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Universal Asymptotic Clone Size Distribution for General Population Growth.
Michael D Nicholson1, Tibor Antal2
1SUPA, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, UK. Michael.Nicholson@ed.ac.uk.
Bulletin of Mathematical Biology
|November 3, 2016
Summary
This study generalizes the Luria-Delbrück model for mutant clone growth beyond exponential wild-type population expansion. Findings suggest power-law distributions are more likely than exponential ones for clone sizes, with implications for cancer metastasis research.
Area of Science:
- Mathematical Biology
- Population Dynamics
- Cancer Research
Background:
- Stochastic mutant clone evolution from deterministic wild-type populations is key in microbial and cancer studies.
- The standard Luria-Delbrück model assumes unrealistic exponential wild-type growth.
- Real-world population growth often deviates from exponential patterns.
Purpose of the Study:
- To generalize the Luria-Delbrück model for various wild-type population growth types.
- To analyze the size distribution of mutant clones under different growth conditions.
- To investigate the applicability of these models to cancer metastasis.
Main Methods:
- Developed a generalized birth-death branching process for mutant evolution.
- Derived exact clone size distribution expressions for exponential, power-law, and logistic wild-type growth.
- Proved a general two-parameter form for long-time clone size distribution, featuring a power-law tail.
Main Results:
- Exact mathematical expressions for clone size distributions were obtained for diverse wild-type growth models.
- A universal power-law decay in the tail of the clone size distribution was proven for a broad range of population growth.
- Analysis of cancer metastasis data supported a power-law tail over an exponential one.
Conclusions:
- The generalized model provides a more realistic framework for studying mutant clone dynamics.
- Power-law distributions are a significant feature of clone size distributions in various biological systems, including cancer.
- This work offers new insights into the mathematical underpinnings of tumor heterogeneity and metastasis.
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