DNA strand displacement is a key reaction in DNA homologous recombination and DNA mismatch repair and is also heavily utilized in DNA-based computation and locomotion. Despite its ubiquity in science and engineering, sequence-dependent effects of displacement kinetics have not been extensively characterized. Here, we measured toehold-mediated strand displacement kinetics using single-molecule fluorescence in the presence of a single basepair mismatch. The apparent displacement rate varied significantly when the mismatch was introduced in the invading DNA strand. The rate generally decreased as the mismatch in the invader was encountered earlier in displacement. Our data indicate that a single base pair mismatch in the invader stalls branch migration and displacement occurs via direct dissociation of the destabilized incumbent strand from the substrate strand. We combined both branch migration and direct dissociation into a model, which we term the concurrent displacement model, and used the first passage time approach to quantitatively explain the salient features of the observed relationship. We also introduce the concept of splitting probabilities to justify that the concurrent model can be simplified into a three-step sequential model in the presence of an invader mismatch. We expect our model to become a powerful tool to design DNA-based reaction schemes with broad functionality.

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Reaching sub-millisecond 3D tracking of individual molecules in living cells would enable direct measurements of diffusion-limited macromolecular interactions under physiological conditions. Here, we present a 3D tracking principle that approaches the relevant regime. The method is based on the true excitation point spread function and cross-entropy minimization for position localization of moving fluorescent reporters. Tests on beads moving on a stage reaches 67 nm lateral and 109 nm axial precision with a time resolution of 0.84 ms at a photon count rate of 60 kHz; the measurements agree with the theoretical and simulated predictions. Our implementation also features a method for microsecond 3D PSF positioning and an estimator for diffusion analysis of tracking data. Finally, we successfully apply these methods to track the Trigger Factor protein in living bacterial cells. Overall, our results show that while it is possible to reach sub-millisecond live-cell single-molecule tracking, it is still hard to resolve state transitions based on diffusivity at this time scale.

Sub-ms 3D tracking of individual molecules in living cells is an important goal for microscopy since it will enable measurements at the scale of diffusion limited macromolecular interactions. Here, we present a 3D tracking principle based on the true excitation point spread function and cross-entropy minimization for position localization of moving fluorescent reporters that approaches the relevant regime. When tested on beads moved on a stage, we reached 67nm lateral and 109nm axial precision with a time resolution of 0.84 ms at a photon count rate of 60kHz, coming close to the theoretical and simulated predictions. A critical step in the implementation was a new method for microsecond 3D PSF positioning that combines 3D holographic beam shaping and electro-optical deflection. For the analysis of tracking data, a new point estimator for diffusion was derived and evaluated by a detailed simulation of the 3D tracking principle applied to a fictive reaction-diffusion process in an E. coli-like geometry. Finally, we successfully applied these methods to track the Trigger Factor protein in living bacterial cells. Overall our results show that it is possible to reach sub-millisecond live-cell single molecule tracking, but that it is still hard to resolve state transitions based on diffusivity at this time scale.