DNA and RNA are versatile construction materials. By appropriately designing the sequence of bases in each strand, synthetic nucleic acid systems can be programmed to self-assemble into complex structures that implement dynamic mechanical tasks. Motivated by the challenge of encoding arbitrary mechanical function into nucleic acid sequences, we are developing a suite of computational algorithms for analyzing the underlying free energy landscapes that control the behavior of a system. This talk will focus on new algorithms for predicting the equilibrium properties of an entire test tube of interacting nucleic acid strands. The utility of the approach will be demonstrated by elucidating the empirical behavior of hybridization chain reaction mechanisms that are under development with application to biosensing, transport, and therapeutics.