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.