Computer modeling 16 S ribosomal RNA

A three-dimensional structure for 16 S RNA has been produced with a computer protocol that is not dependent on human intervention. This protocol improves upon traditional modeling techniques by using distance geometry to fold the molecule in an objective and reproducible fashion. The method is based on the secondary structure of RNA and treats the molecule as a set of double-stranded helices that are linked by flexible single-strands of variable length. Data derived from chemical cross-linking studies of 16 S RNA and tertiary phylogenetic relationships provide the constraints used to fold the molecule into a compact three-dimensional form. Possibly subjective evaluation of the input data are transformed into verifiable quantitative parameters. Relationships based on general locations within the 30 S subunit or on protein-RNA interactions have been specifically excluded. The resolution of the model exceeds that of electron micrographs and approaches that obtained in preliminary X-ray crystal structures. The model size of 245 x 190 x 140 A is compatible with that of the 30 S subunit as determined by electron microscopy. The volume of the model is 1.87 x 10(6) A which is similar to that of the small subunit in a preliminary X-ray crystal structure. The radius of gyration of the model structure of 76 A is intermediate to that seen for partially denatured and fully folded 16 S RNA. Computer graphics are used to display the results in a manner that maximizes the opportunities for human visual interpretation of the models. A format for displaying the structures has been developed that will make it possible for researchers who have not devoted themselves to ribosomal modeling to comprehend and make use of the information that the models embody. On this basis the computer-generated models are compared with models developed by other researchers and with structural data not included in the folding parameter data set.     

A Geometrical Approach in Folding a Pseudoknot Motif within the E. Coli 16S-RNA

Abstract

Except for tRNA, the tertiary structure of RNA molecules are very little known. The many possibilities in the arrangement of different helices in space and the flexibility in the single- stranded loops that connect the helical regions make the modeling of the tertiary structure of RNA molecule a very complex task. Here, we introduce an approach to fold RNA tertiary structure based only on the information of the secondary structure and the stereochemistry of the molecule. This approach was used to construct an atomic structure of a pseudoknot (bases 500–545) in the E. coli 16S RNA. The resulting structure is a closely packed molecule that is consistent with the predicted secondary structure and stereochemically feasible. This new approach is very general and easily adaptable. Experimental data (e.g., NMR, fluorescence energy transfer, etc.), as they become available, can be incorporated directly into the approach to improve the accuracy of the modeled structure.     

RNA secondary structure prediction based on free energy and phylogenetic analysis.

We describe a computational method for the prediction of RNA secondary structure that uses a combination of free energy and comparative sequence analysis strategies. Using a homology-based sequence alignment as a starting point, all favorable pairings with respect to the Turner energy function are identified. Each potentially paired region within a multiple sequence alignment is scored using a function that combines both predicted free energy and sequence covariation with optimized weightings. High scoring regions are ranked and sequentially incorporated to define a growing secondary structure. Using a single set of optimized parameters, it is possible to accurately predict the foldings of several test RNAs defined previously by extensive phylogenetic and experimental data (including tRNA, 5 S rRNA, SRP RNA, tmRNA, and 16 S rRNA). The algorithm correctly predicts approximately 80% of the secondary structure. A range of parameters have been tested to define the minimal sequence information content required to accurately predict secondary structure and to assess the importance of individual terms in the prediction scheme. This analysis indicates that prediction accuracy most strongly depends upon covariational information and only weakly on the energetic terms. However, relatively few sequences prove sufficient to provide the covariational information required for an accurate prediction. Secondary structures can be accurately defined by alignments with as few as five sequences and predictions improve only moderately with the inclusion of additional sequences.     

Modeling active RNA structures using the intersection of conformational space: application to the lead-activated ribozyme.

