In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics, which often provide qualitative and coarsegrained descriptions of genetic regulatory networks. Given a qualitative model of a genetic regulatory network, consisting of a system of PL differential equations and inequality constraints on the parameter values, the method produces a graph of qualitative states and transitions between qualitative states, summarizing the qualitative dynamics of the system. The qualitative simulation method has been implemented in Java in the computer tool Genetic Network Analyzer.

The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their mutual interactions, so-called genetic regulatory networks. In order to gain an understanding of how the behavior of an organism – e.g., the response of a

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The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their interactions, so-called genetic regulatory networks. The concerted efforts of genetics, molecular biology, biochemistry, and physiology have led to the accumulation of enormous amounts of data on the molecular components of genetic regulatory networks and their interactions. Notwithstanding the advances in the mapping of the network structure, surprisingly little is understood about how the dynamic behavior of the system emerges from the interactions between the network components. This has incited an increasingly large group of researchers to turn from the structure to the behavior of genetic regulatory networks, against the background of a broader movement nowadays often referred to as systems biology

Abstract. The switch-like character of the dynamics of genetic regulatory networks has attracted much attention from mathematical biologists and researchers on hybrid systems alike. We extend our previous work on a method for the qualitative analysis of hybrid models of genetic regulatory networks, based on a class of piecewise-affine differential equation (PADE) models, in two directions. First, we present a refinement of the method using a discrete or qualitative abstraction that preserves stronger properties of the dynamics of the PA systems, in particular the sign patterns of the derivatives of the concentration variables. The discrete transition system resulting from the abstraction is a conservative approximation of the dynamics of the PA system and can be computed symbolically. Second, we apply the refined method to a regulatory system whose functioning is not yet well-understood by biologists, the nutritional stress response in the bacterium Escherichia coli. 1

Motivation: New developments in post-genomic technology now provide researchers with the data necessary to study regulatory processes in a holistic fashion at multiple levels of biological organisation. One of the major challenges for the biologist is to integrate and interpret these vast data resources to gain a greater understanding of the structure and function of the molecular processes that mediate adaptive and cell cycle driven changes in gene expression. In order to achieve this biologists require new tools and techniques to allow pathway related data to be modelled and analysed as network structures, providing valuable insights which can then be validated and investigated in the laboratory. Results: We propose a new technique for constructing and analysing qualitative models of genetic regulatory networks based on the Petri net formalism. We take as our starting point the Boolean network approach of treating genes as binary switches and develop a new Petri net model which uses logic minimization to automate the construction of compact qualitative models. Our approach addresses the shortcomings of Boolean networks by providing access to the wide range of existing Petri net analysis techniques and by using non–determinism to cope with incomplete and inconsistent data. The ideas we present are illustrated by a case study in which the genetic regulatory network controlling sporulation in the bacterium Bacillus subtilis is modelled and analysed. Availability: The Petri net model construction tool and the data files for the B. subtilis sporulation case study are available at

Methods developed for the qualitative simulation of dynamical systems have turned out to be powerful tools for studying genetic regulatory networks. A bottleneck in the application of these methods is the analysis of the simulation results. In this paper, we propose a combination of qualitative simulation and model-checking techniques to perform this task correctly and efficiently. By means of the example of the network controlling the initiation of sporulation in B. subtilis, we argue that this approach is well-adapted to the kind of questions biologists habitually ask and the kind of data available to answer these questions. 1

Summary. The experimental study of genetic regulatory networks has made tremendous progress in recent years resulting in a huge amount of data on the molecular interactions in model organisms. It is therefore not possible anymore to intuitively understand how the genes and interactions together influence the behavior of the system. In order to answer such questions, a rigorous modeling and analysis approach is necessary. In this chapter, we present a family of such models and analysis methods enabling us to better understand the dynamics of genetic regulatory networks. We apply such methods to the network that underlies the nutritional stress response of the bacterium E. coli. The functioning and development of living organisms is controlled by large and complex networks of genes, proteins, small molecules, and their interactions, socalled genetic regulatory networks. The study of these networks has recently taken a qualitative leap through the use of modern genomic techniques that allow for the simultaneous measurement of the expression levels of all genes of an organism. This has resulted in an ever growing description of the interactions in the studied genetic regulatory networks. However, it is necessary to go beyond the simple description

Methods developed for the qualitative simulation of dynamical systems have turned out to be powerful tools for studying genetic regulatory networks. A bottleneck in the application of these methods is the analysis of the simulation results. In this paper, we propose a combination of qualitative simulation and model-checking techniques to perform this task systematically and efficiently. We apply our approach to the analysis of the complex network controlling the nutritional stress response in the bacterium Escherichia coli. 1

Invited Review-R1 DNA microarray represents a powerful tool in biomedical discoveries. Harnessing the potential of this technology depends on the development and appropriate use of data mining and statistical tools. Significant current advances have made microarray data mining more versatile. Researchers are no longer limited to default choices that generate suboptimal results. Conflicting results in repeated experiments can be resolved through attention to the statistical details. In the current dynamic environment, there are many choices and potential pitfalls for researchers who intend to incorporate microarrays as a research tool. This review is intended to provide a simple framework to understand the choices and identify the pitfalls. Specifically, this review article discusses the choice of microarray platform, preprocessing raw data, differential expression and validation, clustering, annotation and functional characterization of genes, and pathway construction in light of emergent concepts and tools.