Predicting helical coaxial stacking in RNA multibranch loops

The hypothesis that RNA coaxial stacking can be predicted by free energy minimization using nearest-neighbor parameters is tested. The results show 58.2% positive predictive value (PPV) and 65.7% sensitivity for accuracy of the lowest free energy configuration compared with crystal structures. The probability of each stacking configuration can be predicted using a partition function calculation. Based on the dependence of accuracy on the calculated probability of the stacks, a probability threshold of 0.7 was chosen for predicting coaxial stacks. When scoring these likely stacks, the PPV was 66.7% at a sensitivity of 51.9%. It is observed that the coaxial stacks of helices that are not separated by unpaired nucleotides can be predicted with a significantly higher accuracy (74.0% PPV, 66.1% sensitivity) than the coaxial stacks mediated by noncanonical base pairs (55.9% PPV, 36.5% sensitivity). It is also shown that the prediction accuracy does not show any obvious trend with multibranch loop complexity as measured by three different parameters.     

Promoting RNA helical stacking via A-minor junctions

RNA molecules take advantage of prevalent structural motifs to fold and assemble into well-defined 3D architectures. The A-minor junction is a class of RNA motifs that specifically controls coaxial stacking of helices in natural RNAs. A sensitive self-assembling supra-molecular system was used as an assay to compare several natural and previously unidentified A-minor junctions by native polyacrylamide gel electrophoresis and atomic force microscopy. This class of modular motifs follows a topological rule that can accommodate a variety of interchangeable A-minor interactions with distinct local structural motifs. Overall, two different types of A-minor junctions can be distinguished based on their functional self-assembling behavior: one group makes use of triloops or GNRA and GNRA-like loops assembling with helices, while the other takes advantage of more complex tertiary receptors specific for the loop to gain higher stability. This study demonstrates how different structural motifs of RNA can contribute to the formation of topologically equivalent helical stacks. It also exemplifies the need of classifying RNA motifs based on their tertiary structural features rather than secondary structural features. The A-minor junction rule can be used to facilitate tertiary structure prediction of RNAs and rational design of RNA parts for nanobiotechnology and synthetic biology.     

A molecular dynamics simulation study of coaxial stacking in RNA

We report on unrestrained molecular dynamics simulations of an RNA tetramer binding to a tetra-nucleotide overhang at the 5'-end of an RNA hairpin (nicked structure) and of the corresponding continuous hairpin with Na+ as counterions. The simulations lead to stable structures and in this way a structural model for the coaxially stacked RNA hairpin is generated. The stacking interface in the coaxially stacked nicked hairpin structure is characterized by a reduced twist and shift and a slightly increased propeller twist as compared to the continuous system. This leads to an increased overlap between C22 and G23 in the stacking interface of the nicked structure. In the simulations the continuous RNA hairpin has an almost straight helical axis. On the other hand, the corresponding axis for the nicked structure exhibits a marked kink of 39 degrees. The stacking interface exhibits no increased flexibility as compared to the corresponding base pair step in the continuous structure.     

An examination of coaxial stacking of helical stems in a pseudoknot motif: the gene 32 messenger RNA pseudoknot of bacteriophage T2

The RNA pseudoknot located at the 5' end of the gene 32 messenger RNA of bacteriophage T2 contains two A-form helical stems connected by two loops, in an H-type pseudoknot topology. A combination of multidimensional NMR methods and isotope labeling were used to investigate the pseudoknot structure, resulting in a more detailed structural model than provided by earlier homonuclear NMR studies. Of particular significance, the interface between the stacked helical stems within the pseudoknot motif is described in detail. The two stems are stacked in a coaxial manner, with an approximately 18 degrees rotation of stem1 relative to stem2 about an axis that is parallel to the helical axis. This rotation serves to relieve what would otherwise be a relatively close phosphate-phosphate contact at the junction of the two stems, while preserving the stabilizing effects of base stacking. The ability of the NMR data to determine pseudoknot bending was critically assessed. The data were found to be a modestly precise indicator of pseudoknot bending, with the angle between the helical axes of stem1 and stem2 being in the range of 15+/-15 degrees. Pseudoknot models with bend angles within this range are equally consistent with the data, since they differ by only small amounts in the relatively short-range interproton distances from which the structure was derived. The gene 32 messenger RNA pseudoknot was compared with other RNA structures with coaxial or near-coaxial stacked helical stems.     

