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

A modular, qualitative modelling of regulatory networks using Petri nets

International audienceAdvances in high-throughput technologies have enabled the de-lineation of large networks of interactions that control cellular processes. To understand behavioural properties of these complex networks, mathematical and computational tools are required. The multi-valued logical formalism, initially defined by R. Thomas and co-workers, proved well adapted to account for the qualitative knowledge available on regulatory interactions, and also to perform analyses of their dynamical properties. In this context, we present two representations of logical models in terms of Petri nets. In a first step, we briefly show how logical models of regulatory networks can be transposed into standard (place/transition) Petri nets, and discuss the capabilities of such representation. In the second part, we focus on logical regulatory modules and their composition, demonstrating that a high-level Petri net representation greatly facilitates the modelling of interconnected modules. Doing so, we introduce an explicit means to integrate signals from various interconnected modules, taking into account their spatial distribution. This provides a flexible modelling framework to handle regulatory networks that operate at both intra-and intercellular levels. As an illustration, we describe a simplified model of the segment-polarity module involved in the segmentation of the Drosophila embryo

A review of modelling and verification approaches for computational biology

This paper reviews most frequently used computational modelling approaches and formal verification techniques in computational biology. The paper also compares a number of model checking tools and software suits used in analysing biological systems and biochemical networks and verifiying a wide range of biological properties

Modelling molecular networks: relationships between different formalisms and levels of details

This document is the deliverable 1.3 of French ANR CALAMAR. It presents a study of different formalisms used for modelling and analyzing large molecular regulation networks, their formal links, in terms of mutual encodings and of abstractions, and the corresponding levels of detail captured

09091 Abstracts Collection -- Formal Methods in Molecular Biology

From 23. February to 27. February 2009, the Dagstuhl Seminar 09091 ``Formal Methods in Molecular Biology \u27\u27 was held in Schloss Dagstuhl~--~Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Tools and techniques for multi-valued networks using rewriting logic

PhD ThesisMulti-valued networks (MVNs) are an important, widely used qualitative modelling technique where time and states are discrete. MVNs extend the well-known Boolean networks by providing a more powerful qualitative modelling approach for biological systems by allowing an entity’s state to be within a range of discrete set of values instead of just 0 and 1. They provide a logical framework for qualitatively modelling and analysing control systems and have been successfully applied to biological systems and circuit design. While a range of support tools for developing and analysing MVNs exist, more work is needed to develop tools to support the practical applications of those techniques. One of the frameworks that have been successfully applied to biological systems is Rewriting Logic (RL), an algebraic specification framework that is capable of modelling and analysing the behaviour of dynamic, concurrent systems. The flexibility of RL techniques such as implementation of strategies has allowed it to be successfully used to model a wide range of different formalisms and systems, such as process algebras, Petri nets, and biological systems. RL specification, programming and computation is supported by a range of powerful analysis tools which was one of the motivations for choosing to use RL. We choose Maude as a tool in our work here which is a high-performance reflective language supporting both equational and RL specification. Maude is going to be used through this thesis to model and analyse a range of MVNs using RL. In this thesis we aim to investigate the application of RL to modelling and analysing both synchronous and asynchronous MVNs, thus enabling the application of support tools available for RL. We start by constructing an RL model for MVNs using a translation approach that translates an MVNs set of equations into rewrite rules. We formally show that our translation approach is correct by proving its soundness and completeness. We illustrate the techniques and the developed RL framework for MVNs by presenting a range of case studies which provides a good illustration of the practical application of the developed RL framework. We then introduce an artificial, scalable MVN model in order to allow a range of model sizes to be considered and we investigate the performance of our RL framework. We analyse a larger regulatory network from the literature using our RL framework to give some insights into how it coped with a larger case studyMinistry of Higher Education in Saudi Arabi

Computational Modeling, Formal Analysis, and Tools for Systems Biology.

As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science

SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modelling formalisms and tools

Background: Qualitative frameworks, especially those based on the logical discrete formalism, are increasingly used to model regulatory and signalling networks. A major advantage of these frameworks is that they do not require precise quantitative data, and that they are well-suited for studies of large networks. While numerous groups have developed specific computational tools that provide original methods to analyse qualitative models, a standard format to exchange qualitative models has been missing. Results: We present the Systems Biology Markup Language (SBML) Qualitative Models Package (“qual”), an extension of the SBML Level 3 standard designed for computer representation of qualitative models of biological networks. We demonstrate the interoperability of models via SBML qual through the analysis of a specific signalling network by three independent software tools. Furthermore, the collective effort to define the SBML qual format paved the way for the development of LogicalModel, an open-source model library, which will facilitate the adoption of the format as well as the collaborative development of algorithms to analyse qualitative models. Conclusions: SBML qual allows the exchange of qualitative models among a number of complementary software tools. SBML qual has the potential to promote collaborative work on the development of novel computational approaches, as well as on the specification and the analysis of comprehensive qualitative models of regulatory and signalling networks