Dirk Husmeier

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

TOPALi v2

Summary: TOPALi v2 simplifies and automates the use of several methods for the evolutionary analysis of multiple sequence alignments. Jobs are submitted from a Java graphical user interface as TOPALi web services to either run remotely on high-performance computing clusters or locally (with multiple cores supported). Methods available include model selection and phylogenetic tree estimation using the Bayesian inference and maximum likelihood (ML) approaches, in addition to recombination detection methods. The optimal substitution model can be selected for protein or nucleic acid (standard, or protein-coding using a codon position model) data using accurate statistical criteria derived from ML co-estimation of the tree and the substitution model. Phylogenetic software available includes PhyML, RAxML and MrBayes. Availability: Freely downloadable from http://www.topali.org for Windows, Mac OS X, Linux and Solaris. Contact: iain.milne@scri.ac.uk

TOPALi: software for automatic identification of recombinant sequences within DNA multiple alignments

SUMMARY TOPALi is a new Java graphical analysis application that allows the user to identify recombinant sequences within a DNA multiple alignment (either automatically or via manual investigation). TOPALi allows a choice of three statistical methods to predict the positions of breakpoints due to past recombination. The breakpoint predictions are then used to identify putative recombinant sequences and their relationships to other sequences. In addition to its sophisticated interface, TOPALi can import many sequence formats, estimate and display phylogenetic trees and allow interactive analysis and/or automatic HTML report generation. AVAILABILITY TOPALi is freely available from http://www.bioss.ac.uk/software.html

Reconstructing gene regulatory networks with bayesian networks by combining expression data with multiple sources of prior knowledge.

There have been various attempts to reconstruct gene regulatory networks from microarray expression data in the past. However, owing to the limited amount of independent experimental conditions and noise inherent in the measurements, the results have been rather modest so far. For this reason it seems advisable to include biological prior knowledge, related, for instance, to transcription factor binding locations in promoter regions or partially known signalling pathways from the literature. In the present paper, we consider a Bayesian approach to systematically integrate expression data with multiple sources of prior knowledge. Each source is encoded via a separate energy function, from which a prior distribution over network structures in the form of a Gibbs distribution is constructed. The hyperparameters associated with the different sources of prior knowledge, which measure the influence of the respective prior relative to the data, are sampled from the posterior distribution with MCMC. We have evaluated the proposed scheme on the yeast cell cycle and the Raf signalling pathway. Our findings quantify to what extent the inclusion of independent prior knowledge improves the network reconstruction accuracy, and the values of the hyperparameters inferred with the proposed scheme were found to be close to optimal with respect to minimizing the reconstruction error.

Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move

Applications of Bayesian networks in systems biology are computationally demanding due to the large number of model parameters. Conventional MCMC schemes based on proposal moves in structure space tend to be too slow in mixing and convergence, and have recently been superseded by proposal moves in the space of node orders. A disadvantage of the latter approach is the intrinsic inability to specify the prior probability on network structures explicitly. The relative paucity of different experimental conditions in contemporary systems biology implies a strong influence of the prior probability on the posterior probability and, hence, the outcome of inference. Consequently, the paradigm of performing MCMC proposal moves in order rather than structure space is not entirely satisfactory. In the present article, we propose a new and more extensive edge reversal move in the original structure space, and we show that this significantly improves the convergence of the classical structure MCMC scheme.

Improvements in the reconstruction of time-varying gene regulatory networks

METHOD Dynamic Bayesian networks (DBNs) have been applied widely to reconstruct the structure of regulatory processes from time series data, and they have established themselves as a standard modelling tool in computational systems biology. The conventional approach is based on the assumption of a homogeneous Markov chain, and many recent research efforts have focused on relaxing this restriction. An approach that enjoys particular popularity is based on a combination of a DBN with a multiple changepoint process, and the application of a Bayesian inference scheme via reversible jump Markov chain Monte Carlo (RJMCMC). In the present article, we expand this approach in two ways. First, we show that a dynamic programming scheme allows the changepoints to be sampled from the correct conditional distribution, which results in improved convergence over RJMCMC. Second, we introduce a novel Bayesian clustering and information sharing scheme among nodes, which provides a mechanism for automatic model complexity tuning. RESULTS We evaluate the dynamic programming scheme on expression time series for Arabidopsis thaliana genes involved in circadian regulation. In a simulation study we demonstrate that the regularization scheme improves the network reconstruction accuracy over that obtained with recently proposed inhomogeneous DBNs. For gene expression profiles from a synthetically designed Saccharomyces cerevisiae strain under switching carbon metabolism we show that the combination of both: dynamic programming and regularization yields an inference procedure that outperforms two alternative established network reconstruction methods from the biology literature. AVAILABILITY AND IMPLEMENTATION A MATLAB implementation of the algorithm and a supplementary paper with algorithmic details and further results for the Arabidopsis data can be downloaded from: http://www.statistik.tu-dortmund.de/bio2010.html.

