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

Inferring latent temporal progression and regulatory networks from cross-sectional transcriptomic data of cancer samples

Unraveling molecular regulatory networks underlying disease progression is critically important for understanding disease mechanisms and identifying drug targets. The existing methods for inferring gene regulatory networks (GRNs) rely mainly on time-course gene expression data. However, most available omics data from cross-sectional studies of cancer patients often lack sufficient temporal information, leading to a key challenge for GRN inference. Through quantifying the latent progression using random walks-based manifold distance, we propose a latent-temporal progression-based Bayesian method, PROB, for inferring GRNs from the cross-sectional transcriptomic data of tumor samples. The robustness of PROB to the measurement variabilities in the data is mathematically proved and numerically verified. Performance evaluation on real data indicates that PROB outperforms other methods in both pseudotime inference and GRN inference. Applications to bladder cancer and breast cancer demonstrate that our method is effective to identify key regulators of cancer progression or drug targets. The identified ACSS1 is experimentally validated to promote epithelial-to-mesenchymal transition of bladder cancer cells, and the predicted FOXM1-targets interactions are verified and are predictive of relapse in breast cancer. Our study suggests new effective ways to clinical transcriptomic data modeling for characterizing cancer progression and facilitates the translation of regulatory network-based approaches into precision medicine.

A unifying modelling formalism for the integration of stoichiometric and kinetic models

Current research on systems and synthetic biology relies heavily on mathematical models of the systems under study. The usefulness of such models depends on the quantity and quality of biological data, and on the availability of appropriate modelling formalisms that can gather and accommodate such data so that they can be exploited properly. Given our incomplete knowledge of biological systems and the fact that they consist of many subsystems, biological data are usually uncertain and heterogeneous. These facts hinder the use of mathematical models and computational methods. In the scope of dynamic biological systems, e.g. metabolic networks, this difficulty can be overcome by the novel modelling formalism of flexible nets (FNs). We show that an FN can combine, in a natural way, a stoichiometric model and a kinetic model. Moreover, the resulting net admits nonlinear dynamics and can be analysed in both transient and steady states.

Dynamic gene regulatory network reconstruction and analysis based on clinical transcriptomic data of colorectal cancer

Inferring dynamic regulatory networks that rewire at different stages is a reasonable way to understand the mechanisms underlying cancer development. In this study, we reconstruct the stage-specific gene regulatory networks (GRNs) for colorectal cancer to understand dynamic changes of gene regulations along different disease stages. We combined multiple sets of clinical transcriptomic data of colorectal cancer patients and employed a supervised approach to select initial gene set for network construction. We then developed a dynamical system-based optimization method to infer dynamic GRNs by incorporating mutual information-based network sparsification and a dynamic cascade technique into an ordinary differential equations model. Dynamic GRNs at four different stages of colorectal cancer were reconstructed and analyzed. Several important genes were revealed based on the rewiring of the reconstructed GRNs. Our study demonstrated that reconstructing dynamic GRNs based on clinical transcriptomic profiling allows us to detect the dynamic trend of gene regulation as well as reveal critical genes for cancer development which may be important candidates of master regulators for further experimental test.

Practical steps to digital organism models, from laboratory model species to 'Crops in silico

A recent initiative named 'Crops in silico' proposes that multi-scale models 'have the potential to fill in missing mechanistic details and generate new hypotheses to prioritize directed engineering efforts' in plant science, particularly directed to crop species. To that end, the group called for 'a paradigm shift in plant modelling, from largely isolated efforts to a connected community'. 'Wet' (experimental) research has been especially productive in plant science, since the adoption of Arabidopsis thaliana as a laboratory model species allowed the emergence of an Arabidopsis research community. Parts of this community invested in 'dry' (theoretical) research, under the rubric of Systems Biology. Our past research combined concepts from Systems Biology and crop modelling. Here we outline the approaches that seem most relevant to connected, 'digital organism' initiatives. We illustrate the scale of experimental research required, by collecting the kinetic parameter values that are required for a quantitative, dynamic model of a gene regulatory network. By comparison with the Systems Biology Markup Language (SBML) community, we note computational resources and community structures that will help to realize the potential for plant Systems Biology to connect with a broader crop science community.

