Bayesian learning of sparse gene regulatory networks

Differential equations (DEs) have been the most widespread formalism for gene regulatory network (GRN) modeling, as they offer natural interpretation of biological processes, easy elucidation of gene relationships, and the capability of using efficient parameter estimation methods. However, an important limitation of DEs is their requirement of O(d(2)) parameters where d is the number of genes modeled, which often causes over-parameterization for large d, leading to the over-fitting of data and dense parameter sets that are hard to interpret. This paper presents the first effort to address the over-parameterization problem by applying the sparse Bayesian learning (SBL) method to sparsify the GRN model of DEs. SBL operates on the parsimony principle, with the objective to reduce the number of effective parameters by driving the redundant parameters to zero. The resulting sparse parameter set offers three important advantages for GRN inference: first, the inferred GRNs are more plausible, since the biological counterparts are known to be sparse; second, gene relationships can be more easily elucidated from sparse sets than from dense sets; and third, the solutions become more optimal and consistent, due to the reduction in the volume of solution space. Experiments are conducted on the yeast Saccharomyces cerevisiae time-series gene expression data, in which known regulatory events related to the cell cycle G1/S phase are reliably reproduced.     

Inference of gene pathways using mixture Bayesian networks

Background  

Inference of gene networks typically relies on measurements across a wide range of conditions or treatments. Although one network structure is predicted, the relationship between genes could vary across conditions. A comprehensive approach to infer general and condition-dependent gene networks was evaluated. This approach integrated Bayesian network and Gaussian mixture models to describe continuous microarray gene expression measurements, and three gene networks were predicted.     

Inferring gene networks from time series microarray data using dynamic Bayesian networks

Dynamic Bayesian networks (DBNs) are considered as a promising model for inferring gene networks from time series microarray data. DBNs have overtaken Bayesian networks (BNs) as DBNs can construct cyclic regulations using time delay information. In this paper, a general framework for DBN modelling is outlined. Both discrete and continuous DBN models are constructed systematically and criteria for learning network structures are introduced from a Bayesian statistical viewpoint. This paper reviews the applications of DBNs over the past years. Real data applications for Saccharomyces cerevisiae time series gene expression data are also shown.     

Gene networks inference using dynamic Bayesian networks

This article deals with the identification of gene regulatory networks from experimental data using a statistical machine learning approach. A stochastic model of gene interactions capable of handling missing variables is proposed. It can be described as a dynamic Bayesian network particularly well suited to tackle the stochastic nature of gene regulation and gene expression measurement. Parameters of the model are learned through a penalized likelihood maximization implemented through an extended version of EM algorithm. Our approach is tested against experimental data relative to the S.O.S. DNA Repair network of the Escherichia coli bacterium. It appears to be able to extract the main regulations between the genes involved in this network. An added missing variable is found to model the main protein of the network. Good prediction abilities on unlearned data are observed. These first results are very promising: they show the power of the learning algorithm and the ability of the model to capture gene interactions.     

Experimental design for efficient identification of gene regulatory networks using sparse Bayesian models

Background  

Identifying large gene regulatory networks is an important task, while the acquisition of data through perturbation experiments (e.g., gene switches, RNAi, heterozygotes) is expensive. It is thus desirable to use an identification method that effectively incorporates available prior knowledge – such as sparse connectivity – and that allows to design experiments such that maximal information is gained from each one.     

BNFinder: exact and efficient method for learning Bayesian networks

MOTIVATION: Bayesian methods are widely used in many different areas of research. Recently, it has become a very popular tool for biological network reconstruction, due to its ability to handle noisy data. Even though there are many software packages allowing for Bayesian network reconstruction, only few of them are freely available to researchers. Moreover, they usually require at least basic programming abilities, which restricts their potential user base. Our goal was to provide software which would be freely available, efficient and usable to non-programmers. RESULTS: We present a BNFinder software, which allows for Bayesian network reconstruction from experimental data. It supports dynamic Bayesian networks and, if the variables are partially ordered, also static Bayesian networks. The main advantage of BNFinder is the use exact algorithm, which is at the same time very efficient (polynomial with respect to the number of observations).     

Learning about gene regulatory networks from gene deletion experiments

Gene regulatory networks are a major focus of interest in molecular biology. A crucial question is how complex regulatory systems are encoded and controlled by the genome. Three recent publications have raised the question of what can be learned about gene regulatory networks from microarray experiments on gene deletion mutants. Using this indirect approach, topological features such as connectivity and modularity have been studied.     

