-4’. These torsion angles are completely different from their mean values at three residues, All, U24 and A28 where they are in the trans, trans conformation instead of the usual gauche-, gauche+ conformation. This correlates with the superposition of the canonical fiber-helix upon the U(UA),A structure in Figure 3, which shows that the divergence between the backbones of the two helices starts at phosphate 11 (and its corresponding P19 on the other strand)
Table 2 Average helical parameters and comparison with other structures Groove width?
UWAkA (SD.)
Helix twist (“)
Rise per base-pair (4
Minor (4
Major
Base-pair tilt (“)
Disp.$ (4
33.2 P9)
2.78 (0.23)
10.2 (0.5)
4.1 (2.3)
17.1 (W
36 (6.4)
Fiber model
Poly(A) poly(U) Cl)0
32.7
2.81
11.3
41
16.7
4.4
tRNAs(l tRNAASp (2) tRNAPhe ortho (3) tRNAPhc mono (4)
33.4 33.2 33.5
2.55 2.53 2.41
9.7 98 9.8
3.2 45 45
157 160 16.9
4.5 41 44
A-DNA A-DNA fiber (5) A-DNA oligo. (6) (SD.) r(GCG)d(TATACGC)
32.7 32.9 (0.9) 333
2.56 298 (010) 252
11.0 98 (0.3) 10.2
23 7.0 (1.3) 3.2
22.0 lF2 (1.8) 19.3
4.4 38 (0.3) 4.5
(7)
t Measured as the closest phosphorus to phosphorus distance across the major groove, minus 58 A to account for the phosphate groups van der Waals’ radii. $ Disp. is the displacement of a base-pair (C6.CS vector) from the helix axis. Q References: (1) Arnott et al. (1973); (2) Westhof et al. (1985a); (3) Holbrook et al. (1978); (4) Westhof & Sundaralingam (1986); (,5) values reported by Shakked & Rabinovitch (1986); (6) mean values and S.D. calculated from the compilation of Shakked & Rabinovitch (1986); (7) Wang et al. (1982). (( Average of acceptor stem (base-pairs 1.72 to 7.66) and anticodon stem (base-pairs 27.43 to 31 ‘39).
464
A. C. Dock-Bregeon
et al.
-j--+*14
Figure 3. The structure of U(UA),A, thick lines, ball-and-stick mode, is compared to the fiber model (Arnott et al., 1973), in thin lines. The central block of 5 base-pairs (U6. A23 to UlO A19) were superimposed, and show a good similarity. This view emphasizes that the divergence of the 2 structures starts at precise locations on each strand: Pl 1 and P24. The distances between equivalent positions at the helical ends exceed 3 A. Note also the pinching effect of the kink at Pll
upon the major
groove
(on the left of the Figure),
and at phosphate 24 (and P6). The mean torsion angles, computed excluding All, U24 and the terminal residue A28, are very close to those of the canonical A-RNA structure deduced from fiber diffraction. It is well established now that the shifts in the torsion angles c( and y are strongly anti-correlated in A-type helices (e.g. see Shakked et al., 1983; Conner et al., 1984; Westhof et al., 1985a). This is true also in U(UA),A, as indicated in Figure 5. Since the intervening torsion angle B is always trans, the anticorrelated movements of c( and y lead to a displacement of the base along its normal vector, and to an extended conformation of the backbone. The distance from one phosphorus to the next on the chain (which otherwise averages 5.8 B+O.3), is
28 27
26
25
24
23
22
21
20
19
18
17
Figure 4. The sequence of U(UA),A. Asterisks the conformational changes inducing the kinks.
16
whose widt)h is reduced
extended to 6.4 a for P23-P24 and 6.7 a for PlO-Pll. The extended conformation has also been observed in two A-DNA oligonucleotides, d(CCCCGGGG) (Haran et al., 1987) and d(GCCCGGGC) (Heinemann et al., 1987), at the pyrimidine-purine
Torsion angle about P-O-5’
15
indicate
from a mean value of 4.1 A to 2.1 !I.