Fusing gene expressions and transitive protein-protein interactions for inference of gene regulatory networks

BACKGROUND

Systematic fusion of multiple data sources for Gene Regulatory Networks (GRN) inference remains a key challenge in systems biology. We incorporate information from protein-protein interaction networks (PPIN) into the process of GRN inference from gene expression (GE) data. However, existing PPIN remain sparse and transitive protein interactions can help predict missing protein interactions. We therefore propose a systematic probabilistic framework on fusing GE data and transitive protein interaction data to coherently build GRN.

RESULTS

We use a Gaussian Mixture Model (GMM) to soft-cluster GE data, allowing overlapping cluster memberships. Next, a heuristic method is proposed to extend sparse PPIN by incorporating transitive linkages. We then propose a novel way to score extended protein interactions by combining topological properties of PPIN and correlations of GE. Following this, GE data and extended PPIN are fused using a Gaussian Hidden Markov Model (GHMM) in order to identify gene regulatory pathways and refine interaction scores that are then used to constrain the GRN structure. We employ a Bayesian Gaussian Mixture (BGM) model to refine the GRN derived from GE data by using the structural priors derived from GHMM. Experiments on real yeast regulatory networks demonstrate both the feasibility of the extended PPIN in predicting transitive protein interactions and its effectiveness on improving the coverage and accuracy the proposed method of fusing PPIN and GE to build GRN.

CONCLUSION

The GE and PPIN fusion model outperforms both the state-of-the-art single data source models (CLR, GENIE3, TIGRESS) as well as existing fusion models under various constraints.

Estimating Causal Effects from Nonparanormal Observational Data

One of the basic aims of science is to unravel the chain of cause and effect of particular systems. Especially for large systems, this can be a daunting task. Detailed interventional and randomized data sampling approaches can be used to resolve the causality question, but for many systems, such interventions are impossible or too costly to obtain. Recently, Maathuis et al. (2010), following ideas from Spirtes et al. (2000), introduced a framework to estimate causal effects in large scale Gaussian systems. By describing the causal network as a directed acyclic graph it is a possible to estimate a class of Markov equivalent systems that describe the underlying causal interactions consistently, even for non-Gaussian systems. In these systems, causal effects stop being linear and cannot be described any more by a single coefficient. In this paper, we derive the general functional form of a causal effect in a large subclass of non-Gaussian distributions, called the non-paranormal. We also derive a convenient approximation, which can be used effectively in estimation. We show that the estimate is consistent under certain conditions and we apply the method to an observational gene expression dataset of the Arabidopsis thaliana circadian clock system.

Handling variability and incompleteness of biological data by flexible nets: a case study for Wilson disease

Mathematical models that combine predictive accuracy with explanatory power are central to the progress of systems and synthetic biology, but the heterogeneity and incompleteness of biological data impede our ability to construct such models. Furthermore, the robustness displayed by many biological systems means that they have the flexibility to operate under a range of physiological conditions and this is difficult for many modeling formalisms to handle. Flexible nets (FNs) address these challenges and represent a paradigm shift in model-based analysis of biological systems. FNs can: (i) handle uncertainties, ranges and missing information in concentrations, stoichiometry, network topology, and transition rates without having to resort to statistical approaches; (ii) accommodate different types of data in a unified model that integrates various cellular mechanisms; and (iii) be employed for system optimization and model predictive control. We present FNs and illustrate their capabilities by modeling a well-established system, the dynamics of glucose consumption by a microbial population. We further demonstrate the ability of FNs to take control actions in response to genetic or metabolic perturbations. Having bench-marked the system, we then construct the first quantitative model for Wilson disease—a rare genetic disorder that impairs copper utilization in the liver. We used this model to investigate the feasibility of using vitamin E supplementation therapy for symptomatic improvement. Our results indicate that hepatocytic inflammation caused by copper accumulation was not aggravated by limitations on endogenous antioxidant supplies, which means that treating patients with antioxidants is unlikely to be effective.

In order to study complex dynamical systems, appropriate mathematical models that capture the system features are necessary. Biological systems, in particular, require flexible modeling approaches for their study since they exhibit variable quantifiable responses under different conditions. Moreover, data about a given biological system are often uncertain or unavailable. Here, a group of scientists from the University of Cambridge introduce Flexible Nets (FNs), a novel approach for the modeling, analysis, and control of biological systems. After presenting the FN approach, they show how a well-known system of glucose consumption and utilization by yeast can be modeled, analyzed and controlled. Then, FNs are used to build and analyze the first quantitative and predictive model of Wilson disease (a heritable defect in copper utilization). They demonstrate that FN simulations permit an evaluation of the relative efficacy of different therapeutic options.

