General formulation of Luria-Delbrück distribution of the number of mutants

Bahram Houchmandzadeh (1)

1 BIOP-LIPhy - BIOP - Fluctuations, Régulation et Evolution des Systèmes Vivants

The Luria-Delbrück 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.

Mots clés: Luria-Delbrück

Domaines: Biophysique [physics.bio-ph]; Analyse de données, Statistiques et Probabilités [physics.data-an]

Bahram Houchmandzadeh. General formulation of Luria-Delbrück distribution of the number of mutants. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2015, 92, pp.012719. ⟨hal-01148693v2⟩