General formulation of Luria-Delbr{\"u}ck distribution of the number of mutants

TL;DR

This paper generalizes the Luria-Delbrück distribution to arbitrary growth functions, providing a simple and versatile derivation that accounts for both deterministic and stochastic mutant growth, extending beyond constant growth assumptions.

Contribution

It introduces a new derivation method for the distribution of mutants using wild type bacteria count as the independent variable, applicable to various growth models.

Findings

Derivation for arbitrary growth functions of mutants

Applicable to both deterministic and stochastic growth

Simplifies analysis of mutant distribution in experimental conditions

Abstract

The Luria-Delbr{\"u}ck experiment is a cornerstone of evolutionary theory, demonstrating the randomness of mutations before selection. The distribution of the number of mutants in this experiment has been the subject of intense investigation during the last 70 years. Despite this considerable effort, most of the results have been obtained under the assumption of constant growth rate, which is far from the experimental condition. We derive here the properties of this distribution for arbitrary growth function, for both the deterministic and stochastic growth of the mutants. The derivation we propose uses the number of wild type bacteria as the independent variable instead of time. The derivation is surprisingly simple and versatile, allowing many generalizations to be taken easily into account.