IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i23p3028-d688497.html
   My bibliography  Save this article

Deep Gene Networks and Response to Stress

Author

Listed:
  • Sergey Vakulenko

    (Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia
    These authors contributed equally to this work.)

  • Dmitry Grigoriev

    (CNRS, Mathématiques, Université de Lille, 59655 Villeneuve d’Ascq, France
    These authors contributed equally to this work.)

Abstract

We consider systems of differential equations with polynomial and rational nonlinearities and with a dependence on a discrete parameter. Such systems arise in biological and ecological applications, where the discrete parameter can be interpreted as a genetic code. The genetic code defines system responses to external perturbations. We suppose that these responses are defined by deep networks. We investigate the stability of attractors of our systems under sequences of perturbations (for example, stresses induced by environmental changes), and we introduce a new concept of biosystem stability via gene regulation. We show that if the gene regulation is absent, then biosystems sooner or later collapse under fluctuations. By a genetic regulation, one can provide attractor stability for large times. Therefore, in the framework of our model, we prove the Gromov–Carbone hypothesis that evolution by replication makes biosystems robust against random fluctuations. We apply these results to a model of cancer immune therapy.

Suggested Citation

  • Sergey Vakulenko & Dmitry Grigoriev, 2021. "Deep Gene Networks and Response to Stress," Mathematics, MDPI, vol. 9(23), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3028-:d:688497
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/23/3028/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/23/3028/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. H. Jeong & S. P. Mason & A.-L. Barabási & Z. N. Oltvai, 2001. "Lethality and centrality in protein networks," Nature, Nature, vol. 411(6833), pages 41-42, May.
    2. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    3. Suzanne L. Rutherford & Susan Lindquist, 1998. "Hsp90 as a capacitor for morphological evolution," Nature, Nature, vol. 396(6709), pages 336-342, November.
    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. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    2. Chung-Yen Yu & Yung-Ting Chuang & Hsi-Peng Kuan, 2017. "Understanding Faculty Collaboration and Productivity: A Case Study," Asian Social Science, Canadian Center of Science and Education, vol. 13(3), pages 1-1, March.
    3. Gong, Pulin & van Leeuwen, Cees, 2003. "Emergence of scale-free network with chaotic units," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 679-688.
    4. Ruskin, Heather J. & Burns, John, 2006. "Weighted networks in immune system shape space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 549-555.
    5. P.B., Divya & Lekha, Divya Sindhu & Johnson, T.P. & Balakrishnan, Kannan, 2022. "Vulnerability of link-weighted complex networks in central attacks and fallback strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    6. Cemal Cagatay Bilgin & Shayoni Ray & Banu Baydil & William P Daley & Melinda Larsen & Bülent Yener, 2012. "Multiscale Feature Analysis of Salivary Gland Branching Morphogenesis," PLOS ONE, Public Library of Science, vol. 7(3), pages 1-19, March.
    7. Dan Braha & Yaneer Bar-Yam, 2004. "Information Flow Structure in Large-Scale Product Development Organizational Networks," Industrial Organization 0407012, University Library of Munich, Germany.
    8. Serra, Roberto & Villani, Marco & Agostini, Luca, 2004. "On the dynamics of random Boolean networks with scale-free outgoing connections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 339(3), pages 665-673.
    9. Huaylla, Claudia A. & Nacif, Marcos E. & Coulin, Carolina & Kuperman, Marcelo N. & Garibaldi, Lucas A., 2021. "Decoding information in multilayer ecological networks: The keystone species case," Ecological Modelling, Elsevier, vol. 460(C).
    10. Raghav, Tanu & Jalan, Sarika, 2022. "Random matrix analysis of multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    11. Tracy Chih-Ting Koubkova-Yu & Jung-Chi Chao & Jun-Yi Leu, 2018. "Heterologous Hsp90 promotes phenotypic diversity through network evolution," PLOS Biology, Public Library of Science, vol. 16(11), pages 1-29, November.
    12. Fabio Caccioli & J. Doyne Farmer & Nick Foti & Daniel Rockmore, 2013. "How interbank lending amplifies overlapping portfolio contagion: A case study of the Austrian banking network," Papers 1306.3704, arXiv.org.
    13. Jacob D Feala & Jorge Cortes & Phillip M Duxbury & Andrew D McCulloch & Carlo Piermarocchi & Giovanni Paternostro, 2012. "Statistical Properties and Robustness of Biological Controller-Target Networks," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-11, January.
    14. N. Foti & S. Pauls & Daniel N. Rockmore, 2011. "Stability of the World Trade Web over Time - An Extinction Analysis," Papers 1104.4380, arXiv.org, revised May 2011.
    15. Cajueiro, Daniel O., 2010. "Optimal navigation for characterizing the role of the nodes in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1945-1954.
    16. 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.
    17. Giorgio Jansen & Tanda Qi & Vito Latora & Grigoris D. Amoutzias & Daniela Delneri & Stephen G. Oliver & Giuseppe Nicosia, 2024. "Minimisation of metabolic networks defines a new functional class of genes," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    18. Piaopiao Chen & Agnès H. Michel & Jianzhi Zhang, 2022. "Transposon insertional mutagenesis of diverse yeast strains suggests coordinated gene essentiality polymorphisms," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    19. Zhou, Wei-Xing & Jiang, Zhi-Qiang & Sornette, Didier, 2007. "Exploring self-similarity of complex cellular networks: The edge-covering method with simulated annealing and log-periodic sampling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 741-752.
    20. D. Blanco-Obregon & K. El Marzkioui & F. Brutscher & V. Kapoor & L. Valzania & D. S. Andersen & J. Colombani & S. Narasimha & D. McCusker & P. Léopold & L. Boulan, 2022. "A Dilp8-dependent time window ensures tissue size adjustment in Drosophila," Nature Communications, Nature, vol. 13(1), pages 1-10, December.

    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:gam:jmathe:v:9:y:2021:i:23:p:3028-:d:688497. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.