Basic properties and information theory of Audic-Claverie statistic for analyzing cDNA arrays

Background  

The Audic-Claverie method [1] has been and still continues to be a popular approach for detection of differentially expressed genes in the SAGE framework. The method is based on the assumption that under the null hypothesis tag counts of the same gene in two libraries come from the same but unknown Poisson distribution. The problem is that each SAGE library represents only a single measurement. We ask: Given that the tag count samples from SAGE libraries are extremely limited, how useful actually is the Audic-Claverie methodology? We rigorously analyze the A-C statistic that forms a backbone of the methodology and represents our knowledge of the underlying tag generating process based on one observation.     

A seriation approach for visualization-driven discovery of co-expression patterns in Serial Analysis of Gene Expression (SAGE) data

Background

Serial Analysis of Gene Expression (SAGE) is a DNA sequencing-based method for large-scale gene expression profiling that provides an alternative to microarray analysis. Most analyses of SAGE data aimed at identifying co-expressed genes have been accomplished using various versions of clustering approaches that often result in a number of false positives.

Principal Findings

Here we explore the use of seriation, a statistical approach for ordering sets of objects based on their similarity, for large-scale expression pattern discovery in SAGE data. For this specific task we implement a seriation heuristic we term ‘progressive construction of contigs’ that constructs local chains of related elements by sequentially rearranging margins of the correlation matrix. We apply the heuristic to the analysis of simulated and experimental SAGE data and compare our results to those obtained with a clustering algorithm developed specifically for SAGE data. We show using simulations that the performance of seriation compares favorably to that of the clustering algorithm on noisy SAGE data.

Conclusions

We explore the use of a seriation approach for visualization-based pattern discovery in SAGE data. Using both simulations and experimental data, we demonstrate that seriation is able to identify groups of co-expressed genes more accurately than a clustering algorithm developed specifically for SAGE data. Our results suggest that seriation is a useful method for the analysis of gene expression data whose applicability should be further pursued.     

Overdispersed logistic regression for SAGE: Modelling multiple groups and covariates

Background  

Two major identifiable sources of variation in data derived from the Serial Analysis of Gene Expression (SAGE) are within-library sampling variability and between-library heterogeneity within a group. Most published methods for identifying differential expression focus on just the sampling variability. In recent work, the problem of assessing differential expression between two groups of SAGE libraries has been addressed by introducing a beta-binomial hierarchical model that explicitly deals with both of the above sources of variation. This model leads to a test statistic analogous to a weighted two-sample t-test. When the number of groups involved is more than two, however, a more general approach is needed.     

A comparative analysis of the information content in long and short SAGE libraries

Background  

Serial Analysis of Gene Expression (SAGE) is a powerful tool to determine gene expression profiles. Two types of SAGE libraries, ShortSAGE and LongSAGE, are classified based on the length of the SAGE tag (10 vs. 17 basepairs). LongSAGE libraries are thought to be more useful than ShortSAGE libraries, but their information content has not been widely compared. To dissect the differences between these two types of libraries, we utilized four libraries (two LongSAGE and two ShortSAGE libraries) generated from the hippocampus of Alzheimer and control samples. In addition, we generated two additional short SAGE libraries, the truncated long SAGE libraries (tSAGE), from LongSAGE libraries by deleting seven 5' basepairs from each LongSAGE tag.     

A feature selection approach for identification of signature genes from SAGE data

Background  

One goal of gene expression profiling is to identify signature genes that robustly distinguish different types or grades of tumors. Several tumor classifiers based on expression profiling have been proposed using microarray technique. Due to important differences in the probabilistic models of microarray and SAGE technologies, it is important to develop suitable techniques to select specific genes from SAGE measurements.     

Accurate and unambiguous tag-to-gene mapping in serial analysis of gene expression

Background  

In this study, we present a robust and reliable computational method for tag-to-gene assignment in serial analysis of gene expression (SAGE). The method relies on current genome information and annotation, incorporation of several new features, and key improvements over alternative methods, all of which are important to determine gene expression levels more accurately. The method provides a complete annotation of potential virtual SAGE tags within a genome, along with an estimation of their confidence for experimental observation that ranks tags that present multiple matches in the genome.     

