Leveraging Topological Events in Tracking Graphs for Understanding Particle Diffusion

Abstract

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.