Diagnosing Heterogeneous Dynamics in Single-Molecule/Particle Trajectories with Multiscale Wavelets

Abstract

We describe a simple automated method to extract and quantify transient heterogeneous dynamical changes from large datasets generated in single molecule/particle tracking experiments. Based on wavelet transform, the method transforms raw data to locally match dynamics of interest. This is accomplished using statistically adaptive universal thresholding, whose advantage is to avoid a single arbitrary threshold that might conceal individual variability across populations. How to implement this multiscale method is described, focusing on local confined diffusion separated by transient transport periods or hopping events, with 3 specific examples: in cell biology, biotechnology, and glassy colloid dynamics. This computationallyefficient method can run routinely on hundreds of millions of data points analyzed within an hour on a desktop personal computer.Key words: single molecule imaging, dynamic heterogeneity, wavelet, active transport, electrophoresis, colloid glass 3The experimental study of dynamics has been deeply transformed during the past generation by new technologies that acquire digital images in vast quantities, allowing one to record motion of objects of interest, one-by-one in real space and time. [1][2][3][4][5][6] When datasets of this kind are analyzed, the capacity to track individual objects over a long time allows not only quantification of individual variations within populations but also complex temporal fluctuations of individual moving elements. The valuable information offered by huge datasets goes beyond what can be obtained from the classic ensemble-averaged approach, and has often provided unexpected mechanistic insights. This approach of "deep" statistical imaging has already led to significant progress in a variety of fields, from physical sciences such as diffusion 5-10 and other dynamics in condensed matter, 4,11,12 to biological sciences such as ecology 13 and cell biology. 14-16 Much important work revolves around improving experimental techniques to collect the data. 17-18Here we ask a different question: how to analyze such data for embedded information? For many problems, but not all, it is reasonable to assume random fluctuations with some probabilistic distribution around an average value. However, dynamics in the physical and biological worlds are often heterogeneous. When the statistical character of the process changes intermittently with time due to stochastic switching between coexisting and often competing microscopic processes, 1-16 averaging over these distinct processes may give misleading results.Progress is impeded by the paucity of methods to identify these distinct processes, and to quantify them, especially in the presence of noise in the data. An ideal method would be automated to handle large datasets, involve no judgment on the part of the analyst, and resolve rapid dynamic changes. Also problematical is to select a criterion by which to distinguish random fluctuations from real changes in dynamics; there is no general way to avoid judgment in selecting...

Segmentation of 3D Trajectories Acquired by TSUNAMI Microscope: An Application to EGFR Trafficking

“…As a wealth of information about membrane structure, interior organization, and receptor biology can be derived from the long 3D trajectories acquired by TSUNAMI, a sophisticated tool is needed to segment and classify these trajectories according to their motional modes (34)(35)(36)(37), extract physical parameters of the motion (30,38), and correlate that motion to the surrounding environment (39), all with the goal of understanding the physical scenarios behind the observed motion (40,41). Considerable effort has been devoted to the identification of change points in motion (36) or diffusivity (38) along the same trajectory and to the visualization of spatial regions with different dynamic behaviors (34,35,38,42). Such an analysis is called trajectory segmentation and classification (11), which is often carried out by calculating a number of classification parameters over the trajectory using methods such as rolling window analysis (34,36,43), supervised segmentation (44), mean-squareddisplacement (MSD) curvature (34,35,45,46), maximum likelihood estimator (38), Bayesian methods (47,48), F-statistics (49), hidden Markov model (50,51), and wavelet analysis (42,52).…”

“…Considerable effort has been devoted to the identification of change points in motion (36) or diffusivity (38) along the same trajectory and to the visualization of spatial regions with different dynamic behaviors (34,35,38,42). Such an analysis is called trajectory segmentation and classification (11), which is often carried out by calculating a number of classification parameters over the trajectory using methods such as rolling window analysis (34,36,43), supervised segmentation (44), mean-squareddisplacement (MSD) curvature (34,35,45,46), maximum likelihood estimator (38), Bayesian methods (47,48), F-statistics (49), hidden Markov model (50,51), and wavelet analysis (42,52).…”

Disentangling Random Motion and Flow in a Complex Medium

“…wavelet-based method previously described for identifying actively transported organelles (21). Smoothed local velocities were defined using third-order Savitsky-Golay wavelets with a span of n ¼ 20 (see Section S2).…”

“…A common signal-processing technique for extracting approximate velocities from noisy data is that of wavelet analysis (13,21). This procedure involves taking a sliding window over each trajectory and using a linear combination of data points within that window to approximate the velocity of the particle:ṽ…”

Decorrelation correction for nanoparticle tracking analysis of dilute polydisperse suspensions in bulk flow

“…Choosing the span of the weighting function is commonly subjective, such as in the popular IDL code [12], although first performing an ellipticity analysis on SPT trajectories may offer reasonable values for window span [27]. Less subjective approaches have been recently developed using multiresolution wavelet analysis with universal thresholding, which have been employed to correct spatiotemporally heterogeneous advection of intracellular probes in migrating cells [28] and to identify particular time steps in which displacements are influenced by hydrodynamic interactions in the diffusion of confined probe particles [29]. To process the estimated non-Brownian motion relies on large SPT data sets obtained by tracking large ensembles over numerous time steps.…”