Supporting Information Appendix
نویسندگان
چکیده
Methods Overview.Our computational approaches involve two stages: estimation of knowledge-based statistical potentials and Monte Carlo/ Simulated Annealing (MC/SA) sampling of 3D graphs. In the first stage, we develop knowledge-based statistical potentials based on 3D graph representations of non-redundant solved RNAs and statistical analysis of their 3D geometrical features, from parts to whole, including sizes of helices/hairpins/bulges/junctions, bending and torsion angles between two helices of internal loops, and radii of gyration of the entire RNAs. Three steps are involved in this process of potential development: (i) Non-redundant sets of solvedRNAs are translated to 3Dgraphs and linked to their 2D structures. See below for detailed translation rules of 3D graphs and RNA dataset. (ii) To determine overall helical arrangements, we measure details of local and global geometries and correlate these 3D geometries to 2D structural information. The local geometrical descriptors for RNA include sizes for each building block (helices, hairpins, internal loops, and junctions) and local inter-helical angles (bending and torsion angles). The global geometrical measure of the radius of gyration describes the overall compactness in 3D. We quantify these measures using 3D graphs and relate them to the available 2D information. See below for a coordinate system for 3D graphs, mathematical formulas for measures, and the resulting statistics. (iii) Based on resulting statistics of 3D geometries linked to 2D information, knowledge-based statistical potentials of bending, torsion angles and radii of gyration are calculated and extrapolated by polynomial expansion to handle unrepresented regions of experimental data. See below for the detailed refinement procedures and resulting statistical potentials. In the second stage, to build native-like structures from 2D structures guided by preferred conformations, we employ hierarchical MC/SA sampling approaches where the objective junction is the combination of knowledge-based statistical potentials computed from the first stage. The MC/SA consists of three steps: (i) set-up of initial graphs given a 2D structure by assignment of weighted edges and vertices to the different families of 2D structures (helices, hairpins, internal loops, junctions) and using size measures and junction prediction; (ii) MC/SA sampling of RNA 3D graphs based on two types of moves (restricted and random pivot moves) guided by the knowledge-based potentials; (iii) analysis of resulting sampled graphs using RMSD and by clustering analysis. Detailed procedures are described below.
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