Analysis of signalling pathways using continuous time markov chains

  • Authors:

  • Muffy Calder;Vladislav Vyshemirsky;David Gilbert;Richard Orton

  • Affiliations:

  • Department of Computing Science, University of Glasgow;Bioinformatics Research Centre, University of Glasgow;Bioinformatics Research Centre, University of Glasgow;Bioinformatics Research Centre, University of Glasgow

  • Venue:
  • Transactions on Computational Systems Biology VI
  • Year:
  • 2006

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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.