IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v73y2015icp166-182.html
   My bibliography  Save this article

Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation

Author

Listed:
  • Rabajante, Jomar Fajardo
  • Talaue, Cherryl Ortega

Abstract

Concurrent decision-making model (CDM) of interaction networks with more than two antagonistic components represents various biological systems, such as gene interaction, species competition and mental cognition. The CDM model assumes sigmoid kinetics where every component stimulates itself but concurrently represses the others. Here we prove generic mathematical properties (e.g., location and stability of steady states) of n-dimensional CDM with either symmetric or asymmetric reciprocal antagonism between components. Significant modifications in parameter values serve as biological regulators for inducing steady state switching by driving a temporal state to escape an undesirable equilibrium. Increasing the maximal growth rate and decreasing the decay rate can expand the basin of attraction of a steady state that contains the desired dominant component. Perpetually adding an external stimulus could shut down multi-stability of the system which increases the robustness of the system against stochastic noise. We further show that asymmetric interaction forming a repressilator-type network generates oscillatory behavior.

Suggested Citation

  • Rabajante, Jomar Fajardo & Talaue, Cherryl Ortega, 2015. "Equilibrium switching and mathematical properties of nonlinear interaction networks with concurrent antagonism and self-stimulation," Chaos, Solitons & Fractals, Elsevier, vol. 73(C), pages 166-182.
    • Handle: RePEc:eee:chsofr:v:73:y:2015:i:c:p:166-182
    DOI: 10.1016/j.chaos.2015.01.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077915000259
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2015.01.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Noah J Cowan & Erick J Chastain & Daril A Vilhena & James S Freudenberg & Carl T Bergstrom, 2012. "Nodal Dynamics, Not Degree Distributions, Determine the Structural Controllability of Complex Networks," PLOS ONE, Public Library of Science, vol. 7(6), pages 1-5, June.
    2. Todd S. Macfarlan & Wesley D. Gifford & Shawn Driscoll & Karen Lettieri & Helen M. Rowe & Dario Bonanomi & Amy Firth & Oded Singer & Didier Trono & Samuel L. Pfaff, 2012. "Embryonic stem cell potency fluctuates with endogenous retrovirus activity," Nature, Nature, vol. 487(7405), pages 57-63, July.
    3. Shinya Yamanaka, 2009. "Elite and stochastic models for induced pluripotent stem cell generation," Nature, Nature, vol. 460(7251), pages 49-52, July.
    4. Kyung H Kim & Herbert M Sauro, 2012. "Adjusting Phenotypes by Noise Control," PLOS Computational Biology, Public Library of Science, vol. 8(1), pages 1-14, January.
    5. Kuznetsov, A. & Afraimovich, V., 2012. "Heteroclinic cycles in the repressilator model," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 660-665.
    6. Hannah H. Chang & Martin Hemberg & Mauricio Barahona & Donald E. Ingber & Sui Huang, 2008. "Transcriptome-wide noise controls lineage choice in mammalian progenitor cells," Nature, Nature, vol. 453(7194), pages 544-547, May.
    7. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
    8. Eric H. Davidson, 2010. "Emerging properties of animal gene regulatory networks," Nature, Nature, vol. 468(7326), pages 911-920, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhou, Peipei & Cai, Shuiming & Liu, Zengrong & Chen, Luonan & Wang, Ruiqi, 2013. "Coupling switches and oscillators as a means to shape cellular signals in biomolecular systems," Chaos, Solitons & Fractals, Elsevier, vol. 50(C), pages 115-126.
    2. Miles Miller & Marc Hafner & Eduardo Sontag & Noah Davidsohn & Sairam Subramanian & Priscilla E M Purnick & Douglas Lauffenburger & Ron Weiss, 2012. "Modular Design of Artificial Tissue Homeostasis: Robust Control through Synthetic Cellular Heterogeneity," PLOS Computational Biology, Public Library of Science, vol. 8(7), pages 1-18, July.
    3. Jin Wang & Bo Huang & Xuefeng Xia & Zhirong Sun, 2006. "Funneled Landscape Leads to Robustness of Cell Networks: Yeast Cell Cycle," PLOS Computational Biology, Public Library of Science, vol. 2(11), pages 1-10, November.
