IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v627y2023ics0378437123006775.html
   My bibliography  Save this article

Dynamical transition of phenotypic states in breast cancer system with Lévy noise

Author

Listed:
  • Song, Yi
  • Xu, Wei
  • Wei, Wei
  • Niu, Lizhi

Abstract

Breast cancer cells exhibit three distinct phenotypes: basal, stem-like, and luminal states. These phenotypes are closely associated with the invasion and spread of breast cancer. As breast cancer has a high recurrence rate and rapid progression, it is critical to comprehend the mechanisms responsible for the transition between these states. This paper employs quantitative analysis to investigate the multiple phenotypic transition behaviors of the Lévy-noise-induced kinetic model of breast cancer using the first escape probability. The semi-analytical method of the first escape probability is constructed under Balayage–Dirichlet exterior boundary conditions. The results suggest that noise can trigger a transition from the basal state to the other two states, inducing breast cancer metastasis. Moreover, higher noise intensity promotes the transition from the basal state to the stem-like state, which can lead to tumor seeding. In addition, a larger amplitude with lower frequency of the jump increases the likelihood of transition from the basal state to the luminal state, indicating the formation of new tumors in distant organs that are difficult to treat. The validity and consistency of the proposed method can be verified by numerical simulations.

Suggested Citation

  • Song, Yi & Xu, Wei & Wei, Wei & Niu, Lizhi, 2023. "Dynamical transition of phenotypic states in breast cancer system with Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 627(C).
    • Handle: RePEc:eee:phsmap:v:627:y:2023:i:c:s0378437123006775
    DOI: 10.1016/j.physa.2023.129122
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437123006775
    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.2023.129122?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. Wang, Kang Kang & Wang, Ya Jun & Li, Sheng Hong & Wu, Jian Cheng, 2016. "Stochastic stability and state shifts for a time-delayed cancer growth system subjected to correlated multiplicative and additive noises," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 1-13.
    2. Andrew M. Edwards & Richard A. Phillips & Nicholas W. Watkins & Mervyn P. Freeman & Eugene J. Murphy & Vsevolod Afanasyev & Sergey V. Buldyrev & M. G. E. da Luz & E. P. Raposo & H. Eugene Stanley & Ga, 2007. "Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer," Nature, Nature, vol. 449(7165), pages 1044-1048, October.
    3. Arjun Raj & Charles S Peskin & Daniel Tranchina & Diana Y Vargas & Sanjay Tyagi, 2006. "Stochastic mRNA Synthesis in Mammalian Cells," PLOS Biology, Public Library of Science, vol. 4(10), pages 1-13, September.
    4. Luxuan Yang & Ting Gao & Yubin Lu & Jinqiao Duan & Tao Liu, 2021. "Neural network stochastic differential equation models with applications to financial data forecasting," Papers 2111.13164, arXiv.org, revised Nov 2022.
    5. Wei, Wei & Xu, Wei & Song, Yi & Liu, Jiankang, 2021. "Bifurcation and basin stability of an SIR epidemic model with limited medical resources and switching noise," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Chen, Xiaoli & Wu, Fengyan & Duan, Jinqiao & Kurths, Jürgen & Li, Xiaofan, 2019. "Most probable dynamics of a genetic regulatory network under stable Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 425-436.
    7. Tesfay, Daniel & Wei, Pingyuan & Zheng, Yayun & Duan, Jinqiao & Kurths, Jürgen, 2020. "Transitions between metastable states in a simplified model for the thermohaline circulation under random fluctuations," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    8. He, Danhua & Xu, Liguang, 2022. "Boundedness analysis of stochastic delay differential equations with Lévy noise," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    9. Zhang, Ge & Li, Zhiming & Din, Anwarud, 2022. "A stochastic SIQR epidemic model with Lévy jumps and three-time delays," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    10. Ertugrul M. Ozbudak & Mukund Thattai & Han N. Lim & Boris I. Shraiman & Alexander van Oudenaarden, 2004. "Multistability in the lactose utilization network of Escherichia coli," Nature, Nature, vol. 427(6976), pages 737-740, February.
    11. Wang, Xiao & Duan, Jinqiao & Li, Xiaofan & Song, Renming, 2018. "Numerical algorithms for mean exit time and escape probability of stochastic systems with asymmetric Lévy motion," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 618-634.
