IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v421y2022ics0096300322000029.html
   My bibliography  Save this article

Stability and bifurcations in fractional-order gene regulatory networks

Author

Listed:
  • Kaslik, Eva
  • Rădulescu, Ileana Rodica

Abstract

A fractional-order mathematical model of a large-scale GRN is presented, focusing on the positivity of solutions and on the stability analysis of equilibria based on Matignon’s theorem. With special emphasis on cyclic GRNs, necessary and sufficient conditions are obtained in terms of inequalities involving the system’s parameters and the fractional order, which guarantee the stability of equilibrium points. Based on the stability analysis, the critical values of the fractional order for which Hopf-type bifurcations may occur are detected. In this context, it is shown that oscillatory behavior due to a Hopf-type bifurcation (considering the fractional order as bifurcation parameter) is expected only in the case of an odd number of repressive genes. Numerical examples are given in order to demonstrate the usefulness of the proposed results and to exemplify the effect of the fractional order on the dynamics of cyclic GRNs, additionally revealing that period-doubling bifurcations of limit cycles may also occur in sufficiently large cyclic GRNs.

Suggested Citation

  • Kaslik, Eva & Rădulescu, Ileana Rodica, 2022. "Stability and bifurcations in fractional-order gene regulatory networks," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000029
    DOI: 10.1016/j.amc.2022.126916
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322000029
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.126916?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. Marcel Tigges & Tatiana T. Marquez-Lago & Jörg Stelling & Martin Fussenegger, 2009. "A tunable synthetic mammalian oscillator," Nature, Nature, vol. 457(7227), pages 309-312, January.
    2. Huang, Chengdai & Cao, Jinde & Xiao, Min, 2016. "Hybrid control on bifurcation for a delayed fractional gene regulatory network," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 19-29.
    3. Zang, Hong & Zhang, Tonghua & Zhang, Yanduo, 2015. "Bifurcation analysis of a mathematical model for genetic regulatory network with time delays," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 204-226.
    4. Björn Schwanhäusser & Dorothea Busse & Na Li & Gunnar Dittmar & Johannes Schuchhardt & Jana Wolf & Wei Chen & Matthias Selbach, 2011. "Global quantification of mammalian gene expression control," Nature, Nature, vol. 473(7347), pages 337-342, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Shenglong & Yang, Jikai & Li, Zhiming & Li, Hong-Li & Hu, Cheng, 2023. "New results for dynamical analysis of fractional-order gene regulatory networks with time delay and uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    2. Yang, Juanping & Sheng, Yuhong & Li, Hong-Li & Hu, Cheng, 2023. "Stability and adaptive control-based synchronization of delayed uncertain fractional-order gene regulatory networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    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. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    2. Li, Peiluan & Gao, Rong & Xu, Changjin & Ahmad, Shabir & Li, Ying & Akgül, Ali, 2023. "Bifurcation behavior and PDγ control mechanism of a fractional delayed genetic regulatory model," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Yang, Juanping & Sheng, Yuhong & Li, Hong-Li & Hu, Cheng, 2023. "Stability and adaptive control-based synchronization of delayed uncertain fractional-order gene regulatory networks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Yuping Chen & Jo-Hsi Huang & Connie Phong & James E. Ferrell, 2024. "Viscosity-dependent control of protein synthesis and degradation," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    5. Wang, Xinhe & Lu, Junwei & Wang, Zhen & Li, Yuxia, 2020. "Dynamics of discrete epidemic models on heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    6. Gábor Csárdi & Alexander Franks & David S Choi & Edoardo M Airoldi & D Allan Drummond, 2015. "Accounting for Experimental Noise Reveals That mRNA Levels, Amplified by Post-Transcriptional Processes, Largely Determine Steady-State Protein Levels in Yeast," PLOS Genetics, Public Library of Science, vol. 11(5), pages 1-32, May.
