Robust single-particle tracking in live-cell time-lapse sequences

Abstract

Single-particle tracking (SPT) is often the rate-limiting step in live-cell imaging studies of subcellular dynamics. Here we present a tracking algorithm that addresses the principal challenges of SPT, namely high particle density, particle motion heterogeneity, temporary particle disappearance, and particle merging and splitting. The algorithm first links particles between consecutive frames and then links the resulting track segments into complete trajectories. Both steps are formulated as global combinatorial optimization problems whose solution identifies the overall most likely set of particle trajectories throughout a movie. Using this approach, we show that the GTPase dynamin differentially affects the kinetics of long- and short-lived endocytic structures and that the motion of CD36 receptors along cytoskeleton-mediated linear tracks increases their aggregation probability. Both applications indicate the requirement for robust and complete tracking of dense particle fields to dissect the mechanisms of receptor organization at the level of the plasma membrane.

Figure 1. Tracking particles via spatially and temporally global assignments

(a) Tracks were constructed from an image sequence by detecting particles in each frame (Step 0), linking particles between consecutive frames (Step 1), and then closing gaps and capturing merging and splitting events between the initial track segments (Step 2). (b) Cost matrix controlling particle assignments between frames. λ_ij: cost for linking particle i in frame t to particle j in frame t + 1, x: impossible link whose cost exceeded the cutoff, d: cost for allowing particles in frame t to link to nothing in frame t + 1, b: cost for allowing particles in frame t + 1 to get linked by nothing in frame t. The lower right block is an auxiliary block required to satisfy the topological constraints of the LAP (Supplementary Note 4 online). (c) Cost matrix controlling gap closing, merging and splitting. gIJ: cost for closing a gap between the end of track segment I and the start of track segment J, m_IJ: cost for the end of track segment I merging with a middle point of track segment J, s_IJ: cost for the start of track segment J splitting from a middle point of track segment I. Central cross: links between track segment middle points introduced for merging and splitting were not allowed. The upper and middle right blocks, lower left and middle blocks, and lower right block were as described in (b). In (b) and (c), ‘…’ means index continuation.

Figure 2. Validation of tracking algorithm on simulated tracks

5 simulations of increasing particle density, each combined with 8 detection efficiencies represented by percentages of particles missing from the detection, were used to test the performance of the tracking algorithm. The results shown are the averages over 6 repetitions of each simulation. (a) Criteria to assess particle density as related to tracking: Average nearest neighbor distance (upper panel, left y-axis) and fraction of particles with nearest neighbors closer than twice their average frame-to-frame displacement (upper panel, right y-axis), evaluated at 0% detection misses; average number of potential assignments per particle (middle panel, left y-axis) and fraction of particles with > 1 potential assignment (middle panel, right y-axis) in the frame-to-frame linking step, evaluated at 0% detection misses; average number of potential assignments per track segment (lower panel, left y-axis) and fraction of track segments with > 1 potential assignment (lower panel, right y-axis) in the gap closing, merging and splitting step, evaluated at 20% detection misses (at 0% misses, there are no gaps to close). (b–d) Percentage of true and false positives in particle linking (b), gap closing (c) and merging and splitting (d) relative to the ground truth (GT). (e) P-value of the Kolmogorov-Smirnov test comparing the measured and GT lifetime distributions. The 0.05 significance threshold is indicated by a dashed line. In (b–e), the conditions similar to the experimental data are highlighted with a dotted oval.

Figure 3. Clathrin-coated pit lifetime is regulated by dynamin

(a) TIR-FM image of a BSC1 cell fluorescently labeled with clathrin light chain-EGFP. Scale bar = 5 µm. (b) Clathrin-coated pit (CCP) trajectories in the 10 ×10 µm area indicated by a red box in (a). (c) Normalized lifetime histogram of 21,518 CCP trajectories pooled from 11 control cell movies. Shaded blue and pink areas: second and third data quartiles. (d) CCP lifetimes for control and for alterations of dynamin function (DynOX: Dynamin over-expression, DynKD: Dynamin knockdown). Blue and pink bars: second and third data quartiles. Round black markers: mean. Black error bars: Cell-to-cell standard deviation (calculated for 11 control, 4 DynOX, 15 DynKD and 5 dynasore). KS-test: * p-value < 10⁻⁵, ** p-value < 10⁻¹⁰. (e) Cumulative frequency of CCP lifetimes in control and dynasore treated cells, resulting from tracking with gap closing (as in (b–d)) and without gap closing. (f) CCP lifetimes for control and for alterations of dynamin function resulting from tracking without gap closing.

Figure 4. CD36 receptor aggregation activity depends on motion type

(a) Epifluorescence image of CD36 immuno-labeled in a control macrophage using a primary Fab fragment followed by a Cy3-conjugated secondary Fab fragment. (b) CD36 tracks in a control macrophage. (c) CD36 tracks in a Blebbistatin (Bleb.) treated macrophage. (d) CD36 tracks in a Nocodazole (Noc.) treated macrophage. All tracks are from 10s/100 frame movies. Tracks are classified as linear (red) or random (cyan) (Supplementary Note 10 online). Scale bar = 1 µm. (e) Fraction of particles undergoing linear motion. (f) Two sample trajectories represented as x-coordinate, y-coordinate and amplitude over time, highlighting merging events (green ovals), splitting events (purple ovals) and closed gaps (orange ovals). The two colors (pink and blue) highlight the two track segments brought together by capturing merge and split events. (g) Conditional probabilities of merging and splitting while undergoing linear motion and while undergoing random motion, and ratio of conditional probability while undergoing linear motion to conditional probability while undergoing random motion. In (e) and (g), error bars indicate standard deviation as calculated from a sample of size 200 generated by the bootstrap method. ** p-value < 10⁻¹⁰. Statistics were calculated from 14 control cells (7527 trajectories ≥ 5 frames long), 11 Blebbistatin-treated cells (5148 trajectories ≥ 5 frames long) and 12 Nocodazole-treated cells (4926 trajectories ≥ 5 frames long). Trajectories shorter than 5 frames were excluded as non-classifiable with respect to motion type.