Modeling DNA-Strand Displacement Reactions in the Presence of Base-Pair Mismatches

Toehold-mediated strand displacement is the most abundantly used method to achieve dynamic switching in DNA-based nanotechnology. An "invader" strand binds to the "toehold" overhang of a target strand and replaces a target-bound "incumbent" strand. Here, the complementarity of the invader to the single-stranded toehold provides the free energy bias of the reaction. Despite the widespread use of strand displacement reactions for realizing dynamic DNA nanostructures, variants on the basic motif have not been completely characterized. Here we introduce a simple thermodynamic model, which is capable of quantitatively describing the kinetics of strand displacement reactions in the presence of mismatches, using a minimal set of parameters. Furthermore, our model highlights that base pair fraying and internal loop formation are important mechanisms when involving mismatches in the displacement process. Our model should provide a helpful tool for the rational design of strand-displacement reaction networks.