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: 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.

UNLABELLED: Warp2D is a novel time alignment approach, which uses the overlapping peak volume of the reference and sample peak lists to correct misleading peak shifts. Here, we present an easy-to-use web interface for high-throughput Warp2D batch processing time alignment service using the Dutch Life Science Grid, reducing processing time from days to hours. This service provides the warping function, the sample chromatogram peak list with adjusted retention times and normalized quality scores based on the sum of overlapping peak volume of all peaks. Heat maps before and after time alignment are created from the arithmetic mean of the sum of overlapping peak area rearranged with hierarchical clustering, allowing the quality control of the time alignment procedure. Taverna workflow and command line tool are provided for remote processing of local user data. AVAILABILITY: online data processing service is available at http://www.nbpp.nl/warp2d.html. Taverna workflow is available at myExperiment with title '2D Time Alignment-Webservice and Workflow' at http://www.myexperiment.org/workflows/1283.html. Command line tool is available at http://www.nbpp.nl/Warp2D_commandline.zip. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Mass spectrometry data are subjected to considerable noise. Good noise models are required for proper detection and quantification of peptides. We have characterized noise in both quadrupole time-of-flight (Q-TOF) and ion trap data, and have constructed models for the noise. RESULTS: We find that the noise in Q-TOF data from Applied Biosystems QSTAR fits well to a combination of multinomial and Poisson model with detector dead-time correction. In comparison, ion trap noise from Agilent MSD-Trap-SL is larger than the Q-TOF noise and is proportional to Poisson noise. We then demonstrate that the noise model can be used to improve deisotoping for peptide detection, by estimating appropriate cutoffs of the goodness of fit parameter at prescribed error rates. The noise models also have implications in noise reduction, retention time alignment and significance testing for biomarker discovery.