Role of Self-Loop in Cell-Cycle Network of Budding Yeast

Shu-ichi  Kinoshita; Hiroaki  Yamada

doi:10.4236/ojbiphy.2019.91002

Shu-ichi Kinoshita^1,2, Hiroaki Yamada³

Abstract: Study of network dynamics is very active area in biological and social sciences. However, the relationship between the network structure and the attractors of the dynamics has not been fully understood yet. In this study, we numerically investigated the role of degenerate self-loops on the attractors and its basin size using the budding yeast cell-cycle network model. In the network, all self-loops negatively suppress the node (self-inhibition loops) and the attractors are only fixed points, i.e. point attractors. It is found that there is a simple division rule of the state space by removing the self-loops when the attractors consist only of point attractors. The point attractor with largest basin size is robust against the change of the self-inhibition loop. Furthermore, some limit cycles of period 2 appear as new attractor when a self-activation loop is added to the original network. It is also shown that even in that case, the point attractor with largest basin size is robust.

Keywords: Gene Regulatory Network, Attractors, Budding Yeast, Degenerate Self-Loop

Cite this paper: Kinoshita, S. , Yamada, H. (2019) Role of Self-Loop in Cell-Cycle Network of Budding Yeast. Open Journal of Biophysics, 9, 10-20. doi: 10.4236/ojbiphy.2019.91002.

References

[1] Salgado, H., et al. (2003) RegulonDB v8.0: Omics Data Sets, Evolutionary Conservation, Regulatory Phrases, Cross-Validated Gold Standards and More. Nucleic Acids Research, 41, D203-D213.

[2] Han, B. and Wang, J. (2007) Quantifying Robustness and Dissipation Cost of Yeast Cell Cycle Network: The Funneled Energy Landscape Perspectives. Biophysical Journal, 92, 3755-3763.
https://doi.org/10.1529/biophysj.106.094821

[3] Ferhat, A., et al. (2009) Scalable Steady State Analysis of Boolean Biological Regulatory Networks. PLoS ONE, 12, e7992.

[4] Huang, X., et al. (2013) Boolean Genetic Network Model for the Control of C. elegans Early Embryonic Cell Cycles. BioMedical Engineering OnLine, 12, S1.
https://doi.org/10.1186/1475-925X-12-S1-S1

[5] Tran, V., et al. (2013) On the Underlying Assumptions of Threshold Boolean Networks as a Model for Genetic Regulatory Network Behavior Frontiers in Genetics. Bioinformatics and Computational Biology, 4, Article 263.

[6] Kauffman, S.A. (1969) Metabolic Stability and Epigenesis in Randomly Constructed Genetic Nets. Journal of Theoretical Biology, 22, 437-467.
https://doi.org/10.1016/0022-5193(69)90015-0

[7] Iguchi, K., Kinoshita, S. and Yamada, H.S. (2007) Boolean Dynamics of Kauffman Model with a Scale-Free Network. Journal of Theoretical Biology, 247, 138-151.
https://doi.org/10.1016/j.jtbi.2007.02.010

[8] Kinoshita, S., Iguchi, K. and Yamada, H.S. (2009) Intrinsic Properties of Boolean Dynamics in Complex Networks. Journal of Theoretical Biology, 256, 351-369.
https://doi.org/10.1016/j.jtbi.2008.10.014

[9] Daniels, B.C., et al. (2018) Criticality Distinguishes the Ensemble of Biological Regulatory Networks. Physical Review Letters, 121, 138102.
https://doi.org/10.1103/PhysRevLett.121.138102

[10] Li, F., Long, T., Lu, Y., Ouyang, Q. and Tang, C. (2004) The Yeast Cell-Cycle Network Is Robustly Designed. Proceedings of the National Academy of Sciences of the United States of America, 101, 4781-4786.
https://doi.org/10.1073/pnas.0305937101

[11] Yang, L.J., et al. (2013) Robustness and Backbone Motif of a Cancer Network Regulated by miR-17-92 Cluster during the G1/S Transition. PLoS ONE, 8, 1-9.
https://doi.org/10.1371/journal.pone.0057009

[12] Barberis, M., Todd, R.G. and van der Zee, L. (2016) Advances and Challenges in Logical Modeling of Cell Cycle Regulation: Perspective for Multi-Scale, Integrative Yeast Cell Models. FEMS Yeast Research, 17, fow103.

[13] Luo, X., Xu, L., Han, B. and Wang, J. (2017) Funneled Potential and Flux Landscapes Dictate the Stabilities of Both the States and the Flow: Fission Yeast Cell Cycle. PLOS Computational Biology, 13, e1005710.
https://doi.org/10.1371/journal.pcbi.1005710

[14] Kinoshita, S. and Yamada, H. (2018) The Effect of Removal of Self-Loop for Attractor on Cell Cycle Network. In: Morales, A.J., et al., Eds., Unifying Themes in Complex Systems IX: Proceedings of the Ninth International Conference on Complex Systems, Springer Proceedings in Complexity, Springer Nature Switzerland AG, 346-351.

[15] Goles, E., Montalva, M. and Ruz, G.A. (2013) Deconstruction and Dynamical Robustness of Regulatory Networks: Application to the Yeast Cell Cycle Networks. Bulletin of Mathematical Biology, 75, 939-966.
https://doi.org/10.1007/s11538-012-9794-1

[16] Davidich, M.I. and Bornholdt, S. (2008) Boolean Network Model Predicts Cell Cycle Sequence of Fission Yeast. PLoS ONE, 3, e1672.
https://doi.org/10.1371/journal.pone.0001672

[17] Richard, A. (2015) Fixed Point Theorems for Boolean Networks Expressed in Terms of Forbidden Subnetworks. Theoretical Computer Science, 583, 1-26.
https://doi.org/10.1016/j.tcs.2015.03.038