A compositional approach to performance modelling
A compositional approach to performance modelling
Information Processing Letters
Bio-PEPA: An Extension of the Process Algebra PEPA for Biochemical Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
Relating continuous and discrete PEPA models of signalling pathways
Theoretical Computer Science
Integrated Simulation and Model-Checking for the Analysis of Biochemical Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
Analysis of signalling pathways using continuous time markov chains
Transactions on Computational Systems Biology VI
Beta binders for biological interactions
CMSB'04 Proceedings of the 20 international conference on Computational Methods in Systems Biology
Transactions on Computational Systems Biology VII
Bio-PEPA: A framework for the modelling and analysis of biological systems
Theoretical Computer Science
Bio-PEPA for Epidemiological Models
Electronic Notes in Theoretical Computer Science (ENTCS)
A Model and Analysis of the AKAP Scaffold
Electronic Notes in Theoretical Computer Science (ENTCS)
Relating PDEs in Cylindrical Coordinates and CTMCs with Levels of Concentration
Electronic Notes in Theoretical Computer Science (ENTCS)
Probabilistic approximations of ODEs based bio-pathway dynamics
Theoretical Computer Science
A semantic equivalence for Bio-PEPA based on discretisation of continuous values
Theoretical Computer Science
Analysis of stochastic reaction networks with Markov reward models
Proceedings of the 9th International Conference on Computational Methods in Systems Biology
Adapting rule-based model descriptions for simulating in continuous and hybrid space
Proceedings of the 9th International Conference on Computational Methods in Systems Biology
Multi-scale modelling of biological systems in process algebra with multi-way synchronisation
Proceedings of the 9th International Conference on Computational Methods in Systems Biology
Product Form Approximation of Transient Probabilities in Stochastic Reaction Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
Modelling and analysis of the NF-κB pathway in bio-PEPA
Transactions on Computational Systems Biology XII
A Hybrid Factored Frontier Algorithm for Dynamic Bayesian Networks with a Biopathways Application
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Modular modelling of signalling pathways and their cross-talk
Theoretical Computer Science
Trend-Based analysis of a population model of the AKAP scaffold protein
Transactions on Computational Systems Biology XIV
Quasi product form approximation for markov models of reaction networks
Transactions on Computational Systems Biology XIV
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Bio-PEPA is a recently defined language for the modelling and analysis of biochemical networks. It supports an abstract style of modelling, in which discrete levels of concentration within a species are considered instead of individual molecules. A finer granularity for the system corresponds to a smaller concentration step size and therefore to a greater number of concentration levels. This style of model is amenable to a variety of different analysis techniques, including numerical analysis based on a CMTC with states reflecting the levels of concentration. In this paper we present a formal definition of the CTMC with levels derived from a Bio-PEPA system. Furthermore we investigate the relationship between this CTMC and the system of ordinary differential equations (ODEs) derived from the same model. Using Kurtz's theorem, we show that the set of ODEs derived from the Bio-PEPA model is able to capture the limiting behaviour of the CTMC obtained from the same system. Finally, we define an empirical methodology to find the granularity of the Bio-PEPA system for which the ODE and the CTMC with levels are in a good agreement. The proposed definition is based on a notion of distance between the two models. We demonstrate our approach on a model of the Repressilator, a simple biochemical network with oscillating behaviour.