Circadian systems biology: When time matters

The circadian clock is a powerful endogenous timing system, which allows organisms to fine-tune their physiology and behaviour to the geophysical time. The interplay of a distinct set of core-clock genes and proteins generates oscillations in expression of output target genes which temporally regulate numerous molecular and cellular processes. The study of the circadian timing at the organismal as well as at the cellular level outlines the field of chronobiology, which has been highly interdisciplinary ever since its origins. The development of high-throughput approaches enables the study of the clock at a systems level. In addition to experimental approaches, computational clock models exist which allow the analysis of rhythmic properties of the clock network. Such mathematical models aid mechanistic understanding and can be used to predict outcomes of distinct perturbations in clock components, thereby generating new hypotheses regarding the putative function of particular clock genes. Perturbations in the circadian timing system are linked to numerous molecular dysfunctions and may result in severe pathologies including cancer. A comprehensive knowledge regarding the mechanistic of the circadian system is crucial to develop new procedures to investigate pathologies associated with a deregulated clock.

In this manuscript we review the combination of experimental methodologies, bioinformatics and theoretical models that have been essential to explore this remarkable timing-system. Such an integrative and interdisciplinary approach may provide new strategies with regard to chronotherapeutic treatment and new insights concerning the restoration of the circadian timing in clock-associated diseases.

Uncovering distinct protein-network topologies in heterogeneous cell populations

Background

Cell biology research is fundamentally limited by the number of intracellular components, particularly proteins, that can be co-measured in the same cell. Therefore, cell-to-cell heterogeneity in unmeasured proteins can lead to completely different observed relations between the same measured proteins. Attempts to infer such relations in a heterogeneous cell population can yield uninformative average relations if only one underlying biochemical network is assumed. To address this, we developed a method that recursively couples an iterative unmixing process with a Bayesian analysis of each unmixed subpopulation.

Results

Our approach enables to identify the number of distinct cell subpopulations, unmix their corresponding observations and resolve the network structure of each subpopulation. Using simulations of the MAPK pathway upon EGF and NGF stimulations we assess the performance of the method. We demonstrate that the presented method can identify better than clustering approaches the number of subpopulations within a mixture of observations, thus resolving correctly the statistical relations between the proteins.

Conclusions

Coupling the unmixing of multiplexed observations with the inference of statistical relations between the measured parameters is essential for the success of both of these processes. Here we present a conceptual and algorithmic solution to achieve such coupling and hence to analyze data obtained from a natural mixture of cell populations. As the technologies and necessity for multiplexed measurements are rising in the systems biology era, this work addresses an important current challenge in the analysis of the derived data.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0170-2) contains supplementary material, which is available to authorized users.

Exact likelihood computation in Boolean networks with probabilistic time delays, and its application in signal network reconstruction

MOTIVATION

For biological pathways, it is common to measure a gene expression time series after various knockdowns of genes that are putatively involved in the process of interest. These interventional time-resolved data are most suitable for the elucidation of dynamic causal relationships in signaling networks. Even with this kind of data it is still a major and largely unsolved challenge to infer the topology and interaction logic of the underlying regulatory network.

RESULTS

In this work, we present a novel model-based approach involving Boolean networks to reconstruct small to medium-sized regulatory networks. In particular, we solve the problem of exact likelihood computation in Boolean networks with probabilistic exponential time delays. Simulations demonstrate the high accuracy of our approach. We apply our method to data of Ivanova et al. (2006), where RNA interference knockdown experiments were used to build a network of the key regulatory genes governing mouse stem cell maintenance and differentiation. In contrast to previous analyses of that data set, our method can identify feedback loops and provides new insights into the interplay of some master regulators in embryonic stem cell development.

AVAILABILITY AND IMPLEMENTATION

The algorithm is implemented in the statistical language R. Code and documentation are available at Bioinformatics online.

CONTACT

duemcke@mpipz.mpg.de or tresch@mpipz.mpg.de

SUPPLEMENTARY INFORMATION

Supplementary Materials are available at Bioinfomatics online.

