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Modelling cell adaptation using internal variables: Accounting for cell plasticity in continuum mathematical biology
Marina Pérez-Aliacar1, Jacobo Ayensa-Jiménez2, Manuel Doblaré3
1Mechanical Engineering Department, School of Engineering and Architecture, University of Zaragoza, C/ Maria de Luna, Zaragoza, 50018, Spain; Engineering Research Institute of Aragón (I3A), University of Zaragoza, C/ Mariano Esquillor, Zaragoza, 50018, Spain.
Computers in Biology and Medicine
|August 16, 2023
Summary
Cells adapt to their environment through phenotypic plasticity. This study introduces a mathematical model to simulate cellular adaptation and heterogeneity, crucial for understanding cancer evolution and treatment strategies.
Area of Science:
- Cellular and Molecular Biology
- Mathematical Biology
- Cancer Research
Background:
- Cellular adaptation is a key mechanism for cells to respond to environmental changes, influencing biological processes like cancer evolution.
- Phenotypic plasticity, driven by gene expression changes, underlies cellular adaptation and is critical for understanding tumor progression and therapeutic resistance.
- Cancer stem cells exhibit enhanced proliferation and invasion, highlighting the importance of studying cellular adaptation in oncology.
Purpose of the Study:
- To develop a mathematical framework for simulating phenotypic heterogeneity in cell populations.
- To model the interaction between cells and their microenvironment, specifically chemical species.
- To investigate cellular adaptation mechanisms, including phenotype inheritance and response to stimuli history.
Main Methods:
- A continuum mathematical model using internal variables to represent cell phenotype.
- Derivation of the model from conservation laws to capture phenotype-stimuli relationships and inheritance.
- Application and parametric analysis of the model for glioblastoma adaptation to hypoxia.
Main Results:
- The model successfully simulates phenotypic heterogeneity arising from microenvironmental interactions.
- Parametric analysis revealed the impact of individual parameters on cellular adaptation trends.
- The model reproduced various trends previously reported in scientific literature regarding cellular adaptation.
Conclusions:
- The developed mathematical framework can simulate cellular adaptation and phenotypic heterogeneity.
- The model is adaptable to various cell plasticity problems, provided sufficient cell numbers for continuum variables.
- This framework can aid in exploring cellular adaptation mechanisms and informing treatment strategies.
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