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: Our goal is to construct a model for genetic regulatory networks such that the model class: (i ) incorporates rule-based dependencies between genes; (ii ) allows the systematic study of global network dynamics; (iii ) is able to cope with uncertainty, both in the data and the model selection; and (iv ) permits the quantification of the relative influence and sensitivity of genes in their interactions with other genes.

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.

Abstract—DNA microarray technology has now made it possible to simultaneously monitor the expression levels of thousands of genes during important biological processes and across collections of related samples. Elucidating the patterns hidden in gene expression data offers a tremendous opportunity for an enhanced understanding of functional genomics. However, the large number of genes and the complexity of biological networks greatly increases the challenges of comprehending and interpreting the resulting mass of data, which often consists of millions of measurements. A first step toward addressing this challenge is the use of clustering techniques, which is essential in the data mining process to reveal natural structures and identify interesting patterns in the underlying data. Cluster analysis seeks to partition a given data set into groups based on specified features so that the data points within a group are more similar to each other than the points in different groups. A very rich literature on cluster analysis has developed over the past three decades. Many conventional clustering algorithms have been adapted or directly applied to gene expression data, and also new algorithms have recently been proposed specifically aiming at gene expression data. These clustering algorithms have been proven useful for identifying biologically relevant groups of genes and samples. In this paper, we first briefly introduce the concepts of microarray technology and discuss the basic elements of clustering on gene expression data. In particular, we divide cluster analysis for gene expression data into three categories. Then, we present specific challenges pertinent to each clustering category and introduce several representative approaches. We also discuss the problem of cluster validation in three aspects and review various methods to assess the quality and reliability of clustering results. Finally, we conclude this paper and suggest the promising trends in this field. Index Terms—Microarray technology, gene expression data, clustering.

Motivation: Most approaches to gene expression analysis use real-valued expression data, produced by highthroughput screening technologies, such as microarrays. Often, some measure of similarity must be computed in order to extract meaningful information from the observed data. The choice of this similarity measure frequently has a profound effect on the results of the analysis, yet no standards exist to guide the researcher.

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Abstract. A major challenge in system biology is the automatic inference of gene regulation network topology—an instance of reverse engineering—based on limited local data whose collection is costly and slow. Reverse engineering implies the reconstruction of a hidden system based only on input and output data sets generated by the target system. Here we present a generalized evolutionary algorithm that can reverse engineer a hidden network based solely on input supplied to the network and the output obtained, using a minimal number of tests of the physical system. The algorithm has two stages: the first stage evolves a system hypothesis, and the second stage evolves a new experiment that should be carried out on the target system in order to extract the most information. We present the general algorithm, which we call the estimation-exploration algorithm, and demonstrate it both for the inference of gene regulatory networks without the need to perform expensive and disruptive knockout studies, and the inference of morphological properties of a robot without extensive physical testing. 1

Clustering is one of the most commonly used tools in the analysis of gene expression data (1, 2). The usage in grouping genes is based on the premise that co-expression is a result of co-regulation. It is thus a preliminary step in extracting gene networks and inference of gene function (3, 4). Clustering of experiments can be used to discover novel

Abstract. Recent advances of experimental techniques in biology have led to the production of enormous amounts of data on the dynamics of genetic regulatory networks. In this paper, we present an approach for the identification of PieceWise-Affine (PWA) models of genetic regulatory networks from experimental data, focusing on the reconstruction of switching thresholds associated with regulatory interactions. In particular, our method takes into account geometric constraints specific to models of genetic regulatory networks. We show the feasibility of our approach by the reconstruction of switching thresholds in a PWA model of the carbon starvation response in the bacterium Escherichia coli. 1

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.