This study presents an improved quantitative tool for the analysis of particulate trajectories. Particulate trajectory data appears in several different biological contexts, from the trajectory of chemotaxing bacteria to the nuclear mobility inferred from the trajectory of MS2 spots. Presently, the majority of analyses performed on particulate trajectory data have been limited to mean-squared displacement (MSD) analysis. Although simple, MSD analysis has several pitfalls, including difficulty in selecting between competing methods of motion, handling systems with multiple distinct subpopulations, and parameter extraction from limited time-series data. Here, we provide an alternative to MSD analysis using the jump distance distribution (JDD), which addresses the aforementioned issues. In particular, the method outperforms MSD analysis in the data-poor limit, thereby giving access to a larger range of temporal dynamics. In this work, we construct and validate a derivation of the JDD for different transportation modes and dimensions and implement a parameter estimation and model selection scheme. This scheme is validated, and direct improvements over MSD analysis are shown. Through an analysis of bacterial chemotaxis data, we highlight the JDD's ability to extract parameters at a variety of timescales, as well as extract underlying biological features of interest.
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