Figure P-O-5’)
5. Anti-correlation of torsion and y (about C-5’-C-4’).
angles
c( (about
Structure
of U (UA)
465
6A
Table 3 Torsion
P-i-5’
B
0-5’-C-5’
angles in U( UA) 6A
6 cm.&;m4~ c-4’-C-3’
c-3&-3
i
0-3’-P
x
0-4’-C-I’-N-9-C-4 O-4’-C-I’PN-l-C-2
-71 -75 -57 -71 -63 - 78 -85 -48 -69 155 -59 -42 -56
-177 -174 170 168 -179 -169 -165 -176 165 178 140 177 166
49 59 56 70 53 61 66 43 60 178 64 37 55
99 83 76 83 76 80 78 85 79 80 89 78 93 75
-152 -175 -162 - 162 -142 -152 -159 -155 -171 -135 -114 -136 -139
-75 -65 -69 -86 -73 -66 -71 -81 -61 -70 -103 -91 -87
- 163 -146 - 161 -155 -167 -157 -1.54 - 1.54 -148 -156 178 -1i4 - 163 -155
- 55 -81 -42 -53 -87 -49 -81 -54 -149 -49 -65 -56 -146
151 171 172 168 156 147 166 167 -177 170 147 -178 -162
51 80 37 45 75 51 77 52 127 44 77 44 118
85 83 75 81 83 78 84 81 66 76 79 72 78 83
-95 - 137 -138 -159 -156 -116 -134 -139 -167 -132 -153 -131 -168
-97 -84 - 74 -83 -79 -113 -88 -81 -62 -86 -86 -76 -77
165 -158 -170 -153 -159 -167 -162 -164 - 154 -173 -161 -169 -154 -158
-75 (37)
172 (15)
Ps’r
-162 (11)
(S.D.)
-63 (14)
170 (14)
57 (13)
i
-145 (19) - 147 (18)
-80
(3”:,
RNA fibre$
-62
180
48
83
tRXAASpII
-93
183
74
82
Ul U2 A3 u4 A5 U-e A7 V8 A9 UlO All Ul;! Al 3 Al4 U15 U16 Al7 U18 A19 U20 All U22 A23 U24 A25 U26
A27 A28 Meant (SD.)
MEAN$
(12) (12)
- 161 (10)
-151
-74
-165
-156
-74
-166
-79
(pur) (pyr)
t Average of all values. 2 Average excluding Al 1 and U24, and the terminal residue A28. 3 Arnott et al. (1973). 11Only the residues of the stems were considered; from Westhof et al. (1985).
steps. However, these oligonucleotides are not kinked because the cc,y trans, trans conformation is observed on both strands. In U(UA),A, the trans, trans conformation occurs only in one strand for each kink. The disruption of the base-pairing and the base stacking, which could result from the extension of one chain, is avoided by the kinks. (c) Base-pair (i) Stacking
geometry and stacking
geometries
In A-helices the stacking interactions vary with the sequence; 5’pyrimidine3’purine steps show interstrand stacking of the purines, while B’purineS’pyrimidine steps do not. Figure 6 shows some representative stacking geometries and emphasizes the differences with the fiber model. In 5’A-3’U steps, a movement of the upper base-pair towards the minor groove hampers the overlap of the exocyclic atoms in the major groove. The same
observation was made in d(GGTATACC) (Shakked et al., 1983). At variance, in 5’U-3’A steps a small movement of the upper base-pair is observed towards the major groove. This favors a small intrastrand stacking. The stacking mode is not affected by the crystal environment or the kinks. Figure 6 shows that the stacking patterns are typical of the sequence even at the kinks regions (steps 5 and lo), or at those of the largest twist variations (steps 3. 10 and 12) as indicated in Figure 7. The different helical parameters characterizing the positions of the base-pairs are reported in Table 4. (ii) The slide variations In U(UA),A the slide displays alternating values. The 5’U-3’A steps, with an average slide of l-44 A, show the higher values characteristic of interstrand stacking (in 5’A-3’U steps the average slide is
466
A. C. Dock-Bregeon
t
”
- *
A-U
I
et al.
steps
fibre fibre
step
2
A27 - U2 I U26 - A3 I
step
10
A19 - “10 I “18
step Al7 I U16
- A:1 I
12 - “12 - A13 I
Figure 6. Examples of the stacking patterns in U(UA),A and comparison with the stacking patterns of the fiber model (on the top). Three examples of each kind of sequence (5’AP3’U steps on the left and 5’W3’A steps on the right) are shown. The stacking patterns of the steps (5 and 10) where conformational changes of torsion angles are observed (represented as asterisks on the sequence in Fig. 4) are represented, as well as those where the twist angle is particularly large (step 12) or small (steps 10 and 3) and also steps with medium twist angles (steps 2 and 7). The twist angles variations are plotted in Fig. 7.
j8 36
32 30 28 26
I
Ul d28
Figure 7. Variations the kinks occur.
r
I
12 U2 Ak7
I,
34 A3 U4 d26 Ai5
I
56 *
I
I
I
7
8
A5 U6 A7 U8 u’za At?3 U!?2 Ail
of the twist angles in the structure.