Adaptive networks using learning matrices

Summary The performance of the Learning Matrix (LM) is suitable for the design of adaptive networks of higher complexity. It has been published, how to connect a LM with a generator of patterns (binary or nonbinary) and a ring-counter to result in an automatic classification of the presented patterns. This paper describes, how to connect two LM's to form an Autonomous Learning Matrix Dipole (ALD) and how to organize it, so that it adapts itself to an environment according to a given evaluation scale. For this purpose, a third type of input (beside e and b), namely h seems to be useful. This h-input controls the rate of adaptation of the LM.Using such ALD's, one may design adaptive structures of even higher complexity, for example with an adaptive internal model.The principle of Learning Matrices has been explained in detail (see e.g. IEEE Transactions on Electronic Computers, Vol. EC-12, No. 6, December, 1963, pp. 846–862). Using such learning matrices (LM), one may build up adaptive networks with rather interesting functions. Perhaps they are interesting for the physiologist and psychologist as well as for the engineer. Let us first recall the most essential details of the LM's.

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Zusammenfassung Die Funktion der Lernmatrix (LM) erlaubt den Entwurf adaptiver Netzwerke höherer Komplexität. Es wurde an anderer Stelle schon beschrieben, wie eine LM (binär oder nichtbinär) mit einem Generator für Eigenschaftssätze und einem Ringzähler zusammengeschaltet werden kann, um eine selbsttätige Klassifikation der angebotenen Eigenschaftssätze zu bewirken. Im vorliegenden Aufsatz wird erklärt, wie zwei LM so zusammengeschaltet werden können, dacß sich ein Autonomer Lernmatrix-Dipol (ALD) ergibt, und wie dieser zu organisieren ist, daß er sich einer gegebenen Außenwelt nach Maßgabe einer vorgegebenen Werteskala anpaßt. Zu diesem Zweck erweist sich außer den bisher beschriebenen beiden Zugangen zur LM (nämlich e und b) ein dritter sehr zweckmäßig, nämlich h. Dieser h-Eingang beeinflußt die Lerngeschwindigkeit der LM.Unter Verwendung solcher ALD's kann man adaptive Strukturen noch höherer Komplexität aufbauen, beispielsweise solche mit adaptivem innerem Modell.

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Visiting Professor of Electrical Engineering Stanford University.     

Reconstruction of biogeographic and evolutionary networks using reticulograms

A reticulogram is a general network capable of representing a reticulate evolutionary structure. It is particularly useful for portraying relationships among organisms that may be related in a nonunique way to their common ancestor - relationships that cannot be represented by a dendrogram or a phylogenetic tree. We propose a new method for constructing reticulograms that represent a given distance matrix. Reticulate evolution applies first to phylogenetic problems; it has been found in nature, for example, in the within-species microevolution of eukaryotes and in lateral gene transfer in bacteria. In this paper, we propose a new method for reconstructing reticulation networks and we develop applications of the reticulate evolution model to ecological biogeographic, population microevolutionary, and hybridization problems. The first example considers a spatially constrained reticulogram representing the postglacial dispersal of freshwater fishes in the Québec peninsula; the reticulogram provides a better model of postglacial dispersal than does a tree model. The second example depicts the morphological similarities among local populations of muskrats in a river valley in Belgium; adding supplementary branches to a tree depicting the river network leads to a better representation of the morphological distances among local populations of muskrats than does a tree structure. A third example involves hybrids between plants of the genus Aphelandra.     

Trophoblast-specific gene manipulation using lentivirus-based vectors

The trophoblast layers of the mammalian placenta carry out many complex functions required to pattern the developing embryo and maintain its growth and survival in the uterine environment. Genetic disruption of many gene pathways can result in embryonic lethality because of placental failure, potentially confusing the interpretation of mouse knockout phenotypes. Development of tools to specifically and efficiently manipulate gene expression in the trophoblast lineage would greatly aid understanding of the relative roles of different genetic pathways in the trophoblast versus embryonic lineages. We show that short-term lentivirus-mediated infection of mouse blastocysts can lead to rapid expression of a green fluorescent protein (GFP) transgene specifically in the outer trophoblast progenitors and their later placental derivatives. Efficient trophoblast-specific gene knockdown can also be produced by lentivirus-mediated pol III-driven short hairpin RNA (shRNA) and efficient trophoblast-specific gene knockout by pol II-driven Cre recombinase lentiviral vectors. This lentivirus lineage-specific infection system thus facilitates both gain and loss of function studies during placental development in the mouse and potentially other mammalian species.     