The Pb2+ cleavage of a specific phosphodiester bond in yeast tRNA(Phe) is the classical model of metal-assisted RNA catalysis. In vitro selection experiments have identified a tRNA(Phe) variant, the leadzyme, that is very active in cleavage by Pb2+. We present here a three-dimensional modeling protocol that was used to propose a structure for this ribozyme, and is based on the computation of the intersection of conformational space of sequence variants and the use of chemical modification data. Sequence and secondary structure data were used in a first round of computer modeling that allowed identification of conformations compatible with all known leadzyme variants. Common conformations were then tested experimentally by evaluating the activity of analogues containing modified nucleotides in the catalytic core. These experiments led to a new structural hypothesis that was tested in a second round of computer modeling. The resulting proposal for the active conformation of the leadzyme is consistent with all known structural data. The final model suggests an in-line SN2 attack mechanism and predicts two Pb2+ binding sites. The protocol presented here is generally applicable in modeling RNAs whenever the catalytic or binding activity of structural analogues is known.     

Computational methods for defining the allowed conformational space of 16S rRNA based on chemical footprinting data.

Structural models for 16S ribosomal RNA have been proposed based on combinations of crosslinking, chemical protection, shape, and phylogenetic evidence. These models have been based for the most part on independent data sets and different sets of modeling assumptions. In order to evaluate such models meaningfully, methods are required to explicitly model the spatial certainty with which individual structural components are positioned by specific data sets. In this report, we use a constraint satisfaction algorithm to explicitly assess the location of the secondary structural elements of the 16S RNA, as well as the certainty with which these elements can be positioned. The algorithm initially assumes that these helical elements can occupy any position and orientation and then systematically eliminates those positions and orientations that do not satisfy formally parameterized interpretations of structural constraints. Using a conservative interpretation of the hydroxyl radical footprinting data, the positions of the ribosomal proteins as defined by neutron diffraction studies, and the secondary structure of 16S rRNA, the location of the RNA secondary structural elements can be defined with an average precision of 25 A (ranging from 12.8 to 56.3 A). The uncertainty in individual helix positions is both heterogeneous and dependent upon the number of constraints imposed on the helix. The topology of the resulting model is consistent with previous models based on independent approaches. The result of our computation is a conservative upper bound on the possible positions of the RNA secondary structural elements allowed by this data set, and provides a suitable starting point for refinement with other sources of data or different sets of modeling assumptions.     

Computational approaches for RNA energy parameter estimation

Methods for efficient and accurate prediction of RNA structure are increasingly valuable, given the current rapid advances in understanding the diverse functions of RNA molecules in the cell. To enhance the accuracy of secondary structure predictions, we developed and refined optimization techniques for the estimation of energy parameters. We build on two previous approaches to RNA free-energy parameter estimation: (1) the Constraint Generation (CG) method, which iteratively generates constraints that enforce known structures to have energies lower than other structures for the same molecule; and (2) the Boltzmann Likelihood (BL) method, which infers a set of RNA free-energy parameters that maximize the conditional likelihood of a set of reference RNA structures. Here, we extend these approaches in two main ways: We propose (1) a max-margin extension of CG, and (2) a novel linear Gaussian Bayesian network that models feature relationships, which effectively makes use of sparse data by sharing statistical strength between parameters. We obtain significant improvements in the accuracy of RNA minimum free-energy pseudoknot-free secondary structure prediction when measured on a comprehensive set of 2518 RNA molecules with reference structures. Our parameters can be used in conjunction with software that predicts RNA secondary structures, RNA hybridization, or ensembles of structures. Our data, software, results, and parameter sets in various formats are freely available at http://www.cs.ubc.ca/labs/beta/Projects/RNA-Params.     

