An explicit representation of the Luria-Delbrück distribution

Area of Science:

• Mathematical Biology
• Population Genetics
• Computational Biology

Background:

• Classical Luria-Delbrück models describe mutation distributions in large populations with low mutation rates.
• Existing models have limitations with high mutation rates or arbitrary population sizes.

Purpose of the Study:

• To derive an explicit probability distribution for mutant cells in growing populations.
• To extend existing mutation models to accommodate high mutation rates and arbitrary population sizes.
• To analyze the impact of cell death and dual-mutant daughter cells on mutation dynamics.

Main Methods:

• Development of a discrete model for mutation and population growth.
• Analysis of the model in limiting cases (large populations, small mutation rates).
• Derivation of two distinct limit laws based on the product of mutation rate and population size.

Main Results:

• An explicit probability distribution applicable to arbitrary mutation rates and population sizes.
• Identification of two limit laws governing mutation distributions under different conditions.
• An algorithm for efficient calculation of the mutant cell distribution.

Conclusions:

• The study significantly extends classical mutation distribution models.
• Provides a more comprehensive framework for understanding mutation dynamics in cell populations.
• Offers tools for analyzing fluctuation experiments with broader applicability.