I
9 A9 d0
I
I
‘2
l1
UlO All Ai Ui8
I
I
l2 I3
U12 Al3 Ail Ui6
Al4 Ui5
Asterisks show where the conformational
changes leading to
Structure
Helical
qf U(UA)
Table 4 parameters in U (UA),A Tilt
Disp.
Propeller twist
19.5
3.09
28.8
IT1 A28
165
3.37
152
u2 A27
145
3.39
17.1
A3 1126
15.0
312
19.9
(74 A25
142
3.43
15.9
A5 1u4
205
405
18.1
LJ6. A23
22.1
3.97
18.7
Ai. U22
208
411
19.9
U8.A21
21.7
399
23.3
A9 u20
22.7
3.85
17.6
UlO.Al9
134
3.19
156
All.ClX
13-2
357
20.8
UlZ.Al7
10-l
3.80
21.5
A13-Vl6
1+9
320
14.8
Al4.1Tl5
1.17 (0.31)
17.1 (W
3.58 (0.37)
191 (3.8)
1.55
167
44
13.8
Twist
Rise
Roll
Slide
34.0
309
48
0.51
33.8
281
14.4
1.29
295
2.77
0.0
1.07
368
2-73
131
143
32.3
2.49
6.1
190
32.9
246
11.0
1.54
336
2.77
11.8
098
332
265
16.9
1.34
35.0
25 1
9.2
0.83
26.8
3.19
14.2
1.50
31.4
2.81
26
1.12
380
2.79
136
1.56
34.0
309
5.0
1.07
1-1 82X u2. A27 A3 U26 U4. A25 A5 CT24 * U6. A23 A-7. C22 U8,A21 A9 u20 UIO.Al9 * All.UlX U12.A17 813. L’l6 A14.Ul5 (S.D.)
332 (2.9)
2.78 (023)
Fibret
327
281
Mean
467
6A
9.4 (52) -9.0
Helical parameters were calculated using the program HELIX (Fratini et al., 1982), with the 3 domains Ul . A28 to UlO.Al9 and UlO’A19 to Al4.Ul5 treated separately. Asterisks indicate the positions of the kinks. t Deduced from Arnott et al. (1973).
1.00 A). Globally, slide values are slightly lower than those of the fibre model (1.7 A and 1.4 8, respectively) in agreement with the observation of an improvement of intrastrand stacking. (iii) The roll variations The roll angles are all positive and their values alternate. Values for 5’U-3’A steps are higher (average 13.9”) than those for A-U steps (average 59”), with the exception of the seventh step. This behavior follows Calladine’s predictions (Calladine, 1982; Dickerson, 1983), based upon the rationale that rolling may lessen steric clashes between purines in alternating sequences. The steric clash is avoided for 5’pyrimidine-3’purine sequences by an increase of the roll angle that opens the minor groove. Thus, the two alternating types of sequence in this structure are characterized by different combinations of roll and slide, with high values for 5’U-3’A steps and low values for 5’A-3’U steps, in agreement with the model of Calladine & Drew (1984). (iv) The twist variations The twist angle is mostly influenced by the kinks and not by the sequence (Fig. 7). In the middle of
to A5.1724, A5. U24
the molecule, it is close to the average value (33.2”). At the kink regions compensatory variations appear and are propagated towards the outer parts of the molecule. The observed variations of the twist angle may also be related to the environment in the crystal. The twist changes at step 10, where an intermolecular contact is stabilized through hydrogen bonding between Al 1(O-2’) and a neighboring Ul(O-2). At the other step where the twist angle changes (step 4) a hydrogen bond is observed that involves A25(0-2’). Twist appears to be a means of orienting structural elements to optimize intermolecular interactions. For example, the low twist angle observed at step 10 brings the 0-2’-hydroxyl groups of UlO and All into an orientation that permits simultaneous intermolecular interactions (Fig. 6; compare the O-2’ orientations at step 10, with a low twist angle, and at step 2, with a medium twist). (v) Propeller
twist
Propeller twist shows a high average value of lg.]“, correlating well with the observation of an improvement in intrastrand stacking in this structure. This value is still smaller than that observed in t,he oligo(dA) . oligo(dT) stretches of the B-DNA
468
A. C. Dock-Bregeon
et al.