Predicting coaxial helical stacking in RNA junctions

RNA junctions are important structural elements that form when three or more helices come together in space in the tertiary structures of RNA molecules. Determining their structural configuration is important for predicting RNA 3D structure. We introduce a computational method to predict, at the secondary structure level, the coaxial helical stacking arrangement in junctions, as well as classify the junction topology. Our approach uses a data mining approach known as random forests, which relies on a set of decision trees trained using length, sequence and other variables specified for any given junction. The resulting protocol predicts coaxial stacking within three- and four-way junctions with an accuracy of 81% and 77%, respectively; the accuracy increases to 83% and 87%, respectively, when knowledge from the junction family type is included. Coaxial stacking predictions for the five to ten-way junctions are less accurate (60%) due to sparse data available for training. Additionally, our application predicts the junction family with an accuracy of 85% for three-way junctions and 74% for four-way junctions. Comparisons with other methods, as well applications to unsolved RNAs, are also presented. The web server Junction-Explorer to predict junction topologies is freely available at: http://bioinformatics.njit.edu/junction.     

Prediction of RNA secondary structure based on helical regions distribution

MOTIVATION: RNAs play an important role in many biological processes and knowing their structure is important in understanding their function. Due to difficulties in the experimental determination of RNA secondary structure, the methods of theoretical prediction for known sequences are often used. Although many different algorithms for such predictions have been developed, this problem has not yet been solved. It is thus necessary to develop new methods for predicting RNA secondary structure. The most-used at present is Zuker's algorithm which can be used to determine the minimum free energy secondary structure. However many RNA secondary structures verified by experiments are not consistent with the minimum free energy secondary structures. In order to solve this problem, a method used to search a group of secondary structures whose free energy is close to the global minimum free energy was developed by Zuker in 1989. When considering a group of secondary structures, if there is no experimental data, we cannot tell which one is better than the others. This case also occurs in combinatorial and heuristic methods. These two kinds of methods have several weaknesses. Here we show how the central limit theorem can be used to solve these problems. RESULTS: An algorithm for predicting RNA secondary structure based on helical regions distribution is presented, which can be used to find the most probable secondary structure for a given RNA sequence. It consists of three steps. First, list all possible helical regions. Second, according to central limit theorem, estimate the occurrence probability of every helical region based on the Monte Carlo simulation. Third, add the helical region with the biggest probability to the current structure and eliminate the helical regions incompatible with the current structure. The above processes can be repeated until no more helical regions can be added. Take the current structure as the final RNA secondary structure. In order to demonstrate the confidence of the program, a test on three RNA sequences: tRNAPhe, Pre-tRNATyr, and Tetrahymena ribosomal RNA intervening sequence, is performed. AVAILABILITY: The program is written in Turbo Pascal 7.0. The source code is available upon request. CONTACT: Wujj@nic.bmi.ac.cn or Liwj@mail.bmi.ac.cn      

Isoalloxazine derivatives promote photocleavage of natural RNAs at G.U base pairs embedded within helices.

We have recently shown that isoalloxazine derivatives are able to photocleave RNA specifically at G.U base pairs embedded within a helical stack. The reaction involves the selective molecular recognition of G.U base pairs by the isoalloxazine ring and the removal of one nucleoside downstream of the uracil residue. Divalent metal ions are absolutely required for cleavage. Here we extend our studies to complex natural RNA molecules with known secondary and tertiary structures, such as tRNAs and a group I intron (td). G.U pairs were cleaved in accordance with the phylogenetically and experimentally derived secondary and tertiary structures. Tandem G.U pairs or certain G.U pairs located at a helix extremity were not affected. These new cleavage data, together with the RNA crystal structure, allowed us to perform molecular dynamics simulations to provide a structural basis for the observed specificity. We present a stable structural model for the ternary complex of the G. U-containing helical stack, the isoalloxazine molecule and a metal ion. This model provides significant new insight into several aspects of the cleavage phenomenon, mechanism and specificity for G. U pairs. Our study shows that in large natural RNAs a secondary structure motif made of an unusual base pair can be recognized and cleaved with high specificity by a low molecular weight molecule. This photocleavage reaction thus opens up the possibility of probing the accessibility of G.U base pairs, which are endowed with specific structural and functional roles in numerous structured and catalytic RNAs and interactions of RNA with proteins, in folded RNAs.     