Structures of helical junctions in nucleic acids

Our knowledge of the architectural principles of nucleic acid junctions has seen significant recent advances. The conformation of DNA junctions is now well understood, and this provides a new basis for the analysis of important structural elements in RNA. The most significant new data have come from X-ray crystallography of four-way DNA junctions; incidentally showing the great importance of serendipity in science, since none of the three groups had deliberately set out to crystallise a junction. Fortunately the results confirm, and of course extend, the earlier conformational studies of DNA junctions in almost every detail. This is important, because it means that these methods can be applied with greater confidence to new systems, especially in RNA. Methods like FRET, chemical probing and even the humble polyacrylamide gel can be rapid and very powerful, allowing the examination of a large number of sequence variants relatively quickly. Molecular modelling in conjunction with experiments is also a very important component of the general approach. Ultimately crystallography provides the gold standard for structural analysis, but the other, simple approaches have considerable value along the way. At the beginning of this review I suggested two simple folding principles for branched nucleic acids, and it is instructive to review these in the light of recent data. In brief, these were the tendency for pairwise coaxial stacking of helical arms, and the importance of metal ion interactions in the induction of folding. We see that both are important in a wide range of systems, both in DNA and RNA. The premier example is the four-way DNA junction, which undergoes metal ion-induced folding into the stacked X-structure that is based on coaxial stacking of arms. As in many systems, there are two alternative ways to achieve this depending on the choice of stacking partners. Recent data reveal that both forms often exist in a dynamic equilibrium, and that the relative stability of the two conformers depends upon base sequence extending a significant distance from the junction. The three-way junction has provided a good test of the folding principles. Perfect three-way (3H) DNA junctions seem to defy these principles in that they appear reluctant to undergo coaxial stacking of arms, and exhibit little change in conformation with addition of metal ions. Modelling suggests that such a junction is stereochemically constrained in an extended conformation. However, upon inclusion of a few additional base pairs at the centre (to create a 3HS2 junction for example) the additional stereochemical flexibility allows two arms to undergo coaxial stacking. Such a junction exhibits all the properties consistent with the general folding principles, with ion-induced folding into a form based on pairwise coaxial stacking of arms in one of two different conformers. The three-way junction is therefore very much the exception that proves the rule. It is instructive to compare the folding of corresponding species in DNA and RNA, where we find both similarities and differences. The RNA four-way junction can adopt a structure that is globally similar to the stacked X-structure (Duckett et al. 1995a), and the crystal structure of the DNAzyme shows that the stacked X-conformation can include one helical pair in the A-conformation (Nowakowski et al. 1999). However, modelling suggests that the juxtaposition of strands and grooves will be less satisfactory in RNA, and the higher magnesium ion concentration required to fold the RNA junction indicates a lower stability of the antiparallel form. Perhaps the biggest difference between the properties of the DNA and RNA four-way junctions is the lack of an unstacked structure at low salt concentrations for the RNA species. This clearly reflects a major difference in the electrostatic interactions in the RNA junction. In general the folding of branched DNA provides some good indications on the likely folding of the corresponding RNA species, but caution is required in making the extrapolation because the two polymers are significantly different. A number of studies point to the flexibility and malleability of branched nucleic acids, and this turns out to have particular significance in their interactions with proteins. Proteins such as the DNA junction-resolving enzymes exhibit considerable selectivity for the structure of their substrates, which is still not understood at a molecular level. Despite this, it appears to be universally true that these proteins distort the global, and in some cases at least the local, structure of the junctions. The somewhat perplexing result is that the proteins appear to distort the very property that they recognise. In general it seems that four-way DNA junctions are opened to one extent or another by interaction with proteins. (ABSTRACT TRUNCATED)     

Predicting RNA secondary structures with arbitrary pseudoknots by maximizing the number of stacking pairs.

