Generation and convergence of DNA and RNA structural ensembles

DNA and RNA secondary and higher-order structure plays a central role in biology, medicine, bioengineering, and biomolecular nanotechnology, such as RNA therapeutics, Ribocomputing, and DNA origami. However, the study of nucleic acid secondary structure is demanding, as it spans an exponentially large phase space even when employing a high-level representation of structure. In other words, the low free energy manifold can be vast and have many structures contributing to observable or functional characteristics, such as hybridization efficiency, RNA programming errors, or assembly yield. We develop an approach to generate the equilibrium manifold and a conformational classification that enables testing ensemble convergence at varying degrees of fine graining. The procedure starts with a "seed" ensemble from an Ising-like spin model. This ensemble is transferred into a nucleic acid model (such as, oxDNA or oxRNA, but a fully atomistic description is also possible for smaller scale structures). Replica exchange anneals this seed ensemble. We then classify, via k-means and hierarchical clustering, structures according to a distance measure on the secondary structure. This permits testing both the convergence of the ensemble with respect to the number of members (i.e., the static ensemble) and the time dynamics (i.e., the dynamic ensemble). Nucleic acid ensembles are intractable despite the large growth in computational resources. Our approach efficiently generates an ensemble and endows it with a natural metric for convergence, an approach that can also be employed inhomogeneously to identify and converge regions of hypervariability.