IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v531y2019ics0378437119310325.html
   My bibliography  Save this article

Most probable transition pathways and maximal likely trajectories in a genetic regulatory system

Author

Listed:
  • Cheng, Xiujun
  • Wang, Hui
  • Wang, Xiao
  • Duan, Jinqiao
  • Li, Xiaofan

Abstract

We study the most probable transition pathways and maximal likely trajectories in a genetic regulation model of the transcription factor activator’s concentration evolution, with Gaussian noise and non-Gaussian stable Lévy noise in the synthesis reaction rate taking into account, respectively. We compute the most probable transition pathways by the Onsager–Machlup least action principle, and calculate the maximal likely trajectories by spatially maximizing the probability density of the system path, i.e., the solution of the associated nonlocal Fokker–Planck equation. We have observed the rare most probable transition pathways in the case of Gaussian noise, for certain noise intensity, evolution time scale and system parameters. We have especially studied the maximal likely trajectories starting at the low concentration metastable state, and examined whether they evolve to or near the high concentration metastable state (i.e., the likely transcription regime) for certain parameters, in order to gain insights into the transcription processes and the tipping time for the transcription likely to occur. This enables us: (i) to visualize the progress of concentration evolution (i.e., observe whether the system enters the transcription regime within a given time period); (ii) to predict or avoid certain transcriptions via selecting specific noise parameters in particular regions in the parameter space. Moreover, we have found some peculiar or counter-intuitive phenomena in this gene model system, including: (a) A smaller noise intensity may trigger the transcription process, while a larger noise intensity cannot, under the same asymmetric Lévy noise. This phenomenon does not occur in the case of symmetric Lévy noise; (b) The symmetric Lévy motion always induces transition to high concentration, but certain asymmetric Lévy motions do not trigger the switch to transcription.

Suggested Citation

  • Cheng, Xiujun & Wang, Hui & Wang, Xiao & Duan, Jinqiao & Li, Xiaofan, 2019. "Most probable transition pathways and maximal likely trajectories in a genetic regulatory system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
  • Handle: RePEc:eee:phsmap:v:531:y:2019:i:c:s0378437119310325
    DOI: 10.1016/j.physa.2019.121779
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119310325
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2019.121779?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.

    Citations

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


    Cited by:

    1. Han, Ping & Xu, Wei & Wang, Liang & Zhang, Hongxia & Ma, Shichao, 2020. "Most probable dynamics of the tumor growth model with immune surveillance under cross-correlated noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    2. Yang, Anji & Wang, Hao & Yuan, Sanling, 2023. "Tipping time in a stochastic Leslie predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Tsiairis, Athanasios & Wei, Pingyuan & Chao, Ying & Duan, Jinqiao, 2021. "Maximal likely phase lines for a reduced ice growth model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 569(C).
    4. Hao, Mengli & Jia, Wantao & Wang, Liang & Li, Fuxiao, 2022. "Most probable trajectory of a tumor model with immune response subjected to asymmetric Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

    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:phsmap:v:531:y:2019:i:c:s0378437119310325. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.