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

TL;DR

This paper mathematically analyzes how much information about particle motion can be extracted from post-processed fluorescence tracking data, finding that emission noise dominates the likelihood, thus limiting motion model learning.

Contribution

It provides a formal likelihood framework showing the dominance of emission models over motion models in fluorescence tracking data, questioning the reliability of learned motion models.

Findings

Emission model contributes ~99% to the likelihood

Motion model explains only ~1% of the data

Challenges the validity of current motion model inference methods

Abstract

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 approximately 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.