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PDE MODELS OF ADDER MECHANISMS IN CELLULAR PROLIFERATION
Mingtao Xia1, Chris D Greenman2, Tom Chou3
1Department of Mathematics, UCLA, Los Angeles, CA 90095-1555.
SIAM Journal on Applied Mathematics
|February 28, 2022
Summary
This study unifies cell division models, proposing adder-sizer models to explain cellular proliferation. Mathematical analysis and numerical experiments reveal insights into cell population dynamics and growth correlations.
Area of Science:
- * Biophysics
- * Cell Biology
- * Mathematical Biology
Background:
- * Cell division is a complex process governed by various biochemical and biophysical mechanisms.
- * Existing models (timer, sizer, adder) simplify triggers for cell division based on age, size, or added volume.
- * Understanding cell population dynamics is crucial for biological and medical research.
Purpose of the Study:
- * To propose and analyze unified adder-sizer models for cell division.
- * To investigate the mathematical relationship between adder-sizer and age-size models.
- * To explore cell population dynamics, including effects of correlated growth rates and added size variations.
Main Methods:
- * Development of a 2+1-dimensional partial differential equation (PDE) model.
- * Mathematical proofs for existence and uniqueness of weak solutions.
- * Numerical computation of cell population densities and dynamics.
- * Generalization of the model to incorporate mother-daughter correlations and DNA replication timing.
Main Results:
- * Demonstrated mathematical equivalence between the adder-sizer model and age-size dependent division models.
- * Proved convergence of numerical solutions for the PDE model.
- * Illustrated potential for average cell volume blowup under correlated growth conditions.
- * Explored cell population dynamics with mother-daughter correlated growth rates.
Conclusions:
- * The unified adder-sizer model provides a robust framework for studying cell population structure.
- * The PDE model accurately captures complex dynamics, including correlated growth and cell cycle variations.
- * Findings offer new computational tools for analyzing cell proliferation and growth patterns.
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