Secondary Structure Design for Cotranscriptional 3D RNA Origami Wireframes

We address the task of secondary structure design for de novo 3D RNA origami wireframe structures in a way that takes into account the specifics of a cotranscriptional folding setting. We consider two issues: firstly, avoiding the topological obstacle of "polymerase trapping", where some helical domain cannot be hybridised due to a closed kissing-loop pair blocking the winding of the strand relative to the polymerase-DNA-template complex; and secondly, minimising the number of distinct kissing-loop designs needed, by reusing KL pairs that have already been hybridised in the folding process. For the first task, we present an efficient strand-routing method that guarantees the absence of polymerase traps for any 3D wireframe model, and for the second task, we provide a graph-theoretic formulation of the minimisation problem, show that it is NP-complete in the general case, and outline a branch-and-bound type enumerative approach to solving it. Key concepts in both cases are depth-first search in graphs and the ensuing DFS spanning trees. Both algorithms have been implemented in the DNAforge design tool (https://dnaforge.org) and we present some examples of the results.