In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools for the modeling and simulation of genetic regulatory networks will be indispensable. This paper reviews formalisms that have been employed in mathematical biology and bioinformatics to describe genetic regulatory systems, in particular directed graphs, Bayesian networks, Boolean networks and their generalizations, ordinary and partial differential equations, qualitative differential equations, stochastic equations, and rule-based formalisms. In addition, the paper discusses how these formalisms have been used in the simulation of the behavior of actual regulatory systems.

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.

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The inference of genetic interactions from measured expression data is one of the most challenging tasks of modern functional genomics. When successful, the learned network of regulatory interactions yields a wealth of useful information. An inferred genetic network contains information about the pathway to which a gene belongs and which genes it interacts with. Furthermore, it explains the gene's function in terms of how it influences other genes and indicates which genes are pathway initiators and therefore potential drug targets. Obviously, such wealth comes at a price and that of genetic network modeling is that it is an extremely complex task. Therefore, it is necessary to develop sophisticated computational tools that are able to extract relevant information from a limited set of microarray measurements and integrate this with different information sources, to come up with reliable hypotheses of a genetic regulatory network. Thus far, a multitude of modeling approaches has been proposed for discovering genetic networks. However, it is unclear what the advantages and disadvantages of each of the different approaches are and how their results can be compared. In this review, genetic network models are put in a historical perspective that explains why certain models were introduced. Various modeling assumptions and their consequences are also highlighted. In addition, an overview of the principal differences and similarities between the approaches is given by considering the qualitative properties of the chosen models and their learning strategies. In pharmacogenomics and related areas, a lot of research is directed towards discovering, understanding and/or controlling the outcome of some particular biological pathway. Numerous examples exist where the manipulation of a key enzyme in such a pathway did not lead to the desired effect We know that the structure of complex genetic and biochemical networks lies hidden in the sequence information of our DNA but it is far from trivial to predict gene expression from the sequence code alone. The current availability of microarray measurements of thousands of gene expression levels during the course of an experiment or after the knockout of a gene provides a wealth of complementary information that may be exploited to unravel the complex interplay between genes. It now becomes possible to start answering some of the truly challenging questions in systems biology. For example, is it possible to model these genetic interactions as a large network of interacting elements and can these interactions be effectively learned from measured expression data? Since Kauffman Although the behavior and properties of artificial networks match the observations made in real biological systems well, the field of genetic network modeling has yet to reach its full maturity. The automatic discovery of genetic networks from expression data alone is far from trivial because of the combinatorial nature of the problem and the poor information content of 1 For reasons of brevity, the authors consistently refer only to the first author of each reference.

Clustering is commonly used for analyzing gene expression data. Despite their successes, clustering methods suffer from a number of limitations. First, these methods reveal similarities that exist over all of the measurements, while obscuring relationships that exist over only a subset of the data. Second, clustering methods cannot readily incorporate additional types of information, such as clinical data or known attributes of genes. To circumvent these shortcomings, we propose the use of a single coherent probabilistic model, that encompasses much of the rich structure in the genomic expression data, while incorporating additional information such as experiment type, putative binding sites, or functional information. We show how this model can be learned from the data, allowing us to discover patterns in the data and dependencies between the gene expression patterns and additional attributes. The learned model reveals context-specific relationships, that exist only over a subset of the experiments in the dataset. We demonstrate the power of our approach on synthetic data and on two real-world gene expression data sets for yeast. For example, we demonstrate a novel functionality that falls naturally out of our framework: predicting the “cluster” of the array resulting from a gene mutation based only on the gene’s expression pattern in the context of other mutations.

Motivation: Genetic networks regulate key processes in living cells. Various methods have been suggested to reconstruct network architecture from gene expression data. However, most approaches are based on qualitative models that provide only rough approximations of the underlying events, and lack the quantitative aspects that are critical for understanding the proper function of biomolecular systems. Results: We present fine-grained dynamical models of gene transcription and develop methods for reconstructing them from gene expression data within the framework of a generative probabilistic model. Unlike previous works, we employ quantitative transcription rates, and simultaneously estimate both the kinetic parameters that govern these rates, and the activity levels of unobserved regulators that control them. We apply our approach to expression data sets from yeast and show that we can learn the unknown regulator activity profiles, as well as the binding affinity parameters. We also introduce a novel structure learning algorithm, and demonstrate its power to accurately reconstruct the regulatory network from those data sets.

We propose a statistical method for estimating a gene network based on Bayesian networks from microarray gene expression data together with biological knowledge including protein-protein interactions, protein-DNA interactions, binding site information, existing literature and so on. Unfortunately, microarray data do not contain enough information for constructing gene networks accurately in many cases. Our method adds biological knowledge to the estimation method of gene networks under a Bayesian statistical framework, and also controls the trade-off between microarray information and biological knowledge automatically. We conduct Monte Carlo simulations to show the effectiveness of the proposed method. We analyze Saccharomyces cerevisiae gene expression data as an application. 1.

Abstract. We propose a dynamic Bayesian network and nonparametric regression model for constructing a gene network from time series microarray gene expression data. The proposed method can overcome a shortcoming of the Bayesian network model in the sense of the construction of cyclic regulations. The proposed method can analyze the microarray data as continuous data and can capture even nonlinear relations among genes. It can be expected that this model will give a deeper insight into the complicated biological systems. We also derive a new criterion for evaluating an estimated network from Bayes approach. We demonstrate the effectiveness of our method by analyzing Saccharomyces cerevisiae gene expression data. 1

We present a probabilistic framework that models the process by which transcriptional binding explains the mRNA expression of different genes. Our joint probabilistic model unifies the two key components of this process: the prediction of gene regulation events from sequence motifs in the gene’s promoter region, and the prediction of mRNA expression from combinations of gene regulation events in different settings. Our approach has several advantages. By learning promoter sequence motifs that are directly predictive of expression data, it can improve the identification of binding site patterns. It is also able to identify combinatorial regulation via interactions of different transcription factors. Finally, the general framework allows us to integrate additional data sources, including data from the recent binding localization assays. We demonstrate our approach on the cell cycle data of Spellman et al., combined with the binding localization information of Simon et al. We show that the learned model predicts expression from sequence, and that it identifies coherent co-regulated groups with significant transcription factor motifs. It also provides valuable biological insight into the domain via these co-regulated “modules” and the combinatorial regulation effects that govern their behavior.