articleTimeDelay-ARACNE : Reverse engineering of gene networks from time-course data by an information theoretic approach

Background: One of main aims of Molecular Biology is the gain of knowledge about how molecular components interact each other and to understand gene function regulations. Using microarray technology, it is possible to extract measurements of thousands of genes into a single analysis step having a picture of the cell gene expression. Several methods have been developed to infer gene networks from steady-state data, much less literature is produced about time-course data, so the development of algorithms to infer gene networks from time-series measurements is a current challenge into bioinformatics research area. In order to detect dependencies between genes at different time delays, we propose an approach to infer gene regulatory networks from time-series measurements starting from a well known algorithm based on information theory. Results: In this paper we show how the ARACNE (Algorithm for the Reconstruction of Accurate Cellular Networks) algorithm can be used for gene regulatory network inference in the case of time-course expression profiles. The resulting method is called TimeDelay-ARACNE. It just tries to extract dependencies between two genes at different time delays, providing a measure of these dependencies in terms of mutual information. The basic idea of the proposed algorithm is to detect time-delayed dependencies between the expression profiles by assuming as underlying probabilistic model a stationary Markov Random Field. Less informative dependencies are filtered out using an auto calculated threshold, retaining most reliable connections. TimeDelay-ARACNE can infer small local networks of time regulated gene-gene interactions detecting their versus and also discovering cyclic interactions also when only a medium-small number of measurements are available. We test the algorithm both on synthetic networks and on microarray expression profiles. Microarray measurements concern S. cerevisiae cell cycle, E. coli SOS pathways and a recently developed network for in vivo assessment of reverse engineering algorithms. Our results are compared with ARACNE itself and with the ones of two previously published algorithms: Dynamic Bayesian Networks and systems of ODEs, showing that TimeDelay-ARACNE has good accuracy, recall and F-score for the network reconstruction task. Conclusions: Here we report the adaptation of the ARACNE algorithm to infer gene regulatory networks from timecourse data, so that, the resulting network is represented as a directed graph. The proposed algorithm is expected to be useful in reconstruction of small biological directed networks from time course data. Background In order to understand cellular complexity much attention is placed on large dynamic networks of co-regulated genes at the base of phenotype differences. One of the aims in molecular biology is to make sense of highthroughput data like that from microarray of gene expression experiments. Many important biological processes (e.g., cellular differentiation during development, aging, disease aetiology etc.) are very unlikely controlled by a single gene instead by the underlying complex regulatory interactions between thousands of genes within a fourdimension space. In order to identify these interactions, expression data over time can be exploited. An important open question is related to the development of efficient methods to infer the underlying gene regulation networks (GRN) from temporal gene expression profiles. Inferring, * Correspondence: ceccarelli@unisannio.it 1 Department of Biological and Environmental Studies, University of Sannio, Benevento, I-82100, Italy Full list of author information is available at the end of the article BioMed Central © 2010 Zoppoli et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Zoppoli et al. BMC Bioinformatics 2010, 11:154 http://www.biomedcentral. com/1471-2105/11/154 Page 2 of 15 or reverse-engineering, gene networks can be defined as the process of identifying gene interactions from experimental data through computational analysis. A GRN can be modelled as a graph G = (V, U, D), where V is the set of nodes corresponding to genes, U is the set of unordered pair (undirected edges) and D is the set of ordered pairs D (directed edges). A directed edge dij from vi to vj is present iff there is a causal effect from node vi to node vj. An undirected edge uij represents the mutual association between nodes vi and vj. Gene expression data from microarrays are typically used for this purpose. There are two broad classes of reverse-engineering algorithms [1]: those based on the physical interaction approach which aim at identifying interactions among transcription factors and their target genes (gene-to-sequence interaction) and those based on the influence interaction approach that try to relate the expression of a gene to the expression of the other genes in the cell (gene-to-gene interaction), rather than relating it to sequence motifs found in the promoters. We will refer to the ensemble of these influence interactions as gene networks. Many algorithms have been proposed in the literature to model gene regulatory networks [2] and solve the network inference problem [3]. Ordinary Differential Equations Reverse-engineering algorithms based on ordinary differential equations (ODEs) relate changes in gene transcript concentration to each other and to an external perturbation. Typical perturbations can be for example the treatment with a chemical compound (i.e. a drug), or the over expression or down regulation of particular genes. A set of ODEs, one for each gene, describes gene regulation as a function of other genes. As ODEs are deterministic, the interactions among genes represent causal interactions, rather than statistical dependencies. The ODE-based approaches yield signed directed graphs and can be applied to both steady-state and time-series expression profiles [3,4]. Bayesian Networks A Bayesian network [5] is a graphical model for representing probabilistic relationships among a set of random variables Xi, where i = 1, , n. These relationships are encoded in the structure of a directed acyclic graph G, whose vertexes (or nodes) are the random variables Xi. The relationships between the variables are described by a joint probability distribution P(X1, , Xn). The genes, on which the probability is conditioned, are called the parents of gene i and represent its regulators, and the joint probability density is expressed as a product of conditional probabilities. Bayesian networks cannot contain cycles (i.e. no feedback loops). This restriction is the principal limitation of the Bayesian network model [6]. Dynamic Bayesian networks overcome this limitation [7]. Dynamic Bayesian networks are an extension of Bayesian networks able to infer interactions from a data set consisting of time-series rather than steady-state data. Graphical Gaussian Model Graphical Gaussian model, also known as covariance selection or concentration graph models, assumes multivariate normal distribution for underlying data. The independence graph is defined by a set of pairwise conditional independence relationships calculated using partial correlations as a measure of independence of any two genes that determine the edge-set of the graph [8]. Partial cross correlation has been also used to deal with time delays [9]. Gene Relevance Network Gene relevance networks are based on the covariance graph model. Given a measure of association and defined a threshold value, for all pairs of domain variables (X, Y), association A(X, Y) is computed. Variables X and Y are connected by an undirected edge when association A(X, Y) exceeds the predefined threshold value. One of the measures of association is the mutual information (MI) [10,11], one of the information theory (IT) main tools. In IT approaches, the expression level of a gene is considered as a random variable. MI is the main tool for measuring if and how two genes influence each other. MI between two variables X and Y is also defined as the reduction in uncertainty about a variable X after observing a second random variable Y. Edges in networks derived by information-theoretic approaches represent statistical dependencies among gene expression profiles. As in the case of Bayesian network, the edge does not represent a direct causal interaction between two genes, but only a statistical dependency. It is possible to derive the information-theoretic approach as a method to approximate the joint probability density function of gene expression profiles, as it is performed for Bayesian networks [12-14]. Time-Course Reverse Engineering Availability of time-series gene expression data can be of help in the study of the dynamical properties of molecular networks, by exploiting the causal gene-gene temporal relationships. In the recent literature several dynamic models, such as Probabilistic Boolean Networks (PBN) [15]; Dynamic Bayesian Networks (DBN) [7]; Hidden Markov Model (HMM) [16] Kalfman filters [17]; Ordinary Differential Equations (ODEs) [4,18]; pattern recognition approaches [19]; signal processing approaches [20], model-free approaches [21] and informational approaches [22] have been proposed for reconstructing regulatory networks from time-course gene expression Zoppoli et al. BMC Bioinformatics 2010, 11:154 http://www.biomedcentral. com/1471-2105/11/154 Page 3 of 15 data. Most of them are essentially model-based trying to uncover the dynamics of the system by estimating a series of parameters, such as auto regressive coefficients [20] or the coefficients of state-transition matrix [17] or of a stiffness matrix [4,18]. The model parameters themselves describe the temporal relationships between nodes of the mol