    4. Avraham E Mayo & Yaakov Setty & Seagull Shavit & Alon Zaslaver & Uri Alon, 2006. "Plasticity of the cis-Regulatory Input Function of a Gene," PLOS Biology, Public Library of Science, vol. 4(4), pages 1-1, March.
    5. Ankit Gupta & Mustafa Khammash, 2022. "Frequency spectra and the color of cellular noise," Nature Communications, Nature, vol. 13(1), pages 1-18, December.
    6. Bottani, Samuel & Grammaticos, Basile, 2008. "A simple model of genetic oscillations through regulated degradation," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1468-1482.
    7. Margherita Carletti & Malay Banerjee, 2019. "A Backward Technique for Demographic Noise in Biological Ordinary Differential Equation Models," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    8. Belén de la Hera & Jezabel Varadé & Marta García-Montojo & José Ramón Lamas & Ana de la Encarnación & Rafael Arroyo & Benjamín Fernández-Gutiérrez & Roberto Álvarez-Lafuente & Elena Urcelay, 2013. "Role of the Human Endogenous Retrovirus HERV-K18 in Autoimmune Disease Susceptibility: Study in the Spanish Population and Meta-Analysis," PLOS ONE, Public Library of Science, vol. 8(4), pages 1-7, April.
    9. Masa Tsuchiya & Vincent Piras & Sangdun Choi & Shizuo Akira & Masaru Tomita & Alessandro Giuliani & Kumar Selvarajoo, 2009. "Emergent Genome-Wide Control in Wildtype and Genetically Mutated Lipopolysaccarides-Stimulated Macrophages," PLOS ONE, Public Library of Science, vol. 4(3), pages 1-13, March.
    10. Weiyue Ji & Handuo Shi & Haoqian Zhang & Rui Sun & Jingyi Xi & Dingqiao Wen & Jingchen Feng & Yiwei Chen & Xiao Qin & Yanrong Ma & Wenhan Luo & Linna Deng & Hanchi Lin & Ruofan Yu & Qi Ouyang, 2013. "A Formalized Design Process for Bacterial Consortia That Perform Logic Computing," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-9, February.
    11. Konstantinos I Papadimitriou & Guy-Bart V Stan & Emmanuel M Drakakis, 2013. "Systematic Computation of Nonlinear Cellular and Molecular Dynamics with Low-Power CytoMimetic Circuits: A Simulation Study," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-24, February.
    12. Inés P Mariño & Alexey Zaikin & Joaquín Míguez, 2017. "A comparison of Monte Carlo-based Bayesian parameter estimation methods for stochastic models of genetic networks," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-25, August.
    13. Zhdanov, Vladimir P., 2012. "Periodic perturbation of genetic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 577-587.
    14. Dhiman, Aman & Poria, Swarup, 2018. "Allee effect induced diversity in evolutionary dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 108(C), pages 32-38.
    15. Anyou Wang & Ying Du & Qianchuan He & Chunxiao Zhou, 2013. "A Quantitative System for Discriminating Induced Pluripotent Stem Cells, Embryonic Stem Cells and Somatic Cells," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-10, February.
    16. Chen, Shi-Ming & Xu, Yun-Fei & Nie, Sen, 2017. "Robustness of network controllability in cascading failure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 536-539.
    17. Gautam Dey & Gagan D Gupta & Balaji Ramalingam & Mugdha Sathe & Satyajit Mayor & Mukund Thattai, 2014. "Exploiting Cell-To-Cell Variability To Detect Cellular Perturbations," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-10, March.
    18. Javier Santos-Moreno & Eve Tasiudi & Hadiastri Kusumawardhani & Joerg Stelling & Yolanda Schaerli, 2023. "Robustness and innovation in synthetic genotype networks," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    19. T. Ochiai & J. C. Nacher, 2007. "Stochastic analysis of autoregulatory gene expression dynamics," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 14(4), pages 377-388, November.
    20. Thomas B. Kepler & Timothy C. Elston, 2001. "Stochasticity in Transcriptional Regulation: Origins, Consequences and Mathematical Representations," Working Papers 01-06-033, Santa Fe Institute.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:73:y:2015:i:c:p:166-182. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.