dodecamers d(CGCA,GCG)/d(CGCT,GCG) (Nelson et (zZ., 1987) and d(CGCA,TsGCG) (Co11 et al., 1987): which display average values of 20”. High propeller twist could reflect a larger deformability of A. IT base-pairs, which have only two hydrogen bonds. In the case of the oligo(dA). oligo(dT) stretches, the high propeller twist is stabilized through crossst)rand hydrogen bonds. These are not possible in the case of aiternating AT or AIJ sequences. (d) Packing
arrangement
(i) The two contacts that resemble those seen in A-DNA crystals In the P2,2,2, space group there are three intermolecular contacts, of which two show interactions similar to those observed in A-DNA helices, i.e. the stacking of an end-base-pair on the flat minor groove of a symmetrical molecule (Shakked &
Figure 8. The common building
block of 2 contacts. The core of contact 1 (see Table 5) is represented by the terminal base-pair (here Gl .A28) at the bottom in open lines, and the symmetrical pair at the top (here Al 1 Ul8) in heavy lines. The same interactions are observed in contact 2. where the other terminal base-pair. A14.Ul5 interacts with a symmetrical U4. A25.
Table 5 Intermolecular 5, y, Z-P --x, A9 I d-U20
1 1/2+y,
112-z
A;1
-
UIO+
and salvation
2
U12 I U16 Al?
A’J9
contacts: distances
3
z, y, z-t1/2+x,
c
1/2-g.
A23 z+024 A25 (126 I A’5 lJ\ A: U6
Ul -A28
UlS-Al4
U2 -A21
U16-
--t
x,y,z+1/2-2,
-w
1/2+z
A23*U24.. -
U2
UJ
UlS - Al4 A13
U16-
Al3
+
UlO
A3 -U26 +
-y,
~A2IlJ22
t
A9 t
.,Direct
contacts:,
.... ......................... ............. ......................... ............ .......................... .........
Ul(OZ)-v-w
AII(O2’)
3.0
UlS(C6)
. . . . . U22(027
3.2
AZS(O2’)
___ UJ8(02)
3.0
UlS(CS)
..-.U22(03’)
3.0
A28(03’)
_-- UIS(O2’)
3.0
A9(03’) A9(03’)
. . . . . . UZ(O5’) . . . . . . Ul(C5’)
3.5
UUO2’)--
U12(02P)
U2(02’)---
UI O(O2 ‘) 2.5
A3(02’),,,,
U20(02’)
A28(N3)--??-
)X-i?-
3.3
UlO(O2P)~~~~~~ UI(C5’)
_216_-
A27(N3)
v?k-
AII(N3)
2.9
---
2.6 w;%‘-
34-w
43(02P)
____ A19(02’)
2.9 _* w2L w ~~---S.---_
A3(03~)??-
2.;*
w’N
3.;-
UZO(O2) U20(02’)
-k?--
---3k---;i-
U16(02’)
-_?.6
Ul6(02’)
-Kz.s--‘w=.-
W-m?!-
~6~033
w-.%1 ----
2.5 w -.%.
A9(02p)
--..%I--
A14(02P)
--?“--
U12(01P)
-----
U6(04’) 2c=A5f02,J
--3.8---
AS(N3)
Als(N6)
A14(03’)
A21(04’) U10(03 1) AJI(OZP) I
Ul(O2’)
A17(02’) Al7(03’)
4
W-e!?
3.3
3.2
r’3.0 UZ(O2)
3.3
-?” --- _ W = --2’4 U26(02) ---.---2.9 --A27(04’)
A13(02’)
-?-
A13(N3)
---j;
w -::-
A5((,2 ‘,
2.6
w -m&?--
UJ(O5’)
w ---3! --_-
AZJ(OtPj
W\ 2.s
--3t?m y-?!k
W-2_.!-
U24(02P)
\2.9
Ul5(04)
-~2,L~‘w
Ul6(04)
-?
_____
I 2.5 w --?!s-2:8*.
All(N7)
-3.y
W--55--
A23(OZP) A.1
w’
U12(02P) uls(o4*)--?L
3.5 w - --mm-----_ -----3.6
U22(02’) U22(04’)
Structure of U( UA),A
469
(bf
Figure 9. (a) Packing of U(UA),A. Two contacts are represented; the lower couple of molecules show contact 1 (see Table 5) with the ribose of A28 of the leftmost molecule directed into the minor groove of the symmetrical molecule. The contact is stabilized as shown in Fig. 8, plus 3 additional hydrogen bonds between the close backbones (other views of this contact are provided in Fig. 11). The upper couple of molecules show contact 3, which is different. The cavity between the major grooves of the upper couple of molecules and the region between the 2 lower molecules are the largest solvent domains of the U(UA),A crystals. (b) The third contact, in the same orientation. This contact is formed by van der Waals’ contacts and solvent bridges between the backbone of the upper molecule and the major groove of the other.