    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. Han, Ping & Xu, Wei & Zhang, Hongxia & Wang, Liang, 2022. "Most probable trajectories in the delayed tumor growth model excited by a multiplicative non-Gaussian noise," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Chen, Aimin & Tian, Tianhai & Chen, Yiren & Zhou, Tianshou, 2022. "Stochastic analysis of a complex gene-expression model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Song, Yi & Xu, Wei, 2021. "Asymmetric Lévy noise changed stability in a gene transcriptional regulatory system," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Matthieu Wyart & David Botstein & Ned S Wingreen, 2010. "Evaluating Gene Expression Dynamics Using Pairwise RNA FISH Data," PLOS Computational Biology, Public Library of Science, vol. 6(11), pages 1-14, November.
    5. Lai, Qiang & Norouzi, Benyamin & Liu, Feng, 2018. "Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 230-245.
    6. Tomas Tokar & Jozef Ulicny, 2013. "The Mathematical Model of the Bcl-2 Family Mediated MOMP Regulation Can Perform a Non-Trivial Pattern Recognition," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-8, December.
    7. Paul Miller & Anatol M Zhabotinsky & John E Lisman & Xiao-Jing Wang, 2005. "The Stability of a Stochastic CaMKII Switch: Dependence on the Number of Enzyme Molecules and Protein Turnover," PLOS Biology, Public Library of Science, vol. 3(4), pages 1-1, March.
    8. Butts, David J. & Thompson, Noelle E. & Christensen, Sonja A. & Williams, David M. & Murillo, Michael S., 2022. "Data-driven agent-based model building for animal movement through Exploratory Data Analysis," Ecological Modelling, Elsevier, vol. 470(C).
    9. Stuart Aitken & Marie-Cécile Robert & Ross D Alexander & Igor Goryanin & Edouard Bertrand & Jean D Beggs, 2010. "Processivity and Coupling in Messenger RNA Transcription," PLOS ONE, Public Library of Science, vol. 5(1), pages 1-12, January.
    10. Han, Ping & Xu, Wei & Wang, Liang & Ma, Shichao, 2020. "The most probable response of some prototypical stochastic nonlinear dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    11. Singh, Abhyudai & Vahdat, Zahra & Xu, Zikai, 2019. "Time-triggered stochastic hybrid systems with two timer-dependent resets," OSF Preprints u8fzg, Center for Open Science.
    12. Muir Morrison & Manuel Razo-Mejia & Rob Phillips, 2021. "Reconciling kinetic and thermodynamic models of bacterial transcription," PLOS Computational Biology, Public Library of Science, vol. 17(1), pages 1-30, January.
    13. Tobias May & Lee Eccleston & Sabrina Herrmann & Hansjörg Hauser & Jorge Goncalves & Dagmar Wirth, 2008. "Bimodal and Hysteretic Expression in Mammalian Cells from a Synthetic Gene Circuit," PLOS ONE, Public Library of Science, vol. 3(6), pages 1-7, June.
    14. Danish A. Ahmed & Sergei V. Petrovskii & Paulo F. C. Tilles, 2018. "The “Lévy or Diffusion” Controversy: How Important Is the Movement Pattern in the Context of Trapping?," Mathematics, MDPI, vol. 6(5), pages 1-27, May.
    15. Marc S Sherman & Barak A Cohen, 2014. "A Computational Framework for Analyzing Stochasticity in Gene Expression," PLOS Computational Biology, Public Library of Science, vol. 10(5), pages 1-13, May.
    16. Rajesh Ramaswamy & Ivo F Sbalzarini & Nélido González-Segredo, 2011. "Noise-Induced Modulation of the Relaxation Kinetics around a Non-Equilibrium Steady State of Non-Linear Chemical Reaction Networks," PLOS ONE, Public Library of Science, vol. 6(1), pages 1-10, January.
    17. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    18. Anton J M Larsson & Christoph Ziegenhain & Michael Hagemann-Jensen & Björn Reinius & Tina Jacob & Tim Dalessandri & Gert-Jan Hendriks & Maria Kasper & Rickard Sandberg, 2021. "Transcriptional bursts explain autosomal random monoallelic expression and affect allelic imbalance," PLOS Computational Biology, Public Library of Science, vol. 17(3), pages 1-16, March.
    19. Yang, Anji & Wang, Hao & Yuan, Sanling, 2023. "Tipping time in a stochastic Leslie predator–prey model," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    20. Yang, Yi & Huang, Jin, 2024. "Double fast algorithm for solving time-space fractional diffusion problems with spectral fractional Laplacian," Applied Mathematics and Computation, Elsevier, vol. 475(C).

    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:627:y:2023:i:c:s0378437123006775. 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: 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.