Joint learning of gene functions--a Bayesian network model approach

In this paper, we develop a machine learning system for determining gene functions from heterogeneous data sources using a Weighted Naive Bayesian network (WNB). The knowledge of gene functions is crucial for understanding many fundamental biological mechanisms such as regulatory pathways, cell cycles and diseases. Our major goal is to accurately infer functions of putative genes or Open Reading Frames (ORFs) from existing databases using computational methods. However, this task is intrinsically difficult since the underlying biological processes represent complex interactions of multiple entities. Therefore, many functional links would be missing when only one or two sources of data are used in the prediction. Our hypothesis is that integrating evidence from multiple and complementary sources could significantly improve the prediction accuracy. In this paper, our experimental results not only suggest that the above hypothesis is valid, but also provide guidelines for using the WNB system for data collection, training and predictions. The combined training data sets contain information from gene annotations, gene expressions, clustering outputs, keyword annotations, and sequence homology from public databases. The current system is trained and tested on the genes of budding yeast Saccharomyces cerevisiae. Our WNB model can also be used to analyze the contribution of each source of information toward the prediction performance through the weight training process. The contribution analysis could potentially lead to significant scientific discovery by facilitating the interpretation and understanding of the complex relationships between biological entities.     

AtCAST, a tool for exploring gene expression similarities among DNA microarray experiments using networks

The comparison of gene expression profiles among DNA microarray experiments enables the identification of unknown relationships among experiments to uncover the underlying biological relationships. Despite the ongoing accumulation of data in public databases, detecting biological correlations among gene expression profiles from multiple laboratories on a large scale remains difficult. Here, we applied a module (sets of genes working in the same biological action)-based correlation analysis in combination with a network analysis to Arabidopsis data and developed a 'module-based correlation network' (MCN) which represents relationships among DNA microarray experiments on a large scale. We developed a Web-based data analysis tool, 'AtCAST' (Arabidopsis thaliana: DNA Microarray Correlation Analysis Tool), which enables browsing of an MCN or mining of users' microarray data by mapping the data into an MCN. AtCAST can help researchers to find novel connections among DNA microarray experiments, which in turn will help to build new hypotheses to uncover physiological mechanisms or gene functions in Arabidopsis.     

Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks

MOTIVATION: Bayesian networks have been applied to infer genetic regulatory interactions from microarray gene expression data. This inference problem is particularly hard in that interactions between hundreds of genes have to be learned from very small data sets, typically containing only a few dozen time points during a cell cycle. Most previous studies have assessed the inference results on real gene expression data by comparing predicted genetic regulatory interactions with those known from the biological literature. This approach is controversial due to the absence of known gold standards, which renders the estimation of the sensitivity and specificity, that is, the true and (complementary) false detection rate, unreliable and difficult. The objective of the present study is to test the viability of the Bayesian network paradigm in a realistic simulation study. First, gene expression data are simulated from a realistic biological network involving DNAs, mRNAs, inactive protein monomers and active protein dimers. Then, interaction networks are inferred from these data in a reverse engineering approach, using Bayesian networks and Bayesian learning with Markov chain Monte Carlo. RESULTS: The simulation results are presented as receiver operator characteristics curves. This allows estimating the proportion of spurious gene interactions incurred for a specified target proportion of recovered true interactions. The findings demonstrate how the network inference performance varies with the training set size, the degree of inadequacy of prior assumptions, the experimental sampling strategy and the inclusion of further, sequence-based information. AVAILABILITY: The programs and data used in the present study are available from http://www.bioss.sari.ac.uk/~dirk/Supplements     

Growing Bayesian network models of gene networks from seed genes

MOTIVATION: For the last few years, Bayesian networks (BNs) have received increasing attention from the computational biology community as models of gene networks, though learning them from gene-expression data is problematic. Most gene-expression databases contain measurements for thousands of genes, but the existing algorithms for learning BNs from data do not scale to such high-dimensional databases. This means that the user has to decide in advance which genes are included in the learning process, typically no more than a few hundreds, and which genes are excluded from it. This is not a trivial decision. We propose an alternative approach to overcome this problem. RESULTS: We propose a new algorithm for learning BN models of gene networks from gene-expression data. Our algorithm receives a seed gene S and a positive integer R from the user, and returns a BN for the genes that depend on S such that less than R other genes mediate the dependency. Our algorithm grows the BN, which initially only contains S, by repeating the following step R + 1 times and, then, pruning some genes; find the parents and children of all the genes in the BN and add them to it. Intuitively, our algorithm provides the user with a window of radius R around S to look at the BN model of a gene network without having to exclude any gene in advance. We prove that our algorithm is correct under the faithfulness assumption. We evaluate our algorithm on simulated and biological data (Rosetta compendium) with satisfactory results.