We have recently introduced an experimental method for the design and production of RNA-origami nanostructures that fold up from a single strand while the RNA is being enzymatically produced, commonly referred to as cotranscriptional folding. To realize a general and scalable architecture we have developed a theoretical framework for determining RNA crossover geometries, long-distance interactions, and strand paths that are topologically compatible with cotranscriptional folding. Here, we introduce a simple parameterized model for the A-form helix and use it to determine the geometry and base-pair spacing for the five types of RNA double-crossover molecules and the curvature resulting from crossovers between multiple helices. We further define a set of paranemic loop-loop and end-to-end interactions compatible with the design of folding paths for RNA structures with arbitrary shape and programmable curvature. Finally, we take inspiration from space-filling curves in mathematics to design strand paths that have high-locality, programmed folding kinetics to avoid topological traps, and structural repeat units that might be used to create infinite RNA ribbons and squares by rolling circle transcription.
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