    7. Suran Kim & Sungjin Min & Yi Sun Choi & Sung-Hyun Jo & Jae Hun Jung & Kyusun Han & Jin Kim & Soohwan An & Yong Woo Ji & Yun-Gon Kim & Seung-Woo Cho, 2022. "Tissue extracellular matrix hydrogels as alternatives to Matrigel for culturing gastrointestinal organoids," Nature Communications, Nature, vol. 13(1), pages 1-21, December.
    8. Lingling Li & Dongxian Jiang & Qiao Zhang & Hui Liu & Fujiang Xu & Chunmei Guo & Zhaoyu Qin & Haixing Wang & Jinwen Feng & Yang Liu & Weijie Chen & Xue Zhang & Lin Bai & Sha Tian & Subei Tan & Chen Xu, 2023. "Integrative proteogenomic characterization of early esophageal cancer," Nature Communications, Nature, vol. 14(1), pages 1-28, December.
    9. Thomas C. J. Tan & Van Kelly & Xiaoyan Zou & David Wright & Tony Ly & Rose Zamoyska, 2022. "Translation factor eIF5a is essential for IFNγ production and cell cycle regulation in primary CD8+ T lymphocytes," Nature Communications, Nature, vol. 13(1), pages 1-16, December.
    10. Katharina Clemm von Hohenberg & Sandra Müller & Sibylle Schleich & Matthias Meister & Jonathan Bohlen & Thomas G. Hofmann & Aurelio A. Teleman, 2022. "Cyclin B/CDK1 and Cyclin A/CDK2 phosphorylate DENR to promote mitotic protein translation and faithful cell division," Nature Communications, Nature, vol. 13(1), pages 1-14, December.
    11. Jonathan J. Swietlik & Stefanie Bärthel & Chiara Falcomatà & Diana Fink & Ankit Sinha & Jingyuan Cheng & Stefan Ebner & Peter Landgraf & Daniela C. Dieterich & Henrik Daub & Dieter Saur & Felix Meissn, 2023. "Cell-selective proteomics segregates pancreatic cancer subtypes by extracellular proteins in tumors and circulation," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    12. Ryosuke Ishimura & Afnan H. El-Gowily & Daisuke Noshiro & Satoko Komatsu-Hirota & Yasuko Ono & Mayumi Shindo & Tomohisa Hatta & Manabu Abe & Takefumi Uemura & Hyeon-Cheol Lee-Okada & Tarek M. Mohamed , 2022. "The UFM1 system regulates ER-phagy through the ufmylation of CYB5R3," Nature Communications, Nature, vol. 13(1), pages 1-16, December.
    13. Lukas Aufinger & Johann Brenner & Friedrich C. Simmel, 2022. "Complex dynamics in a synchronized cell-free genetic clock," Nature Communications, Nature, vol. 13(1), pages 1-9, December.
    14. Sébastien Durand & Marion Bruelle & Fleur Bourdelais & Bigitha Bennychen & Juliana Blin-Gonthier & Caroline Isaac & Aurélia Huyghe & Sylvie Martel & Antoine Seyve & Christophe Vanbelle & Annie Adrait , 2023. "RSL24D1 sustains steady-state ribosome biogenesis and pluripotency translational programs in embryonic stem cells," Nature Communications, Nature, vol. 14(1), pages 1-17, December.
    15. 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.
    16. Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
    17. Rune B Jakobsen & Esben Østrup & Xiaolan Zhang & Tarjei S Mikkelsen & Jan E Brinchmann, 2014. "Analysis of the Effects of Five Factors Relevant to In Vitro Chondrogenesis of Human Mesenchymal Stem Cells Using Factorial Design and High Throughput mRNA-Profiling," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-13, May.
    18. Beatrice T. Laudenbach & Karsten Krey & Quirin Emslander & Line Lykke Andersen & Alexander Reim & Pietro Scaturro & Sarah Mundigl & Christopher Dächert & Katrin Manske & Markus Moser & Janos Ludwig & , 2021. "NUDT2 initiates viral RNA degradation by removal of 5′-phosphates," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    19. Gao, Bo & Deng, Zheng-hong & Zhao, Da-wei & Song, Qun, 2017. "State analysis of Boolean control networks with impulsive and uncertain disturbances," Applied Mathematics and Computation, Elsevier, vol. 301(C), pages 187-192.
    20. McNutt Patrick & Gut Ian & Hubbard Kyle & Beske Phil, 2015. "A novel method to prioritize RNAseq data for post-hoc analysis based on absolute changes in transcript abundance," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 14(3), pages 227-241, June.

    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:apmaco:v:421:y:2022:i:c:s0096300322000029. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.