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Stochastic multi-step cell size homeostasis model for cycling human cells
Sayeh Rezaee1, Cesar Nieto1, Abhyudai Singh2
1Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA.
Arxiv
|January 8, 2026
Summary
Cells maintain a consistent size each cycle, a principle preserved even with growth saturation. This study extends cell size control theory beyond exponential growth, revealing how growth laws impact cell populations.
Area of Science:
- Cell Biology
- Quantitative Biology
- Theoretical Biology
Background:
- Cell size homeostasis is crucial for cellular function.
- The adder principle, where cells add a constant size per cycle, explains this homeostasis.
- Existing models often assume exponential growth.
Purpose of the Study:
- To extend the adder principle framework to include growth saturation.
- To investigate the impact of a general Hill-type growth law on cell size dynamics.
- To analyze stochastic multi-step adder models and their effect on cell proliferation.
Main Methods:
- Developed a stochastic multi-step adder model incorporating a Hill-type growth function.
- Derived exact analytical expressions for moments of cell size distributions.
- Analyzed clonal proliferation dynamics under growth saturation.
Main Results:
- Growth saturation increases mean cell size and slightly reduces fluctuations.
- The adder property is preserved despite growth saturation.
- Growth saturation influences single-cell size statistics and population variability.
Conclusions:
- The adder principle is robust and extends beyond exponential growth.
- Growth laws, not just scaling, determine size variability.
- This work provides a generalized framework for cell proliferation dynamics.
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