Analysis of signalling pathways using continuous time Markov chains

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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 (https://doi.org/10.1007/11880646_3)

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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.

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