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

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, 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 focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. 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 subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763

Differential kinetochore protein requirements for establishment versus propagation of centromere activity in Saccharomyces cerevisiae

Dicentric chromosomes undergo a breakage–fusion–bridge cycle as a consequence of having two centromeres on the same chromatid attach to opposite spindle poles in mitosis. Suppression of dicentric chromosome breakage reflects loss of kinetochore function at the kinetochore–microtubule or the kinetochore–DNA interface. Using a conditionally functional dicentric chromosome in vivo, we demonstrate that kinetochore mutants exhibit quantitative differences in their degree of chromosome breakage. Mutations in chl4/mcm17/ctf17 segregate dicentric chromosomes through successive cell divisions without breakage, indicating that only one of the two centromeres is functional. Centromere DNA introduced into the cell is unable to promote kinetochore assembly in the absence of CHL4. In contrast, established centromeres retain their segregation capacity for greater than 25 generations after depletion of Chl4p. The persistent mitotic stability of established centromeres reveals the presence of an epigenetic component in kinetochore segregation. Furthermore, this study identifies Chl4p in the initiation and specification of a heritable chromatin state

Centromeric Heterochromatin: The Primordial Segregation Machine

Centromeres are specialized domains of heterochromatin that provide the foundation for the kinetochore. Centromeric heterochromatin is characterized by specific histone modifications, a centromere-specific histone H3 variant (CENP-A), and the enrichment of cohesin, condensin, and topo-isomerase II. Centromere DNA varies orders of magnitude in size from 125 bp (budding yeast) to several megabases (human). In metaphase, sister kinetochores on the surface of replicated chromosomes face away from each other, where they establish microtubule attachment and bi-orientation. Despite the disparity in centromere size, the distance between separated sister kinetochores is remarkably conserved (approximately 1 μm) throughout phylogeny. The centromere functions as a molecular spring that resists microtubule-based extensional forces in mitosis. This review explores the physical properties of DNA in order to understand how the molecular spring is built and how it contributes to the fidelity of chromosome segregation

Centromeres: unique chromatin structures that drive chromosome segregation

Fidelity during chromosome segregation is essential to prevent aneuploidy. The proteins and chromatin at the centromere form a unique site for kinetochore attachment and allow the cell to sense and correct errors during chromosome segregation. Centromeric chromatin is characterized by distinct chromatin organization, epigenetics, centromere-associated proteins and histone variants. These include the histone H3 variant centromeric protein A (CENPA), the composition and deposition of which have been widely investigated. Studies have examined the structural and biophysical properties of the centromere and have suggested that the centromere is not simply a ‘landing pad’ for kinetochore formation, but has an essential role in mitosis by assembling and directing the organization of the kinetochore

Lessons learned from counting molecules: how to lure CENP-A into the kinetochore

Chromosome segregation requires the assembly of a multi-protein complex at the centromere, known as the kinetochore, along with re-organization of the cytoskeleton from an anastomosing microtubule network into a highly polarized bipolar spindle. Electron microscopy of chemically preserve

The polarity and dynamics of microtubule assembly in the budding yeast Saccharomyces cerevisiae

Microtubule assembly in Saccharomyces cerevisiae is initiated from sites within spindle pole bodies (SPBs) in the nuclear envelope. Microtubule plus ends are thought to be organized distal to the SPBs, while minus ends are proximal. Several hypotheses for the function of microtubule motor proteins in force generation and regulation of microtubule assembly propose that assembly and disassembly occur at minus ends as well as at plus ends. Here we analyse microtubule assembly relative to the SPBs in haploid yeast cells expressing green fluorescent protein fused to α-tubulin, a microtubule subunit. Throughout the cell cycle, analysis of fluorescent speckle marks on cytoplasmic astral microtubules reveals that there is no detectable assembly or disassembly at minus ends. After laser-photobleaching, metaphase spindles recover about 63% of the bleached fluorescence, with a half-life of about 1 minute. After anaphase onset, photobleached marks in the interpolar spindle are persistent and do not move relative to the SPBs. In late anaphase, the elongated spindles disassemble at the microtubule plus ends. These results show for astral and anaphase interpolar spindle microtubules, and possibly for metaphase spindle microtubules, that microtubule assembly and disassembly occur at plus, and not minus, ends

Mechanisms of force generation by end-on kinetochore-microtubule attachments

Generation of motile force is one of the main functions of the eukaryotic kinetochore during cell division. In recent years, the KMN network of proteins (Ndc80 complex, Mis12 complex and KNL-1 complex) has emerged as a highly conserved core microtubule-binding complex at the kinetochore. It plays a major role in coupling force generation to microtubule plus-end polymerization and depolymerization. In this review, we discuss current theoretical mechanisms of force generation, and then focus on emerging information about mechanistic contributions from the Ndc80 complex in eukaryotes, and the microtubule-binding Dam1/DASH complex from fungi. New information has also become available from super-resolution light microscopy on the protein architecture of the kinetochore-microtubule attachment site in both budding yeast and humans, which provides further insight into the mechanism of force generation. We briefly discuss potential contributions of motors, other microtubule-associated proteins, and microtubule depolymerases. Using the above evidence, we present speculative models of force generation at the kinetochore

Design Features of a Mitotic Spindle: Balancing Tension and Compression at a Single Microtubule Kinetochore Interface in Budding Yeast

Accurate segregation of duplicated chromosomes ensures that daughter cells get one and only one copy of each chromosome. Errors in chromosome segregation result in aneuploidy and have severe consequences on human health. Incorrect chromosome number and chromosomal instability are hallmarks of tumor cells. Hence, segregation errors are thought to be a major cause of tumorigenesis. A study of the physical mechanical basis of chromosome segregation is essential to understand the processes that can lead to errors. Tremendous progress has been made in recent years in identifying the proteins necessary for chromosome movement and segregation, but the mechanism and structure of critical force generating components and the molecular basis of centromere stiffness remain poorly understood

Bending the Rules: Widefield Microscopy and the Abbe Limit of Resolution

One of the most fundamental concepts of microscopy is that of resolution–the ability to clearly distinguish two objects as separate. Recent advances such as structured illumination microscopy (SIM) and point localization techniques including photoactivated localization microscopy (PALM), and stochastic optical reconstruction microscopy (STORM) strive to overcome the inherent limits of resolution of the modern light microscope. These techniques, however, are not always feasible or optimal for live cell imaging. Thus, in this review, we explore three techniques for extracting high resolution data from images acquired on a widefield microscope–deconvolution, model convolution, and Gaussian fitting. Deconvolution is a powerful tool for restoring a blurred image using knowledge of the point spread function (PSF) describing the blurring of light by the microscope, although care must be taken to ensure accuracy of subsequent quantitative analysis. The process of model convolution also requires knowledge of the PSF to blur a simulated image which can then be compared to the experimentally acquired data to reach conclusions regarding its geometry and fluorophore distribution. Gaussian fitting is the basis for point localization microscopy, and can also be applied to tracking spot motion over time or measuring spot shape and size. All together, these three methods serve as powerful tools for high-resolution imaging using widefield microscopy