The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no performance guarantee and can handle only limited types of pseudoknots. In this paper, we initiate the study of predicting RNA secondary structures with a maximum number of stacking pairs while allowing arbitrary pseudoknots. We obtain two approximation algorithms with worst-case approximation ratios of 1/2 and 1/3 for planar and general secondary structures, respectively. For an RNA sequence of n bases, the approximation algorithm for planar secondary structures runs in O(n(3)) time while that for the general case runs in linear time. Furthermore, we prove that allowing pseudoknots makes it NP-hard to maximize the number of stacking pairs in a planar secondary structure. This result is in contrast with the recent NP-hard results on psuedoknots which are based on optimizing some general and complicated energy functions.     

Efficiency of coaxial stacking depends on the DNA duplex structure

Thermodynamic parameters of coaxial stacking at complementary helix-helix interfaces GX*pYG/CZVC (X,Y=A,C,T,G;*-nick) created by contiguous oligonucleotide hybridization were determined. The data obtained were compared to the thermodynamic parameters of coaxial stacking at the interfaces CX*pYC/GZVG. Multiple linear regression analysis has revealed that the free-energy increments of interaction for the contacts GX*pYG/CZVC and CX*pYC/GZVG can be described by a set of uniform Delta G degrees(X*pY/ZV) values. The difference in the observed free-energy of the coaxial stacking between the two sets is defined by the contribution from the factors reflecting structural differences between compared DNA duplexes.     

Base extrusion is found at helical junctions between right- and left-handed forms of DNA and RNA

Base extrusion is a major structural feature at the junction between B- and Z-DNA (the B–Z junction) where a base pair is broken, and the two bases are extruded from the double helix. Despite the demonstration of base extrusion at the B–Z junction, it is not clear whether a similar base extrusion occurs at other types of junctions involving the left-handed Z conformation. Here, we investigate structural changes of bases at three Z-form junctions: DNA B–Z and Z–Z and RNA A–Z junctions. By monitoring fluorescently labeled duplex nucleic acids using 2-aminopurines at various positions relative to the junction point, we show that base extrusion occurs not only at the DNA B–Z junction, but also at the RNA A–Z and DNA Z–Z junctions. Our data suggest that base extrusion is a general feature of Z-form nucleic-acid junctions.     

The influence of nearest neighbours on the efficiency of coaxial stacking at contiguous stacking hybridization of oligodeoxyribonucleotides

Contiguous stacking hybridization of oligodeoxyribonucleotides with a stem of preformed minihairpin structure of a DNA template was studied with the use of UV-melting technique. It was shown that the free-energy of the coaxial stacking interaction (deltaG degrees ST at 37 degrees C, 1 M NaCl, pH 7.4) at the complementary interface XA*pTY/ZATV (an asterisk stands for a nick) strongly depends on the type of nearest neighbor bases X and Y flanking the nicked dinucleotide step. The maximum efficiency of the coaxial stacking was observed for the PuA*pTPy/PuATPy interface, whereas the minimum efficiency was obtained for the PyA*pTPu/PyATPu interface. A 5'-phosphate residue in the nick enhances the coaxial stacking. In dependence on duplex structure the observed efficiency of A*T/AT coaxial stacking varied from (- 0.97 kcal/mol) for unphosphorylated TA*TA/TATA interface to three-fold higher value (- 2.78 kcal/mol) for GA*pTT/AATC interface.     

Stabilization of RNA stacking by pseudouridine.

