Abstract
Probabilistic Model Checking (PMC) is a technique that is used for the specification and analysis of unpredictable and complex systems. It can be applied directly to biological systems that show these characteristics. In this paper, PMC is used to model and analyze the effects of the palytoxin toxin (PTX) in transmembrane ionic transport systems, cellular structures responsible for exchanging ions through the plasma membrane. The correct behavior of these systems is necessary for all animal cells, otherwise the individual could present diseases and syndromes. We have discovered that high concentrations of ATP could inhibit PTX action, therefore individuals with ATP insufficiency, such as brain disorders (i.e. stroke), are more susceptible to the toxin. This type of analysis can provide a better understanding of how cell transport systems behave, give a better comprehension of these systems, and can lead to the discovery and development of new drugs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
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)
Campbell, N.A., Reece, J.B., Mitchell, L.G.: Biology, 5th edn. (1999)
Chapman, J.B., Johnson, E.A., Kootsey, J.M.: Electrical and biochemical properties of an enzyme model of the sodium pump. Membrane Biology (1983)
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)
Karp, G.: Cell and Molecular Biology, 5th edn. (2008)
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)
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’08, 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., Infantosi, A.F.C., Almeida, A.C.G.: Palytoxin and the sodium/potassium pump-phosphorylation and potassium interaction. Physical Biology (2009)
Tosteson, M., Thomas, J., Arnadottir, J., Tosteson, D.: Effects of palytoxin on cation occlusion and phosphorylation of the (na + /k + )-atpase. Journal of Membrane Biology 192, 181–189 (2003), 10.1007/s00232-002-1074-9
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Braz, F.A.F., Cruz, J.S., Faria-Campos, A.C., Campos, S.V.A. (2012). A Probabilistic Model Checking Approach to Investigate the Palytoxin Effects on the Na + /K + -ATPase. In: de Souto, M.C., Kann, M.G. (eds) Advances in Bioinformatics and Computational Biology. BSB 2012. Lecture Notes in Computer Science(), vol 7409. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31927-3_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-31927-3_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31926-6
Online ISBN: 978-3-642-31927-3
eBook Packages: Computer ScienceComputer Science (R0)