A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In part I, we illustrate...

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.

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Abstract. This paper examines the influence of the Raf Kinase Inhibitor Protein (RKIP) on the Extracellular signal Regulated Kinase (ERK) signalling pathway [5] through modelling in a Markovian process algebra, PEPA [11]. Two models of the system are presented, a reagentcentric view and a pathway-centric view. The models capture functionality at the level of subpathway, rather than at a molecular level. Each model affords a different perspective of the pathway and analysis. We demonstrate the two models to be formally equivalent using the timingaware bisimulation defined over PEPA models and discuss the biological significance. 1

A bigraphical reactive system (BRS) involves bigraphs, in which the nesting of nodes represents locality, independently of the edges connecting them; it also allows bigraphs to reconfigure themselves. BRSs aim to provide a uniform way to model spatially distributed systems that both compute and communicate. In this memorandum we develop their static and dynamic theory. In Part I we illustrate...

The genomic sequencing of hundreds of organisms including homo sapiens, and the exponential growth in gene expression and proteomic data for many species has revolutionized research in biology. However, the computational analysis of these burgeoning datasets has been hampered by the sparse successes in combinations of data sources, representations, and algorithms. Here we propose the application of symbolic toolsets from the formal methods community to problems of biological interest, particularly signaling pathways, and more specifically mammalian mitogenic and stress responsive pathways. The results of formal symbolic analysis with extremely efficient representations of biological networks provide insights with potential biological impact. In particular, novel hypotheses may be generated which could lead to wet lab validation of new signaling possibilities. We demonstrate the graphic representation of the results of formal analysis of pathways, including navigational abilities, and describe the logical underpinnings of the approach. In summary, we propose and provide an initial description of an algebra and logic of signaling pathways and biologically plausible abstractions that provide the foundation for the application of highpowered tools such as model checkers to problems of biological interest. 1

Abstract. Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway. 1

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.

Abstract. Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations impractical. In contrast, agentbased or concurrent languages, such as κ [1–3] or the closely related BioNetGen language [4–10], describe biological interactions in terms of rules, thereby avoiding the combinatorial explosion besetting differential equations. Rules are expressed in an intuitive graphical form that transparently represents biological knowledge. In this way, rules become a natural unit of model building, modification, and discussion. We illustrate this with a sizeable example obtained from refactoring two models of EGF receptor signalling that are based on differential equations [11, 12]. An exciting aspect of the agent-based approach is that it naturally lends itself to the identification and analysis of the causal structures that deeply shape the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. In particular, one can adapt the notions of causality and conflict, familiar from concurrency theory, to κ, our representation language of choice. Using the EGF receptor model as an example, we show how causality enables the formalization of the colloquial concept of pathway and, perhaps more surprisingly, how conflict can be used to dissect the signalling dynamics to obtain a qualitative handle on the range of system behaviours. By taming the combinatorial explosion, and exposing the causal structures and key kinetic junctures in a model, agent- and rule-based representations hold promise for making modelling more powerful, more perspicuous, and of appeal to a wider audience. 1

Abstract. Differential equations are a classical approach for biochemical system modelling and have frequently been used to describe reactions of interest in biochemical pathways. Process algebras have also been applied in a small number of cases to describe such systems. In this paper we establish a connection between these approaches. This has the benefit of allowing process algebra models to be validated against trusted ODEs or, conversely, allowing ODEs derived from process algebra models to be evaluated and compared using bisimulation or other methods. In addition the process algebra models may now be efficiently solved using numerical differential equations procedures such as adaptive fifth-order Runge-Kutta. 1