Motivation: Reconstruction of gene regulatory networks (GRNs), which explicitly represent the causality of developmental or regulatory process, is of utmost interest and has become a challenging computational problem for understanding the complex regulatory mechanisms in cellular systems. However, all existing methods of inferring GRNs from gene expression profiles have their strengths and weaknesses. In particular, many properties of GRNs, such as topology sparseness and non-linear dependence, are generally in regulation mechanism but seldom are taken into account simultaneously in one computational method.Results: In this work, we present a novel method for inferring GRNs from gene expression data considering the non-linear dependence and topological structure of GRNs by employing path consistency algorithm (PCA) based on conditional mutual information (CMI). In this algorithm, the conditional dependence between a pair of genes is represented by the CMI between them. With the general hypothesis of Gaussian distribution underlying gene expression data, CMI between a pair of genes is computed by a concise formula involving the covariance matrices of the related gene expression profiles. The method is validated on the benchmark GRNs from the DREAM challenge and the widely used SOS DNA repair network in Escherichia coli. The cross-validation results confirmed the effectiveness of our method (PCA-CMI), which outperforms significantly other previous methods. Besides its high accuracy, our method is able to distinguish direct (or causal) interactions from indirect associations.Availability: All the source data and code are available at: http://csb.shu.edu.cn/subweb/grn.htm.Contact: lnchen@sibs.ac.cn; zpliu@sibs.ac.cnSupplementary information: Supplementary data are available at Bioinformatics online.

Quantitatively identifying direct dependencies between variables is an important task in data analysis, in particular for reconstructing various types of networks and causal relations in science and engineering. One of the most widely used criteria is partial correlation, but it can only measure linearly direct association and miss nonlinear associations. However, based on conditional independence, conditional mutual information (CMI) is able to quantify nonlinearly direct relationships among variables from the observed data, superior to linear measures, but suffers from a serious problem of underestimation, in particular for those variables with tight associations in a network, which severely limits its applications. In this work, we propose a new concept, “partial independence,” with a new measure, “part mutual information” (PMI), which not only can overcome the problem of CMI but also retains the quantification properties of both mutual information (MI) and CMI. Specifically, we first defined PMI to measure nonlinearly direct dependencies between variables and then derived its relations with MI and CMI. Finally, we used a number of simulated data as benchmark examples to numerically demonstrate PMI features and further real gene expression data from Escherichia coli and yeast to reconstruct gene regulatory networks, which all validated the advantages of PMI for accurately quantifying nonlinearly direct associations in networks.

Mutual information (MI), a quantity describing the nonlinear dependence between two random variables, has been widely used to construct gene regulatory networks (GRNs). Despite its good performance, MI cannot separate the direct regulations from indirect ones among genes. Although the conditional mutual information (CMI) is able to identify the direct regulations, it generally underestimates the regulation strength, i.e. it may result in false negatives when inferring gene regulations. In this work, to overcome the problems, we propose a novel concept, namely conditional mutual inclusive information (CMI2), to describe the regulations between genes. Furthermore, with CMI2, we develop a new approach, namely CMI2NI (CMI2-based network inference), for reverse-engineering GRNs. In CMI2NI, CMI2 is used to quantify the mutual information between two genes given a third one through calculating the Kullback–Leibler divergence between the postulated distributions of including and excluding the edge between the two genes. The benchmark results on the GRNs from DREAM challenge as well as the SOS DNA repair network in Escherichia coli demonstrate the superior performance of CMI2NI. Specifically, even for gene expression data with small sample size, CMI2NI can not only infer the correct topology of the regulation networks but also accurately quantify the regulation strength between genes. As a case study, CMI2NI was also used to reconstruct cancer-specific GRNs using gene expression data from The Cancer Genome Atlas (TCGA). CMI2NI is freely accessible at http://www.comp-sysbio.org/cmi2ni.

Motivation: Reconstruction of gene regulatory networks (GRNs) is of utmost interest to biologists and is vital for understanding the complex regulatory mechanisms within the cell. Despite various methods developed for reconstruction of GRNs from gene expression profiles, they are notorious for high false positive rate owing to the noise inherited in the data, especially for the dataset with a large number of genes but a small number of samples.Results: In this work, we present a novel method, namely NARROMI, to improve the accuracy of GRN inference by combining ordinary differential equation-based recursive optimization (RO) and information theory-based mutual information (MI). In the proposed algorithm, the noisy regulations with low pairwise correlations are first removed by using MI, and the redundant regulations from indirect regulators are further excluded by RO to improve the accuracy of inferred GRNs. In particular, the RO step can help to determine regulatory directions without prior knowledge of regulators. The results on benchmark datasets from Dialogue for Reverse Engineering Assessments and Methods challenge and experimentally determined GRN of Escherichia coli show that NARROMI significantly outperforms other popular methods in terms of false positive rates and accuracy.Availability: All the source data and code are available at: http://csb.shu.edu.cn/narromi.htm.Contact: lnchen@sibs.ac.cn, hao@info.univ-angers.fr and zhaoxingming@gmail.com.Supplementary information: Supplementary data are available at Bioinformatics online.