Sufficient burn-in for Gibbs samplers for a hierarchical random effects model

We consider Gibbs and block Gibbs samplers for a Bayesian hierarchical version of the one-way random effects model. Drift and minorization conditions are established for the underlying Markov chains. The drift and minorization are used in conjunction with results from J. S. Rosenthal [J. Amer. Statist. Assoc. 90 (1995) 558-566] and G. O. Roberts and R. L. Tweedie [Stochastic Process. Appl. 80 (1999) 211-229] to construct analytical upper bounds on the distance to stationarity. These lead to upper bounds on the amount of burn-in that is required to get the chain within a prespecified (total variation) distance of the stationary distribution. The results are illustrated with a numerical example

Evaluation of Formal posterior distributions via Markov chain arguments

We consider evaluation of proper posterior distributions obtained from improper prior distributions. Our context is estimating a bounded function $\phi$ of a parameter when the loss is quadratic. If the posterior mean of $\phi$ is admissible for all bounded $\phi$, the posterior is strongly admissible. We give sufficient conditions for strong admissibility. These conditions involve the recurrence of a Markov chain associated with the estimation problem. We develop general sufficient conditions for recurrence of general state space Markov chains that are also of independent interest. Our main example concerns the $p$-dimensional multivariate normal distribution with mean vector $\theta$ when the prior distribution has the form $g(\|\theta\|^2) d\theta$ on the parameter space $\mathbb{R}^p$. Conditions on $g$ for strong admissibility of the posterior are provided.Comment: Published in at http://dx.doi.org/10.1214/07-AOS542 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Appendix to "Approximating perpetuities"

An algorithm for perfect simulation from the unique solution of the distributional fixed point equation $Y=_d UY + U(1-U)$ is constructed, where $Y$ and $U$ are independent and $U$ is uniformly distributed on $[0,1]$. This distribution comes up as a limit distribution in the probabilistic analysis of the Quickselect algorithm. Our simulation algorithm is based on coupling from the past with a multigamma coupler. It has four lines of code

Two distinct types of neuronal asymmetries are controlled by the Caenorhabditis elegans zinc finger transcription factor die-1

Left/right asymmetric features of animals are either randomly distributed on either the left or right side within a population ("antisymmetries") or found stereotypically on one particular side of an animal ("directional asymmetries"). Both types of asymmetries can be found in nervous systems, but whether the regulatory programs that establish these asymmetries share any mechanistic features is not known. We describe here an unprecedented molecular link between these two types of asymmetries in Caenorhabditis elegans. The zinc finger transcription factor die-1 is expressed in a directionally asymmetric manner in the gustatory neuron pair ASE left (ASEL) and ASE right (ASER), while it is expressed in an antisymmetric manner in the olfactory neuron pair AWC left (AWCL) and AWC right (AWCR). Asymmetric die-1 expression is controlled in a fundamentally distinct manner in these two neuron pairs. Importantly, asymmetric die-1 expression controls the directionally asymmetric expression of gustatory receptor proteins in the ASE neurons and the antisymmetric expression of olfactory receptor proteins in the AWC neurons. These asymmetries serve to increase the ability of the animal to discriminate distinct chemosensory inputs

In-vivo evidence that high mobility group box 1 exerts deleterious effects in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine model and Parkinson's disease which can be attenuated by glycyrrhizin

Acknowledgements Samples were obtained from the Neuro Biobank of the University of Tuebingen, Germany (http://www.hih-tuebingen.de/nd/biobank/for-researchers/). This biobank is supported by the Hertie Institute and the DZNE. We are grateful to the staff of the Medical Research Facility for their help with the animal care. We thank Dr. Kinnari Sathe for her help with the experiments. We thank Claire A. Walker for assisting with western blot analysis. This study was supported by: Tenovus Scotland, Parkinson's Disease Foundation, Royal Society 2006/R1, NHS Endowment 14-42, and Wellcome Trust WT080782MF.Peer reviewedPublisher PD

Mesoscopic organization reveals the constraints governing C. elegans nervous system

One of the biggest challenges in biology is to understand how activity at the cellular level of neurons, as a result of their mutual interactions, leads to the observed behavior of an organism responding to a variety of environmental stimuli. Investigating the intermediate or mesoscopic level of organization in the nervous system is a vital step towards understanding how the integration of micro-level dynamics results in macro-level functioning. In this paper, we have considered the somatic nervous system of the nematode Caenorhabditis elegans, for which the entire neuronal connectivity diagram is known. We focus on the organization of the system into modules, i.e., neuronal groups having relatively higher connection density compared to that of the overall network. We show that this mesoscopic feature cannot be explained exclusively in terms of considerations, such as optimizing for resource constraints (viz., total wiring cost) and communication efficiency (i.e., network path length). Comparison with other complex networks designed for efficient transport (of signals or resources) implies that neuronal networks form a distinct class. This suggests that the principal function of the network, viz., processing of sensory information resulting in appropriate motor response, may be playing a vital role in determining the connection topology. Using modular spectral analysis, we make explicit the intimate relation between function and structure in the nervous system. This is further brought out by identifying functionally critical neurons purely on the basis of patterns of intra- and inter-modular connections. Our study reveals how the design of the nervous system reflects several constraints, including its key functional role as a processor of information.Comment: Published version, Minor modifications, 16 pages, 9 figure

