A Model for the Proliferation–Quiescence Transition in Human Cells
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. Deregulati...
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MDPI AG
2022-07-01
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| Online Access: | https://www.mdpi.com/2227-7390/10/14/2426 |
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| author | Kudzanayi Z. Mapfumo Jane C. Pagan’a Victor Ogesa Juma Nikos I. Kavallaris Anotida Madzvamuse |
| author_facet | Kudzanayi Z. Mapfumo Jane C. Pagan’a Victor Ogesa Juma Nikos I. Kavallaris Anotida Madzvamuse |
| author_sort | Kudzanayi Z. Mapfumo |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>b</mi><mo>−</mo><mi>E</mi><mn>2</mn><mi>F</mi></mrow></semantics></math></inline-formula> 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi></mrow></semantics></math></inline-formula>). The derived predictions confirm experimental observations. |
| first_indexed | 2024-03-09T13:26:10Z |
| format | Article |
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| language | English |
| last_indexed | 2024-03-09T13:26:10Z |
| publishDate | 2022-07-01 |
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| series | Mathematics |
| spelling | doaj.art-4df9adb1e136414485b31e7c8c6f72db2023-11-30T21:23:35ZengMDPI AGMathematics2227-73902022-07-011014242610.3390/math10142426A Model for the Proliferation–Quiescence Transition in Human CellsKudzanayi Z. Mapfumo0Jane C. Pagan’a1Victor Ogesa Juma2Nikos I. Kavallaris3Anotida Madzvamuse4Department of Mathematics and Computational Sciences, University of Zimbabwe, Harare P.O. Box MP167, ZimbabweDepartment of Statistics and Mathematics, Bindura University of Science Education, Bindura P.O. Box 1020, ZimbabweMechanical Engineering Department, University of Zaragoza, Edificio Betancourt, Campus Rio Ebro, E-50018 Zaragoza, SpainDepartment of Mathematics and Computer Science, Faculty of Health, Science and Technology, Karlstad University, 651 88 Karlstad, SwedenDepartment of Mathematics, University of Sussex, Pevensey III, Brighton BN1 9QH, UKThe 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><mi>b</mi><mo>−</mo><mi>E</mi><mn>2</mn><mi>F</mi></mrow></semantics></math></inline-formula> 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 (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>F</mi></mrow></semantics></math></inline-formula>). The derived predictions confirm experimental observations.https://www.mdpi.com/2227-7390/10/14/2426cell cycleproliferationquiescencesystem of ODEsbifurcation analysisnumerical bifurcation analysis |
| spellingShingle | Kudzanayi Z. Mapfumo Jane C. Pagan’a Victor Ogesa Juma Nikos I. Kavallaris Anotida Madzvamuse A Model for the Proliferation–Quiescence Transition in Human Cells Mathematics cell cycle proliferation quiescence system of ODEs bifurcation analysis numerical bifurcation analysis |
| title | A Model for the Proliferation–Quiescence Transition in Human Cells |
| title_full | A Model for the Proliferation–Quiescence Transition in Human Cells |
| title_fullStr | A Model for the Proliferation–Quiescence Transition in Human Cells |
| title_full_unstemmed | A Model for the Proliferation–Quiescence Transition in Human Cells |
| title_short | A Model for the Proliferation–Quiescence Transition in Human Cells |
| title_sort | model for the proliferation quiescence transition in human cells |
| topic | cell cycle proliferation quiescence system of ODEs bifurcation analysis numerical bifurcation analysis |
| url | https://www.mdpi.com/2227-7390/10/14/2426 |
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