The Distance Precision Matrix: computing networks from non-linear relationships.

MOTIVATION: Full-order partial correlation, a fundamental approach for network reconstruction, e.g. in the context of gene regulation, relies on the precision matrix (the inverse of the covariance matrix) as an indicator of which variables are directly associated. The precision matrix assumes Gaussian linear data and its entries are zero for pairs of variables that are independent given all other variables. However, there is still very little theory on network reconstruction under the assumption of non-linear interactions among variables. RESULTS: We propose Distance Precision Matrix, a network reconstruction method aimed at both linear and non-linear data. Like partial distance correlation, it builds on distance covariance, a measure of possibly non-linear association, and on the idea of full-order partial correlation, which allows to discard indirect associations. We provide evidence that the Distance Precision Matrix method can successfully compute networks from linear and non-linear data, and consistently so across different datasets, even if sample size is low. The method is fast enough to compute networks on hundreds of nodes. AVAILABILITY AND IMPLEMENTATION: An R package DPM is available at https://github.molgen.mpg.de/ghanbari/DPM. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Reconstruction of gene networks using prior knowledge.

BACKGROUND: Reconstructing gene regulatory networks (GRNs) from expression data is a challenging task that has become essential to the understanding of complex regulatory mechanisms in cells. The major issues are the usually very high ratio of number of genes to sample size, and the noise in the available data. Integrating biological prior knowledge to the learning process is a natural and promising way to partially compensate for the lack of reliable expression data and to increase the accuracy of network reconstruction algorithms. RESULTS: In this manuscript, we present PriorPC, a new algorithm based on the PC algorithm. PC algorithm is one of the most popular methods for Bayesian network reconstruction. The result of PC is known to depend on the order in which conditional independence tests are processed, especially for large networks. PriorPC uses prior knowledge to exclude unlikely edges from network estimation and introduces a particular ordering for the conditional independence tests. We show on synthetic data that the structural accuracy of networks obtained with PriorPC is greatly improved compared to PC. CONCLUSION: PriorPC improves structural accuracy of inferred gene networks by using soft priors which assign to edges a probability of existence. It is robust to false prior which is not avoidable in the context of biological data. PriorPC is also fast and scales well for large networks which is important for its applicability to real data.

Inference of interactions between chromatin modifiers and histone modifications: from ChIP-Seq data to chromatin-signaling.

Chromatin modifiers and histone modifications are components of a chromatin-signaling network involved in transcription and its regulation. The interactions between chromatin modifiers and histone modifications are often unknown, are based on the analysis of few genes or are studied in vitro. Here, we apply computational methods to recover interactions between chromatin modifiers and histone modifications from genome-wide ChIP-Seq data. These interactions provide a high-confidence backbone of the chromatin-signaling network. Many recovered interactions have literature support; others provide hypotheses about yet unknown interactions. We experimentally verified two of these predicted interactions, leading to a link between H4K20me1 and members of the Polycomb Repressive Complexes 1 and 2. Our results suggest that our computationally derived interactions are likely to lead to novel biological insights required to establish the connectivity of the chromatin-signaling network involved in transcription and its regulation.

Finding associations among histone modifications using sparse partial correlation networks.

Histone modifications are known to play an important role in the regulation of transcription. While individual modifications have received much attention in genome-wide analyses, little is known about their relationships. Some authors have built Bayesian networks of modifications, however most often they have used discretized data, and relied on unrealistic assumptions such as the absence of feedback mechanisms or hidden confounding factors. Here, we propose to infer undirected networks based on partial correlations between histone modifications. Within the partial correlation framework, correlations among two variables are controlled for associations induced by the other variables. Partial correlation networks thus focus on direct associations of histone modifications. We apply this methodology to data in CD4+ cells. The resulting network is well supported by common knowledge. When pairs of modifications show a large difference between their correlation and their partial correlation, a potential confounding factor is identified and provided as explanation. Data from different cell types (IMR90, H1) is also exploited in the analysis to assess the stability of the networks. The results are remarkably similar across cell types. Based on this observation, the networks from the three cell types are integrated into a consensus network to increase robustness. The data and the results discussed in the manuscript can be found, together with code, on http://spcn.molgen.mpg.de/index.html.

PROmiRNA: a new miRNA promoter recognition method uncovers the complex regulation of intronic miRNAs.

