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Abstract. The existing approaches used to identify the relevant pathways in a given condition do not consider a number of important biological factors such as magnitude of each gene’s expression change, their position and interactions in the given pathways, etc. Recently, an impact analysis approach was proposed that considers these crucial biological factors to analyze regulatory pathways at systems biology level. This approach calculates perturbations induced by each gene in a pathway, and propagates them through the entire pathway to compute an impact factor for the given pathway. Here we propose an alternative approach that uses a linear system to compute the impact factor. Our proposed approach eliminates the possible stability problems when the perturbations are propagated through a pathway that contains positive feedback loops. Additionally, the proposed approach is able to consider the type of genes when calculating the impact factors. 1

Consider the gene ranking problem of replicated microarray time course experiments where there are multiple biological conditions, and genes of interest are those whose temporal profiles are different across conditions. We derive the multi-sample multivariate empirical Bayes statistic for rank-ing genes in the order of differential expression, from both longitudinal and cross-sectional replicated developmental microarray time course data. Our longitudinal multi-sample model assumes that time course replicates are i.i.d. multivariate normal vectors. On the other hand, we construct our cross-sectional model using a normal regression framework with any appro-priate basis for the design matrices. In both cases, we use natural conjugate priors in our empirical Bayes setting which guarantee closed form solutions 1 for the posterior odds. Our simulations and two case studies using pub-lished worm and mouse microarray time course datasets indicate that the proposed approaches work well.

BATS is a user-friendly software for Bayesian Analysis of Time Series microarray experiments based on the novel, truly functional and fully Bayesian approach proposed in Angelini et at. (2006). The software is specifically designed for time series data. It allows an user to automatically identify and rank differentially expressed genes and to estimate their expression profiles. BATS successfully manages various technical difficulties which arise in microarray time-course experiments, such as a small number of observations, non-uniform sampling intervals, and presence of missing or multiple data. BATS can carry out analysis with both simulated and real experimental data. It also handles data from different platforms. 1 Availability: BATS is written in Matlab and executable in Windows (Macintosh and Linux version are currently under development). It is freely available upon request from the authors. 1

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application in solanaceous species

Research article

The vegetative cells of the filamentous cyanobacterium Nostoc punctiforme can differentiate into three mutually exclusive cell types: nitrogen-fixing heterocysts, spore-like akinetes, and motile hormogomium filaments. A DNA microarray consisting of 6,893 N. punctiforme genes was used to identify the global transcription patterns at single time points in the three developmental states, compared to those in ammonium-grown time zero cultures. Analysis of ammonium-grown cultures yielded a transcriptome of 2,935 genes, which is nearly twice the size of a soluble proteome. The NH4-grown transcriptome was enriched in genes encoding core metabolic functions. A steady-state N2-grown (heterocyst-containing) culture showed differential transcription of 495 genes, 373 of which were up-regulated. The majority of the up-regulated genes were predicted from studies of heterocyst differentiation and N2 fixation; other genes are candidates for more detailed genetic analysis. Three days into the developmental process, akinetes showed a similar number of differentially expressed genes (497 genes), which were equally up- and down-regulated. The down-regulated genes were enriched in core metabolic functions, consistent with entry into a nongrowth state. There were relatively few adaptive genes up-regulated in 3-day akinetes, and there was little overlap with putative heterocyst developmental genes. There were 1,827 differentially transcribed genes in 24-h hormogonia, which was nearly fivefold greater than the number in akinete-forming or N2-fixing cultures. The majority of the up-regulated adaptive

DNA microarray experiments provide a high throughput way to measure mRNA levels of thousands of genes simultaneously. This technology has been refined during the last 10 years and is now an important tool for molecular biologists. From a statistical point of view, the analysis of data generated with DNA microarrays is far from straightforward. The experiments involve several consecutive steps, each inducing systematic effects and differences in precision. Moreover, microarrays are both time consuming and expensive, so only few replicates are usually made. Thus, thousands of variables are observed only a few times each and there is a pressing need for quality assessments, which makes traditional statistical methods unsuitable. In this thesis a new method for analysis of paired DNA microarray experiments is presented. The method is based on a generalised linear model with a variance structure which consists of both a gene-independent covariance matrix and a gene-dependent scaling factor. To increase the precision, the latter is assumed to follow a prior distribution with a shape hyperparameter. These assumption makes the method suitable for handling data with quality variations and/or few replicates. Estimators for the covariance matrix as well as the hyperparameter are constructed and general likelihood ratio tests for differentially expressed genes are derived. Simulated datasets are used to show that the method