Abstract
We demonstrate the effects of embedding subgraphs in a Boolean network, which is one of the discrete dynamic models for transcriptional regulatory networks. After comparing the dynamic properties of networks embedded with seven different subgraphs including feedback and feedforward subgraphs, we found that complexity of the state space increases with longer lengths of attractors, and the number of attractors is reduced for networks with more feedforward subgraphs. In addition, feedforward subgraphs can provide higher mutual information with lower entropy in a temporal program of gene expression. Networks with the other six subgraphs show opposite effects on network dynamics. This is roughly consistent with Thomas’s conjecture. These results suggest that feedforward subgraph is favorable local structure in complex biological networks.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barabási, A.-L., Oltvai, Z.N.: Network biology: Understanding the cell’s functional organization. Nature Genetics 5, 101–112 (2004)
Newman, M., Barabási, A.-L., Watts, D.J.: The Structure and Dynamics of Networks. Princeton University Press, Princeton (2006)
Alon, U.: An Introduction to Systems Biology. Chapman & Hall/CRC (2006)
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298, 824–827 (2002)
Kauffman, S.A.: The Origins of Order. Oxford University Press, Oxford (1993)
Oosawa, C., Savageau, M.A.: Effects of alternative connectivity on behavior of randomly constructed Boolean networks. Physica D 170, 143–161 (2002)
Harris, S., Sawhill, B., Wuensche, A., Kauffman, S.: A model of transcriptional regulatory networks based on biases in the observed regulation rules. Complexity 7, 23–40 (2002)
Raeymakers, L.: Dynamics of Boolean Networks Controlled by Biologically Meaningful Functions. J. Theor. Biol. 218, 331–341 (2002)
Setty, Y., Mayo, A.E., Surette, M.G., Alon, U.: Detailed map of cis-regulatory input function. Proc. Natl. Acad. Sci. 100, 7702–7707 (2003)
Nikolajewa, S., Friedel, M., Wilhelm, T.: Boolean networks with biologically relevant rules show ordered behavior. BioSystems 90, 40–47 (2007)
Oosawa, C., Takemoto, K., Savageau, M.A.: Effects of feedback and feedforward loops on dynamics of transcriptional regulatory model networks. In: Proceedings of the 13th International Symposium on Artificial Life and Robotics, pp. 885–890, http://arxiv.org/abs/0711.2730v2 [arXiv:0711.2730]
Krawitz, P., Shmulevich, I.: Basin Entropy in Boolean Ensembles. Phys. Rev. Lett. 98, 158701 (2007)
Oosawa, C., Takemoto, K., Matsumoto, S., Savageau, M.A.: Local cause of coherence in Boolean networks. In: Proceedings of the 12th International Symposium on Artificial Life and Robotics, pp. 621–626 (2007), http://arxiv.org/abs/nlin/0611049 [nlin/0611049]
Oosawa, C.: Roles of hubs in Boolean networks. In: Proceedings of the 15th IEEE International Workshop on Nonlinear Dynamics of Electrical Systems, pp. 245–248 (2007), http://arxiv.org/abs/nlin/0703033 [nlin/0703033]
Thomas, R., Thieffry, D., Kaufman, D.: Dynamical behaviour of biological regulatory networks I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state. Bulletin of Mathematical Biology 57, 247–276 (1995)
Sontag, E.D.: Monotone and near-monotone biochemical networks. Syst. Synth. Biol. 1, 59–87 (2007)
Sontag, E.D., Veliz-Cuba, A., Laubenbacher, R., Jarrah, A.S.: The effect of negative feedback subgraphs on the dynamics of Boolean networks, http://arxiv.org/abs/0707.3468v2 [arXiv:0707.3468]
Mangan, S., Alon, U.: Structure and function of the feed-forward loop network motif. Proc. Natl. Acad. Sci. 100, 11980–11985 (2003)
Balázsi, G., Barabśi, A.-L., Oltvai, Z.N.: Topological units of environmental signal processing in the transcriptional regulatory network of Escherichia coli. Proc. Natl. Acad. Sci. 102, 7841–7846 (2005)
Moreira, A.A., Amaral, L.A.N.: Canalizing kauffman networks: Nonergodicity and its effect on their critical behavior. Phys. Rev. Lett. 94, 218702 (2005)
Aldana, M., Cluzel, P.: A natural class of robust networks. Proc. Natl. Acad. Sci. 100, 8710–8714 (2003)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oosawa, C., Savageau, M.A., Jarrah, A.S., Laubenbacher, R.C., Sontag, E.D. (2008). Stabilizing and Destabilizing Effects of Embedding 3-Node Subgraphs on the State Space of Boolean Networks. In: Umeo, H., Morishita, S., Nishinari, K., Komatsuzaki, T., Bandini, S. (eds) Cellular Automata. ACRI 2008. Lecture Notes in Computer Science, vol 5191. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79992-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-79992-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79991-7
Online ISBN: 978-3-540-79992-4
eBook Packages: Computer ScienceComputer Science (R0)