Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments.

Christopher P Calderon,Kerry Bloom,Yanchang Wang

doi:10.1371/journal.pone.0137633

Christopher P Calderon, Kerry Bloom + Show 1 more

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https://doi.org/10.1371/journal.pone.0137633

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Abstract

Understanding the basis for intracellular motion is critical as the field moves toward a deeper understanding of the relation between Brownian forces, molecular crowding, and anisotropic (or isotropic) energetic forcing. Effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study discusses limitations in currently popular analysis methods (e.g., mean square displacement-based analyses) and how new techniques can be used to systematically analyze Single Particle Tracking (SPT) data experiencing abrupt state changes in time or space. The approach is to track GFP tagged chromatids in metaphase in live yeast cells and quantitatively probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes can be induced by various sources including: microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, and DNA-based molecular machines including polymerases and protein exchange complexes such as chaperones and chromatin remodeling complexes. Simulations aiming to show the relevance of the approach to more general SPT data analyses are also studied. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for “ground-truth” and/or subjective information.

Highlights

We demonstrate how the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS) framework developed by Fox and co-workers [32] can be used to deduce the direction and magnitude of different forces that contribute to molecular motion in living cells [23]
We have demonstrated the utility of the HDP-SLDS method of Fox et al [32] in automatically segmenting Single Particle Tracking (SPT) data into different dynamical regimes
When applied to experimental data, we demonstrated how new quantitative information can be extracted about transient forces experienced during mitosis in live yeast cells; the method explicitly accounts for the statistical effects of measurement noise on top of “thermal” or “process” noise

Summary

Introduction

Recent advances in optical microscopy [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] have inspired numerous analysis methods aiming to quantify the motion of individual molecules in live cells [17,18,19,20,21,22,23,24,25,26,27,28,29]. The resolution afforded by current optical microscopes allows researchers to more reliably measure two-dimensional (2D) [17, 27, 28] and three-dimensional (3D) [23] position vs time data in Single Particle Tracking (SPT) experiments. This permits researchers to probe in vivo forces without introducing external perturbations into the system. We demonstrate how the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS) framework developed by Fox and co-workers [32] can be used to deduce the direction and magnitude of different forces that contribute to molecular motion in living cells [23]. The approach presented shows promise in both (I) accelerating the scientific discovery process (i.e., statistically significant changes in dynamics can be reliably detected) and (II) automating preprocessing tasks required when analyzing and segmenting large SPT data sets

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