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A Model for the Proliferation–Quiescence Transition in Human Cells

Author

Listed:
  • Kudzanayi Z. Mapfumo

    (Department of Mathematics and Computational Sciences, University of Zimbabwe, Harare P.O. Box MP167, Zimbabwe
    These authors contributed equally to this work.)

  • Jane C. Pagan’a

    (Department of Statistics and Mathematics, Bindura University of Science Education, Bindura P.O. Box 1020, Zimbabwe
    These authors contributed equally to this work.)

  • Victor Ogesa Juma

    (Mechanical Engineering Department, University of Zaragoza, Edificio Betancourt, Campus Rio Ebro, E-50018 Zaragoza, Spain
    These authors contributed equally to this work.)

  • Nikos I. Kavallaris

    (Department of Mathematics and Computer Science, Faculty of Health, Science and Technology, Karlstad University, 651 88 Karlstad, Sweden
    These authors contributed equally to this work.)

  • Anotida Madzvamuse

    (Department of Mathematics, University of Sussex, Pevensey III, Brighton BN1 9QH, UK
    Department of Mathematics, University of Johannesburg, Johannesburg 2006, South Africa
    Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC V6T 1Z2, Canada
    Conceived the research study.)

Abstract

The process of revitalising quiescent cells in order for them to proliferate plays a pivotal role in the repair of worn-out tissues as well as for tissue homeostasis. This process is also crucial in the growth, development and well-being of higher multi-cellular organisms such as mammals. Deregulation of proliferation-quiescence transition is related to many diseases, such as cancer. Recent studies have revealed that this proliferation–quiescence process is regulated tightly by the R b − E 2 F bistable switch mechanism. Based on experimental observations, in this study, we formulate a mathematical model to examine the effect of the growth factor concentration on the proliferation–quiescence transition in human cells. Working with a non-dimensionalised model, we prove the positivity, boundedness and uniqueness of solutions. To understand model solution behaviour close to bifurcation points, we carry out bifurcation analysis, which is further illustrated by the use of numerical bifurcation analysis, sensitivity analysis and numerical simulations. Indeed, bifurcation and numerical analysis of the model predicted a transition between bistable and stable states, which are dependent on the growth factor concentration parameter ( G F ). The derived predictions confirm experimental observations.

Suggested Citation

  • Kudzanayi Z. Mapfumo & Jane C. Pagan’a & Victor Ogesa Juma & Nikos I. Kavallaris & Anotida Madzvamuse, 2022. "A Model for the Proliferation–Quiescence Transition in Human Cells," Mathematics, MDPI, vol. 10(14), pages 1-24, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2426-:d:860885
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    References listed on IDEAS

    as
    1. Michael B. Kastan & Jiri Bartek, 2004. "Cell-cycle checkpoints and cancer," Nature, Nature, vol. 432(7015), pages 316-323, November.
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