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This article is part of the supplement: Proceedings of the 6th International Conference of the Brazilian Association for Bioinformatics and Computational Biology (X-meeting 2010)

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Modeling and analysis of cell membrane systems with probabilistic model checking

Mirlaine A Crepalde, Alessandra C Faria-Campos and Sérgio VA Campos*

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Department of Computer Science, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte, MG, Brazil

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Citation and License

BMC Genomics 2011, 12(Suppl 4):S14  doi:10.1186/1471-2164-12-S4-S14

Published: 22 December 2011



Recently there has been a growing interest in the application of Probabilistic Model Checking (PMC) for the formal specification of biological systems. PMC is able to exhaustively explore all states of a stochastic model and can provide valuable insight into its behavior which are more difficult to see using only traditional methods for system analysis such as deterministic and stochastic simulation. In this work we propose a stochastic modeling for the description and analysis of sodium-potassium exchange pump. The sodium-potassium pump is a membrane transport system presents in all animal cell and capable of moving sodium and potassium ions against their concentration gradient.


We present a quantitative formal specification of the pump mechanism in the PRISM language, taking into consideration a discrete chemistry approach and the Law of Mass Action aspects. We also present an analysis of the system using quantitative properties in order to verify the pump reversibility and understand the pump behavior using trend labels for the transition rates of the pump reactions.


Probabilistic model checking can be used along with other well established approaches such as simulation and differential equations to better understand pump behavior. Using PMC we can determine if specific events happen such as the potassium outside the cell ends in all model traces. We can also have a more detailed perspective on its behavior such as determining its reversibility and why its normal operation becomes slow over time. This knowledge can be used to direct experimental research and make it more efficient, leading to faster and more accurate scientific discoveries.