Kennard, 1985; Wang & Teng, 1988). However, the presence of the 2’-hydroxyl groups modifies the interatomic contacts. Both interactions are based upon a similar pattern, represented in Figure 8, and stabilized through hydrogen bonding. In each case, the ribose of the terminal adenine points into the minor groove of the symmetrically related molecule and interacts with an uridine O-2. A second inter-
action involves the terminal uridine O-2 and the 0-2’.hydroxyl of the other adenine. In the case of the contact involving the Ul .A28 terminal basepair there are three additional intermolecular interactions. All of them consist of hydrogen bonds involving 0-2’-hydroxyl groups. The distances between interacting atoms in the intermolecular contacts are given in Table 5.
470
A. C. Dock-Bregeon
et al.
(a)
I
P14
P28
P28
&I4
Figure distances
10. General view of the salvation up to 3.4 d. (a) The major groove.
of the grooves. Broken (b) The minor groove.
@ lines
represent
possible
1.’PI4
hydrogen
bonds.
with
Structure
of U (UA)
(ii) The third contact The third contact, represented in Figure 9, is different; it brings the major grooves of two symmetrical molecules face to face with each other. A few van der Waals’ interactions are observed between the backbones at Ul and A9, UlO of the symmetrical molecule, and between the backbone at U22 and the major groove near the terminal A14. U15 base-pairs. The contact is further stabilized by solvent bridges between the backbone at U22-U24 and the major groove of the symmetrical molecule. The contact is described further in Table 5.
(e) SoZwation
(i) Distribution of solvent molecules Of the 91 solvent molecules identified per duplex, 65 are in direct contact with the atoms of the RNA, with distances of 2.3 to 3.6 A. Of the remaining 26 molecules, 14 are bound to first-shell solvent molea fragmentary second cules and constitute hydration layer. The other 12 are more distant. About 32% of the solvent molecules are located in the major groove, 6% are in the minor groove and 60% are near the backbone. The clear identification of cations proved surprisingly difficult, since the crystallization was very dependent on high magnesium concentration. This could either be due to lack of resolution, or reflect a delocalization of the cations, forming an electrostatic shield in the crystal assembly without having necessarily any defined site. (ii) Solvation of the major groove The solvent molecules found in the deep major groove of the RNA molecule form a continuous column around which the helix wraps. A general view is given in Figure 10(a). Adenines are much more hydrated than uridines, with 12 N-7 atom sites and 2 N-6 atom sites occupied, whereas there are only two O-4 atom sites occupied. We do not observe higher-order organization of solvent molecules comparable to the fused pentagons observed in the alternating TA or B’UA stretches of A-DNA structures (Kennard et al., 1986). Two-water bridges of the type A(N7). . . Wl . . . W2.. .O-1P lie between adenine N-7 and 0-1P of the same residue (at A19 and A25) or of adjacent residues (at A7-U6). A onewater bridge of the same type is observed at A27 and at A28, at the end of the molecule. In this case, the two solvent molecules bound to the consecutive N-7 atoms are spanned by a solvent molecule of the second layer. (iii) Solvation of the backbone The solvation of the phosphate-oxygen backbone shows that both 0-1P and 0-2P atoms are hydrated, with about 60% of the possible sites occupied, while the ester oxygens are less hydrated. The terminal 3’ and 5’ hydroxyl groups are solvated. The solvent molecules interacting with anionic
471
6A
oxygens of the phosphate groups are most often monodentate. We see only two bridges between adjacent phosphate groups as expected from Saenger et al. (1986). This is possibly a consequence of the tight packing of the U(UA),A crystals, since the only stretches of backbone that lack close neighbors are U8 to Al3 and U18 to U24, in the cavity between the major grooves of the third contact. There is a one-water interstrand bridge between A5 and U18, while other examples of interstrand bridges reported thus far are two-water bridges (Westhof, 1987, 1988; Westhof et al., 19856). It spans the narrowest part of the major groove and is probably related to the pinching effect of the kink upon the groove. This bridge is flanked by two additional two-solvent bridges. The backbone is also the anchor point of intermolecular bridges, especially in the packing contact described above as the third contact. Table 5 shows the interatomic distances concerning a group of seven solvent molecules connecting U24(0-2P) to the major groove of a symmetric molecule. These are linked in one stretch of continuous density in a 2F,,,- Fcalc map contoured at 8% of the maximum value. Other stretches of continuous density are observed in solvent regions between the RNA molecules. It may be recalled here that no spermine was used in the crystallization medium. of the minor groove (iv) Solvation The solvation of the bases in the minor groove shows a regular pattern (Fig. 10(b)), with solvent molecules running along the gutter-like groove. In contrast to the situation in the major groove, both base-types are hydrated, at N-3 for adenines and at O-2 for uridines. The minor groove is intimately involved in two packing contacts and Figure 11 shows the solvation in one of these contacts. The economics of the hydration are remarkable, with most of the solvent molecules shared between the two symmetrical RNA molecules.
