Bayesian Sample Size Determination for Single-Particle Tracking of Pathogens in Biological Fluids

Abstract

Single-particle tracking (SPT) experiments measure 2-dimensional particle position with a high-resolution digital camera, capturing microsecond motion. SPT has allowed novel investigation of membrane dynamics, enzymology, subdiffusion processes in proteins, and serves as a burgeoning application of statistical modelling. While particle tracking statistical methodology has shown great promise, the literature is comparatively scarce for methods that determine the necessary number of particles to track to assess a relevant scientific hypothesis. This work addresses this gap by providing a Bayesian sample size determination (SSD) algorithm. Namely, this work proceeds in two-stages, (1) model training and (2) the SSD algorithm. A single-trajectory location-scale model incorporating fractional Brownian motion is fit using maximum likelihood estimation for each 2-dimensional SPT trajectory. Subsequently, a multiple-trajectory hierarchical model is fit to capture different particle dynamics caused by fluid heterogeneity. A Bayesian SSD algorithm follows to evaluate scientific relevance based on population-level mean-squared displacement. The performance of the SSD algorithm is first studied under a simulation environment. Three simplified SSD algorithms are presented to accelerate computation. Following this, experimental data of 3,707 fluorescently labelled herpes-simplex virus trajectories are studied across five separate antibody concentrations ranging 0-1000 mg/L. A detailed analysis on the practical use of the SSD algorithm provides insight into virus dynamics as a function of antibody concentration.