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Probabilistic Model Checking for Systems Biology - PRISM

Probabilistic Model Checking for Systems Biology - PRISM

Probabilistic Model Checking for Systems Biology -

DRAFTProbabilistic Model Checkingfor Systems BiologyMarta Kwiatkowska 1 , Gethin Norman 2 , and David Parker 11 Oxford University Computing Laboratory, Parks Road, Oxford, OX1 3QD, UK2 Department of Computing Science, University of Glasgow, Glasgow, G12 8RZ, UKAbstract. Probabilistic model checking is a technique for formally verifyingquantitative properties of systems that exhibit stochastic behaviour.In this chapter, we show how this approach can be applied to the study ofbiological systems such as biochemical reaction networks and signallingpathways. We present an introduction to the state-of-the-art probabilisticmodel checking tool PRISM using a case study based on the FibroblastGrowth Factor (FGF) signalling pathway.1 IntroductionProbabilistic model checking is a formal verification technique for the analysis ofsystems with stochastic characteristics. It is based on the exhaustive constructionand analysis of a probabilistic model, typically a Markov chain or Markov process,of some real-life system. This allows various quantitative properties of thesystem’s behaviour, such as performance or reliability, to be analysed automaticallyunder a range of different scenarios or parameters. The results can then beused to identify anomalies, faults or other points of interest in the systems beingmodelled. Probabilistic model checking has been used to study a wide array ofsystems including randomised communication protocols such as Bluetooth andFirewire, security protocols for anonymity and contract signing, dynamic powermanagement schemes and NAND multiplexing for nanotechnology.In this chapter we focus on how probabilistic model checking can be usedto study the behaviour of biological systems such as biochemical reaction networksand signalling pathways which, under certain assumptions, are well suitedto being modelled as discrete stochastic systems. We give an introduction toprobabilistic model checking and to the software tool PRISM [10, 17] which implementsthese techniques and, using a selection of examples of increasing complexity,demonstrate how PRISM can used as a framework for the modelling andanalysis of biological pathways. The approaches introduced in this chapter shouldnot be viewed as a substitute for the classical approaches based on simulationand differential equations. Rather, the techniques should be used in conjunctionwith these classical approaches to obtain a more detailed understanding of thecomplex interactions and behaviour of biological pathways.The chapter is organised as follows. Section 2 presents an overview of probabilisticmodel checking, including descriptions of continuous-time Markov chains,

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