The fixed-size Luria-Delbruck model with a nonzero death rate

Area of Science:

• Evolutionary biology
• Mathematical modeling
• Cellular biology

Background:

• The Luria-Delbruck model traditionally analyzes mutant distribution over a fixed time.
• Many biological applications, such as in-vivo oncology, involve measurable colony size rather than fixed time.

Purpose of the Study:

• To determine the expected number of mutants in a stochastically growing cell colony of a specific size (N).
• To analyze the impact of cell death rates on mutant accumulation.
• To compare fixed-size and fixed-time models for mutant distribution.

Main Methods:

• Developed a variant of the Luria-Delbruck model focusing on colony size (N) instead of time.
• Derived analytical results for the mean and partial results for the variance of mutants.
• Designed an efficient computational method for calculating the mean number of mutants for large colony sizes and arbitrary death rates.

Main Results:

• A higher cell death rate leads to a greater number of mutants in a population of a given size.
• Larger populations exhibit a higher percentage of mutants, indicating mutations act as a selection force even without a selective advantage.
• The traditional fixed-time model approximates the fixed-size model when stochastic effects are minimal.

Conclusions:

• Colony size is a critical factor in understanding mutant accumulation, particularly in in-vivo scenarios.
• Cell death rate significantly influences the number of mutants, contrary to models assuming only growth.
• The developed computational method provides a robust tool for analyzing mutant frequencies in large populations.