Bayesian Inference to Discriminate Motion Models from Particle Trajectories

Abstract

Quantitative analysis of particle motion from particle tracking datasets--such as cell trajectories during embryonic development, receptor dynamics in cell membranes, and chromosome and kinetochore motions during spindle assembly--is a powerful approach to revealing the mechanism of transport in biological systems. However, inferring motion models from single-particle trajectories (SPTs) is non-trivial due to noise from both sampling limitations and heterogeneity in biological samples. We present two complementary approaches based on Bayesian inference to perform objective and automated analysis of SPTs. The first is a multiple hypothesis testing approach to determine the most likely mode of motion from mean-square displacement (MSD) curves derived from particle trajectories. This approach handles a large set of competing motion models--including diffusion, anomalous diffusion, confined diffusion, and directed motion--and determines which model is most justified by the evidence present in the available MSD curves. Because noise in MSD curves is highly correlated, we find that explicitly modeling the noise covariance matrix using multiple independent curves is essential for accurately determining model probabilities. The second approach fits raw particle trajectories with a Hidden Markov Model (HMM) to determine the most likely diffusion coefficient and velocity at each step along a trajectory, enabling the identification of transient motion states and dynamic transitions between motion models. These methods avoid overfitting by using an objective Bayesian framework to penalize model complexity and account for noise. These automated methods naturally scale to large numbers of particle trajectories, making them ideal for classifying motion in high-throughput screens of SPTs.