Clustering DNA and RNA molecular dynamics ensembles via secondary structure

Macromolecular structure is central to biology. Yet, not all biomolecules have a well-defined fold. Intrinsically disordered regions are ubiquitous, conveying a versatility to function even in otherwise folded structures. For nucleic acids, entropic disorder is manifest in regions of incomplete base pairing (e.g., during transcription) and for long molecules (i.e., beyond the persistence length). To classify the resulting ensembles, we develop a method to cluster based on secondary structure, focusing specifically on DNA and RNA. The number of basepairs to reorganize furnishes a proper distance metric for structures of the same topology (e.g., without knots). This permits clustering of any type, from k-means to hierarchical to density-based methods. We demonstrate this by showing the broad distribution of secondary structure of a fragment of the M13 bacteriophage DNA and by revealing the hidden order in an RNA Holliday junction. This clustering approach is connected to energy barriers from disrupting hybridization and recognizes structures that differ only by, for example, internal reorientation as the same, compressing the vast free-energy landscape from entropic disorder.