Reconstructing Generalized Logical Networks of Transcriptional Regulation in Mouse Brain from Temporal Gene Expression Data

Hindawi Publishing Corporation EURASIP Journal on Bioinformatics and Systems Biology Volume 2009, Article ID 545176, 13 pages doi:10.1155/2009/545176 Research Article Reconstructing Generalized Logical Networks of Transcriptional Regulation in Mouse Brain from Temporal Gene Expression Data Mingzhou (Joe) Song,1 Chris K. Lewis,1 Eric R. Lance,1 Elissa J. Chesler,2 Roumyana Kirova Yordanova,3 Michael A. Langston,4 Kerrie H. Lodowski,5 and Susan E. Bergeson6 1 Department of Computer Science, New Mexico State University, Las Cruces, NM 88003, USA 2 Systems Genetics Group, Biosciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA 3 Department of Applied Genomics, Bristol-Myers Squibb R&D, P.O. Box 5400, Princeton, NJ 08543, USA 4 Department of Computer Science, University of Tennessee, Knoxville, TN 37996, USA 5 Department of Pharmacology, School of Medicine, Case Western Reserve University, Cleveland, OH 44106, USA 6 Department of Pharmacology and Neuroscience, Texas Tech University, Lubbock, TX 79430, USA Correspondence should be addressed to Mingzhou (Joe) Song, Received 1 June 2008; Revised 8 September 2008; Accepted 12 December 2008 Recommended by Dirk Repsilber Gene expression time course data can be used not only to detect differentially expressed genes but also to find temporal associations among genes. The problem of reconstructing generalized logical networks to account for temporal dependencies among genes and environmental stimuli from transcriptomic data is addressed. A network reconstruction algorithm was developed that uses statistical significance as a criterion for network selection to avoid false-positive interactions arising from pure chance. The multinomial hypothesis testing-based network reconstruction allows for explicit specification of the false-positive rate, unique from all extant network inference algorithms. The method is superior to dynamic Bayesian network modeling in a simulation study. Temporal gene expression data from the brains of alcohol-treated mice in an analysis of the molecular response to alcohol are used for modeling. Genes from major neuronal pathways are identified as putative components of the alcohol response mechanism. Nine of these genes have associations with alcohol reported in literature. Several other potentially relevant genes, compatible with independent results from literature mining, may play a role in the response to alcohol. Additional, previously unknown gene interactions were discovered that, subject to biological verification, may offer new clues in the search for the elusive molecular mechanisms of alcoholism. Copyright © 2009 Mingzhou (Joe) Song et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction The regulation of transcription occurring in an intriguingly complex biological system involves multiple interacting regulatory processes in gene regulatory networks (GRNs). Modeling transcriptional regulation requires algorithms that retain information about regulatory interactions. The generalized logical network (GLN) is a generative model that can be reconstructed from temporal trajectories, for example, from data collected in time-series studies of gene expression. Because these data capture information on temporal antecedence, the approach can be used to develop stronger hypotheses about casual relations among transcrip- tional events than one would be able to derive from mere correlation analyses. We designed a GLN reconstruction algorithm that differs from previous approaches because it makes use of hypothesis testing on the multinomial distribution to establish directed connections among genes. Our statistical approach allows explicit control of false positives by specifying a desirable alpha level, while other criteria used in network reconstruction, such as the Bayesian information criterion (BIC) used in dynamic Bayesian networks (DBNs) reconstruction and the coefficient of determination (COD) used in Boolean networks (BNs) reconstruction, do not explicitly enforce false-positive rate control. 2 GLNs also allow more aspects of systems to be studied than other network models by enabling (1) adaptive description for interactions among variables, (2) nonlinear interaction patterns, and (3) finite steady states, attractor basins, and state transition diagrams. The software CellNetAnalyzer [1] allows a user to draft a GLN from existing knowledge. Our method allows such networks to be reconstructed and derived solely from data-driven approaches. GLNs have the further advantage that they do not require parametric assumptions, unlike stochastic logical networks [2] which discretize differential equations based on strong assumptions. Additionally, our implementation of GLN modeling focuses on network reconstruction from temporal gene expression data, which can be used complementarily with network property analysis algorithms such as the network walking algorithm [3], and literature mining tools such as those reviewed in [4]. GLN is a dynamical system model to characterize interactions among discrete variables over discrete time. It is a directed graph, with nodes representing the discrete variables and each having a generalized truth table (gtt). The gtt for a node X maps all possible combinations of parent node values to values of X. Related modeling paradigms with different emphases have also been applied to biological data and are compared and contrasted with the GLN below. (i) Temporal probabilistic networks. The dynamic Bayesian network (DBN) is an extension of Bayesian networks, which incorporates time transitions between Bayesian networks. A DBN describes temporal statistical dependencies among genes. DBNs have been successful in extracting probabilistic dependencies among genes in GRNs [5–7]. Certain DBNs can even be converted to probabilistic Boolean networks [8]. However, DBN is an indirect tool to understand system dynamics since it does not explicitly describe temporal relations among entities in a functional form, while a GLN provides immediate functional relationships among variables. (ii) Continuous dynamical system models. Differential equations in both deterministic [9, 10] and stochastic [11] formulations have been used to model interactions in GRNs in continuous time. The E-Cell Project [12, 13] uses differential equations to target knowledge-based reproduction, not data-driven reconstruction, of intracellular biochemical and molecular interactions within a single cell. The stochastic master equations relate state probabilities by differential equations, impractical for biological systems involving many variables because of the computational burden. Recent research has been focusing on improving the scalability of such models [14]. (iii) Discrete dynamical system models. The Boolean network (BN) [ (...truncated)