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DNA strand displacement systems have proven themselves to be fertilesubstrates for the design of programmable molecular machinery and circuitry.Domain-level reaction enumerators provide the foundations for molecularprogramming languages by formalizing DNA strand displacement mechanisms andmodeling interactions at the "domain" level - one level of abstraction abovemodels that explicitly describe DNA strand sequences. Unfortunately, themost-developed models currently only treat pseudo-linear DNA structures, whilemany systems being experimentally and theoretically pursued exploit a muchbroader range of secondary structure configurations. Here, we describe a newdomain-level reaction enumerator that can handle arbitrary non-pseudoknottedsecondary structures and reaction mechanisms including association anddissociation, 3-way and 4-way branch migration, and direct as well as remotetoehold activation. To avoid polymerization that is inherent when consideringgeneral structures, we employ a time-scale separation technique that holds inthe limit of low concentrations. This also allows us to "condense" the detailedreactions by eliminating fast transients, with provable guarantees ofcorrectness for the set of reactions and their kinetics. We hope that the newreaction enumerator will be used in new molecular programming languages,compilers, and tools for analysis and verification that treat a wider varietyof mechanisms of interest to experimental and theoretical work. We haveimplemented this enumerator in Python, and it is included in the DyNAMiCWorkbench Integrated Development Environment.

A domain-level DNA strand displacement reaction enumerator allowing arbitrary non-pseudoknotted secondary structures