Conformational entropy of the RNA phosphate backbone and its contribution to the folding free energy.

While major contributors to the free energy of RNA tertiary structures such as basepairing, base-stacking, and charge and counterion interactions have been studied extensively, little is known about the intrinsic free energy of the backbone. To assess the magnitude of the entropic strains along the phosphate backbone and their impact on the folding free energy, we have formulated a mathematical treatment for computing the volume of the main-chain torsion-angle conformation space between every pair of nucleobases along any sequence to compute the corresponding backbone entropy. To validate this method, we have compared the computed conformational entropies against a statistical free energy analysis of structures in the crystallographic database from several-thousand backbone conformations between nearest-neighbor nucleobases as well as against extensive computer simulations. Using this calculation, we analyzed the backbone entropy of several ribozymes and riboswitches and found that their entropic strains are highly localized along their sequences. The total entropic penalty due to steric congestions in the backbone for the native fold can be as high as 2.4 cal/K/mol per nucleotide for these medium and large RNAs, producing a contribution to the overall free energy of up to 0.72 kcal/mol per nucleotide. For these RNAs, we found that low-entropy high-strain residues are predominantly located at loops with tight turns and at tertiary interaction platforms with unusual structural motifs.

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.