Abstract
When analyzing the state space attractors and their basin of attraction, two main methods have been used: the synchronous update method and the asynchronous update method. Although its simplicity, the synchronous update fails to consider various time scales of the chemical processes between the components within the network. To overcome this limitations, several asynchronous methods have been developed. In this work, we use two different asynchronous methods to study the dynamics of the wild-type and perturbed Klotho gene and carry out comparative results with previously published results. Prior evidence shows that the system develops oscillations and a fixed point. The numerical results of the both asynchronous methods show that, the system’s oscillations disappear and the system undergo in only one time-invariant fixed point, leading to an extended attractor. This work aims to highlight different behavior of the Klotho gene under various internal and external perturbations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Trairatphisan, P., et al.: Recent development and biomedical applications of probabilistic Boolean networks. Cell Commun. Signal. 11(1) (2013)
Chaves, M., Sontag, E.D., Albert, R.: Methods of robustness analysis for Boolean models of gene control networks. arXiv:0605004 (2006)
Saadatpour, A., Albert, I., Albert, R.: Attractor analysis of asynchronous Boolean models of signal transduction networks. J. Theor. Biol. 266(4), 641–656 (2010)
Saadatpour, A., Albert, R.: Boolean modeling of biological regulatory networks: a methodology tutorial. Methods 62(1), 3–12 (2013)
Kauffman, Stuart A.: The Origins of Order: Self Organization and Selection in Evolution. Oxford University Press, USA (1993)
Thomas, R.: On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations. In: Numerical Methods in the Study of Critical Phenomena, pp. 180–193. Springer, Berlin, Heidelberg (1981)
Shmulevich, I., et al.: Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2), 261–274 (2002)
Shmulevich, I., Dougherty, E.R., Zhang, W.: From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. Proc. IEEE 90(11), 1778–1792 (2002)
Mestl, T., Plahte, E., Omholt, S.W.: A mathematical framework for describing and analysing gene regulatory networks. J. Theor. Biol. 176(2), 291–300 (1995)
Marku, M., Ifti, M., Koçiaj, I., Klotilda, N.: Dynamical Analysis of Synchronous Boolean Model of the Klotho Gene Complex Networks and Their Applications (2016)
Kuro-o, M.: Klotho and aging. Biochimica et Biophysica Acta (BBA)-General Subjects, vol. 1790, no. 10, pp. 1049–1058 (2009)
Quarles, L.D.: Role of FGF23 in vitamin D and phosphate metabolism: implications in chronic kidney disease. Exp. Cell Res. 318(9), 1040–1048 (2012)
Haussler, M.R., et al.: The role of vitamin D in the FGF23, klotho, and phosphate bone-kidney endocrine axis. Rev. Endocr. Metab. Dis. 13(1), 57–69 (2012)
Wiese, R., Eiglsperger, M., Kaufmann, M.: yfiles-visualization and automatic layout of graphs. In: Graph Drawing Software, pp. 173–191. Springer, Berlin, Heidelberg (2004)
Albert, I., et al.: Boolean network simulations for life scientists. Source Code Biol. Med. 3(1) (2008)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Marku, M., Koçiaj, I., Nikaj, K., Ifti, M. (2017). Attractor Analysis of the Asynchronous Boolean Model of the Klotho Gene Regulatory Network. In: Gonçalves, B., Menezes, R., Sinatra, R., Zlatic, V. (eds) Complex Networks VIII. CompleNet 2017. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-54241-6_22
Download citation
DOI: https://doi.org/10.1007/978-3-319-54241-6_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54240-9
Online ISBN: 978-3-319-54241-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)