Discarding duplicate ditags in LongSAGE analysis may introduce significant error

Background  

During gene expression analysis by Serial Analysis of Gene Expression (SAGE), duplicate ditags are routinely removed from the data analysis, because they are suspected to stem from artifacts during SAGE library construction. As a consequence, naturally occurring duplicate ditags are also removed from the analysis leading to an error of measurement.     

Simulation methods with extended stability for stiff biochemical Kinetics

Background  

With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of individual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ, whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ-leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows.     

SAGE: String-overlap Assembly of GEnomes

Background

De novo genome assembly of next-generation sequencing data is one of the most important current problems in bioinformatics, essential in many biological applications. In spite of significant amount of work in this area, better solutions are still very much needed.

Results

We present a new program, SAGE, for de novo genome assembly. As opposed to most assemblers, which are de Bruijn graph based, SAGE uses the string-overlap graph. SAGE builds upon great existing work on string-overlap graph and maximum likelihood assembly, bringing an important number of new ideas, such as the efficient computation of the transitive reduction of the string overlap graph, the use of (generalized) edge multiplicity statistics for more accurate estimation of read copy counts, and the improved use of mate pairs and min-cost flow for supporting edge merging. The assemblies produced by SAGE for several short and medium-size genomes compared favourably with those of existing leading assemblers.

Conclusions

SAGE benefits from innovations in almost every aspect of the assembly process: error correction of input reads, string-overlap graph construction, read copy counts estimation, overlap graph analysis and reduction, contig extraction, and scaffolding. We hope that these new ideas will help advance the current state-of-the-art in an essential area of research in genomics.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-302) contains supplementary material, which is available to authorized users.     

Modeling the distribution of new MRI cortical lesions in multiple sclerosis longitudinal studies

Objective

Recent studies have shown the relevance of the cerebral grey matter involvement in multiple sclerosis (MS). The number of new cortical lesions (CLs), detected by specific MRI sequences, has the potential to become a new research outcome in longitudinal MS studies. Aim of this study is to define the statistical model better describing the distribution of new CLs developed over 12 and 24 months in patients with relapsing-remitting (RR) MS.

Methods

Four different models were tested (the Poisson, the Negative Binomial, the zero-inflated Poisson and the zero-inflated Negative Binomial) on a group of 191 RRMS patients untreated or treated with 3 different disease modifying therapies. Sample size for clinical trials based on this new outcome measure were estimated by a bootstrap resampling technique.

Results

The zero-inflated Poisson model gave the best fit, according to the Akaike criterion to the observed distribution of new CLs developed over 12 and 24 months both in each treatment group and in the whole RRMS patients group adjusting for treatment effect.

Conclusions

The sample size calculations based on the zero-inflated Poisson model indicate that randomized clinical trials using this new MRI marker as an outcome are feasible.     

Transcriptional profiling of inductive mesenchyme to identify molecules involved in prostate development and disease

Background  

The mesenchymal compartment plays a key role in organogenesis, and cells within the mesenchyme/stroma are a source of potent molecules that control epithelia during development and tumorigenesis. We used serial analysis of gene expression (SAGE) to profile a key subset of prostatic mesenchyme that regulates prostate development and is enriched for growth-regulatory molecules.     

Limitations of Poisson statistics in describing radioactive decay

ObjectivesThe assumption that nuclear decays are governed by Poisson statistics is an approximation. This approximation becomes unjustified when data acquisition times longer than or even comparable with the half-lives of the radioisotope in the sample are considered. In this work, the limits of the Poisson-statistics approximation are investigated.MethodsThe formalism for the statistics of radioactive decay based on binomial distribution is derived. The theoretical factor describing the deviation of variance of the number of decays predicated by the Poisson distribution from the true variance is defined and investigated for several commonly used radiotracers such as ¹⁸F, ¹⁵O, ⁸²Rb, ¹³N, ^99mTc, ¹²³I, and ²⁰¹Tl.ResultsThe variance of the number of decays estimated using the Poisson distribution is significantly different than the true variance for a 5-minute observation time of ¹¹C, ¹⁵O, ¹³N, and ⁸²Rb.ConclusionsDurations of nuclear medicine studies often are relatively long; they may be even a few times longer than the half-lives of some short-lived radiotracers. Our study shows that in such situations the Poisson statistics is unsuitable and should not be applied to describe the statistics of the number of decays in radioactive samples. However, the above statement does not directly apply to counting statistics at the level of event detection. Low sensitivities of detectors which are used in imaging studies make the Poisson approximation near perfect.