Bayesian Estimation of Diffusion Constants from Single Particle Tracking Data

Abstract

Single particle tracking (SPT) is an important tool for investigating the mobility of proteins on cell surfaces. Typically, the analysis of such trajectories involves the calculation of the Mean Squared Displacement (MSD) versus time interval and the resulting curve is fit to extract the diffusion constant. However, MSD analysis cannot easily handle correctly the variability in localization precisions and trajectory intermittency that occurs when tracking intermittent probes such as quantum dots. We have developed an analysis of SPT trajectories that takes into account the effects of missing data, finite exposure time of the camera, and variable localization precision. We have derived a recursion relation that can be used to calculate the probability of the observed trajectory given diffusion constant and the assumption of free Brownian motion. using the method of Bayesian data analysis, we calculate the posterior distribution of the diffusion constant and use this to provide credible intervals for the estimated parameter. We compare the performance of this Bayesian estimator with that of a traditional MSD analysis. In systems with large localization errors, the Bayesian method provides a more accurate estimate of the diffusion constant. We demonstrate the performance of the estimator using simulated data, experimental data collected with known trajectories created using a piezoelectric nanostage, and data collected from various membrane proteins on live cell membranes.