Analysis of internal loops within the RNA secondary structure in almost quadratic time

MOTIVATION: Evaluating all possible internal loops is one of the key steps in predicting the optimal secondary structure of an RNA molecule. The best algorithm available runs in time O(L(3)), L is the length of the RNA. RESULTS: We propose a new algorithm for evaluating internal loops, its run-time is O(M(*)log(2)L), M < L(2) is a number of possible nucleotide pairings. We created a software tool Afold which predicts the optimal secondary structure of RNA molecules of lengths up to 28 000 nt, using a computer with 2 Gb RAM. We also propose algorithms constructing sets of conditionally optimal multi-branch loop free (MLF) structures, e.g. the set that for every possible pairing (x, y) contains an optimal MLF structure in which nucleotides x and y form a pair. All the algorithms have run-time O(M(*)log(2)L).     

Equilibrium and kinetics of the thermal unfolding of yeast 5S ribosomal RNA.

The equilibrium and kinetics of thermal unfolding of yeast 5S ribosomal RNA have been studied by optical methods, in a low ionic strength environment without Mg2+, to follow the disruption of the secondary structure base pairs in the molecule. The equilibrium results demonstrated that all of the helical regions melted simultaneously, and the kinetics of the thermal unfolding were first order. These findings suggest the validity of the two-state approximation for the unfolding reaction under the present conditions. The total number of secondary structure base pairs estimated from our experiment was consistent with that contained in the conformational model based on the Raman spectrum rather than that in the one derived by the enzymic digestion method. Taking our results on the kinetic behavior of the thermal unfolding overall, we propose that the 5S RNA has a partly melted secondary structure under the solvent conditions used.     

Secondary structure model for 23S ribosomal RNA.

A secondary structure model for 23S ribosomal RNA has been constructed on the basis of comparative sequence data, including the complete sequences from E. coli. Bacillus stearothermophilis, human and mouse mitochondria and several partial sequences. The model has been tested extensively with single strand-specific chemical and enzymatic probes. Long range base-paired interactions organize the molecule into six major structural domains containing over 100 individual helices in all. Regions containing the sites of interaction with several ribosomal proteins and 5S RNA have been located. Segments of the 23S RNA structure corresponding to eucaryotic 5.8S and 25 RNA have been identified, and base paired interactions in the model suggest how they are attached to 28S RNA. Functionally important regions, including possible sites of contact with 30S ribosomal subunits, the peptidyl transferase center and locations of intervening sequences in various organisms are discussed. Models for molecular 'switching' of RNA molecules based on coaxial stacking of helices are presented, including a scheme for tRNA-23S RNA interaction.     

How RNA folds.

We describe the RNA folding problem and contrast it with the much more difficult protein folding problem. RNA has four similar monomer units, whereas proteins have 20 very different residues. The folding of RNA is hierarchical in that secondary structure is much more stable than tertiary folding. In RNA the two levels of folding (secondary and tertiary) can be experimentally separated by the presence or absence of Mg2+. Secondary structure can be predicted successfully from experimental thermodynamic data on secondary structure elements: helices, loops, and bulges. Tertiary interactions can then be added without much distortion of the secondary structure. These observations suggest a folding algorithm to predict the structure of an RNA from its sequence. However, to solve the RNA folding problem one needs thermodynamic data on tertiary structure interactions, and identification and characterization of metal-ion binding sites. These data, together with force versus extension measurements on single RNA molecules, should provide the information necessary to test and refine the proposed algorithm.     

Comparative photocross-linking analysis of the tertiary structures of Escherichia coli and Bacillus subtilis RNase P RNAs.