(v) Hydration
of the 2’-OH
groups
Half of the 0-2’-hydroxyl groups lie within hydrogen bonding distance of one or more solvent molecules. Four of them bridge 0-2’-hydroxyl groups to O-2 or N-3 atoms of the adjacent base in the minor groove, and two others bridge 0-2’-hydroxyl groups to the next O-4’ in the 3’ direction. This last type of bridge has also been observed in r(ApU) (Seeman et al., 1976). The intramolecular solvent bridges involving O-2’ groups are not, however, as frequently observed as in the case of tRNAs (Westhof et al., 1988) although the resolution is better. The difference is probably linked to the tightness of the crystal packing in U(UA),A. The analysis of the packing contacts (Table 5) shows the important participation of 0-2’.hydroxyl groups. Indeed, 12 of them participate in direct intermolecular hydrogen bonds and three more in solventmediated intermolecular bridges. Therefore, the structure of U(UA),A represents a model of an interacting RNA molecule.
472
A. C. Dock-Bregeon
(b)
et al.
4
Figure 11. Solvation of the first contact, involving the minor groove. The close interconnection of the symmetrical molecules is reinforced by the solvent. (a) Pairs Ul . A28, U2. A27 and residue A3 in open lines, pairs UlO. A19, Al 1. U18 and residues U12 and U20 in heavy lines. The orientation emphasizes the participation of the 0-2’-hydroxyl groups in the interaction. (b) A perpendicular view where the same residues except U12 are shown.
4. Discussion This crystal structure provides the best information on an RNA helix at the atomic level. The functional role of specific groups like 2’-hydroxyl can be verified. They are expected to play an important role in the preference of RNA molecules for A-type helices, since they sterically hinder the C-2’endo conformation and may further stabilize the C-Q’-endo conformation by hydrogen bonding with the ribose O-4’ of the next residue in the 3’-direction. Such hydrogen bonds have been reported in tRNAs (Jack et al., 1976; Holbrook et al., 1978; Westhof et al., 1985a). They are also observed in U(UA),A, where one third of the 0-2’(n) groups interact with O-4’(n + l), with distances averaging 3.3 A. The sequence chosen is particularly repetitive. Previous examples of alternating AT stretches were provided by the structures of d(GGTATACC) (Shakked et al., 1983) and r(GCG)d(TATACGC) (Wang et al., 1982). These show a distinct behavior for each type of sequence: the 5’T-3’A steps have low twist angles, high slide, and high roll values, while the 5’A-3’T steps have medium twist angles, low slide and negligible roll values (Shakked &
Rabinovitch, 1986). In U(UA,)A, this observation holds for the slide and the roll values, but the twist angles variations are quite different. No sequence information seems to be directly reflected by the backbone in this structure. For example, the torsion angle x about the glycosidic bond may vary according to the nature of the base, as in the crystal structure of d(GGGGCCCC) (McCall et al., 1985), where higher values were observed for guanine than for cytidine residues. Here they are alike: -161”(g) for adenines and -161”(8) for uridines. It seems that in this RNA structure, as in a previous study on DNA (Shakked & Rabinovitch, 1986), the effects of the sequence upon the conformation of the sugar-phosphate backbone are not clearly apparent. Even when the sequence is highly symmetrical, this structure is definitely asymmetrical. The superposition of one strand (Ul to A14) upon the other (U15 to A28) shows a r.m.s. distance between equivalent atoms of 1.7 A. This reflects the differences in the environment of each strand in the crystal lattice. Therefore, the two kinks are also different, as illustrated by the analysis of the rise per basepair (Table 3). At All, the rise is 3.2 A, increasing from the average value of 2.8 A, while at U24 it
Structure of U ( UA) 6A decreases to 2.5 A. This difference is related t$o the different amplitude of the conformational change of torsion angles a,y at each kink. These kinks reflect degrees of freedom also observed in larger RNA molecules like tRNAs. The correlated change of the cr,y angles observed at the kinks is seen also in tRNAs, especially for the G. U base-pairs, with the example of G30 in tRNAASp (Westhof et aE., 1985) or G4 in tRNAPh’ (Sussman et aZ., 1978)? but also at less specific sequences like G51 or G53 in the T-stem of tRNAAsp. The final model confirms that the major groove is narrow and deep and the minor groove broad and shallow. Moreover, 0-2’-hydroxyl groups point towards the minor groove, which becomes, therefore, the preferred site for intermolecular interactions and sequence-specific recognition. The particularities of this structure, which significantly differs from the fiber model, are most probably to the high related temperature of crystallization. The present model reflects, therefore, one of many possible states of the molecule, which could eventually be analyzed by a molecular dynamics study in which both the fiber and the crystal structures would be states to be reproduced. This would enable us to gain further insight into the fascinating variability of the RNA molecule.
