Super-resolved trajectory-derived nanoclustering analysis using spatiotemporal indexing

Abstract

Single-molecule localization microscopy techniques are emerging as vital tools to unravel the nanoscale world of living cells by understanding the spatiotemporal organization of protein clusters at the nanometer scale. Current analyses define spatial nanoclusters based on detections but neglect important temporal information such as cluster lifetime and recurrence in "hotspots" on the plasma membrane. Spatial indexing is widely used in video games to detect interactions between moving geometric objects. Here, we use the R-tree spatial indexing algorithm to determine the overlap of the bounding boxes of individual molecular trajectories to establish membership in nanoclusters. Extending the spatial indexing into the time dimension allows the resolution of spatial nanoclusters into multiple spatiotemporal clusters. Using spatiotemporal indexing, we found that syntaxin1a and Munc18-1 molecules transiently cluster in hotspots, offering insights into the dynamics of neuroexocytosis. Nanoscale spatiotemporal indexing clustering (NASTIC) has been implemented as a free and open-source Python graphic user interface.

Fig. 1. Schematic representation of clustering algorithms as applied to molecular trajectories.

a Molecular trajectory data, with each trajectory’s spatial centroid indicated with a dot. b DBSCAN. Multiple molecular centroids present within a defined radius (red circles) are considered clustered. The most effective radius (ε) and the minimum number of centroids within it (MinPts) are determined empirically. c Voronoï tessellation. Tiles are drawn around each centroid such that the distance from any point within the tile is closer to its centroid than to any other centroid. Molecular centroids with tile areas less than an empirically determined threshold (red) are considered clustered. d Spatial indexing. Clustered molecules are determined by overlapping 2D bounding regions (red), defining the spatial extent of each molecular trajectory. e Spatiotemporal indexing. This panel represents the data in panel (d) rotated 90° around its y-axis to highlight the temporal component of each centroid. Each trajectory bounding region is assigned a user-defined “thickness” in the time dimension. Overlapping 3D bounding regions represent spatiotemporally clustered molecules. f Molecular trajectory composed of individual detections. g Spatiotemporal centroid representing the trajectory’s average position in space and time. h Convex hull (blue) defining the spatial extent of the trajectory. i Simplified 2D spatial bounding box (blue square) based on the approximate radius (r) of the convex hull (red circle). j 3D spatiotemporal bounding box of user-defined “thickness” in the time dimension. k R-tree spatiotemporal index of all trajectory bounding boxes. Discrete clusters of overlapping bounding boxes are indicated in color, and unclustered boxes are in gray. l 3D clusters of trajectories associated with overlapping bounding boxes. m 2D representation of clustered trajectories. Colored polygons represent the spatial convex hull of all detections comprising each of the clustered trajectories. Clusters are colored according to the averaged detection time of their component trajectories, allowing the assignment of overlapping clusters (green and blue) occupying the same spatial extent at different times. n Nanoscale spatiotemporal indexing clustering (NASTIC) of simulated trajectory data described in “Optimum parameters for spatiotemporal clustering” using r = 1.2, t = 20 s. Cluster boundaries represent the extent of the detections associated with clustered trajectories and are colored according to the average detection time. The inset displays a zoomed view of a single cluster against a background of unclustered trajectories, with trajectory centroids indicated with a dot. o Heatmap of averaged metrics (cluster number, cluster radius, trajectories per cluster and the number of clustered trajectories, see Supplementary Fig. 3). Each pixel represents the average log₂ ratio of the experimental observed (EXP) value for a given r/t pair to the ground truth (GT). Pale regions indicate r/t pairs which return cluster metrics close to the ground truth. The approximate inflection point where the pale line transitions to horizontal is indicated with a dotted box. Source data are provided as a Source Data file.

Fig. 2. Comparison of clustering algorithms.

a–c Resolution of spatiotemporal clusters in simulated data as described in “Comparison of clustering algorithms using simulated trajectory data”. a Clustering using NASTIC using r = 1.2, t = 20 s. Insets highlight different classes of clustering: (i) distinct clusters resolved in space and time; (ii) spatially overlapping clusters resolved in time; (iii) clusters with a degree of spatial and temporal overlap; (iv) clusters which overlap in space and time. 3D (x, y, t) projections of highlighted clusters (i–iii) and the associated detection times (lower panels) demonstrate distinct temporal clustering. b DBSCAN spatial clustering using ε = 0.055 μm and MinPts = 3. c Voronoï tessellation spatial clustering. Trajectories with an associated Voronoï tile area <0.004 μm² were considered clustered. In all analyses, a cluster is defined as three or more proximal centroids. d–g Comparison of cluster metrics returned by NASTIC, DBSCAN and Voronoï tessellation from synthetic data simulating 10 acquisitions as described in “Comparison of clustering algorithms using simulated trajectory data”. d Total trajectories in clusters, e Total unique clusters, f Average cluster radius (nm) and g Average trajectories in a cluster. Black bars represent the ground truth (GT) in the simulated data, colored bars represent the metrics returned by DBSCAN (ε = 0.05 μm, MinPts = 3, orange), Voronoï tessellation (tile threshold 0.01 μm², green) and NASTIC (r = 1.2, t = 20 s, blue). Error bars show the standard error of the mean (SEM) across 10 datasets. The dotted black line shows the average value in the input synthetic data. h–l Comparison of the ability of different algorithms to return metrics matching the ground truth as the density of unclustered background detection increases in a synthetic dataset. Source data are provided as a Source Data file.

Fig. 3. Resolution of spatiotemporal clustering in live-cell molecular trajectory data.

