Computational Proposal for Tracking Multiple Molecules in a Multifocus Confocal Setup

Statistical analysis of fluorescence intensity transients with Bayesian methods

Molecular movement and interactions at the single-molecule level, particularly in live cells, are often studied using fluorescence correlation spectroscopy (FCS). While powerful, FCS has notable drawbacks: It requires high laser intensities and long acquisition times, increasing phototoxicity, and often relies on problematic statistical assumptions in data fitting. We introduce fluorescence intensity trace statistical analysis (FITSA), a Bayesian method that directly analyzes fluorescence intensity traces. FITSA offers faster, more stable convergence than previous approaches and provides robust parameter estimation from far shorter measurements than conventional FCS. Our results demonstrate that FITSA achieves comparable precision to FCS while requiring substantially fewer photons. This advantage becomes even more pronounced when accounting for statistical dependencies in FCS analysis, which are often overlooked but necessary for accurate error estimation. By reducing laser exposure, FITSA minimizes phototoxicity effects, representing a major advancement in the quantitative analysis of molecular processes across fields.

Single-molecule reaction-diffusion

We propose capturing reaction-diffusion on a molecule-by-molecule basis from the fastest acquirable timescale, namely individual photon arrivals. We illustrate our method on the intrinsically disordered human protein linker histone H1.0 and its chaperone prothymosin α, as these diffuse through an illuminated confocal spot and interact, forming larger ternary complexes on millisecond timescales. Most importantly, single-molecule reaction-diffusion (smRD) reveals single-molecule properties without the requirement to trap or otherwise confine molecules to surfaces. We achieve smRD within a Bayesian paradigm and term our method Bayes-smRD. Bayes-smRD is further free of the average, bulk results inherent to analyzing long photon arrival traces by fluorescence correlation spectroscopy. In learning from mere thousands of photon arrivals, continuous spatial positions, and discrete conformational and photophysical state changes, Bayes-smRD estimates kinetic parameters on a molecule-by-molecule basis with two to three orders of magnitude less data than tools such as fluorescence correlation spectroscopy, thereby also dramatically reducing sample photodamage.

BNP-Track: a framework for superresolved tracking

Superresolution tools, such as PALM and STORM, provide nanoscale localization accuracy by relying on rare photophysical events, limiting these methods to static samples. By contrast, here, we extend superresolution to dynamics without relying on photodynamics by simultaneously determining emitter numbers and their tracks (localization and linking) with the same localization accuracy per frame as widefield superresolution on immobilized emitters under similar imaging conditions (≈50 nm). We demonstrate our Bayesian nonparametric track (BNP-Track) framework on both in cellulo and synthetic data. BNP-Track develops a joint (posterior) distribution that learns and quantifies uncertainty over emitter numbers and their associated tracks propagated from shot noise, camera artifacts, pixelation, background and out-of-focus motion. In doing so, we integrate spatiotemporal information into our distribution, which is otherwise compromised by modularly determining emitter numbers and localizing and linking emitter positions across frames. For this reason, BNP-Track remains accurate in crowding regimens beyond those accessible to other single-particle tracking tools.

Fluorescence Microscopy: a statistics-optics perspective

Fundamental properties of light unavoidably impose features on images collected using fluorescence microscopes. Modeling these features is ever more important in quantitatively interpreting microscopy images collected at scales on par or smaller than light's wavelength. Here we review the optics responsible for generating fluorescent images, fluorophore properties, microscopy modalities leveraging properties of both light and fluorophores, in addition to the necessarily probabilistic modeling tools imposed by the stochastic nature of light and measurement.

Single-Molecule Reaction-Diffusion

We propose to capture reaction-diffusion on a molecule-by-molecule basis from the fastest acquirable timescale, namely individual photon arrivals. We illustrate our method on intrinsically disordered human proteins, the linker histone H1.0 as well as its chaperone prothymosin α , as these diffuse through an illuminated confocal spot and interact forming larger ternary complexes on millisecond timescales. Most importantly, single-molecule reaction-diffusion, smRD, reveals single molecule properties without trapping or otherwise confining molecules to surfaces. We achieve smRD within a Bayesian paradigm and term our method Bayes-smRD. Bayes-smRD is further free of the average, bulk, results inherent to the analysis of long photon arrival traces by fluorescence correlation spectroscopy. In learning from thousands of photon arrivals continuous spatial positions and discrete conformational and photophysical state changes, Bayes-smRD estimates kinetic parameters on a molecule-by-molecule basis with two to three orders of magnitude less data than tools such as fluorescence correlation spectroscopy thereby also dramatically reducing sample photodamage.

BNP-Track: A framework for superresolved tracking

Assessing dynamic processes at single molecule scales is key toward capturing life at the level of its molecular actors. Widefield superresolution methods, such as STORM, PALM, and PAINT, provide nanoscale localization accuracy, even when distances between fluorescently labeled single molecules ("emitters") fall below light's diffraction limit. However, as these superresolution methods rely on rare photophysical events to distinguish emitters from both each other and background, they are largely limited to static samples. In contrast, here we leverage spatiotemporal correlations of dynamic widefield imaging data to extend superresolution to simultaneous multiple emitter tracking without relying on photodynamics even as emitter distances from one another fall below the diffraction limit. We simultaneously determine emitter numbers and their tracks (localization and linking) with the same localization accuracy per frame as widefield superresolution does for immobilized emitters under similar imaging conditions (≈50nm). We demonstrate our results for both in cellulo data and, for benchmarking purposes, on synthetic data. To this end, we avoid the existing tracking paradigm relying on completely or partially separating the tasks of emitter number determination, localization of each emitter, and linking emitter positions across frames. Instead, we develop a fully joint posterior distribution over the quantities of interest, including emitter tracks and their total, otherwise unknown, number within the Bayesian nonparametric paradigm. Our posterior quantifies the full uncertainty over emitter numbers and their associated tracks propagated from origins including shot noise and camera artefacts, pixelation, stochastic background, and out-of-focus motion. Finally, it remains accurate in more crowded regimes where alternative tracking tools cannot be applied.