A current challenge in RNA structure prediction is the description of global helical arrangements compatible with a given secondary structure. Here we address this problem by developing a hierarchical graph sampling/data mining approach to reduce conformational space and accelerate global sampling of candidate topologies. Starting from a 2D structure, we construct an initial graph from size measures deduced from solved RNAs and junction topologies predicted by our data-mining algorithm RNAJAG trained on known RNAs. We sample these graphs in 3D space guided by knowledge-based statistical potentials derived from bending and torsion measures of internal loops as well as radii of gyration for known RNAs. Graph sampling results for 30 representative RNAs are analyzed and compared with reference graphs from both solved structures and predicted structures by available programs. This comparison indicates promise for our graph-based sampling approach for characterizing global helical arrangements in large RNAs: graph rmsds range from 2.52 to 28.24 Å for RNAs of size 25-158 nucleotides, and more than half of our graph predictions improve upon other programs. The efficiency in graph sampling, however, implies an additional step of translating candidate graphs into atomic models. Such models can be built with the same idea of graph partitioning and build-up procedures we used for RNA design.RNA 3D graph | Monte Carlo simulated annealing | RNA 3D prediction T he heightened interest in RNA biology with demonstrated successful applications to medicine and technology has presented new challenges to computational scientists in RNA structure prediction. Though general automated prediction of RNA tertiary (3D) structure from the primary sequence remains elusive, many effective approaches exist for analyzing and describing 3D RNA structures as well as predicting reasonably 3D aspects of small RNAs, ranging from coarse-grained modeling (1) to various structure assembly (2), energy minimization (3), molecular dynamics (4), and other conformational sampling approaches (5, 6).Interest in RNA structure prediction and its modular architecture has also led to many analyses of RNA local structure (7-12). In particular, several studies have focused on the helical arrangements formed by internal loops, important points of flexibility that can affect the overall 3D shape of RNAs. Indeed, the bending and torsion of helical arms connected by internal loops define unique helical conformations, as analyzed by AlHashimi and coworkers (7), Tang and Draper (8), Hagerman and coworkers (9), and Olson and coworkers (10). Recently, Pyle and coworkers (11) reported a pseudotorsional angle database from local RNA backbone geometry, and Sim and Levitt (12) cataloged preferred helical arrangements among nucleotide fragment assemblies given a secondary (2D) conformation. However, extensive topological and geometrical analyses over a large diverse set of RNAs do not exist.To such endeavors, mathematical and computational tools have been applied, including gra...