Reconstruction of biological networks by incorporating prior knowledge into Bayesian network models

Bayesian network model is widely used for reverse engineering of biological network structures. An advantage of this model is its capability to integrate prior knowledge into the model learning process, which can lead to improving the quality of the network reconstruction outcome. Some previous works have explored this area with focus on using prior knowledge of the direct molecular links, except for a few recent ones proposing to examine the effects of molecular orderings. In this study, we propose a Bayesian network model that can integrate both direct links and orderings into the model. Random weights are assigned to these two types of prior knowledge to alleviate bias toward certain types of information. We evaluate our model performance using both synthetic data and biological data for the RAF signaling network, and illustrate the significant improvement on network structure reconstruction of the proposing models over the existing methods. We also examine the correlation between the improvement and the abundance of ordering prior knowledge. To address the issue of generating prior knowledge, we propose an approach to automatically extract potential molecular orderings from knowledge resources such as Kyoto Encyclopedia of Genes and Genomes (KEGG) database and Gene Ontology (GO) annotation.

Learning the local Bayesian network structure around the ZNF217 oncogene in breast tumours

In this study, we discuss and apply a novel and efficient algorithm for learning a local Bayesian network model in the vicinity of the ZNF217 oncogene from breast cancer microarray data without having to decide in advance which genes have to be included in the learning process. ZNF217 is a candidate oncogene located at 20q13, a chromosomal region frequently amplified in breast and ovarian cancer, and correlated with shorter patient survival in these cancers. To properly address the difficulties in managing complex gene interactions given our limited sample, statistical significance of edge strengths was evaluated using bootstrapping and the less reliable edges were pruned to increase the network robustness. We found that 13 out of the 35 genes associated with deregulated ZNF217 expression in breast tumours have been previously associated with survival and/or prognosis in cancers. Identifying genes involved in lipid metabolism opens new fields of investigation to decipher the molecular mechanisms driven by the ZNF217 oncogene. Moreover, nine of the 13 genes have already been identified as putative ZNF217 targets by independent biological studies. We therefore suggest that the algorithms for inferring local BNs are valuable data mining tools for unraveling complex mechanisms of biological pathways from expression data. The source code is available at http://www710.univ-lyon1.fr/∼aaussem/Software.html.

Graphical modelling of molecular networks underlying sporadic inclusion body myositis

Here we present a novel statistical methodology that allows us to analyze gene expression data that have been collected from a number of different cases or conditions in a unified framework. Using a Bayesian nonparametric framework we develop a hierarchical model wherein genes can maintain a shared set of interactions between different cases, whilst also exhibiting behaviour that is unique to specific cases, sets of conditions, or groups of data points. By doing so we are able to not only combine data from different cases but also to discern the unique regulatory interactions that differentiate the cases. We apply our method to clinical data collected from patients suffering from sporadic Inclusion Body Myositis (sIBM), as well as control samples, and demonstrate the ability of our method to infer regulatory interactions that are unique to the disease cases of interest. The method thus balances the statistical need to include as many patients and controls as possible, and the clinical need to maintain potentially cryptic differences among patients and between patients and controls at the regulatory level.

Sparse time series chain graphical models for reconstructing genetic networks

We propose a sparse high-dimensional time series chain graphical model for reconstructing genetic networks from gene expression data parametrized by a precision matrix and autoregressive coefficient matrix. We consider the time steps as blocks or chains. The proposed approach explores patterns of contemporaneous and dynamic interactions by efficiently combining Gaussian graphical models and Bayesian dynamic networks. We use penalized likelihood inference with a smoothly clipped absolute deviation penalty to explore the relationships among the observed time course gene expressions. The method is illustrated on simulated data and on real data examples from Arabidopsis thaliana and mammary gland time course microarray gene expressions.

Learning contextual gene set interaction networks of cancer with condition specificity

Background

Identifying similarities and differences in the molecular constitutions of various types of cancer is one of the key challenges in cancer research. The appearances of a cancer depend on complex molecular interactions, including gene regulatory networks and gene-environment interactions. This complexity makes it challenging to decipher the molecular origin of the cancer. In recent years, many studies reported methods to uncover heterogeneous depictions of complex cancers, which are often categorized into different subtypes. The challenge is to identify diverse molecular contexts within a cancer, to relate them to different subtypes, and to learn underlying molecular interactions specific to molecular contexts so that we can recommend context-specific treatment to patients.

