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. Key words: genetic regulatory networks, mathematical modeling, simulation, computational biology.

motivation: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using highthroughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.

Motivation: Transcriptional activation in eukaryotic organisms normally requires combinatorial interactions of multiple transcription factors. Though several methods exist for identification of individual protein binding site patterns in DNA sequences, there are few methods for discovery of binding site patterns for cooperatively acting factors. Here we present an algorithm, Co-Bind (for COperative BINDing) , for discovering DNA target sites for cooperatively acting transcription factors. The method utilizes a Gibbs sampling strategy to model the cooperativity between two transcription factors and defines position weight matrices for the binding sites. Sequences from both the training set and the entire genome are taken into account, in order to discriminate against commonly occurring patterns in the genome, and produce patterns which are significant only in the training set. Results: We have tested Co-Bind on semi-synthetic and real data sets to show it can efficiently identify DNA target site patterns for cooperatively binding transcription factors. In cases where binding site patterns are weak and cannot be identified by other available methods, Co-Bind, by virtue of modeling the cooperativity between factors, can identify those sites efficiently. Though developed to model protein-- DNA interactions, the scope of Co-Bind may be extended to combinatorial, sequence specific, interactions in other macromolecules. Availability: The program is available upon request from the authors or may be downloaded from http://ural.wustl. edu. Contact: dg@genetics.wustl.edu; stormo@genetics.wustl.edu 1

In this paper, the regulatory interactions between genes are modeled by a linear genetic network that is estimated from gene expression data. The inference of such a genetic network is hampered by the dimensionality problem. This problem is inherent in all gene expression data since the number of genes by far exceeds the number of measured time points. Consequently, there are infinitely many solutions that fit the data set perfectly. In this paper, this problem is tackled by combining genes with similar expression profiles in a single prototypical `gene'. Instead of modeling the genes individually, the relations between prototypical genes are modeled. In this way, genes that cannot be distinguished based on their expression profiles are grouped together and their common control action is modeled instead. This process reduces the number of signals and imposes a structure on the model that is supported by the fact that biological genetic networks are thought to be redun...

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The segmentation gene network of Drosophila consists of maternal and zygotic factors that generate, by transcriptional (cross-) regulation, expression patterns of increasing complexity along the anterior-posterior axis of the embryo. Using known binding site information for maternal and zygotic gap transcription factors, the computer algorithm Ahab recovers known segmentation control elements (modules) with excellent success and predicts many novel modules within the network and genome-wide. We show that novel module predictions are highly enriched in the network and typically clustered proximal to the promoter, not only upstream, but also in intronic space and downstream. When placed upstream of a reporter gene, they consistently drive patterned blastoderm expression, in most cases faithfully producing one or more pattern elements of the endogenous gene. Moreover, we demonstrate for the entire set of known and newly validated modules that Ahab’s prediction of binding sites correlates well with the expression patterns produced by the modules, revealing basic rules governing their composition. Specifically, we show that maternal factors consistently act as activators and that gap factors act as repressors, except for the bimodal factor Hunchback. Our data suggest a simple context-dependent rule for its switch from repressive to activating function. Overall, the composition of modules appears well fitted to the spatiotemporal distribution of their positive and negative input factors. Finally, by comparing Ahab predictions with different categories of transcription factor input, we confirm the global regulatory structure of the segmentation gene network, but find odd skipped behaving like a

Boolean networks are a popular model class for capturing the interactions of genes and global dynamical behavior of genetic regulatory networks. Recently, a significant amount of attention has been focused on the inference or identification of the model structure from gene expression data. We consider the Consistency as well as Best-Fit Extension problems in the context of inferring the networks from data. The latter approach is especially useful in situations when gene expression measurements are noisy and may lead to inconsistent observations. We propose simple efficient algorithms that can be used to answer the Consistency Problem and find one or all consistent Boolean networks relative to the given examples. The same method is extended to learning gene regulatory networks under the Best-Fit Extension paradigm. We also introduce a simple and fast way of finding all Boolean networks having limited error size in the Best-Fit Extension Problem setting. We apply the inference methods to a real gene expression data set and present the results for a selected set of genes.

Currently, the need arises for tools capable of unraveling the functionality of genes based on the analysis of microarray measurements. Modeling genetic interactions by means of genetic network models provides a methodology to infer functional relationships between genes. Although a wide variety of different models have been introduced so far, it remains, in general, unclear what the strengths and weaknesses of each of these approaches are and where these models overlap and differ. This paper compares different genetic modeling approaches that attempt to extract the gene regulation matrix from expression data. A taxonomy of continuous genetic network models is proposed and the following important characteristics are suggested and employed to compare the models: (1) inferential power; (2) predictive power; (3) robustness; (4) consistency; (5) stability and (6) computational cost. Where possible, synthetic time series data are employed to investigate some of these properties. The comparison shows that although genetic network modeling might provide valuable information regarding genetic interactions, current models show disappointing results on simple artificial problems. For now, the simplest models are favored because they generalize better, but more complex models will probably prevail once their bias is more thoroughly understood and their variance is better controlled.

A major problem associated with the reverse engineering of genetic networks from micro-array data is how to reliably nd genetic interactions when faced with a relatively small number of arrays compared to the number of genes. To cope with this dimensionality problem, it is imperative to employ additional (biological) knowledge about real genetic networks, such as limited connectivity, redundancy, stability and robustness, to sensibly constrain the modeling process. In previous

and biological knowledge