A Model for the Proliferation–Quiescence Transition in Human Cells

Kudzanayi Z. Mapfumo, Jane C. Pagan’a, Victor Ogesa Juma, Nikos I. Kavallaris and Anotida Madzvamuse
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Kudzanayi Z. Mapfumo: Department of Mathematics and Computational Sciences, University of Zimbabwe, Harare P.O. Box MP167, Zimbabwe
Jane C. Pagan’a: Department of Statistics and Mathematics, Bindura University of Science Education, Bindura P.O. Box 1020, Zimbabwe
Victor Ogesa Juma: Mechanical Engineering Department, University of Zaragoza, Edificio Betancourt, Campus Rio Ebro, E-50018 Zaragoza, Spain
Nikos I. Kavallaris: Department of Mathematics and Computer Science, Faculty of Health, Science and Technology, Karlstad University, 651 88 Karlstad, Sweden
Anotida Madzvamuse: Department of Mathematics, University of Sussex, Pevensey III, Brighton BN1 9QH, UK

Mathematics, 2022, vol. 10, issue 14, 1-24

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.

Keywords: cell cycle; proliferation; quiescence; system of ODEs; bifurcation analysis; numerical bifurcation analysis; sensitivity analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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