RNA conformational sampling. I. Single-nucleotide loop closure

We consider the loop-closure problem for nucleic acids and describe an efficient numerical algorithm for closing single-nucleotide loops in nucleic acids. Using six new internal coordinates to represent the nucleotide conformation, which we call the R-representation, the original closure problem with six free torsion angles in each nucleotide can be reduced to one with only four degrees of freedom. Simple numerical techniques have been used to solve the resulting loop-closure equations, and a test of the closure algorithm on a set of RNAs consisting of more than 7000 nucleotides was able to regenerate the native torsion angles in every nucleotide in the test set without exception. We show how the conformational probability density transforms when the original torsion angle representation is mapped onto the new R-representation. We also present statistical evidence showing that the delta and nu(2) torsion angles are coupled, and how this coupling affects the conformation probability density in the R-representation. In addition to the backbone, the same loop-closure algorithm can also be applied to close the ribose ring. The algorithm is freely available at http://tyrosine.use.edu/closure.