SMAUG: Analyzing single-molecule tracks with nonparametric Bayesian statistics

Abstract

<jats:title>Abstract</jats:title><jats:p>Single-molecule fluorescence microscopy probes nanoscale, subcellular biology in real time. Existing methods for analyzing single-particle tracking data provide dynamical information, but can suffer from supervisory biases and high uncertainties. Here, we introduce a new approach to analyzing single-molecule trajectories: the <jats:underline>S</jats:underline>ingle-<jats:underline>M</jats:underline>olecule <jats:underline>A</jats:underline>nalysis by <jats:underline>U</jats:underline>nsupervised <jats:underline>G</jats:underline>ibbs sampling (SMAUG) algorithm, which uses nonparametric Bayesian statistics to uncover the whole range of information contained within a single-particle trajectory (SPT) dataset. Even in complex systems where multiple biological states lead to a number of observed mobility states, SMAUG provides the number of mobility states, the average diffusion coefficient of single molecules in that state, the fraction of single molecules in that state, the localization noise, and the probability of transitioning between two different states. In this paper, we provide the theoretical background for the SMAUG analysis and then we validate the method using realistic simulations of SPT datasets as well as experiments on a controlled <jats:italic>in vitro</jats:italic> system. Finally, we demonstrate SMAUG on real experimental systems in both prokaryotes and eukaryotes to measure the motions of the regulatory protein TcpP in <jats:italic>Vibrio cholerae</jats:italic> and the dynamics of the B-cell receptor antigen response pathway in lymphocytes. Overall, SMAUG provides a mathematically rigorous approach to measuring the real-time dynamics of molecular interactions in living cells.</jats:p><jats:sec><jats:title>Statement of Significance</jats:title><jats:p>Super-resolution microscopy allows researchers access to the motions of individual molecules inside living cells. However, due to experimental constraints and unknown interactions between molecules, rigorous conclusions cannot always be made from the resulting datasets when model fitting is used. SMAUG (Single-Molecule Analysis by Unsupervised Gibbs sampling) is an algorithm that uses Bayesian statistical methods to uncover the underlying behavior masked by noisy datasets. This paper outlines the theory behind the SMAUG approach, discusses its implementation, and then uses simulated data and simple experimental systems to show the efficacy of the SMAUG algorithm. Finally, this paper applies the SMAUG method to two model living cellular systems—one bacterial and one mammalian—and reports the dynamics of important membrane proteins to demonstrate the usefulness of SMAUG to a variety of systems.</jats:p></jats:sec>

Following the messenger: Recent innovations in live cell single molecule fluorescence imaging

“…More recently, nonparametric methods have been reported that uncover a range of possible diffusion states within a single particle track, independent of pre‐defined parameters. For example, the Single Molecule Analysis by Unsupervised Gibbs Sampling algorithm provides the number of mobility states, the fraction, and the average diffusion coefficient of each state, as well as the probability of transitioning between two states (Karslake et al, ). Alternatively, background fluctuations arising from out‐of‐focus fluorescence or diffusion in the Z ‐direction can be addressed by the newly developed Single‐Molecule Accurate LocaLization by LocAl Background Subtraction algorithm (Isaacoff, Li, Lee, & Biteen, ).…”

A Bayesian framework for the detection of diffusive heterogeneity

“…Other packages with information theoretic frameworks for trajectory analysis have been released; for example, the Single-Molecule Analysis by Unsupervised Gibbs sampling ("SMAUG") software package [9] also uses Bayesian estimation to characterize diffusive environments. However, our package is unique because it is intended specifically to provide lightweight trajectory analysis and prediction that can be used by those with a biological background to inform microscopy experiment design, without requiring deep statistical or computational knowledge.…”

“…By mapping the diffusivity estimates from each trajectory (value most probable from posterior distribution) to the spatial region where the tracked substrate was localized, the user can build up a spatial mapping of the diffusivity. While frameworks exist for spatial mapping of the physical properties of cells, such as nanorheology of injected particles [15] and SMAUG [9], these techniques respectively require an extensive and invasive experimental design or in-depth knowledge of computational Bayesian inference. Our tool offers an approachable framework for experimental design of studies to probe the spatial variation of physical properties of the cell.…”

Extracting Transition Rates in Particle Tracking Using Analytical Diffusion Distribution Analysis

“…We benchmark this analysis method, with simulation of transitioning particles and implement modifications that account for specific experimental challenges, such as varying tracking windows and confinement effects within the cell. Furthermore, we compare anaDDA to a different kinetic analysis tools that use Bayesian statistics or unsupervised Gibbs sampling to infer state transitions from the data 27,28 . We study the effects of confinement and tracking parameters on the fitting of the distribution coefficient distribution and re-analyse previously published sptPALM data of DNA interacting proteins, obtain their kinetic parameters, and reveal that fast DNA probing interactions were hidden in the published data.…”