Modelling non-stationary gene regulatory processes with a non-homogeneous Bayesian network and the allocation sampler

METHOD The objective of the present article is to propose and evaluate a probabilistic approach based on Bayesian networks for modelling non-homogeneous and non-linear gene regulatory processes. The method is based on a mixture model, using latent variables to assign individual measurements to different classes. The practical inference follows the Bayesian paradigm and samples the network structure, the number of classes and the assignment of latent variables from the posterior distribution with Markov Chain Monte Carlo (MCMC), using the recently proposed allocation sampler as an alternative to RJMCMC. RESULTS We have evaluated the method using three criteria: network reconstruction, statistical significance and biological plausibility. In terms of network reconstruction, we found improved results both for a synthetic network of known structure and for a small real regulatory network derived from the literature. We have assessed the statistical significance of the improvement on gene expression time series for two different systems (viral challenge of macrophages, and circadian rhythms in plants), where the proposed new scheme tends to outperform the classical BGe score. Regarding biological plausibility, we found that the inference results obtained with the proposed method were in excellent agreement with biological findings, predicting dichotomies that one would expect to find in the studied systems. AVAILABILITY Two supplementary papers on theoretical (T) and experi-mental (E) aspects and the datasets used in our study are available from http://www.bioss.ac.uk/associates/marco/supplement/

Gene regulatory network reconstruction by Bayesian integration of prior knowledge and/or different experimental conditions.

There have been various attempts to improve the reconstruction of gene regulatory networks from microarray data by the systematic integration of biological prior knowledge. Our approach is based on pioneering work by Imoto et al. where the prior knowledge is expressed in terms of energy functions, from which a prior distribution over network structures is obtained in the form of a Gibbs distribution. The hyperparameters of this distribution represent the weights associated with the prior knowledge relative to the data. We have derived and tested a Markov chain Monte Carlo (MCMC) scheme for sampling networks and hyperparameters simultaneously from the posterior distribution, thereby automatically learning how to trade off information from the prior knowledge and the data. We have extended this approach to a Bayesian coupling scheme for learning gene regulatory networks from a combination of related data sets, which were obtained under different experimental conditions and are therefore potentially associated with different active subpathways. The proposed coupling scheme is a compromise between (1) learning networks from the different subsets separately, whereby no information between the different experiments is shared; and (2) learning networks from a monolithic fusion of the individual data sets, which does not provide any mechanism for uncovering differences between the network structures associated with the different experimental conditions. We have assessed the viability of all proposed methods on data related to the Raf signaling pathway, generated both synthetically and in cytometry experiments.

Non-homogeneous dynamic Bayesian networks for continuous data

Classical dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption and cannot deal with non-homogeneous temporal processes. Various approaches to relax the homogeneity assumption have recently been proposed. The present paper presents a combination of a Bayesian network with conditional probabilities in the linear Gaussian family, and a Bayesian multiple changepoint process, where the number and location of the changepoints are sampled from the posterior distribution with MCMC. Our work improves four aspects of an earlier conference paper: it contains a comprehensive and self-contained exposition of the methodology; it discusses the problem of spurious feedback loops in network reconstruction; it contains a comprehensive comparative evaluation of the network reconstruction accuracy on a set of synthetic and real-world benchmark problems, based on a novel discrete changepoint process; and it suggests new and improved MCMC schemes for sampling both the network structures and the changepoint configurations from the posterior distribution. The latter study compares RJMCMC, based on changepoint birth and death moves, with two dynamic programming schemes that were originally devised for Bayesian mixture models. We demonstrate the modifications that have to be made to allow for changing network structures, and the critical impact that the prior distribution on changepoint configurations has on the overall computational complexity.

Detection of Recombination in DNA Multiple Alignments with Hidden Markov Models

Conventional phylogenetic tree estimation methods assume that all sites in a DNA multiple alignment have the same evolutionary history. This assumption is violated in data sets from certain bacteria and viruses due to recombination, a process that leads to the creation of mosaic sequences from different strains and, if undetected, causes systematic errors in phylogenetic tree estimation. In the current work, a hidden Markov model (HMM) is employed to detect recombination events in multiple alignments of DNA sequences. The emission probabilities in a given state are determined by the branching order (topology) and the branch lengths of the respective phylogenetic tree, while the transition probabilities depend on the global recombination probability. The present study improves on an earlier heuristic parameter optimization scheme and shows how the branch lengths and the recombination probability can be optimized in a maximum likelihood sense by applying the expectation maximization (EM) algorithm. The novel algorithm is tested on a synthetic benchmark problem and is found to clearly outperform the earlier heuristic approach. The paper concludes with an application of this scheme to a DNA sequence alignment of the argF gene from four Neisseria strains, where a likely recombination event is clearly detected.