### Abstract

Original language | English |
---|---|

Pages (from-to) | 44-67 |

Number of pages | 24 |

Journal | Lecture Notes in Computer Science |

Volume | 4220/2006 |

DOIs | |

Publication status | Published - 2006 |

### Fingerprint

### Keywords

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

### Cite this

*Lecture Notes in Computer Science*,

*4220/2006*, 44-67. https://doi.org/10.1007/11880646_3

}

*Lecture Notes in Computer Science*, vol. 4220/2006, pp. 44-67. https://doi.org/10.1007/11880646_3

**Analysis of signalling pathways using continuous time Markov chains.** / Calder, Muffy; Vyshemirsky, Vladislav; Gilbert, David; Orton, Richard.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Analysis of signalling pathways using continuous time Markov chains

AU - Calder, Muffy

AU - Vyshemirsky, Vladislav

AU - Gilbert, David

AU - Orton, Richard

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - systems biology

KW - mathematical modelling

KW - signalling pathways

KW - Markov chain

U2 - 10.1007/11880646_3

DO - 10.1007/11880646_3

M3 - Article

VL - 4220/2006

SP - 44

EP - 67

JO - Lecture Notes in Computer Science

JF - Lecture Notes in Computer Science

SN - 0302-9743

ER -