Abstract
Single particle tracking (SPT) enables the investigation of biomolecular dynamics at a high temporal and spatial resolution in living cells, and the analysis of these SPT datasets can reveal biochemical interactions and mechanisms. Still, how to make the best use of these tracking data for a broad set of experimental conditions remains an analysis challenge in the field. Here, we develop a new SPT analysis framework: NOBIAS (NOnparametric Bayesian Inference for Anomalous Diffusion in Single-Molecule Tracking), which applies nonparametric Bayesian statistics and deep learning approaches to thoroughly analyze SPT datasets. In particular, NOBIAS handles complicated live-cell SPT data for which: the number of diffusive states is unknown, mixtures of different diffusive populations may exist within single trajectories, symmetry cannot be assumed between the x and y directions, and anomalous diffusion is possible. NOBIAS provides the number of diffusive states without manual supervision, it quantifies the dynamics and relative populations of each diffusive state, it provides the transition probabilities between states, and it assesses the anomalous diffusion behavior for each state. We validate the performance of NOBIAS with simulated datasets and apply it to the diffusion of single outer-membrane proteins in Bacteroides thetaiotaomicron. Furthermore, we compare NOBIAS with other SPT analysis methods and find that, in addition to these advantages, NOBIAS is robust and has high computational efficiency and is particularly advantageous due to its ability to treat experimental trajectories with asymmetry and anomalous diffusion.
Highlights
The biophysical dynamics of biomolecules reflect the biochemical interactions in the system, and these dynamics can be quantified within a dataset of single-particle trajectories obtained by tracking individual molecules
The posterior results of the Hierarchical Dirichlet Process (HDP)-Hidden Markov Models (HMMs) module are shown in scatter plots of the inferred D and weight fraction from each iteration after the inferred number of states converges
The black crosses indicate the ground truth diffusion coefficient and weight fraction for each diffusive state; the posterior samples of the Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) model for the two states after convergence are distributed around the true values
Summary
The biophysical dynamics of biomolecules reflect the biochemical interactions in the system, and these dynamics can be quantified within a dataset of single-particle trajectories obtained by tracking individual molecules. SPT trajectory datasets have been assumed to be Brownian, such that the mean squared displacement, MSD, of each track is linearly proportional to the time lag, τ, and the diffusion coefficient, D, can be calculated from a linear fit to this curve (Qian et al, 1991; Saxton, 1997) This Brownian motion assumption works accurately for freely diffusing molecules in solution. In the complicated cellular environment, multiple diffusive states, each characterized by an average D, can exist—for instance due to binding and unbinding events—and molecules can transition between different states to produce heterogeneity even within single trajectories To reveal these heterogeneous dynamics, probability distribution-based methods such as cumulative probability distribution (Schütz et al, 1997; Mazza et al, 2012), have been applied. These corrections include localization error (Michalet and Berglund, 2012), confinement (Kusumi et al, 1993), motion blur (Berglund, 2010; Deschout et al, 2012), and out-of-focus effects (Lindén et al, 2017) in the probability model
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