Anchored Brownian motion and Bayesian methods for the analysis of single particle tracking data

We present a novel statistical method and a prototype computational implementation for estimating the diffusion coefficient from single particle tracking (SPT) data. Our method is based on anchored Brownian motion, which is a novel representation that relaxes the restrictions of conventional Brownian motion. In particular, rather than forcing the trajectories under analysis to pass through a fixed spatiotemporal origin that can bias SPT inference, our model introduces an explicit anchoring time and position that are uncertain and estimated simultaneously with the other quantities of SPT interest, avoiding the introduction of bias. Our method is fully developed in Bayesian terms and allows for robust estimation of the diffusion coefficient and quantification of the uncertainty propagated from limited data quantity and quality as appropriate for the analysis of live-cell SPT data. We compare our methods with conventional Brownian motion and demonstrate superior performance in estimating the correct value of the diffusion coefficient. Finally, we benchmark our methods with SPT data from in cellulo and in silico experiments.