Multistep Track Segmentation and Motion Classification for Transient Mobility Analysis

Abstract

Molecular interactions are often transient and might change within the window of observation, leading to changes in molecule movement. Therefore, accurate motion analysis often requires transient motion classification. Here we present an accurate and computationally efficient transient mobility analysis framework, termed "divide-and-conquer moment scaling spectrum" (DC-MSS). DC-MSS works in a multistep fashion: 1) it utilizes a local movement descriptor throughout a track to divide it into initial segments of putatively different motion classes; 2) it classifies these segments via moment scaling spectrum (MSS) analysis of molecule displacements; and 3) it uses the MSS analysis results to refine the track segmentation. This strategy uncouples the initial identification of motion switches from motion classification, allowing DC-MSS to circumvent the sensitivity-accuracy tradeoff of classic rolling window approaches for transient motion analysis, while at the same time harnessing the classification power of MSS analysis. Testing of DC-MSS demonstrates that it detects switches among free diffusion, confined diffusion, directed diffusion, and immobility with great sensitivity. To illustrate the utility of DC-MSS, we have applied it to single-particle tracks of the transmembrane protein CD44 on the surface of macrophages, revealing actin cortex-dependent transient mobility changes.

Figure 1

The three steps of DC-MSS: Initial Track Segmentation, Initial Segment Classification, and Final Segmentation and Classification. Illustration uses a 250-frame simulated track that switches among immobility (brown) and confined (blue), free (cyan) and directed (magenta) diffusion. Red x symbols on track and red bars in timelines indicate detected motion switches in each analysis step. Timeline t is in frames. (Black) Unclassified. (Inset) Zoom of enclosed area.

Figure 2

Differences between CD44 and FcγR mobility are diminished upon actin perturbation. (a) Example tracks (400 frames/12 s duration) and state diagrams describing CD44 and FcγR mobility classes and their interconversion in unperturbed cells and cells treated with latrunculin A (1 μM for 5 min). Each mobility class is shown as a circle with circle area proportional to the class probability (indicated inside/next to circle). Arrows between circles and adjacent numbers indicate the switching rate between mobility classes, with arrow thickness and color strength proportional to the rate. Scale bars, 500 nm. Track and circle colors: cyan, free; blue, confined; brown, immobile; magenta, directed. (b) Boxplots of diffusion coefficient distribution for free and confined track segments for each condition. Boxplot description: red central mark shows median; box edges show 25th and 75th percentiles; dashed whiskers extend to the most extreme data points not designated as “outliers”; and notch emanating from median indicates the 95% confidence interval around the median, shown for visual aid. (c) Boxplots of confinement radius distribution for immobile and confined track segments for each condition. Boxplot description is as in (b). In all panels, results are from N = 1274, 1302, 1485, and 2872 tracks of duration ≥20 frames for unperturbed CD44, CD44+latrunculin A, unperturbed FcγR, and FcγR+latrunculin A, respectively. The tracks for each condition come from 22 to 30 cells, collected over three independent experiments.