RNA folding pathways from all-atom simulations with a variationally improved history-dependent bias

Abstract

Atomically detailed simulations of RNA folding have proven very challenging in view of the difficulties of developing realistic force fields and the intrinsic computational complexity of sampling rare conformational transitions. As a step forward in tackling these issues, we extend to RNA an enhanced path-sampling method previously successfully applied to proteins. In this scheme, the information about the RNA's native structure is harnessed by a soft history-dependent biasing force promoting the generation of productive folding trajectories in an all-atom force field with explicit solvent. A rigorous variational principle is then applied to minimize the effect of the bias. Here, we report on an application of this method to RNA molecules from 20 to 47 nucleotides long and increasing topological complexity. By comparison with analog simulations performed on small proteins with similar size and architecture, we show that the RNA folding landscape is significantly more frustrated, even for relatively small chains with a simple topology. The predicted RNA folding mechanisms are found to be consistent with the available experiments and some of the existing coarse-grained models. Due to its computational performance, this scheme provides a promising platform to efficiently gather atomistic RNA folding trajectories, thus retain the information about the chemical composition of the sequence.

Figure 1

Probability distributions of the fraction of native contacts Q and the RMSD to the crystal native structures, estimated from a frequency histogram of the productive rMD folding trajectories for four different macromolecules: (A) HHR, (B) protein TRP-CGE, (C) tmRNA fragment, and (D) protein WW domain. In all cases, trajectories were terminated immediately after entering the native region (gray areas). To see this figure in color, go online.

Figure 2

Folding pathways of (A) the HHR hairpin and (B) the tmRNA pseudoknot. (A) Left: typical mechanism of hairpin formation, from two independent trajectories. The color bands indicate the time order of formation of contacts between nucleotides in the hairpin. The hairpin zipping initiates at the hairpin tip and proceeds toward the termini. Representative snapshots are shown on the right. (B) Left: the progressive formation of tmRNA structural elements is shown as a function of the fraction of native contacts, Q, for two typical productive trajectories. The curves indicate the percentage of established native contacts in stems 1 and 2. Canonical and noncanonical nonnative contacts are shown too, normalized by 10 to have a comparable scale with native contacts. In the first example (top), stem 1 (blue) forms first, followed by stem 2 (orange). In the second example (bottom), the order is reversed. Representative snapshots of the two folding pathways are shown on the right, adopting the same color code convention as in the plots on the left. To see this figure in color, go online.

Figure 3

Formation of native secondary structural elements as a function of the fraction of native contacts (Q) for hTR. Three separate productive folding pathways emerge. In (A) stem 2 (yellow) forms first, followed by the formation of part of loop 2 (green), of the triplets (red), and, finally, the formation of stem 1 (blue). In (B) and (C) stem 1 forms before stem 2, but in (B) the first elements that forms are the triplets, while in (C) the first element is stem 1 directly. The right panel shows representative structures from each pathway toward the experimental structure, which is the rightmost structure on the right in the middle row (magnified). To see this figure in color, go online.

Figure 4

Initial unfolded structures for the three considered RNA molecules. The corresponding .pdb files are available for download as Supporting material. To see this figure in color, go online.