Data-driven techniques for detecting dynamical state changes in noisily measured 3D single-molecule trajectories.

Christopher Calderon

doi:10.3390/molecules191118381

Christopher Calderon

Open Access

https://doi.org/10.3390/molecules191118381

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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.

Highlights

Single-molecule experiments have a rich history in both life and physical science investigations [1,2,3,4,5,6,7,8,9]
Recall that the vbSPT technique is a variational approximation to a classic hidden Markov Modeling (HMM) model; note that the current publicly available software implementation of vbSPT does not account for all statistical effects induced by Gaussian measurement noise and vbSPT relies on post analysis model selection criteria to select the number of hidden states
We show the vbSPT results obtained when the exact Data Generating Process (DGP) parameters are provided to the algorithm. (Recall that this algorithm was not tailored for this type of data and it consistently picks one state; the vbSPT technique is the most similar approach to the Hierarchical Dirichlet Processes (HDP)-SLDS commonly currently used by the single particle tracking (SPT) community in the author’s opinion.) As can be readily observed, the base measure parameters can strongly influence the state segmentation inference and a “properly tuned” HDP-SLDS state estimator can have impressive performance in detecting subtle changes in trajectories containing spatially dependent forces, thermal noise, and measurement noise

Summary

Introduction

Single-molecule experiments have a rich history in both life and physical science investigations [1,2,3,4,5,6,7,8,9]. A surge of publications in optical microscopy techniques applied to monitor single-molecules in live cells [11,21,22,23,24,25,26,27,28] has generated much excitement because recent advances in optical imaging allow researchers to (relatively) noninvasively monitor biological molecules in their native environment With both in vitro and in vivo single-molecule measurements, researchers must account for various complex features including inherent thermal fluctuations, inter- and intra-trajectory “heterogeneity” (induced by unresolved conformational degrees of freedom and/or a time changing micro-environment [29]), statistical artifacts introduced by the experimental apparatus, amongst other complications [10,11]

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