Real-time single-molecule 3D tracking in E. coli based on cross-entropy minimization

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.