Data-Driven Techniques for Detecting Dynamical State Changes in Noisily Measured 3D Single-Molecule Trajectories

Abstract

Optical microscopes and nanoscale probes (AFM, optical tweezers, etc.) afford researchers tools capable of quantitatively exploring how molecules interact with one another in live cells. The analysis of in vivo single-molecule experimental data faces numerous challenges due to the complex, crowded, and time changing environments associated with live cells. Fluctuations and spatially varying systematic forces experienced by molecules change over time; these changes are obscured by “measurement noise” introduced by the experimental probe monitoring the system. In this article, we demonstrate how the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS) of Fox et al. [IEEE Transactions on Signal Processing 59] can be used to detect both subtle and abrupt state changes in time series containing “thermal” and “measurement” noise. The approach accounts for temporal dependencies induced by random and “systematic overdamped” forces. The technique does not require one to subjectively select the number of “hidden states” underlying a trajectory in an a priori fashion. The number of hidden states is simultaneously inferred along with change points and parameters characterizing molecular motion in a data-driven fashion. We use large scale simulations to study and compare the new approach to state-of-the-art Hidden Markov Modeling techniques. Simulations mimicking single particle tracking (SPT) experiments are the focus of this study.

Keywords

• single particle tracking
• hierarchical Dirichlet processes
• switching linear dynamical systems
• measurement/localization noise effects
• nonparametric Bayesian techniques
• prior sensitivity