Estimating Gene Interactions Using Information Theoretic Functionals

With an abundance of data resulting from high-throughput technologies, like DNA microarrays, a race has been on the last few years, to determine the structures and functions of genes and their products, the proteins. Inference of gene interactions, lies in the core of these efforts. In all this activity, three important research issues have emerged. First, in much of the current literature on gene regulatory networks, dependencies among variables in our case genes - are assumed to be linear in nature, when in fact, in real-life scenarios this is seldom the case. This disagreement leads to systematic deviation and biased evaluation. Secondly, although the problem of undersampling, features in every piece of work as one of the major causes for poor results, in practice it is overlooked and rarely addressed explicitly. Finally, inference of network structures, although based on rigid mathematical foundations and computational optimizations, often displays poor fitness values and biologically unrealistic link structures, due - to a large extend - to the discovery of pairwise only interactions. In our search for robust, nonlinear measures of dependency, we advocate that mutual information and related information theoretic functionals (conditional mutual information, total correlation) are possibly the most suitable candidates to capture both linear and nonlinear interactions between variables, and resolve higher order dependencies. To address these issues, we researched and implemented under a common framework, a selection nonparametric estimators of mutual information for continuous variables. The focus of their assessment was, their robustness to the limited sample sizes and their expansibility to higher dimensions - important for the detection of more complex interaction structures. Two different assessment scenaria were performed, one with simulated data and one with bootstrapping the estimators in state-of-the-art network inference algorithms and monitor their predictive power and sensitivity. The tests revealed that, in small sample size regimes, there is a significant difference in the performance of different estimators, and naive methods such as uniform binning, gave consistently poor results compared with more sophisticated methods. Finally, a custom, modular mechanism is proposed, for the inference of gene interactions, targeting the identi cation of some of the most common substructures in genetic networks, that we believe will help improve accuracy and predictability scores

The EM Algorithm and the Rise of Computational Biology

In the past decade computational biology has grown from a cottage industry with a handful of researchers to an attractive interdisciplinary field, catching the attention and imagination of many quantitatively-minded scientists. Of interest to us is the key role played by the EM algorithm during this transformation. We survey the use of the EM algorithm in a few important computational biology problems surrounding the "central dogma"; of molecular biology: from DNA to RNA and then to proteins. Topics of this article include sequence motif discovery, protein sequence alignment, population genetics, evolutionary models and mRNA expression microarray data analysis.Comment: Published in at http://dx.doi.org/10.1214/09-STS312 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Bagging Statistical Network Inference from Large-Scale Gene Expression Data

Modern biology and medicine aim at hunting molecular and cellular causes of biological functions and diseases. Gene regulatory networks (GRN) inferred from gene expression data are considered an important aid for this research by providing a map of molecular interactions. Hence, GRNs have the potential enabling and enhancing basic as well as applied research in the life sciences. In this paper, we introduce a new method called BC3NET for inferring causal gene regulatory networks from large-scale gene expression data. BC3NET is an ensemble method that is based on bagging the C3NET algorithm, which means it corresponds to a Bayesian approach with noninformative priors. In this study we demonstrate for a variety of simulated and biological gene expression data from S. cerevisiae that BC3NET is an important enhancement over other inference methods that is capable of capturing biochemical interactions from transcription regulation and protein-protein interaction sensibly. An implementation of BC3NET is freely available as an R package from the CRAN repository

Statistical inference from large-scale genomic data

This thesis explores the potential of statistical inference methodologies in their applications in functional genomics. In essence, it summarises algorithmic findings in this field, providing step-by-step analytical methodologies for deciphering biological knowledge from large-scale genomic data, mainly microarray gene expression time series. This thesis covers a range of topics in the investigation of complex multivariate genomic data. One focus involves using clustering as a method of inference and another is cluster validation to extract meaningful biological information from the data. Information gained from the application of these various techniques can then be used conjointly in the elucidation of gene regulatory networks, the ultimate goal of this type of analysis. First, a new tight clustering method for gene expression data is proposed to obtain tighter and potentially more informative gene clusters. Next, to fully utilise biological knowledge in clustering validation, a validity index is defined based on one of the most important ontologies within the Bioinformatics community, Gene Ontology. The method bridges a gap in current literature, in the sense that it takes into account not only the variations of Gene Ontology categories in biological specificities and their significance to the gene clusters, but also the complex structure of the Gene Ontology. Finally, Bayesian probability is applied to making inference from heterogeneous genomic data, integrated with previous efforts in this thesis, for the aim of large-scale gene network inference. The proposed system comes with a stochastic process to achieve robustness to noise, yet remains efficient enough for large-scale analysis. Ultimately, the solutions presented in this thesis serve as building blocks of an intelligent system for interpreting large-scale genomic data and understanding the functional organisation of the genome

Efficient reverse-engineering of a developmental gene regulatory network

This is the final version of the article. Available from the publisher via the DOI in this record.Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.Funding: The laboratory of Johannes Jaeger and this study in particular was funded by the MEC-EMBL agreement for the EMBL/CRG Research Unit in Systems Biology, by Grant 153 (MOPDEV) of the ERANet: ComplexityNET program, by SGR Grant 406 from the Catalan funding agency AGAUR, by grant BFU2009-10184 from the Spanish Ministry of Science, and by European Commission grant FP7-KBBE-2011-5/289434 (BioPreDyn). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

A temporal switch model for estimating transcriptional activity in gene expression