References Arnott,
S.. Hukins;
Biochem.
Biophys.
D. W. L. & Dover, Res. Commun.
S. D. (1972).
48, 1392-1399.
Amott, S.. Hukins, D. W. L., Dover, S. D., Fuller. W. & Hodgson. A. R. (1973). J. Mol. Biol. 81, 107-122. Calladine. C. R. (1982). J. Mol. Biol. 161, 343-352. Calladine. C. R. & Drew. H. R. (1984). J. Mol. BioZ. 178, 7733782. Catlin. J. C. & Cramer, F. (1973). J. Organ. Chem. 38, 245-250. Cech, T. R. (1987). Science, 236, 1532-1539. (~011.M., Frederick, C. A., Wang, A. H. J. & Rich, A. (1987). Proc. Nat. Acad. Sci., U.S.A. 84, 8385-8389. Conner, I%. N., Yoon, C.. Dickerson, J. L. & Dickerson, R. E. (1984). J. Mol. BioZ. 174, 663-695. Dickerson. R. E. (1983). J. Mol. BioZ. 166, 419-441. Dickerson. R. E., Kopka, M. L. & Pjura, P. (1985). In Biological Macromolecutes & Assemblies (Jurnak, F. A. $ McPherson, A., eds), vol. 2, pp. 377126, Wiley, New York. Dickerson. R. E., Kopka, M. L. & Pjura, P. (1987). In DXA--Ligand Interactions (Guschlbauer, W. $ Saenger. W., eds). pp. 45-62, Plenum Publishing Corporation, New York. Fratini. A. V., Kopka, M. L., Drew, H. R. & Dickerson, R. E. (1982). J. BioZ. Chem. 257, 14686-14705. Freier. S. M., Kierzek, R.. Jaeger, J. A., Sugimoto, N., Caruthers, M. H., Neilson,,T. $ Turner, D. H. (1986). Proc. Nat. Acad.
Sci., U.S.A.
83, 9373-9377.
Gough, G. R., Collier, K. ,J.. Weith, H. L. & Gilham, P. T. (1979). iVucZ. Acids Res. 7, 1955-1964. Gough, G. R.. Nadeau. ,J. G., Gilham, P. T., Singleton, C. K. Sr Weith. H. I,. (1980). NucZ. Acids Res. Symp. no. 7, 99-102. Gough, G. R.. Brunden, M. J. & Gilham, P. T. (1983). Tetrahrdron Letters. 24, 5321-5324.
473
Hall, K., Cruz, P., Tinoco, I., Jr, Jovin, T. M. & van de Sande, J. H. (1984). Nature (London), 311, 584-586. Haran, T. E., Shakked, Z., Wang, A. H. J. & Rich, A. (1987). J. Biomol. Struck Dynam. 5, 199-217. Hayes, J. A., Brunden, M. J., Gilham, P. T. & Gough, G. R. (1985). Tetrahedron Letters, 26, 2407-2410. Heinemann, U., Lauble, H., Frank, R. & Blocker. H. (1987). NucZ. Acids Res. 22, 9531-9550. Hendrickson, W. A. (1985). Methods Enzymol. 115, 252-270. Hendrickson, W. A. & Konnert, J. H. (1980). In Computing in CrystaZZography (Diamond, R., Ramaseshan, S. & Venkatesan, K., eds), pp. 13011323. The Indian Academy of Sciences, Bangalore. Hingerty, B., Brown, R. 8. & Jack. A. (1978). J. Mol. BioZ. 124, 523-534. Holbrook, S. R.. Sussman, J. L., Warrant, R. W. & Kim, S. H. (1978). J. Mol. BioZ. 123, 631-660. Itakura, K., Bahl, C. P.; Katagiri, N., Michniewicz, J. J., Wightman, R. & Narang, S. A. (1973). Canud. J. Chem. 51, 3649-3651. Jack, A., Ladner, J. E. & Klug, A. (1976). J. Mol. BioZ. 108, 619649. Jones, T. A. (1978). J. AppZ. Crystallogr. 11, 268-272. Kennard, O., Cruse, W. B. T., Nachman,
Dynam.
