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A Moments-Based Analytical Approach for Cell Size Homeostasis
César Nieto1, Cesar Augusto Vargas-Garcia2, Abhyudai Singh3
1Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716 USA.
IEEE Control Systems Letters
|August 13, 2025
Summary
This study reveals that regulated cell division rates are crucial for maintaining stable cell size. Stochastic Hybrid Systems modeling shows that size-dependent division rates, unlike size-independent ones, prevent unbounded increases in cell size variance.
Area of Science:
- Quantitative Biology
- Cellular Dynamics
- Mathematical Modeling
Background:
- Cell size regulation is fundamental for cellular function and organism development.
- Previous models often simplified the complex dynamics of cell growth and division.
- Understanding cell size homeostasis is key to deciphering cellular robustness.
Purpose of the Study:
- To explore and model the mechanisms governing single-cell size dynamics and homeostasis.
- To investigate the impact of different division rate strategies on cell size variability.
- To develop a framework for parameter estimation from experimental cell size data.
Main Methods:
- Utilized Stochastic Hybrid Systems (SHS) to model continuous cell growth and discrete division events.
- Analyzed scenarios with size-independent and size-dependent division rates.
- Derived exact formulas for steady-state moments (mean, variance, skewness) of cell size.
Main Results:
- A size-independent division rate leads to unbounded increases in cell size variance over time.
- A division rate proportional to cell size (the 'adder' model) achieves cell size homeostasis.
- Multi-stage division processes and uneven daughter cell partitioning were modeled, showing reduced variability with more stages.
Conclusions:
- Cell size homeostasis is achieved through specific size-dependent division control mechanisms.
- The SHS framework provides quantitative insights into cell size variability reduction.
- The study offers a method for parameter estimation, aiding experimental validation and understanding of cell size regulation.
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