The effect of the modified nucleoside pseudouridine (psi) on RNA structure was compared with uridine. The extent of base stacking in model RNA oligonucleotides was measured by 1H NMR, UV, and CD spectroscopy. The UV and CD results indicate that the model single-stranded oligoribonucleotides AAUA and AA psi A form stacked structures in solution and the CD results for AA psi A are consistent with a general A-form helical conformation. The AA psi A oligomer exhibits a greater degree of UV hypochromicity over the temperature range 5-55 degrees C, consistent with a better stacked, more A-form structure compared with AAUA. The extent of stacking for each nucleotide residue was inferred from the percent 3'-endo sugar conformation as indicated by the H1'-H2' NMR scalar coupling. This indirect indication of stacking was confirmed by sequential NOE experiments. NMR measurements as a function of temperature indicate that pseudouridine forms a more stable base stacking arrangement than uridine, an effect that is propagated throughout the helix to stabilize stacking of neighboring purine nucleosides. The N1-H imino proton in AA psi A exchanges slowly with solvent, suggesting a role for the extra imino proton in stabilizing the conformation of pseudouridine. These results show that the conformational stabilization is an intrinsic property of pseudouridine occurring at the nucleotide level. The characteristics of pseudouridine in these models are consistent with earlier studies on intact rRNA, indicating that pseudouridine probably performs the same stabilizing function in most structural contexts.     

Parallel multiplex thermodynamic analysis of coaxial base stacking in DNA duplexes by oligodeoxyribonucleotide microchips

Parallel thermodynamic analysis of the coaxial stacking effect of two bases localized in one strand of DNA duplexes has been performed. Oligonucleotides were immobilized in an array of three-dimensional polyacrylamide gel pads of microchips (MAGIChips‘). The stacking effect was studied for all combinations of two bases and assessed by measuring the increase in melting temperature and in the free energy of duplexes formed by 5mers stacked to microchip-immobilized 10mers. For any given interface, the effect was studied for perfectly paired bases, as well as terminal mismatches, single base overlaps, single and double gaps, and modified terminal bases. Thermodynamic parameters of contiguous stacking determined by using microchips closely correlated with data obtained in solution. The extension of immobilized oligonucleotides with 5,6-dihydroxyuridine, a urea derivative of deoxyribose, or by phosphate, decreased the stacking effect moderately, while extension with FITC or Texas Red virtually eliminated stacking. The extension of the immobilized oligonucleotides with either acridine or 5-nitroindole increased stacking to mispaired bases and in some GC-rich interfaces. The measurements of stacking parameters were performed in different melting buffers. Although melting temperatures of AT- and GC-rich oligonucleotides in 5 M tetramethylammonium chloride were equalized, the energy of stacking interaction was significantly diminished.     

Conformational flexibility of four-way junctions in RNA

Helical junctions are common architectural features in RNA. They are particularly important in autonomously folding molecules, as exemplified by the hairpin ribozyme. We have used single-molecule fluorescence spectroscopy to study the dynamic properties of the perfect (4H) four-way helical junction derived from the hairpin ribozyme. In the presence of Mg(2+), the junction samples parallel and antiparallel conformations and both stacking conformers, with a bias towards one antiparallel stacking conformer. There is continual interconversion between the forms, such that there are several transitions per second under physiological conditions. Our data suggest that interconversion proceeds via an open intermediate with reduced cation binding in which coaxial stacking between helices is disrupted. The rate of interconversion becomes slower at higher Mg(2+) concentrations, yet the activation barrier decreases under these conditions, indicating that entropic effects are important. Transitions also occur in the presence of Na(+) only; however, the coaxial stacking appears incomplete under these conditions. The polymorphic and dynamic character of the four-way RNA junction provides a source of structural diversity, from which particular conformations required for biological function might be stabilised by additional RNA interactions or protein binding.     

Predicting RNA pseudoknot folding thermodynamics

Based on the experimentally determined atomic coordinates for RNA helices and the self-avoiding walks of the P (phosphate) and C₄ (carbon) atoms in the diamond lattice for the polynucleotide loop conformations, we derive a set of conformational entropy parameters for RNA pseudoknots. Based on the entropy parameters, we develop a folding thermodynamics model that enables us to compute the sequence-specific RNA pseudoknot folding free energy landscape and thermodynamics. The model is validated through extensive experimental tests both for the native structures and for the folding thermodynamics. The model predicts strong sequence-dependent helix-loop competitions in the pseudoknot stability and the resultant conformational switches between different hairpin and pseudoknot structures. For instance, for the pseudoknot domain of human telomerase RNA, a native-like and a misfolded hairpin intermediates are found to coexist on the (equilibrium) folding pathways, and the interplay between the stabilities of these intermediates causes the conformational switch that may underlie a human telomerase disease.     

