Qualitative simulation predicts the set of possible behaviors...

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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This paper describes the implementation of predicate abstraction techniques to automatically compute symbolic backward reachable sets of high dimensional piecewise a#ne hybrid automata, used to model Delta-Notch biological cell signaling networks. These automata are analyzed by creating an abstraction of the hybrid model, which is a finite state discrete transition system, and then performing the computation on the abstracted system. All the steps, from model generation to the simplification of the reachable set, have been automated using a variety of decision procedure and theorem-proving tools. The concluding example computes the reach set for a four cell network with 8 continuous and 256 discrete states. This demonstrates the feasibility of using these tools to compute on high dimensional hybrid automata, to provide deeper insight into realistic biological systems.

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. We present a procedure for constructing sound finite-state discrete abstractions of hybrid systems. This procedure uses ideas from predicate abstraction to abstract the discrete dynamics and qualitative reasoning to abstract the continuous dynamics of the hybrid system. It relies on the ability to decide satisfiability of quantifier-free formulas in some theory rich enough to encode the hybrid system. We characterize the sets of predicates that can be used to create high quality abstractions and we present new approaches to discover such useful sets of predicates. Under certain assumptions, the abstraction procedure can be applied compositionally to abstract a hybrid system described as a composition of two hybrid automata. We show that the constructed abstractions are always sound, but are relatively complete only under certain assumptions.

The paper discusses an approach to construct discrete abstractions of hybrid systems by means of qualitative reasoning. The work is performed in the context of a modeling language for hybrid systems Charon.Weintroduce a qualitativeversion of the language and describe the abstraction technique using a motivational example. The resulting abstract model is conservative and can be used to analyze properties of the original hybrid system.

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

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

We present a technique based on the use of the quanti er elimination decision procedure for real closed elds and simple theorem proving to construct a series of successively ner qualitative abstractions of hybrid automata. The resulting abstractions are always discrete transition systems which can then be used by any traditional analysis tool.