MOTIVATION: Gaussian graphical models (GGMs) are network representations of random variables (as nodes) and their partial correlations (as edges). GGMs overcome the challenges of high-dimensional data analysis by using shrinkage methodologies. Therefore, they have become useful to reconstruct gene regulatory networks from gene-expression profiles. However, it is often ignored that the partial correlations are 'shrunk' and that they cannot be compared/assessed directly. Therefore, accurate (differential) network analyses need to account for the number of variables, the sample size, and also the shrinkage value, otherwise, the analysis and its biological interpretation would turn biased. To date, there are no appropriate methods to account for these factors and address these issues. RESULTS: We derive the statistical properties of the partial correlation obtained with the Ledoit-Wolf shrinkage. Our result provides a toolbox for (differential) network analyses as (i) confidence intervals, (ii) a test for zero partial correlation (null-effects) and (iii) a test to compare partial correlations. Our novel (parametric) methods account for the number of variables, the sample size and the shrinkage values. Additionally, they are computationally fast, simple to implement and require only basic statistical knowledge. Our simulations show that the novel tests perform better than DiffNetFDR-a recently published alternative-in terms of the trade-off between true and false positives. The methods are demonstrated on synthetic data and two gene-expression datasets from Escherichia coli and Mus musculus. AVAILABILITY AND IMPLEMENTATION: The R package with the methods and the R script with the analysis are available in https://github.com/V-Bernal/GeneNetTools. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: In systems biology, it is important to reconstruct regulatory networks from quantitative molecular profiles. Gaussian graphical models (GGMs) are one of the most popular methods to this end. A GGM consists of nodes (representing the transcripts, metabolites or proteins) inter-connected by edges (reflecting their partial correlations). Learning the edges from quantitative molecular profiles is statistically challenging, as there are usually fewer samples than nodes ('high dimensional problem'). Shrinkage methods address this issue by learning a regularized GGM. However, it remains open to study how the shrinkage affects the final result and its interpretation. RESULTS: We show that the shrinkage biases the partial correlation in a non-linear way. This bias does not only change the magnitudes of the partial correlations but also affects their order. Furthermore, it makes networks obtained from different experiments incomparable and hinders their biological interpretation. We propose a method, referred to as 'un-shrinking' the partial correlation, which corrects for this non-linear bias. Unlike traditional methods, which use a fixed shrinkage value, the new approach provides partial correlations that are closer to the actual (population) values and that are easier to interpret. This is demonstrated on two gene expression datasets from Escherichia coli and Mus musculus. CONCLUSIONS: GGMs are popular undirected graphical models based on partial correlations. The application of GGMs to reconstruct regulatory networks is commonly performed using shrinkage to overcome the 'high-dimensional problem'. Besides it advantages, we have identified that the shrinkage introduces a non-linear bias in the partial correlations. Ignoring this type of effects caused by the shrinkage can obscure the interpretation of the network, and impede the validation of earlier reported results.

MOTIVATION: Strand-seq is a specialized single-cell DNA sequencing technique centered around the directionality of single-stranded DNA. Computational tools for Strand-seq analyses must capture the strand-specific information embedded in these data. RESULTS: Here we introduce breakpointR, an R/Bioconductor package specifically tailored to process and interpret single-cell strand-specific sequencing data obtained from Strand-seq. We developed breakpointR to detect local changes in strand directionality of aligned Strand-seq data, to enable fine-mapping of sister chromatid exchanges, germline inversion and to support global haplotype assembly. Given the broad spectrum of Strand-seq applications we expect breakpointR to be an important addition to currently available tools and extend the accessibility of this novel sequencing technique. AVAILABILITY AND IMPLEMENTATION: R/Bioconductor package https://bioconductor.org/packages/breakpointR. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: One of the main goals in systems biology is to learn molecular regulatory networks from quantitative profile data. In particular, Gaussian graphical models (GGMs) are widely used network models in bioinformatics where variables (e.g. transcripts, metabolites or proteins) are represented by nodes, and pairs of nodes are connected with an edge according to their partial correlation. Reconstructing a GGM from data is a challenging task when the sample size is smaller than the number of variables. The main problem consists in finding the inverse of the covariance estimator which is ill-conditioned in this case. Shrinkage-based covariance estimators are a popular approach, producing an invertible 'shrunk' covariance. However, a proper significance test for the 'shrunk' partial correlation (i.e. the GGM edges) is an open challenge as a probability density including the shrinkage is unknown. In this article, we present (i) a geometric reformulation of the shrinkage-based GGM, and (ii) a probability density that naturally includes the shrinkage parameter. RESULTS: Our results show that the inference using this new 'shrunk' probability density is as accurate as Monte Carlo estimation (an unbiased non-parametric method) for any shrinkage value, while being computationally more efficient. We show on synthetic data how the novel test for significance allows an accurate control of the Type I error and outperforms the network reconstruction obtained by the widely used R package GeneNet. This is further highlighted in two gene expression datasets from stress response in Eschericha coli, and the effect of influenza infection in Mus musculus. AVAILABILITY AND IMPLEMENTATION: https://github.com/V-Bernal/GGM-Shrinkage. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: ChIP-chip and ChIP-seq technologies provide genome-wide measurements of various types of chromatin marks at an unprecedented resolution. With ChIP samples collected from different tissue types and/or individuals, we can now begin to characterize stochastic or systematic changes in epigenetic patterns during development (intra-individual) or at the population level (inter-individual). This requires statistical methods that permit a simultaneous comparison of multiple ChIP samples on a global as well as locus-specific scale. Current analytical approaches are mainly geared toward single sample investigations, and therefore have limited applicability in this comparative setting. This shortcoming presents a bottleneck in biological interpretations of multiple sample data. RESULTS: To address this limitation, we introduce a parametric classification approach for the simultaneous analysis of two (or more) ChIP samples. We consider several competing models that reflect alternative biological assumptions about the global distribution of the data. Inferences about locus-specific and genome-wide chromatin differences are reached through the estimation of multivariate mixtures. Parameter estimates are obtained using an incremental version of the Expectation-Maximization algorithm (IEM). We demonstrate efficient scalability and application to three very diverse ChIP-chip and ChIP-seq experiments. The proposed approach is evaluated against several published ChIP-chip and ChIP-seq software packages. We recommend its use as a first-pass algorithm to identify candidate regions in the epigenome, possibly followed by some type of second-pass algorithm to fine-tune detected peaks in accordance with biological or technological criteria. AVAILABILITY: R source code is available at http://gbic.biol.rug.nl/supplementary/2009/ChromatinProfiles/. Access to Chip-seq data: GEO repository GSE17937.