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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

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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.