Abstract
Automatic verification techniques such as Probabilistic Model Checking (PMC) have been successfully applied in the specification and analysis of stochastic systems. Some biological systems show these characteristics, allowing PMC usage in unexpected fields. We present and analyze a probabilistic model for palytoxin toxin (PTX) effects on cell transport systems, structures which exchange ions across the plasma membrane. Several diseases are linked to their irregular behavior and their study could help drug development. The model developed in this work shows that as sodium concentration increases, PTX action enhances, suggesting that individuals with diets high in sodium are more vulnerable to PTX. An opposite effect is observed when the potassium concentration increases. PMC can help significantly in the understanding of how cell transport systems behave, suggesting novel experiments which otherwise might be overlooked by biologists.
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References
Aidley, D.J., Stanfield, P.R.: Ion channels: molecules in action. Cambridge University Press (1996)
Artigas, P., Gadsby, D.C.: Large diameter of palytoxin-induced na/k pump channels and modulation of palytoxin interaction by na/k pump ligands. J. Gen. Physiol. (2004)
Braz, F.A.F., Cruz, J.S., Faria-Campos, A.C., Campos, S.V.A.: A Probabilistic Model Checking Approach to Investigate the Palytoxin Effects on the Na + /K + -ATPase. In: de Souto, M.C.P., Kann, M.G. (eds.) BSB 2012. LNCS, vol. 7409, pp. 84–96. Springer, Heidelberg (2012)
Chapman, J.B., Johnson, E.A., Kootsey, J.M.: Electrical and biochemical properties of an enzyme model of the sodium pump. Membrane Biology (1983)
Ciocchetta, F., Hillston, J.: Bio-pepa: A framework for the modelling and analysis of biological systems. Theoretical Computer Science (2009)
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching-time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)
Clarke, E.M., Faeder, J.R., Langmead, C.J., Harris, L.A., Jha, S.K., Legay, A.: Statistical Model Checking in BioLab: Applications to the Automated Analysis of T-Cell Receptor Signaling Pathway. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 231–250. Springer, Heidelberg (2008)
Crepalde, M., Faria-Campos, A., Campos, S.: Modeling and analysis of cell membrane systems with probabilistic model checking. BMC Genomics 12(suppl. 4), S14 (2011), http://www.biomedcentral.com/1471-2164/12/S4/S14
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)
Hernández, J.A., Chifflet, S.: Eletrogenic properties of the sodium pump in a dynamic model of membrane transport. Membrane Biology 176, 41–52 (2000)
Holzmann, G.J.: The SPIN Model Checker: Primer and Reference Manual, 1st edn. Addison-Wesley Professional (September 2003)
Kwiatkowska, M., Heath, J.: Biological pathways as communicating computer systems. Journal of Cell Science 122(16), 2793–2800 (2009)
Kwiatkowska, M., Norman, G., Parker, D.: Quantitative Verification Techniques for Biological Processes. In: Algorithmic Bioprocesses. Springer (2009)
Kwiatkowska, M., Norman, G., Parker, D.: Probabilistic Model Checking for Systems Biology. In: Symbolic Systems Biology, pp. 31–59. Jones and Bartlett (2010)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM 4.0: Verification of Probabilistic Real-Time Systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 585–591. Springer, Heidelberg (2011)
Nelson, D.L., Cox, M.M.: Lehninger Principles of Biochemistry, 3rd edn. (2000)
Oka, C., Cha, C.Y., Noma, A.: Characterization of the cardiac na+/k+ pump by development of a comprehensive and mechanistic model. Journal of Theoretical Biology 265(1), 68–77 (2010), http://www.sciencedirect.com/science/article/pii/S0022519310002274
Post, R., Refyvary, C., Kume, S.: Activation by adenosine triphosphate in the phosphorylation kinetics of sodium and potassium ion transport adenosine triphosphatase. J. Biol. Chem.
Queille, J.P., Sifakis, J.: A temporal logic to deal with fairness in transition systems. In: 23rd Annual Symposium on Foundations of Science, SFCS 2008, pp. 217–225 (1982)
Rodrigues, A.M., Almeida, A.C.G., Infantosi, A.F., Teixeira, H.Z., Duarte, M.A.: Model and simulation of na+/k+ pump phosphorylation in the presence of palytoxin. Computational Biology and Chemistry 32(1), 5–16 (2008)
Rodrigues, A.M., Almeida, A.C.G., Infantosi, A.F.C.: Effect of palytoxin on the sodium-potassium pump: model and simulation. Physical Biology 5(3), 036005 (2008), http://stacks.iop.org/1478-3975/5/i=3/a=036005
Rodrigues, A.M., Infantosi, A.F.C., Almeida, A.C.G.: Palytoxin and the sodium/potassium pump-phosphorylation and potassium interaction. Physical Biology (2009)
Sadava, D., Heller, H., Orians, G., Purves, W., Hillis, D.: Life: The Science of Biology. Sinauer Associates (2006)
Yamada, K., Inagaki, N.: ATP-sensitive K+ channels in the brain: Sensors of hypoxic conditions. Physiology 17(3), 127–130 (2002)
Younes, H.L.S.: Ymer: A Statistical Model Checker. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 429–433. Springer, Heidelberg (2005)
Younes, H., Kwiatkowska, M., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. International Journal on Software Tools for Technology Transfer (STTT) 8(3), 216–228 (2006)
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Braz, F.A.F., Cruz, J.S., Faria-Campos, A.C., Campos, S.V.A. (2012). Palytoxin Inhibits the Sodium-Potassium Pump – An Investigation of an Electrophysiological Model Using Probabilistic Model Checking. In: Gheyi, R., Naumann, D. (eds) Formal Methods: Foundations and Applications. SBMF 2012. Lecture Notes in Computer Science, vol 7498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33296-8_5
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DOI: https://doi.org/10.1007/978-3-642-33296-8_5
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