Computing Symbolic Steady States of Boolean Networks
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.
Unable to display preview. Download preview PDF.
- 1.Wang, R.-S., Saadatpour, A., Albert, R.: Boolean modeling in systems biology: an overview of methodology and applications. Physical Biology 9(5), 055001 (2012)Google Scholar
- 4.Crama, Y., Hammer, P.L.: Boolean functions: theory, algorithms, and applications, vol. 142. Cambridge University Press (2011)Google Scholar
- 6.Kauffman, S.A.: The origins of order: Self organization and selection in evolution. Oxford University Press, USA (1993)Google Scholar
- 8.Dick, R.: Quine-McCluskey two-level logic minimization method (2008), http://pypi.python.org/pypi/qm/0.2 (accessed in April 2014)
- 9.Gurobi Optimization, Inc.: Gurobi optimizer reference manual (2014)Google Scholar
- 10.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)Google Scholar
- 11.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)Google Scholar