Christian Laing

Computational approaches to RNA structure prediction, analysis, and design

RNA molecules are important cellular components involved in many fundamental biological processes. Understanding the mechanisms behind their functions requires RNA tertiary structure knowledge. Although modeling approaches for the study of RNA structures and dynamics lag behind efforts in protein folding, much progress has been achieved in the past two years. Here, we review recent advances in RNA folding algorithms, RNA tertiary motif discovery, applications of graph theory approaches to RNA structure and function, and in silico generation of RNA sequence pools for aptamer design. Advances within each area can be combined to impact many problems in RNA structure and function.

Computational approaches to 3D modeling of RNA

Many exciting discoveries have recently revealed the versatility of RNA and its importance in a variety of functions within the cell. Since the structural features of RNA are of major importance to their biological function, there is much interest in predicting RNA structure, either in free form or in interaction with various ligands, including proteins, metabolites and other molecules. In recent years, an increasing number of researchers have developed novel RNA algorithms for predicting RNA secondary and tertiary structures. In this review, we describe current experimental and computational advances and discuss recent ideas that are transforming the traditional view of RNA folding. To evaluate the performance of the most recent RNA 3D folding algorithms, we provide a comparative study in order to test the performance of available 3D structure prediction algorithms for an RNA data set of 43 structures of various lengths and motifs. We find that the algorithms vary widely in terms of prediction quality across different RNA lengths and topologies; most predictions have very large root mean square deviations from the experimental structure. We conclude by outlining some suggestions for future RNA folding research.

Analysis of four-way junctions in RNA structures

RNA secondary structures can be divided into helical regions composed of canonical Watson-Crick and related base pairs, as well as single-stranded regions such as hairpin loops, internal loops, and junctions. These elements function as building blocks in the design of diverse RNA molecules with various fundamental functions in the cell. To better understand the intricate architecture of three-dimensional (3D) RNAs, we analyze existing RNA four-way junctions in terms of base-pair interactions and 3D configurations. Specifically, we identify nine broad junction families according to coaxial stacking patterns and helical configurations. We find that helices within junctions tend to arrange in roughly parallel and perpendicular patterns and stabilize their conformations using common tertiary motifs such as coaxial stacking, loop-helix interaction, and helix packing interaction. Our analysis also reveals a number of highly conserved base-pair interaction patterns and novel tertiary motifs such as A-minor-coaxial stacking combinations and sarcin/ricin motif variants. Such analyses of RNA building blocks can ultimately help in the difficult task of RNA 3D structure prediction.

Annotation of tertiary interactions in RNA structures reveals variations and correlations

RNA tertiary motifs play an important role in RNA folding and biochemical functions. To help interpret the complex organization of RNA tertiary interactions, we comprehensively analyze a data set of 54 high-resolution RNA crystal structures for motif occurrence and correlations. Specifically, we search seven recognized categories of RNA tertiary motifs (coaxial helix, A-minor, ribose zipper, pseudoknot, kissing hairpin, tRNA D-loop/T-loop, and tetraloop-tetraloop receptor) by various computer programs. For the nonredundant RNA data set, we find 613 RNA tertiary interactions, most of which occur in the 16S and 23S rRNAs. An analysis of these motifs reveals the diversity and variety of A-minor motif interactions and the various possible loop-loop receptor interactions that expand upon the tetraloop-tetraloop receptor. Correlations between motifs, such as pseudoknot or coaxial helix with A-minor, reveal higher-order patterns. These findings may ultimately help define tertiary structure restraints for RNA tertiary structure prediction. A complete annotation of the RNA diagrams for our data set is available at http://www.biomath.nyu.edu/motifs/.

Tertiary motifs revealed in analyses of higher-order RNA junctions.

