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.

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.

Recent progress in high-throughput data-production technologies pushes research toward systems biology, focusing on the global interaction between the components of biomolecular processes. In this article we present a formal modelling environment for

We introduce a formalism to represent and analyze protein-protein and protein-DNA interaction networks. We illustrate the expressivity of this language, by proposing a formal counterpart of Kohn's compilation on the mammalian cell cycle control. This e#ectively turns an otherwise static knowledge into a discrete transition system incorporating a qualitative description of the dynamics. We then propose to use the Computation Tree Logic CTL as a query language for querying the possible behaviours of the system. We provide examples of biologically relevant queries expressed in CTL about the mammalian cell cycle control and show the e#ectiveness of symbolic model checking tools to evaluate CTL queries in this context.

This paper describes the modeling language CHARON for modular design of interacting hybrid systems. The language allows specification of architectural as well as behavioral hierarchy and discrete as well as continuous activities. The modular structure of the language is not merely syntactic, but is exploited by analysis tools and is supported by a formal semantics with an accompanying compositional theory of refinement. We illustrate the benefits of CHARON in the design of embedded control software using examples from automated highways concerning vehicle coordination

Abstract. Model checking is an automatic method for deciding if a circuit or a program, expressed as a concurrent transition system, satisfies a set of properties expressed in a temporal logic such as CTL. In this paper we argue that symbolic model checking is feasible in systems biology and that it shows some advantages over simulation for querying and validating formal models of biological processes. We report our experiments on using the symbolic model checker NuSMV and the constraint-based model checker DMC, for the modeling and querying of two biological processes: a qualitative model of the mammalian cell cycle control after Kohn's diagrams, and a quantitative model of gene expression regulation. 1 Introduction In recent years, Biology has clearly engaged an elucidation work of high-level biological processes in terms of their biochemical basis at the molecular level. The mass production of post genomic data, such as ARN expression, protein production and protein-protein interaction, raises the need of a strong parallel effort on the formal representation of biological processes. Metabolism networks, extracellular and intracellular signaling pathways, and gene expression regulation networks, are very complex dynamical systems. Annotating data bases with qualitative and quantitative information about the dynamics of biological systems, will not be sufficient to integrate and efficiently use the current knowledge about these systems. The design of formal tools for modeling biomolecular processes and for reasoning about their dynamics seems to be a mandatory research path to which the field of formal verification in computer science may contribute a lot.

The paper presents a new calculus suitable to describe microbiological systems and their evolution. We use the calculus to model interactions among bacteria and bacteriophage viruses, and to reason on their properties.

who are interested in the interdisciplinary methods and applications relevant to the analysis, design and management of complex systems. 15 St. Mary’s St. Brookline MA 02446 l 617.358.1295 l www.bu.edu/systems

Systems biology is a new area in biology that aims at achieving a systems-level understanding of biological systems. While current genome projects provide a huge amount of data on genes or proteins, lots of research is still necessary to understand how the dierent parts of a biological system interact in order to perform complex biological functions.

Abstract. In this article we present the Biochemical Abstract Machine BIOCHAM and advocate its use as a formal modeling environment for networks biology. Biocham provides a precise semantics to biomolecular interaction maps. Based on this formal semantics, the Biocham system offers automated reasoning tools for querying the temporal properties of the system under all its possible behaviors. We present the main features of Biocham, provide details on a simple example of the MAPK signaling cascade and prove some results on the equivalence of models w.r.t. their temporal properties. 1 Introduction In networks biology, the complexity of the systems at hand (metabolic net-works, extracellular and intracellular networks, networks of gene regulation) clearly shows the necessity of software tools for reasoning globally about bio-logical systems [1]. Several formalisms have been proposed in recent years for modeling biochemical processes either qualitatively [2-4] or quantitatively [5-9].State-of-the-art tools integrate a graphical user interface and a simulator, yet few formal tools are available for reasoning about these processes and provingproperties about them. Our focus in Biocham has been on the design of a biochemical rule language and a query language of the model in temporal logic,that are intended to be used by biologists. Biocham has been designed in the framework of the ARC CPBIO on "ProcessCalculi and Biology of Molecular Networks " [10] which aims at pushing forward a declarative and compositional approach to modeling languages in SystemsBiology. Biocham is a language and a programming environment for modeling biochemical systems, making simulations, and checking temporal properties. Itis composed of: