The Combination of Symbolic and Numerical Computation or Three-Dimensional Modeling of RNA

Abstract

Three-dimensional (3-D) structural models of RNA are essential for understanding of the cellular roles played by RNA. Such models have been obtained by a technique based on a constraint satisfaction algorithm that allows for the facile incorporation of secondary and other structural information. The program generates 3-D structures of RNA with atomic-level resolution that can be refined by numerical techniques such as energy minimization. The precision of this technique was evaluated by comparing predicted transfer RNA loop and RNA pseudoknot structures with known or consensus structures. The root-mean-square deviation (2.0 to 3.0 angstroms before minimization) between predicted and control structures reveal this system to be an effective method in modeling RNA.

FR3D: finding local and composite recurrent structural motifs in RNA 3D structures

“…Major and co-workers pioneered the combined geometric and symbolic approach to analyze RNA 3D structure [13,36]. Their program MC-Annotate uses 4 × 4 homogeneous transformation matrices (HTM) to calculate the relative positions and orientations of pairs of bases in an RNA structure.…”

Probing RNA Structure with Chemical Reagents and Enzymes

“…Computer-based energy minimization algorithms have proven extremely useful in predicting simple RNA structures or in providing multiple local folding possibilities in larger RNAs (Gautheret et al 1990;Gorodkin et al 1997;Major et al 1991;Malhotra et al 1993;Walter et al 1994;Zuker 1989). The folding algorithms suffer from several severe limitations in predicting longer RNAs, however, tending to miss long-distance interactions and lacking sufficient predictions of non-standard interactions among nucleotides.…”

RNAML: A standard syntax for exchanging RNA information

“…secondary structure (specification of helices and single-stranded regions in the sequence)+ 4+ Other servers, perhaps specializing in the detection of pseudoknots, add further annotation to the file+ 5+ Send the file to a program that performs covariation analyses of multiple alignments to predict or confirm secondary structure, as well as long-range tertiary interactions+ The computational results are inserted into the file+ 6+ Send the file to a three-dimensional modeling program, such as MC-Sym (Major et al+, 1991), to build fragments of the molecule's structure and assign Cartesian coordinates to parts of the molecule based on its secondary structure+ The program adds these coordinates to the growing file+ 7+ Perform laboratory experiments to confirm or contradict all or part of the structure and add a trace of these results into the file+ 8+ Finally, a modeling program (or modeler) combines all the fragments into a single structural hypothesis [e+g+, using Manip (Massire & Westhof, 1999)] and supplements the file with the remaining coordinates (perhaps changing existing coordinates) that are necessary to fully express the model+ By the end of this process, the file has grown in size and richness of information, and because conformance to the RNAML format has been maintained throughout, the file can be "recycled" at any time through any of the mentioned programs to recompute features or update information+ With time, the file should accurately represent a summary of our accumulated knowledge on a given RNA molecule+ Note that the RNAML syntax is intended to provide and exchange RNA information among programs; some specific program arguments and constraints must be dealt with separately+ Alternately to this iterative scenario, a RNAML document can be created to maintain annotations of existing structures determined by experimental methods and thus serve as a repository for storing analyses and observations made on the predetermined RNA+ A RNAML document can also be used to carry only a restricted portion of information about an RNA molecule that is of concern for a particular study+ Ultimately, the resulting documents can be disseminated to interested parties, all while following a standardized and familiar syntax+…”