Computational Proposal for Tracking Multiple Molecules in a Multifocus Confocal Setup

Single-molecule tracking continues to provide new insights into the fundamental rules governing biology. Despite continued technical advances in fluorescent and nonfluorescent labeling, as well as in data analysis, direct observations of trajectories and multimolecular interactions in dense environments remain merely aspirational. While confocal methods provide a means to deduce dynamical parameters, such as diffusion coefficients, with high temporal resolution, they do so at the expense of spatial resolution. Indeed, on account of a confocal volume's symmetry, typically only distances from the center of the confocal spot can be deduced. Motivated by the need for true three-dimensional high speed tracking in densely labeled environments, we propose a computational tool for tracking many fluorescent molecules traversing multiple, closely spaced, confocal measurement volumes. We achieve this by directly using single-photon arrival times to inform our likelihood and exploit Hamiltonian Monte Carlo to efficiently sample trajectories from our posterior within a Bayesian nonparametric paradigm. A nonparametric paradigm here is warranted, as the number of molecules present are a priori unknown. Taken together, we provide a Bayesian nonparametric computational framework for multifocus tracking (BNP-MFT) for multiple molecules at once, below the diffraction limit (the width of a confocal spot), in three dimensions at submillisecond or faster time scales.