Abstract
Asymptotic behavior is often of particular interest when analyzing asynchronous Boolean networks representing biological systems such as signal transduction or gene regulatory networks. Methods based on a generalization of the steady state notion, the so-called symbolic steady states, can be exploited to investigate attractor properties as well as for model reduction techniques conserving attractors. In this paper, we propose a novel optimization-based method for computing all maximal symbolic steady states and motivate their use. n particular, we add a new result yielding a lower bound for the number of cyclic attractors and illustrate the methods with a short study of a MAPK pathway model.
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
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Wang, R.-S., Saadatpour, A., Albert, R.: Boolean modeling in systems biology: an overview of methodology and applications. Physical Biology 9(5), 055001 (2012)
Dubrova, E., Teslenko, M.: A SAT-based algorithm for finding attractors in synchronous boolean networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB) 8(5), 1393–1399 (2011)
Siebert, H.: Analysis of discrete bioregulatory networks using symbolic steady states. Bulletin of Mathematical Biology 73, 873–898 (2011)
Crama, Y., Hammer, P.L.: Boolean functions: theory, algorithms, and applications, vol. 142. Cambridge University Press (2011)
Fogelman-Soulie, F.: Parallel and sequential computation on boolean networks. Theoretical Computer Science 40, 275–300 (1985)
Kauffman, S.A.: The origins of order: Self organization and selection in evolution. Oxford University Press, USA (1993)
Akutsu, T., Yang, Z., Hayashida, M., Tamura, T.: Integer programming-based approach to attractor detection and control of boolean networks. IEICE Transactions on Information and Systems 95(12), 2960–2970 (2012)
Dick, R.: Quine-McCluskey two-level logic minimization method (2008), http://pypi.python.org/pypi/qm/0.2 (accessed in April 2014)
Gurobi Optimization, Inc.: Gurobi optimizer reference manual (2014)
Grieco, L., Calzone, L., Bernard-Pierrot, I., Radvanyi, F., Kahn-Perlès, B., Thieffry, D.: Integrative modelling of the influence of mapk network on cancer cell fate decision. PLoS Computational Biology 9(10), e1003286 (2013)
Gershenson, C.: Updating schemes in random boolean networks: Do they really matter. In: Artificial Life IX Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems, pp. 238–243. MIT Press (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Klarner, H., Bockmayr, A., Siebert, H. (2014). Computing Symbolic Steady States of Boolean Networks. In: Wąs, J., Sirakoulis, G.C., Bandini, S. (eds) Cellular Automata. ACRI 2014. Lecture Notes in Computer Science, vol 8751. Springer, Cham. https://doi.org/10.1007/978-3-319-11520-7_59
Download citation
DOI: https://doi.org/10.1007/978-3-319-11520-7_59
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11519-1
Online ISBN: 978-3-319-11520-7
eBook Packages: Computer ScienceComputer Science (R0)