Single particle tracking (SPT) of fluorescent molecules provides significant insights into the diffusion and relative motion of tagged proteins and other structures of interest in biology. However, despite the latest advances in high‐resolution microscopy, individual particles are typically not distinguished from clusters of particles. This lack of resolution obscures potential evidence for how merging and splitting of particles affect their diffusion and any implications on the biological environment. The particle tracks are typically decomposed into individual segments at observed merge and split events, and analysis is performed without knowing the true count of particles in the resulting segments. Here, we address the challenges in analyzing particle tracks in the context of cancer biology. In particular, we study the tracks of KRAS protein, which is implicated in nearly 20% of all human cancers, and whose clustering and aggregation have been linked to the signaling pathway leading to uncontrolled cell growth. We present a new analysis approach for particle tracks by representing them as tracking graphs and using topological events – merging and splitting, to disambiguate the tracks. Using this analysis, we infer a lower bound on the count of particles as they cluster and create conditional distributions of diffusion speeds before and after merge and split events. Using thousands of time‐steps of simulated and in‐vitro SPT data, we demonstrate the efficacy of our method, as it offers the biologists a new, detailed look into the relationship between KRAS clustering and diffusion speeds.

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Single particle tracking (SPT) is an indispensable tool for scientific studies. However, SPT for datasets with a high density of particles is still challenging, especially for the study of particle interactions where the point spread functions (PSFs) are overlapping. In this study, we present spt-PRIS, a new SPT solution where we apply compressive sensing to SPT by integrating the progressive refinement method on sparse recovery (PRIS) into the framework of the state-of-the-art SPT algorithm (uTrack). We systematically characterized and validated spt-PRIS performance using simulations, applied it to the experimental data of membrane-bound KRAS4b proteins in either 2-lipid or 8-lipid membrane supported lipid bilayers (SLB), and compared the results to the conventional method (uTrack). Our results show that spt-PRIS is effective for SPT when the data contains overlapping PSFs and provides unprecedented information about KRAS4b subpopulations. spt-PRIS is helpful for a broad range of scientific studies where precise and fast high-density localization is beneficial. spt-PRIS is also flexible for extensions for multi-species, multi-multi-channel, and multi-dimensional SPT methods with the generalization of PRIS reconstruction schemes.

Fig. 1: Left to right: A connected graph of ridge-like structures is extracted from the Morse-Smale complex (MSC), containing a superset of the possible neuron segments in the data. Our MSC-guided semi-automatic tracing tool enables users to rapidly trace paths and view a live preview as they do so (orange line). When satisfied with the trace, they can add it to the reconstruction (white line).