Bacterial ribonuclease P contains a catalytic RNA subunit that cleaves precursor sequences from the 5' ends of pre-tRNAs. The RNase P RNAs from Bacillus subtilis and Escherichia coli each contain several unique secondary structural elements not present in the other. To understand better how these phylogenetically variable elements affect the global architecture of the ribozyme, photoaffinity cross-linking studies were carried out. Photolysis of photoagents attached at homologous sites in the two RNAs results in nearly identical cross-linking patterns, consistent with the homology of the RNAs and indicating that these RNAs contain a common, core tertiary structure. Distance constraints were used to derive tertiary structure models using a molecular mechanics-based modeling protocol. The resulting superimposition of large sets of equivalent models provides a low resolution (5-10 A) structure for each RNA. Comparison of these structure models shows that the conserved core helices occupy similar positions in space. Variably present helical elements that may play a role in global structural stability are found at the periphery of the core structure. The P5.1 and P15.1 helical elements, unique to the B.subtilis RNase P RNA, and the P6/16/17 helices, unique to the E.coli RNA, occupy similar positions in the structure models and, therefore, may have analogous structural function.     

Interconversion between Parallel and Antiparallel Conformations of a 4H RNA junction in Domain 3 of Foot-and-Mouth Disease Virus IRES Captured by Dynamics Simulations

RNA junctions are common secondary structural elements present in a wide range of RNA species. They play crucial roles in directing the overall folding of RNA molecules as well as in a variety of biological functions. In particular, there has been great interest in the dynamics of RNA junctions, including conformational pathways of fully base-paired 4-way (4H) RNA junctions. In such constructs, all nucleotides participate in one of the four double-stranded stem regions, with no connecting loops. Dynamical aspects of these 4H RNAs are interesting because frequent interchanges between parallel and antiparallel conformations are thought to occur without binding of other factors. Gel electrophoresis and single-molecule fluorescence resonance energy transfer experiments have suggested two possible pathways: one involves a helical rearrangement via disruption of coaxial stacking, and the other occurs by a rotation between the helical axes of coaxially stacked conformers. Employing molecular dynamics simulations, we explore this conformational variability in a 4H junction derived from domain 3 of the foot-and-mouth disease virus internal ribosome entry site (IRES); this junction contains highly conserved motifs for RNA-RNA and RNA-protein interactions, important for IRES activity. Our simulations capture transitions of the 4H junction between parallel and antiparallel conformations. The interconversion is virtually barrier-free and occurs via a rotation between the axes of coaxially stacked helices with a transient perpendicular intermediate. We characterize this transition, with various interhelical orientations, by pseudodihedral angle and interhelical distance measures. The high flexibility of the junction, as also demonstrated experimentally, is suitable for IRES activity. Because foot-and-mouth disease virus IRES structure depends on long-range interactions involving domain 3, the perpendicular intermediate, which maintains coaxial stacking of helices and thereby consensus primary and secondary structure information, may be beneficial for guiding the overall organization of the RNA system in domain 3.     

The hydrodynamic shape, conformation, and molecular model of Escherichia coli ribosomal 5 S RNA.

The structure of ribosomal 5 S RNA has been examined using several physical biochemical techniques. Hydrodynamic measurements yield a s020,omega and [eta] of 5.5 x 10(-13) x and 6.9 ml/g, respectively. Other parameters calculated from these values indicate the shape of 5 S RNA is consistent with that of a prolate ellipsoid 160 A in length and 32 A wide. Sedimentation equilibrium results show that 5 S RNA exists as a monomer in the reconstitution buffer with an apparent molecular weight of 44,000. Ultraviolet absorption difference spectra show that approximately 75% of the bases in 5 S RNA are involved in base pairing, and of these base pairs 70% are G-C and 30% are A-U. These results on the overall shape and secondary structure of 5 S RNA have been incorporated with the results of other investigators as to the possible location of single-stranded and double-stranded helical regions, and a molecular model for 5 S RNA is proposed. The molecular model consists of three double helices in the shape of a prolate ellipsoid, with two of the double helical regions at one end of the molecule. The structure is consistent with the available data on the structure and function of 5 S RNA and bears similarity to the molecular model proposed by Osterberg et al. ((1976) Eur. J. Biochem. 68, 481-487) based on small angle x-ray scattering results and the secondary structure proposed by Madison ((1968) Annu. Rev. Biochem. 37, 131-148).