Sx1a-mEos2 sptPALM data acquired at 50 Hz over 320 s. Clustering using NASTIC using r = 1.2, t = 20 s. a Raw acquisition data showing all molecular detections, with the region of interest (ROI) highlighted in yellow. b Spatiotemporal clustering of the selected trajectories within the ROI of (a), with a region highlighted with a dotted white box for enlargement in (c). c Enlargement of highlighted area in (b) showing individual trajectories and their centroids, with clusters highlighted and color-coded according to their time in the acquisition. The dotted box highlights a hotspot of repeated clustering. d 2D Kernel density estimation of the detections associated with the selected trajectories, with brighter blobs corresponding to higher density. e Instantaneous diffusion coefficient, with each trajectory colored according to the gradient of the first four time points in its mean square displacement (MSD). f 3D plot of the selected trajectories, rotated to show the temporal separation of the clusters highlighted in (c). g 1D plot of the selected trajectories where each vertical bar represents a single trajectory, colored according to its cluster status (top panel) or instantaneous diffusion coefficient (bottom panel). h MSD curves of clustered and unclustered trajectories from the ROI displayed in (b). Each point represents the average MSD of the indicated number of trajectories. Error bars indicate the standard error of the mean (SEM). i, j NASTIC clusters of Sx1a-mEos2 comprise “confined” molecules. The entire 17,598 trajectories dataset, as visualized in (a), was selected for analysis. i K-means clustering of MSD and vector autoregression metrics for each trajectory was used to assign them into confined (orange) and unconfined (purple). j Venn diagram showing the degree to which clustered trajectories established by NASTIC are represented by confined trajectories established using vector autoregression (VAR). Source data are provided as a Source Data file.

Fig. 4. NASTIC spatiotemporal metrics. Sx1a-mEos2 sptPALM data acquired at 50 Hz over 320 s analyzed by NASTIC.

a Contour plot of the kernel density estimator (KDE) for the spatiotemporal centroids of all 17,598 trajectories in the Sx1a-mEos2 dataset projected into the x–y plane. Green dots mark local maxima. b Orthogonal projection of Sx1a-mEos2 trajectories highlighting VAR confined trajectories (bright green) to emphasize the temporal columns of clustered trajectories. c Trajectories within 0.2 µm of the local maxima, as shown in (a), are represented as temporal vertical columns. d Column-wise 1D scatter plots of centroids projected onto the temporal axis for a random selection of 40 columns with significant non-uniform detections of Sx1a (p-value > 0.01/409 using Kolmogorov–Smirnov test for non-uniformity). e Probability of cluster overlap using DBSCAN of cluster centroids identified by NASTIC, ε = 0.001–0.083 μm (average cluster radius) and MinPts = 2. Monte Carlo simulation (N = 50) using 172 randomly distributed cluster centroids was used to establish the degree of random overlap of clusters of the same number and density as the experimental data. The dotted red line indicates the average overlap probability and translucent red indicates the standard error of the mean. The left and right dotted vertical lines represent 0.001 μm and 0.083 μm, respectively. At 0.001 μm, two clusters must essentially completely overlap to be considered as a hotspot, as illustrated by the overlapping circles. At 0.083 μm, two clusters are considered members of a hotspot if their edges touch, as indicated pictorially by the two touching circles. f Average number of clusters in a hotspot as a function of distance. g Average time between clusters in a hotspot as a function of distance. h Number of unique spatiotemporal clusters observed at 1 s intervals over the 320 s acquisition. Source data are provided as a Source Data file.

Fig. 5. NASTIC of trajectory segments (segNASTIC).

a Schematic representation of trajectory segment thresholding based on overlap with segments from other trajectories. b Sx1a-EGFP imaged by uPAINT using Atto-647-labeled anti-GFP nanobodies in PC12 cells. Spatiotemporal clusters were identified using spatiotemporal indexing of trajectory bounding boxes using r = 1.2 and t = 20 s. Each colored cluster boundary represents the convex hull of the detections belonging to all trajectories in the cluster. c Pseudo-density map of trajectory segment overlap, with each trajectory colored according to the number of overlaps with other trajectory segments, as determined by spatiotemporal indexing of segment bounding boxes. d Spatiotemporal clusters identified using thresholded segments t = 20 s. Each colored cluster represents the convex hull of detections belonging to the clustered segments. All trajectories containing clustered segments are shown in the same color as the cluster. Source data are provided as a Source Data file.

Fig. 6. Two-color NASTIC (NASTIC2C) of simulated trajectory data.

a Individual molecular “detections” colored according to molecule 1 (cyan) or molecule 2 (magenta). The dotted box represents the area expanded to show regions representing detections from both colors occupying the same spatial extent (arrows) and expanded in (b) to show clusters. b Spatiotemporal clusters identified by spatiotemporal indexing of combined trajectory bounding boxes using r = 1.2 and t = 20 s. Each colored cluster boundary represents the convex hull of the detections belonging to all trajectories in the cluster. Clusters are colored according to the relative proportions of component molecules, with pure cyan and pure magenta indicating clusters consisting solely of molecule 1 or molecule 2, respectively. Dotted lines represent hotspots of repeated cluster formation. The dotted white box represents an area of spatiotemporal overlap expanded in two and three dimensions in (c) and (d), respectively, to show the resolution of spatiotemporally overlapping clusters into discrete clusters with different molecular compositions. e Mean square displacement (MSD) curves of clustered and unclustered trajectories from each simulated dataset. Each point represents the average MSD of the indicated number of trajectories. Error bars indicate the standard error of the mean (SEM). f Distribution of the relative contribution of color 2 across the 436 observed spatiotemporal clusters. g, h Experimentally observed co-clustering of Munc18-1-mEos2 (green) and Syntaxin-GFP-Atto647 (orange). Source data are provided as a Source Data file.