A Jump Distance Based Parameter Inference Scheme for Particulate Trajectories in Biological Settings

Mean square displacement (MSD) analysis has been the standard for analyzing single molecule or particulate trajectories, where its shortcomings have been overlooked in light of its simplicity. The Jump Distance Distribution (JDD) has been proposed by others in the past as a new way to analyze these trajectories, but has not been sufficiently fleshed out in all dimensions or given a robust analysis on performance and how it compares to MSD analyses. We present the forms of the JDD in 1, 2, and 3 dimensions for three different models of motion: pure diffusion, directed diffusion, and anomalous diffusion. We also discuss how to select between competing models using Bayesian model selection, and verify our method through simulation. Through this, we have a method that is superior to MSD analysis, particularly in the data-poor limit. This method works across a wide range of parameters, which should make it broadly applicable to any system where the underlying motion is stochastic. We finish with an application to the method to ms2 trajectories in the early Drosophila embryo.