Abstracting Asynchronous Multi-Valued Networks: An Initial Investigation

Multi-valued networks provide a simple yet expressive qualitative state based modelling approach for biological systems. In this paper we develop an abstraction theory for asynchronous multi-valued network models that allows the state space of a model to be reduced while preserving key properties of the model. The abstraction theory therefore provides a mechanism for coping with the state space explosion problem and supports the analysis and comparison of multi-valued networks. We take as our starting point the abstraction theory for synchronous multi-valued networks which is based on the finite set of traces that represent the behaviour of such a model. The problem with extending this approach to the asynchronous case is that we can now have an infinite set of traces associated with a model making a simple trace inclusion test infeasible. To address this we develop a decision procedure for checking asynchronous abstractions based on using the finite state graph of an asynchronous multi-valued network to reason about its trace semantics. We illustrate the abstraction techniques developed by considering a detailed case study based on a multi-valued network model of the regulation of tryptophan biosynthesis in Escherichia coli.Comment: Presented at MeCBIC 201

An Abstraction Theory for Qualitative Models of Biological Systems

Multi-valued network models are an important qualitative modelling approach used widely by the biological community. In this paper we consider developing an abstraction theory for multi-valued network models that allows the state space of a model to be reduced while preserving key properties of the model. This is important as it aids the analysis and comparison of multi-valued networks and in particular, helps address the well-known problem of state space explosion associated with such analysis. We also consider developing techniques for efficiently identifying abstractions and so provide a basis for the automation of this task. We illustrate the theory and techniques developed by investigating the identification of abstractions for two published MVN models of the lysis-lysogeny switch in the bacteriophage lambda.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

A High-Level Petri Net Framework for Multi-Valued Genetic Regulatory Networks

To understand the function of genetic regulatory networks in the development of cellular systems, we must not only realise the individual network entities, but also the manner by which they interact. Multi-valued networks are a promising qualitative approach for modelling such genetic regulatory networks, providing an interesting compromise between the simplicity of Boolean models and more detailed quantitative models. However, at present multi-valued networks lack the formal analysis techniques and tools required to comprehensively investigate a genetic regulatory model. This is compounded by the fact that little appears to be known about the relationship between multi-valued models and their more abstract Boolean counterparts. We present a flexible formal framework for modelling and analysing multi-valued genetic regulatory networks using high-level Petri nets. We propose an approach for translating a multi-valued model in to a corresponding compact highlevel Petri net model using logic minimization techniques and consider coping with the problem of incomplete data that often occurs in practice. We demonstrate ou

A High-Level Petri Net Framework for Genetic Regulatory Networks

To understand the function of genetic regulatory networks in the development of cellular systems, we must not only realise the individual network entities, but also the manner by which they interact. Multi-valued networks are a promising qualitative approach for modelling such genetic regulatory networks, however, at present they have limited formal analysis techniques and tools. We present a flexible formal framework for modelling and analysing multi-valued genetic regulatory networks using high-level Petri nets and logic minimization techniques. We demonstrate our approach with a detailed case study in which part of the genetic regulatory network responsible for the carbon starvation stress response in Escherichia coli is modelled and analysed. We then compare and contrast this multivalued model to a corresponding Boolean model and consider their formal relationship

A Case for Using Signal Transition Graphs for Analysing and Refining Genetic Networks

In order to understand and analyse genetic regulatory networks (GRNs), the complex control structures which regulate cellular systems, well supported qualitative formal modelling techniques are required. In this paper, we make a case that biological systems can be qualitatively modelled by speed-independent circuits. We apply techniques from asynchronous circuit design, based on Signal Transition Graphs (STGs), to modelling, visualising and analysing GRNs. STGs are a Petri net based model that has been extensively used in asynchronous circuit design. We investigate how the sufficient conditions ensuring that an STG can be implemented by a speed-independent circuit can be interpreted in the context of GRNs. We observe that these properties provide important insights into a model and highlight areas which need to be refined. Thus, STGs provide a well supported formal framework for GRNs that allows realistic models to be incrementally developed and analysed. We demonstrate the proposed STG approach with a case study of constructing and analysing a speed-independent circuit specification for the lysis-lysogeny switch in phage λ