RNA junctions are secondary-structure elements formed when three or more helices come together. They are present in diverse RNA molecules with various fundamental functions in the cell. To better understand the intricate architecture of three-dimensional (3D) RNAs, we analyze currently solved 3D RNA junctions in terms of base-pair interactions and 3D configurations. First, we study base-pair interaction diagrams for solved RNA junctions with 5 to 10 helices and discuss common features. Second, we compare these higher-order junctions to those containing 3 or 4 helices and identify global motif patterns such as coaxial stacking and parallel and perpendicular helical configurations. These analyses show that higher-order junctions organize their helical components in parallel and helical configurations similar to lower-order junctions. Their sub-junctions also resemble local helical configurations found in three- and four-way junctions and are stabilized by similar long-range interaction preferences such as A-minor interactions. Furthermore, loop regions within junctions are high in adenine but low in cytosine, and in agreement with previous studies, we suggest that coaxial stacking between helices likely forms when the common single-stranded loop is small in size; however, other factors such as stacking interactions involving noncanonical base pairs and proteins can greatly determine or disrupt coaxial stacking. Finally, we introduce the ribo-base interactions: when combined with the along-groove packing motif, these ribo-base interactions form novel motifs involved in perpendicular helix-helix interactions. Overall, these analyses suggest recurrent tertiary motifs that stabilize junction architecture, pack helices, and help form helical configurations that occur as sub-elements of larger junction networks. The frequent occurrence of similar helical motifs suggest natures finite and perhaps limited repertoire of RNA helical conformation preferences. More generally, studies of RNA junctions and tertiary building blocks can ultimately help in the difficult task of RNA 3D structure prediction.

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.

Conservation of writhe helicity under anti-parallel reconnection.

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to the recombination in polymer physics and DNA biology. By using fundamental results in topological fluid mechanics, the helicity of a flux tube can be calculated in terms of writhe and twist contributions. Here we show that the writhe is conserved under anti-parallel reconnection. Hence, for a pair of interacting flux tubes of equal flux, if the twist of the reconnected tube is the sum of the original twists of the interacting tubes, then helicity is conserved during reconnection. Thus, any deviation from helicity conservation is entirely due to the intrinsic twist inserted or deleted locally at the reconnection site. This result has important implications for helicity and energy considerations in various physical contexts.

Computing the writhe on lattices

Given a polygonal closed curve on a lattice or space group, we describe a method for computing the writhe of the curve as the average of weighted projected writhing numbers of the polygon in a few directions. These directions are determined by the lattice geometry, the weights are determined by areas of regions on the unit 2-sphere, and the regions are formed by the tangent indicatrix to the polygonal curve. We give a new formula for the writhe of polygons on the face centred cubic lattice and prove that the writhe of polygons on the body centred cubic lattice, the hexagonal simple lattice, and the diamond space group is always a rational number, and discuss applications to ring polymers.

Shape analysis for automated sulcal classification and parcellation of MRI data

Abstract We describe geometric invariants that characterize the shape of curves and surfaces in 3D space: curvature, Gauss integrals and moments. We apply these invariants to neuroimaging data to determine if they have application for automatically classifying and parcellating cortical data. The curves of sulci and gyri on the cortical surface can be obtained by reconstructing cortical surface representations of the human brain from magnetic resonance imaging (MRI) data. We reconstructed gray matter surfaces for 15 subjects, traced 10 sulcal curves on each surface and computed geometric invariants for each curve. These geometric features were used classify the curves into sulcal and hemispheric classes. The best classification results were obtained when moment-based features were computed on the sulcal curves in native space. Gauss integral measures showed that they were useful for differentiating the hemispheric location of a single sulcus. These promising results may indicate that moment invariants are useful for characterizing shape on a global scale. Gauss integral invariants are potentially useful measures for characterizing cortical shape on a local, rather than global scale. Gauss integrals have found biological significance in characterizing proteins so it is worthwhile to consider their possible application to neuroscientific data.

THE WRITHE OF ORIENTED POLYGONAL GRAPHS

Given an edge-oriented polygonal graph in ℝ3, we describe a method for computing the writhe as the average of weighted directional writhe numbers of the graph in a few directions. These directions are determined by the graph and the weights are determined by areas of path-connected open regions on the unit sphere. Within each open region, the directional writhe is constant. We obtain a closed formula which extends the formula for the writhe of a polygon in ℝ3, including the important special case of writhe of embedded open arcs.