Motivation: The analysis and mechanistic modelling of time series gene expression data provided by techniques such as microarrays, NanoString, reverse transcription–polymerase chain reaction and advanced sequencing are invaluable for developing an understanding of the variation in key biological processes. We address this by proposing the estimation of a flexible dynamic model, which decouples temporal synthesis and degradation of mRNA and, hence, allows for transcriptional activity to switch between different states. Results: The model is flexible enough to capture a variety of observed transcriptional dynamics, including oscillatory behaviour, in a way that is compatible with the demands imposed by the quality, time-resolution and quantity of the data. We show that the timing and number of switch events in transcriptional activity can be estimated alongside individual gene mRNA stability with the help of a Bayesian reversible jump Markov chain Monte Carlo algorithm. To demonstrate the methodology, we focus on modelling the wild-type behaviour of a selection of 200 circadian genes of the model plant Arabidopsis thaliana. The results support the idea that using a mechanistic model to identify transcriptional switch points is likely to strongly contribute to efforts in elucidating and understanding key biological processes, such as transcription and degradation

Partial mixture model for tight clustering of gene expression time-course

Background: Tight clustering arose recently from a desire to obtain tighter and potentially more informative clusters in gene expression studies. Scattered genes with relatively loose correlations should be excluded from the clusters. However, in the literature there is little work dedicated to this area of research. On the other hand, there has been extensive use of maximum likelihood techniques for model parameter estimation. By contrast, the minimum distance estimator has been largely ignored. Results: In this paper we show the inherent robustness of the minimum distance estimator that makes it a powerful tool for parameter estimation in model-based time-course clustering. To apply minimum distance estimation, a partial mixture model that can naturally incorporate replicate information and allow scattered genes is formulated. We provide experimental results of simulated data fitting, where the minimum distance estimator demonstrates superior performance to the maximum likelihood estimator. Both biological and statistical validations are conducted on a simulated dataset and two real gene expression datasets. Our proposed partial regression clustering algorithm scores top in Gene Ontology driven evaluation, in comparison with four other popular clustering algorithms. Conclusion: For the first time partial mixture model is successfully extended to time-course data analysis. The robustness of our partial regression clustering algorithm proves the suitability of the ombination of both partial mixture model and minimum distance estimator in this field. We show that tight clustering not only is capable to generate more profound understanding of the dataset under study well in accordance to established biological knowledge, but also presents interesting new hypotheses during interpretation of clustering results. In particular, we provide biological evidences that scattered genes can be relevant and are interesting subjects for study, in contrast to prevailing opinion

Algebraic shortcuts for leave-one-out cross-validation in supervised network inference

Supervised machine learning techniques have traditionally been very successful at reconstructing biological networks, such as protein-ligand interaction, protein-protein interaction and gene regulatory networks. Many supervised techniques for network prediction use linear models on a possibly nonlinear pairwise feature representation of edges. Recently, much emphasis has been placed on the correct evaluation of such supervised models. It is vital to distinguish between using a model to either predict new interactions in a given network or to predict interactions for a new vertex not present in the original network. This distinction matters because (i) the performance might dramatically differ between the prediction settings and (ii) tuning the model hyperparameters to obtain the best possible model depends on the setting of interest. Specific cross-validation schemes need to be used to assess the performance in such different prediction settings. In this work we discuss a state-of-the-art kernel-based network inference technique called two-step kernel ridge regression. We show that this regression model can be trained efficiently, with a time complexity scaling with the number of vertices rather than the number of edges. Furthermore, this framework leads to a series of cross-validation shortcuts that allow one to rapidly estimate the model performance for any relevant network prediction setting. This allows computational biologists to fully assess the capabilities of their models

A model-based optimization framework for the inference of regulatory interactions using time-course DNA microarray expression data

<p>Abstract</p> <p>Background</p> <p>Proteins are the primary regulatory agents of transcription even though mRNA expression data alone, from systems like DNA microarrays, are widely used. In addition, the regulation process in genetic systems is inherently non-linear in nature, and most studies employ a time-course analysis of mRNA expression. These considerations should be taken into account in the development of methods for the inference of regulatory interactions in genetic networks.</p> <p>Results</p> <p>We use an S-system based model for the transcription and translation process. We propose an optimization-based regulatory network inference approach that uses time-varying data from DNA microarray analysis. Currently, this seems to be the only model-based method that can be used for the analysis of time-course "relative" expressions (expression ratios). We perform an analysis of the dynamic behavior of the system when the number of experimental samples available is varied, when there are different levels of noise in the data and when there are genes that are not considered by the experimenter. Our studies show that the principal factor affecting the ability of a method to infer interactions correctly is the similarity in the time profiles of some or all the genes. The less similar the profiles are to each other the easier it is to infer the interactions. We propose a heuristic method for resolving networks and show that it displays reasonable performance on a synthetic network. Finally, we validate our approach using real experimental data for a chosen subset of genes involved in the sporulation cascade of <it>Bacillus anthracis</it>. We show that the method captures most of the important known interactions between the chosen genes.</p> <p>Conclusion</p> <p>The performance of any inference method for regulatory interactions between genes depends on the noise in the data, the existence of unknown genes affecting the network genes, and the similarity in the time profiles of some or all genes. Though subject to these issues, the inference method proposed in this paper would be useful because of its ability to infer important interactions, the fact that it can be used with time-course DNA microarray data and because it is based on a non-linear model of the process that explicitly accounts for the regulatory role of proteins.</p