3, 623-647.
Lawson, T. G., Regnier, F. E. & Weith, H. 1~. (1983). Anal. Biochem. 133, 85-93. Lohrmann, R. & Khorana, H. G. (1964). J. Amer. t’hem. Sot., 86, 4188-4194. McCall, M., Brown, T. & Kennard, 0. (1985). J. Mol. BioZ. 183, 385-396. Nadeau, J. G. & Gilham. P. T. (1985). Nucl. Acids Re.s. 13, 8259-8274. Nakamura, Y., Fijii. S., Urata, H., Uesugi, S., Ikehara, M. & Tonita. K. (1985). NucE. Acids ~Symp. ser. 16, 29-35. Nelson, H. C. M.. Finch, J. T., Luisi. B. F. & Klug, A. (1987). Nature (London), 330, 221-226. North, A. C. T., Phillips, D. C. & Matthews, F. S. (1968). Acta Crystallogr. sect. A, 24, 351-359. Ohtsuka, E., Tanaka, S. & Ikehara, M. (1974). NucZ. Acids Res. 1, 1351-1357. Ohtsuka, E.; Tanaka, S. & Ikehara, M. (1977). Chem. Pharm.
Bull.
25, 949-959.
Rabinovitch,
D. & Shakked, Z. (1984). Acta Crystallogr. sect. A, 40, 195-200. Rosenberg. J. M., Seeman, N. C., Day, R. 0. bz Rich, A. (1976). J. Mol. BioZ. 104, 145-167. Saenger, W. S. (1984). In Principles of Nucleic Acids Structure (Cantor, C. R.. ed.), pp. 220-241, SpringerVerlag, New York. Saenger, W., Hunter, W. N. & Kennard, 0. (1986). Sature (London),
324, 385-388.
Seeman? N. C., Rosenberg, J. M., Suddath. F. L.. Kim, J. J. P. & Rich, A. (1976). ,I. Xol. Biol. 104. 109-144. Shakked, Z. & Kennard, 0. (1985). In Biological &ZacromoZecuZes & Assemblies (Jurnak, F. A. & McPherson, A., eds). vol. 2, pp. l-36, Wiley, New York. Shakked, Z. & Rabinovitch, D. (1986). Progr. Biophys. Mol. BioZ. 47, 159-195. Shakked, Z.. Rabinovitch, D., Kennard, 0.. Cruse, W. B. T., Salisbury, S. A. & Viswamitra, M. A. (1983). J. Mol. BioZ. 166, 183-201. Sung, W. L. & Narang, S. A. (1982). Canad. J. (Ihem. 60, 111-120.
474
A. C. Dock-Bregeon
Sussman, J. L. (1985). Methods Enzymol. 115, 271-303. Sussman, J. L., Holbrook, S. R., Wade Warrant, R., Church, G. M. & Kim, S. H. (1978). J. Mol. Biol. 123, 607-630. Tinoco, I. Jr, Davis, P. W., Hardin, C. C., Puglisi, J. D., Walker, G. T. & Wyatt, J. (1987). Cold Spring Harbor Symp. Quant. Biol. 52, 135-146. Wang, A. H. J. & Rich, A. (1985). In Biological Macromolecules & Assemblies (Jurnak, F. A. 6 McPherson, A., eds), vol. 2, pp. 127-170, Wiley, New York. Wang, A. H. J. & Teng, M. K. (1988). ,I. Crystal Growth, 90, 295-310. Wang, A. H. J., Fujii, S., van Boom, J. H., van der Marel, Edited
et al.
G. A., van Boeckel, S. A. A. & Rich, A. (1982). Nature (London), 299, 601-604. Westhof, E. (1987). Int. J. Biol. Macromol. 9, 186-192. Westhof, E. (1988). Annu. Rev. Biophys. Chem. 17, 125-144. Westhof, E. & Sundaralingam, M. (1986). Biochemistry, 25, 4868-4878. Westhof, E., Dumas, P. 6 Moras, D. (1985a). J. Mol. Biol. 184, 119-145. Westhof, E., Prange, T., Chevrier, B. & Moras, D. (19856). Biochimie, 67, 811-817. Westhof, E., Dumas, P. & Moras, D. (1988). Biochimie, 70, 145-165.
by A. Klug