RNA Conformational Sampling: II. Arbitrary Length Multinucleotide Loop Closure

In this paper, we describe how the inverse kinematic solution to the loop closure problem may be generalized to reclose a RNA segment of arbitrary length containing any number of nucleotides without disturbing the atomic positions of the rest of the molecule. This generalization is made possible by representing the boundary conditions of the closure in terms of a set of virtual coordinates called RETO, allowing the inverse kinematics to be reduced from the original six-variable/six-constraint problem to a four-variable/four-constraint problem. Based on this generalized closure solution, a new Monte Carlo algorithm has been formulated and implemented in a fully atomistic RNA simulation capable of moving loops of arbitrary lengths using torsion angle updates exclusively. Combined with other conventional Monte Carlo moves, this new algorithm is able to sample large-scale RNA chain conformations much more efficiently. The utility of this new class of Monte Carlo moves in generating large-loop conformational rearrangements is demonstrated in the simulated unfolding of the full-length hammerhead ribozyme with a bound substrate.