Results

In this study, we describe a novel method to discern molecular interactions specific to certain molecular contexts. Unlike conventional approaches to build modular networks of individual genes, our focus is to identify cancer-generic and subtype-specific interactions between contextual gene sets, of which each gene set share coherent transcriptional patterns across a subset of samples, termed contextual gene set. We then apply a novel formulation for quantitating the effect of the samples from each subtype on the calculated strength of interactions observed. Two cancer data sets were analyzed to support the validity of condition-specificity of identified interactions. When compared to an existing approach, the proposed method was much more sensitive in identifying condition-specific interactions even in heterogeneous data set. The results also revealed that network components specific to different types of cancer are related to different biological functions than cancer-generic network components. We found not only the results that are consistent with previous studies, but also new hypotheses on the biological mechanisms specific to certain cancer types that warrant further investigations.

Conclusions

The analysis on the contextual gene sets and characterization of networks of interaction composed of these sets discovered distinct functional differences underlying various types of cancer. The results show that our method successfully reveals many subtype-specific regions in the identified maps of biological contexts, which well represent biological functions that can be connected to specific subtypes.

Biostatistical approaches for the reconstruction of gene co-expression networks based on transcriptomic data

Techniques in molecular biology have permitted the gathering of an extremely large amount of information relating organisms and their genes. The current challenge is assigning a putative function to thousands of genes that have been detected in different organisms. One of the most informative types of genomic data to achieve a better knowledge of protein function is gene expression data. Based on gene expression data and assuming that genes involved in the same function should have a similar or correlated expression pattern, a function can be attributed to those genes with unknown functions when they appear to be linked in a gene co-expression network (GCN). Several tools for the construction of GCNs have been proposed and applied to plant gene expression data. Here, we review recent methodologies used for plant gene expression data and compare the results, advantages and disadvantages in order to help researchers in their choice of a method for the construction of GCNs.

Inference of temporally varying Bayesian networks

MOTIVATION

When analysing gene expression time series data, an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Although some approaches have addressed this problem previously in the literature, many are not well suited to the sequential nature of the data.

RESULTS

Here, we present a method that allows us to infer regulatory network structures that may vary between time points, using a set of hidden states that describe the network structure at a given time point. To model the distribution of the hidden states, we have applied the Hierarchical Dirichlet Process Hidden Markov Model, a non-parametric extension of the traditional Hidden Markov Model, which does not require us to fix the number of hidden states in advance. We apply our method to existing microarray expression data as well as demonstrating is efficacy on simulated test data.

Issues impacting genetic network reverse engineering algorithm validation using small networks

Genetic network reverse engineering has been an area of intensive research within the systems biology community during the last decade. With many techniques currently available, the task of validating them and choosing the best one for a certain problem is a complex issue. Current practice has been to validate an approach on in-silico synthetic data sets, and, wherever possible, on real data sets with known ground-truth. In this study, we highlight a major issue that the validation of reverse engineering algorithms on small benchmark networks very often results in networks which are not statistically better than a randomly picked network. Another important issue highlighted is that with short time series, a small variation in the pre-processing procedure might yield large differences in the inferred networks. To demonstrate these issues, we have selected as our case study the IRMA in-vivo synthetic yeast network recently published in Cell. Using Fisher's exact test, we show that many results reported in the literature on reverse-engineering this network are not significantly better than random. The discussion is further extended to some other networks commonly used for validation purposes in the literature. The results presented in this study emphasize that studies carried out using small genetic networks are likely to be trivial, making it imperative that larger real networks be used for validating and benchmarking purposes. If smaller networks are considered, then the results should be interpreted carefully to avoid over confidence. This article is part of a Special Issue entitled: Computational Methods for Protein Interaction and Structural Prediction.

Modeling formalisms in Systems Biology

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future.

Improvements in the reconstruction of time-varying gene regulatory networks: dynamic programming and regularization by information sharing among genes

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.

Constructing non-stationary Dynamic Bayesian Networks with a flexible lag choosing mechanism

Background

Dynamic Bayesian Networks (DBNs) are widely used in regulatory network structure inference with gene expression data. Current methods assumed that the underlying stochastic processes that generate the gene expression data are stationary. The assumption is not realistic in certain applications where the intrinsic regulatory networks are subject to changes for adapting to internal or external stimuli.

Results

In this paper we investigate a novel non-stationary DBNs method with a potential regulator detection technique and a flexible lag choosing mechanism. We apply the approach for the gene regulatory network inference on three non-stationary time series data. For the Macrophages and Arabidopsis data sets with the reference networks, our method shows better network structure prediction accuracy. For the Drosophila data set, our approach converges faster and shows a better prediction accuracy on transition times. In addition, our reconstructed regulatory networks on the Drosophila data not only share a lot of similarities with the predictions of the work of other researchers but also provide many new structural information for further investigation.

