Explicit Distance Geometry: Identification of all the Degrees of Freedom in a Large RNA Molecule

Abstract

An alternative approach to distance geometry ("explicit" distance geometry) is being developed for problems, such as the modeling of RNA folding in the ribosome, where relatively few distances are known. The approach explicitly identifies minimal sets of additional distances that can be added to a distance matrix in order to calculate structures that are consistent with all the known information without distorting the original input data. These additional distances are bounded to the extent possible by the known distances. These explicitly added distances can be treated as degrees of freedom and used to explore the full range of alternative foldings consistent with the original input in an organized way. The present paper establishes that it is practical to explicitly determine such degrees of freedom for even very large RNAs. To demonstrate the feasibility of the approach tRNA was represented as a simple undirected graph containing all relevant information represented in the usual cloverleaf secondary structure and nine base-base tertiary interactions. Using a three atom representation for each residue a total of 206 degrees of freedom are explicitly identified. To accomplish this a graph theoretic approach was used in which a minimal covering cycle basis was determined.

Modeling large RNAs and ribonucleoprotein particles using molecular mechanics techniques

“…We believe this is one of the major advantages of a molecular mechanics approach, because shape information can be included in the potential function . It is not clear how such information might be included in approaches based on disapproach incorporating both high and low-resolution data Biophysical Journal 1 792 tance geometry (Hubbard and Hearst, 1991a), distance ma-trices (Hadwiger and Fox, 1991), or exhaustive conformational searching (Major et al, 1991;Gautheret et al, 1993).…”

“…Several different computer-based approaches to the problem of 3-D RNA folding are being pursued by other researchers (Malhotra et al, 1993). These include methods based on distance geometry (Hubbard and Hearst, 1991a, b), distance matrix (Hadwiger and Fox, 1991), and conformational searching with constraint satisfaction (Major et al, 1991;Gautheret et al, 1993). Only one of these has been applied to the 16S ribosomal RNA (Hubbard and Hearst, 1991a), and, in contrast with our models , those models did not include the ribosomal proteins.…”

Modeling the three-dimensional structure of RNA.

“…Therefore, evaluation of the conformational space of the entire molecule, taking into account the three-dimensional constraints, is a complex task. Recently, distance geometry has been applied to address this question (10), but the approach is limited to pseudoatom molecular representation.…”