Analysis of signalling pathways using continuous time Markov chains

Muffy Calder, Vladislav Vyshemirsky, David Gilbert, Richard Orton

Research output: Contribution to journalArticlepeer-review

53 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)44-67
Number of pages24
JournalLecture Notes in Computer Science
Publication statusPublished - 2006


  • systems biology
  • mathematical modelling
  • signalling pathways
  • Markov chain


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