How Easy Is It to Learn Motion Models from Widefield Fluorescence Single Particle Tracks?

Motion models (i.e., transition probability densities) are often deduced from fluorescence widefield tracking experiments by analyzing single-particle trajectories post-processed from data. This analysis immediately raises the question: To what degree is our ability to learn motion models impacted by analyzing post-processed trajectories versus raw measurements? To answer this question, we mathematically formulate a data likelihood for diffraction-limited fluorescence widefield tracking experiments. In particular, we make the likelihood's dependence on the motion model versus the emission (or measurement) model explicit. The emission model describes how photons emitted by biomolecules are distributed in space according to the optical point spread function, with intensities subsequently integrated over a pixel, and convoluted with camera noise. Logic dictates that if the likelihood is primarily informed by the motion model, it should be straightforward to learn the motion model from the post-processed trajectory. Contrarily, if the majority of the likelihood is dominated by the emission model, the post-processed trajectory inferred from data is primarily informed by the emission model, and very little information on the motion model permeates into the post-processed trajectories analyzed downstream to learn motion models. Indeed, we find that for typical diffraction-limited fluorescence experiments, the emission model often robustly contributes ≈99% to the likelihood, leaving motion models to explain a meager ≈1% of the data. This result immediately casts doubt on our ability to reliably learn motion models from post-processed data, raising further questions on the significance of motion models learned thus far from post-processed single-particle trajectories from single-molecule widefield fluorescence tracking experiments.