Diffusion analysis of single particle trajectories in a Bayesian nonparametrics framework

Abstract

Single particle tracking (SPT), where individual molecules are fluorescently labelled and followed over time, is an important tool that allows the spatiotemporal dynamics of subcellular biological systems to be studied at very fine temporal and spatial resolution. Mathematical models of particle motion are typically based on Brownian diffusion, reflecting the noisy environment that biomolecules typically inhabit. In order to study changes in particle behaviour within individual tracks, Hidden Markov models (HMM) featuring multiple diffusive states have been used as a descriptive tool for SPT data. However, such models are typically specified with an a-priori defined number of particle states and it has not been clear how such assumptions have affected their outcomes. Here, we propose a method for simultaneously inferring the number of diffusive states alongside the dynamic parameters governing particle motion. Our method is an infinite HMM (iHMM) within the general framework of Bayesian non-parametric models. We directly extend previous applications of these concepts in molecular biophysics to the SPT framework and propose and test an additional constraint with the goal of accelerating convergence and reducing computational time. We test our iHMM using simulated data and apply it to a previously-analyzed large SPT dataset for B cell receptor motion on the plasma membrane of B cells of the immune system.