# Analysis of signalling pathways using continuous time Markov chains

Calder, Muffy and Vyshemirsky, Vladislav and Gilbert, David and Orton, Richard
(2006)
*Analysis of signalling pathways using continuous time Markov chains.*
Lecture Notes in Computer Science, 4220/2006.
pp. 44-67.
ISSN 0302-9743

## Abstract

We describe a quantitative modelling and analysis approach for signal transduction networks. We illustrate the approach with an example, the RKIP inhibited ERK pathway [CSK+03]. Our models are high level descriptions of continuous time Markov chains: proteins are modelled by synchronous processes and reactions by transitions. Concentrations are modelled by discrete, abstract quantities. The main advantage of our approach is that using a (continuous time) stochastic logic and the PRISM model checker, we can perform quantitative analysis such as what is the probability that if a concentration reaches a certain level, it will remain at that level thereafter? or how does varying a given reaction rate affect that probability? We also perform standard simulations and compare our results with a traditional ordinary differential equation model. An interesting result is that for the example pathway, only a small number of discrete data values is required to render the simulations practically indistinguishable.

Item type: | Article |
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ID code: | 36121 |

Keywords: | systems biology, mathematical modelling, signalling pathways , Markov chain, Probabilities. Mathematical statistics, Theoretical Computer Science, Computer Science(all) |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 28 Nov 2011 09:42 |

Last modified: | 27 Apr 2016 17:57 |

URI: | http://strathprints.strath.ac.uk/id/eprint/36121 |