Conclusions

Compared with recent proposed non-stationary DBNs methods, our approach has better structure prediction accuracy By detecting potential regulators, our method reduces the size of the search space, hence may speed up the convergence of MCMC sampling.

Analysis of lifestyle and metabolic predictors of visceral obesity with Bayesian Networks

Background

The aim of this study was to provide a framework for the analysis of visceral obesity and its determinants in women, where complex inter-relationships are observed among lifestyle, nutritional and metabolic predictors. Thirty-four predictors related to lifestyle, adiposity, body fat distribution, blood lipids and adipocyte sizes have been considered as potential correlates of visceral obesity in women. To properly address the difficulties in managing such interactions given our limited sample of 150 women, bootstrapped Bayesian networks were constructed based on novel constraint-based learning methods that appeared recently in the statistical learning community. Statistical significance of edge strengths was evaluated and the less reliable edges were pruned to increase the network robustness. To allow accessible interpretation and integrate biological knowledge into the final network, several undirected edges were afterwards directed with physiological expertise according to relevant literature.

Results

Extensive experiments on synthetic data sampled from a known Bayesian network show that the algorithm, called Recursive Hybrid Parents and Children (RHPC), outperforms state-of-the-art algorithms that appeared in the recent literature. Regarding biological plausibility, we found that the inference results obtained with the proposed method were in excellent agreement with biological knowledge. For example, these analyses indicated that visceral adipose tissue accumulation is strongly related to blood lipid alterations independent of overall obesity level.

Conclusions

Bayesian Networks are a useful tool for investigating and summarizing evidence when complex relationships exist among predictors, in particular, as in the case of multifactorial conditions like visceral obesity, when there is a concurrent incidence for several variables, interacting in a complex manner. The source code and the data sets used for the empirical tests are available at http://www710.univ-lyon1.fr/~aaussem/Software.html.

Modelling nonstationary gene regulatory processes

An important objective in systems biology is to infer gene regulatory networks from postgenomic data, and dynamic Bayesian networks have been widely applied as a popular tool to this end. The standard approach for nondiscretised data is restricted to a linear model and a homogeneous Markov chain. Recently, various generalisations based on changepoint processes and free allocation mixture models have been proposed. The former aim to relax the homogeneity assumption, whereas the latter are more flexible and, in principle, more adequate for modelling nonlinear processes. In our paper, we compare both paradigms and discuss theoretical shortcomings of the latter approach. We show that a model based on the changepoint process yields systematically better results than the free allocation model when inferring nonstationary gene regulatory processes from simulated gene expression time series. We further cross-compare the performance of both models on three biological systems: macrophages challenged with viral infection, circadian regulation in Arabidopsis thaliana, and morphogenesis in Drosophila melanogaster.

An introduction to Gaussian Bayesian networks

The extraction of regulatory networks and pathways from postgenomic data is important for drug -discovery and development, as the extracted pathways reveal how genes or proteins regulate each other. Following up on the seminal paper of Friedman et al. (J Comput Biol 7:601-620, 2000), Bayesian networks have been widely applied as a popular tool to this end in systems biology research. Their popularity stems from the tractability of the marginal likelihood of the network structure, which is a consistent scoring scheme in the Bayesian context. This score is based on an integration over the entire parameter space, for which highly expensive computational procedures have to be applied when using more complex -models based on differential equations; for example, see (Bioinformatics 24:833-839, 2008). This chapter gives an introduction to reverse engineering regulatory networks and pathways with Gaussian Bayesian networks, that is Bayesian networks with the probabilistic BGe scoring metric [see (Geiger and Heckerman 235-243, 1995)]. In the BGe model, the data are assumed to stem from a Gaussian distribution and a normal-Wishart prior is assigned to the unknown parameters. Gaussian Bayesian network methodology for analysing static observational, static interventional as well as dynamic (observational) time series data will be described in detail in this chapter. Finally, we apply these Bayesian network inference methods (1) to observational and interventional flow cytometry (protein) data from the well-known RAF pathway to evaluate the global network reconstruction accuracy of Bayesian network inference and (2) to dynamic gene expression time series data of nine circadian genes in Arabidopsis thaliana to reverse engineer the unknown regulatory network topology for this domain.