Qualitative Simulation of Genetic Regulatory Networks: Method and Application

Computer modeling and simulation are indispensable for understanding the functioning of an organism on a molecular level. We present an implemented method for the qualitative simulation of large and complex genetic regulatory networks. The method allows a broad range of regulatory interactions between genes to be represented and has been applied to the analysis of a real network of biological interest, the network controlling the inititation of sporulation in the bacterium B. subtilis. Introduction It is now commonly accepted in biology that most interesting properties of an organism emerge from the interactions among its genes, proteins, metabolites, and other molecules. This implies that, in order to understand the functioning of an organism, the networks of interactions involved in gene regulation, metabolism, signal transduction, and other cellular and intercellular processes need to be elucidated. A genetic regulatory network consists of a set of genes and their mutual regulatory interactions. The interactions arise from the fact that genes code for proteins that may control the expression of other genes, for instance by activating or inhibiting DNA transcription (Lewin 1999). The study of genetic regulatory networks has received a major impetus from the recent development of experimental techniques permitting the spatiotemporal expression levels of genes to be rapidly measured in a massively parallel way (Brown & Botstein 1999). However, in addition to experimental tools, computer tools for the modeling and simulation of gene regulation processes will be indispensable (de Jong 2000; McAdams & Arkin 1998; Smolen, Baxter, & Byrne 2000). As most genetic regulatory systems of interest involve many genes connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. Currently, only a few regulatory networks are wellunderstood on the molecular level. In addition, quantitative information on kinetic parameters and molecular concentrations are seldom available. This has stimulated an interest in A shorter version of this paper appears in the Proceedings of the 17th International Joint Conference on Artificial Intelligence, IJCAI-01, Seattle, Washington, USA, 4-10 August, 2001. modeling and simulation techniques developed within qualitative reasoning (QR) (Heidtke & Schulze-Kremer 1998; Trelease, Henderson, & Park 1999). A major problem with these approaches, based on well-known methods like QSIM (Kuipers 1994) and QPT (Forbus 1984), is their lack of upscalability. Following approaches in mathematical biology, de Jong and Page (2000) have proposed a qualitative simulation method capable of handling large and complex networks. The aim of this paper is to generalize the latter method and to demonstrate its applicability to real networks of biological interest. The generalization of the method allows a broader range of regulatory interactions between genes to be expressed. This enables more complex systems to be analyzed, such as the network of interactions controlling the inititation of sporulation in the bacterium Bacillus subtilis. We have simulated the sporulation network using a model constructed from published reports of experiments. The simulations reveal that an additional interaction, proposed in the literature before but not yet experimentally identified, may be involved. In the next section, we will discuss the class of equations being used to model genetic regulatory networks. The third section describes the qualitative simulation algorithm, focusing on the representation of the qualitative state of a regulatory system and the determination of state transitions by the simulation algorithm. The subsequent sections present the results of the analysis of the sporulation network as well as a discussion of the method in the context of related work. Modeling genetic regulatory networks Approximations of regulatory interactions In order to model a genetic regulatory network, we first have to describe the regulatory interactions in an empirically valid and mathematically rigorous way. Consider a DNA-binding protein encoded by gene , activating the expression of a target gene . The rate of transcription of as a function of the concentration of the regulatory protein follows a sigmoid curve (Yagil & Yagil 1971). Below a threshold concentration the gene is hardly expressed at all, whereas above this threshold its expression rapidly saturates. Sigmoid curves are also found in the case of more complex regulatory mechanisms. Consider the proteins J and K that form a dimer repressing the transcription of gene (Fig. 1(b)). Analysis of a kinetic model of this regulatory mechanism reveals that the rate of expression of depends in a sigmoidal fashion on the total concentrations and of J and K, respectively. That is, both J and K need to be available above their threshold concentrations for to be repressed.