Adaptive Mixture Modelling Metropolis Methods for Bayesian Analysis of Non-linear State-Space Models.

We describe a strategy for Markov chain Monte Carlo analysis of non-linear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis-Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the non-linearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.

Opening Basement Membrane Gaps During C. elegans Uterine-Vulval Attachment

The basement membrane (BM) is a highly conserved form of extracellular matrix that underlies or surrounds and supports most animal tissues. BMs are crossed by cells during various remodeling events in development, immune surveillance, or during cancer metastasis. Because BMs are dense and not easily penetrable, most of these cells must open a gap in order to facilitate their migration. The mechanisms by which cells execute these changes are poorly understood. A developmental event that requires the opening of a BM gap is C. elegans uterine-vulval connection. The anchor cell (AC), a specialized uterine cell, creates a de novo BM gap. Subsequent widening of the BM gap involves the underlying vulval precursor cells (VPCs) and the π cells, uterine neighbors of the AC through non-proteolytic BM sliding. Using forward and reverse genetic screening, transcriptome profiling, and live-cell imaging, I investigated how the cells in these tissues accomplish BM gap formation. In Chapter 2, I identify two potentially novel regulators of BM breaching, isolated through a large-scale forward genetic screen and characterize the invasion defect in these mutants. In Chapter 3, I describe single-cell transcriptome sequencing of the invasive AC. In Chapter 4, I describe the role of the π cells in opening the nascent BM gap. A complete developmental pathway for this process has been elucidated: the AC induces the π fate through Notch signaling, after which the π cells upregulate the Sec14 family protein CTG-1, which in turn restricts the trafficking of DGN-1 (dystroglycan), a laminin receptor, allowing the BM to slide. Chapter 5 outlines the implications of these discoveries.