3D maps of RNA interhelical junctions

More than 50% of RNA secondary structure is estimated to be A-form helices, which are linked together by various junctions. Here we describe a protocol for computing three interhelical Euler angles describing the relative orientation of helices across RNA junctions. 5' and 3' helices, H1 and H2, respectively, are assigned based on the junction topology. A reference canonical helix is constructed using an appropriate molecular builder software consisting of two continuous idealized A-form helices (iH1 and iH2) with helix axis oriented along the molecular Z-direction running toward the positive direction from iH1 to iH2. The phosphate groups and the carbon and oxygen atoms of the sugars are used to superimpose helix H1 of a target interhelical junction onto the corresponding iH1 of the reference helix. A copy of iH2 is then superimposed onto the resulting H2 helix to generate iH2'. A rotation matrix R is computed, which rotates iH2' into iH2 and expresses the rotation parameters in terms of three Euler angles α(h), β(h) and γ(h). The angles are processed to resolve a twofold degeneracy and to select an overall rotation around the axis of the reference helix. The three interhelical Euler angles define clockwise rotations around the 5' (-γ(h)) and 3' (α(h)) helices and an interhelical bend angle (β(h)). The angles can be depicted graphically to provide a 'Ramachandran'-type view of RNA global structure that can be used to identify unusual conformations as well as to understand variations due to changes in sequence, junction topology and other parameters.     

Helical stacking in DNA three-way junctions containing two unpaired pyrimidines: proton NMR studies.

The proton NMR spectra of DNA three-way junction complexes (TWJ) having unpaired pyrimidines, 5'-TT- and 5'-TC- on one strand at the junction site were assigned from 2D NOESY spectra acquired in H2O and D2O solvents and homonuclear 3D NOESY-TOCSY and 3D NOESY-NOESY in D2O solvent. TWJ are the simplest branched structures found in biologically active nucleic acids. Unpaired nucleotides are common features of such structures and have been shown to stabilize junction formation. The NMR data confirm that the component oligonucleotides assemble to form conformationally homogeneous TWJ complexes having three double-helical, B-form arms. Two of the helical arms stack upon each other. The unpaired pyrimidine bases lie in the minor groove of one of the helices and are partly exposed to solvent. The coaxial stacking arrangement deduced is different from that determined by Rosen and Patel (Rosen, M.A., and D.J. Patel. 1993. Biochemistry. 32:6576-6587) for a DNA three-way junction having two unpaired cytosines, but identical to that suggested by Welch et al. (Welch, J. B., D. R. Duckett, D. M. J. Lilley. 1993. Nucleic Acids Res. 21:4548-4555) on the basis of gel electrophoretic studies of DNA three-way junctions containing unpaired adenosines and thymidines.     

Coplanar and coaxial orientations of RNA bases and helices

Electrostatic interactions, base-pairing, and especially base-stacking dominate RNA three-dimensional structures. In an A-form RNA helix, base-stacking results in nearly perfect parallel orientations of all bases in the helix. Interestingly, when an RNA structure containing multiple helices is visualized at the atomic level, it is often possible to find an orientation such that only the edges of most bases are visible. This suggests that a general aspect of higher level RNA structure is a coplanar arrangement of base-normal vectors. We have analyzed all solved RNA crystal structures to determine the degree to which RNA base-normal vectors are globally coplanar. Using a statistical test based on the Watson-Girdle distribution, we determined that 330 out of 331 known RNA structures show statistically significant (p < 0.05; false discovery rate [FDR] = 0.05) coplanar normal vector orientations. Not surprisingly, 94% of the helices in RNA show bipolar arrangements of their base-normal vectors (p < 0.05). This allows us to compute a mean axis for each helix and compare their orientations within an RNA structure. This analysis revealed that 62% (208/331) of the RNA structures exhibit statistically significant coaxial packing of helices (p < 0.05, FDR = 0.08). Further analysis reveals that the bases in hairpin loops and junctions are also generally planar. This work demonstrates coplanar base orientation and coaxial helix packing as an emergent behavior of RNA structure and may be useful as a structural modeling constraint.