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A novel mathematical model of heterogeneous cell proliferation
Sean T Vittadello1,2, Scott W McCue3, Gency Gunasingh4
1School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, Australia. sean.vittadello@unimelb.edu.au.
Journal of Mathematical Biology
|March 13, 2021
Summary
This study introduces a new mathematical model for heterogeneous cell proliferation, incorporating asymmetric cell division and state switching. The model reveals that switching parameters significantly influence long-term cell population dynamics.
Area of Science:
- Mathematical Biology
- Cellular Dynamics
- Population Modeling
Background:
- Cell populations exhibit heterogeneity due to varying proliferation rates.
- Asymmetric cell division and state switching are key drivers of this heterogeneity.
- Existing models often simplify these complex cellular processes.
Purpose of the Study:
- To develop a novel mathematical model for heterogeneous cell proliferation.
- To incorporate asymmetric cell division and induced switching between proliferative states.
- To analyze the impact of these processes on cell population dynamics.
Main Methods:
- Development of a system of two coupled delay differential equations with distributed time delays.
- Mathematical analysis including proofs of nonnegativity, boundedness, existence, and uniqueness of solutions.
- Analysis of local stability characteristics of equilibrium points and identification of bifurcation parameters.
Main Results:
- The model successfully captures heterogeneous cell proliferation with slow and fast-proliferating subpopulations.
- Parameters governing induced switching were identified as bifurcation parameters, controlling long-term behavior.
- Numerical simulations confirmed theoretical findings and highlighted the importance of transient dynamics.
Conclusions:
- The novel mathematical model provides a framework for understanding heterogeneous cell proliferation.
- Induced switching is a critical factor determining the long-term evolution of cell populations.
- Transient dynamics play a crucial role in the observed behavior of experimental cell populations.
Keywords:
Asymmetric cell divisionDelay differential equationDistributed time delayInduced switchingIntegrodifferential equationTransient dynamicsMore Related Videos
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