Uncovering Hidden Dynamics In Live-Cell Single Molecule Data With Bayesian Statistics

Single-molecule imaging techniques localize and track individual molecules inside living cells with nanometer precision and millisecond timing; this capability has allowed researchers to investigate many open questions across biology. However, single-molecule image analysis is fundamentally limited by a priori model selection, parameter unidentifiability, and other supervisory biases. To address these issues, we have developed an analysis framework for Single-Particle Tracking data based on nonparametric Bayesian inference. By encoding any information we have about the system into the “prior”, iteratively determining the maximal parameter values and data selection by the likelihood, and allowing the model to shrink and expand dynamically, we use the data itself to learn about the system and uncover properties or dynamics that would be hidden by other methods. This method offers a flexible and simple way to allow the data to dictate the appropriate model structure instead of having the experimenter impose a rigid structure beforehand. Here we first validate this method by determining (a) the number of diffusive populations, (b) the average diffusion coefficient for each term, (c) the population weight fraction for each term, and (d) the rates of conversion from one term to another in simulations of heterogeneous diffusion. We then extend our investigations to simple experimental systems, and finally we apply our algorithm to determine the model and dynamics of the membrane-bound keystone virulence protein TcpP in live Vibrio cholerae cells.