The regulation of intragenic miRNAs by their own intronic promoters is one of the open problems of miRNA biogenesis. Here, we describe PROmiRNA, a new approach for miRNA promoter annotation based on a semi-supervised statistical model trained on deepCAGE data and sequence features. We validate our results with existing annotation, PolII occupancy data and read coverage from RNA-seq data. Compared to previous methods PROmiRNA increases the detection rate of intronic promoters by 30%, allowing us to perform a large-scale analysis of their genomic features, as well as elucidate their contribution to tissue-specific regulation. PROmiRNA can be downloaded from http://promirna.molgen.mpg.de.

Estimation of pairwise sequence similarity of mammalian enhancers with word neighbourhood counts.

MOTIVATION: The identity of cells and tissues is to a large degree governed by transcriptional regulation. A major part is accomplished by the combinatorial binding of transcription factors at regulatory sequences, such as enhancers. Even though binding of transcription factors is sequence-specific, estimating the sequence similarity of two functionally similar enhancers is very difficult. However, a similarity measure for regulatory sequences is crucial to detect and understand functional similarities between two enhancers and will facilitate large-scale analyses like clustering, prediction and classification of genome-wide datasets. RESULTS: We present the standardized alignment-free sequence similarity measure N2, a flexible framework that is defined for word neighbourhoods. We explore the usefulness of adding reverse complement words as well as words including mismatches into the neighbourhood. On simulated enhancer sequences as well as functional enhancers in mouse development, N2 is shown to outperform previous alignment-free measures. N2 is flexible, faster than competing methods and less susceptible to single sequence noise and the occurrence of repetitive sequences. Experiments on the mouse enhancers reveal that enhancers active in different tissues can be separated by pairwise comparison using N2. CONCLUSION: N2 represents an improvement over previous alignment-free similarity measures without compromising speed, which makes it a good candidate for large-scale sequence comparison of regulatory sequences. AVAILABILITY: The software is part of the open-source C++ library SeqAn (www.seqan.de) and a compiled version can be downloaded at http://www.seqan.de/projects/alf.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Predicting the outcome of renal transplantation.

OBJECTIVE: Renal transplantation has dramatically improved the survival rate of hemodialysis patients. However, with a growing proportion of marginal organs and improved immunosuppression, it is necessary to verify that the established allocation system, mostly based on human leukocyte antigen matching, still meets today's needs. The authors turn to machine-learning techniques to predict, from donor-recipient data, the estimated glomerular filtration rate (eGFR) of the recipient 1 year after transplantation. DESIGN: The patient's eGFR was predicted using donor-recipient characteristics available at the time of transplantation. Donors' data were obtained from Eurotransplant's database, while recipients' details were retrieved from Charité Campus Virchow-Klinikum's database. A total of 707 renal transplantations from cadaveric donors were included. MEASUREMENTS: Two separate datasets were created, taking features with <10% missing values for one and <50% missing values for the other. Four established regressors were run on both datasets, with and without feature selection. RESULTS: The authors obtained a Pearson correlation coefficient between predicted and real eGFR (COR) of 0.48. The best model for the dataset was a Gaussian support vector machine with recursive feature elimination on the more inclusive dataset. All results are available at http://transplant.molgen.mpg.de/. LIMITATIONS: For now, missing values in the data must be predicted and filled in. The performance is not as high as hoped, but the dataset seems to be the main cause. CONCLUSIONS: Predicting the outcome is possible with the dataset at hand (COR=0.48). Valuable features include age and creatinine levels of the donor, as well as sex and weight of the recipient.

Histone modification levels are predictive for gene expression.

Histones are frequently decorated with covalent modifications. These histone modifications are thought to be involved in various chromatin-dependent processes including transcription. To elucidate the relationship between histone modifications and transcription, we derived quantitative models to predict the expression level of genes from histone modification levels. We found that histone modification levels and gene expression are very well correlated. Moreover, we show that only a small number of histone modifications are necessary to accurately predict gene expression. We show that different sets of histone modifications are necessary to predict gene expression driven by high CpG content promoters (HCPs) or low CpG content promoters (LCPs). Quantitative models involving H3K4me3 and H3K79me1 are the most predictive of the expression levels in LCPs, whereas HCPs require H3K27ac and H4K20me1. Finally, we show that the connections between histone modifications and gene expression seem to be general, as we were able to predict gene expression levels of one cell type using a model trained on another one.