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. An understanding of the underlying free energy landscapes of these systems is crucial for their design, characterization, and control. 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 a new class of DNA-based instrument-free biosensors that are under development in our lab.