HiNO: An Approach for Inferring Hierarchical Organization from Regulatory Networks

BACKGROUND: Gene expression as governed by the interplay of the components of regulatory networks is indeed one of the most complex fundamental processes in biological systems. Although several methods have been published to unravel the hierarchical structure of regulatory networks, weaknesses such as the incorrect or inconsistent assignment of elements to their hierarchical levels, the incapability to cope with cyclic dependencies within the networks or the need for a manual curation to retrieve non-overlapping levels remain unsolved. METHODOLOGY/RESULTS: We developed HiNO as a significant improvement of the so-called breadth-first-search (BFS) method. While BFS is capable of determining the overall hierarchical structures from gene regulatory networks, it especially has problems solving feed-forward type of loops leading to conflicts within the level assignments. We resolved these problems by adding a recursive correction approach consisting of two steps. First each vertex is placed on the lowest level that this vertex and its regulating vertices are assigned to (downgrade procedure). Second, vertices are assigned to the next higher level (upgrade procedure) if they have successors with the same level assignment and have themselves no regulators. We evaluated HiNO by comparing it with the BFS method by applying them to the regulatory networks from Saccharomyces cerevisiae and Escherichia coli, respectively. The comparison shows clearly how conflicts in level assignment are resolved in HiNO in order to produce correct hierarchical structures even on the local levels in an automated fashion. CONCLUSIONS: We showed that the resolution of conflicting assignments clearly improves the BFS-method. While we restricted our analysis to gene regulatory networks, our approach is suitable to deal with any directed hierarchical networks structure such as the interaction of microRNAs or the action of non-coding RNAs in general. Furthermore we provide a user-friendly web-interface for HiNO that enables the extraction of the hierarchical structure of any directed regulatory network. AVAILABILITY: HiNO is freely accessible at http://mips.helmholtz-muenchen.de/hino/

The transcriptional response of Caenorhabditis elegans to ivermectin exposure identifies novel genes involved in the response to reduced food intake

We have examined the transcriptional response of Caenorhabditis elegans following exposure to the anthelmintic drug ivermectin (IVM) using whole genome microarrays and real-time QPCR. Our original aim was to identify candidate molecules involved in IVM metabolism and/or excretion. For this reason the IVM tolerant strain, DA1316, was used to minimise transcriptomic changes related to the phenotype of drug exposure. However, unlike equivalent work with benzimidazole drugs, very few of the induced genes were members of xenobiotic metabolising enzyme families. Instead, the transcriptional response was dominated by genes associated with fat mobilization and fatty acid metabolism including catalase, esterase, and fatty acid CoA synthetase genes. This is consistent with the reduction in pharyngeal pumping, and consequential reduction in food intake, upon exposure of DA1316 worms to IVM. Genes with the highest fold change in response to IVM exposure, cyp-37B1, mtl-1 and scl-2, were comparably up-regulated in response to short–term food withdrawal (4 hr) independent of IVM exposure, and GFP reporter constructs confirm their expression in tissues associated with fat storage (intestine and hypodermis). These experiments have serendipitously identified novel genes involved in an early response of C. elegans to reduced food intake and may provide insight into similar processes in higher organisms

A Genome-Wide RNAi Screen for Factors Involved in Neuronal Specification in Caenorhabditis elegans

One of the central goals of developmental neurobiology is to describe and understand the multi-tiered molecular events that control the progression of a fertilized egg to a terminally differentiated neuron. In the nematode Caenorhabditis elegans, the progression from egg to terminally differentiated neuron has been visually traced by lineage analysis. For example, the two gustatory neurons ASEL and ASER, a bilaterally symmetric neuron pair that is functionally lateralized, are generated from a fertilized egg through an invariant sequence of 11 cellular cleavages that occur stereotypically along specific cleavage planes. Molecular events that occur along this developmental pathway are only superficially understood. We take here an unbiased, genome-wide approach to identify genes that may act at any stage to ensure the correct differentiation of ASEL. Screening a genome-wide RNAi library that knocks-down 18,179 genes (94% of the genome), we identified 245 genes that affect the development of the ASEL neuron, such that the neuron is either not generated, its fate is converted to that of another cell, or cells from other lineage branches now adopt ASEL fate. We analyze in detail two factors that we identify from this screen: (1) the proneural gene hlh-14, which we find to be bilaterally expressed in the ASEL/R lineages despite their asymmetric lineage origins and which we find is required to generate neurons from several lineage branches including the ASE neurons, and (2) the COMPASS histone methyltransferase complex, which we find to be a critical embryonic inducer of ASEL/R asymmetry, acting upstream of the previously identified miRNA lsy-6. Our study represents the first comprehensive, genome-wide analysis of a single neuronal cell fate decision. The results of this analysis provide a starting point for future studies that will eventually lead to a more complete understanding of how individual neuronal cell types are generated from a single-cell embryo