Heterogeneous model for superdiffusive movement of dense core vesicles in C. elegans

Transport of dense core vesicles (DCVs) in neurons is crucial for distributing molecules like neuropeptides and growth factors. We studied the experimental trajectories of dynein-driven directed movement of DCVs in the ALA neuron in C. elegans over a duration of up to 6 seconds. We analysed the DCV movement in three strains of C. elegans: (1) with normal kinesin-1 function, (2) with reduced function in kinesin light chain 2 (KLC-2), and (3) a null mutation in kinesin light chain 1 (KLC-1). We find that DCVs move superdiffusively with displacement variance \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$var(x) \sim t<^>2$$\end{document} in all three strains with low reversal rates and frequent immobilization of DCVs. The distribution of DCV displacements fits a beta-binomial distribution with the mean and the variance following linear and quadratic growth patterns, respectively. We propose a simple heterogeneous random walk model to explain the observed superdiffusive retrograde transport behaviour of DCV movement. This model involves a random probability with the beta density for a DCV to resume its movement or remain in the same position. To validate our model further, we measure the first passage time for a DCV to reach a certain threshold for the first time. According to the model, the first passage time distribution should follow a beta-negative binomial distribution with the same parameters as the DCV displacement distributions. Our experimental data confirm this prediction.