The Kinetic Theory of Mutation Rates

Lorenzo Pareschi, Giuseppe Toscani*

*Corresponding author for this work

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The Luria–Delbrück mutation model is a cornerstone of evolution theory and has been mathematically formulated in a number of ways. In this paper, we illustrate how this model of mutation rates can be derived by means of classical statistical mechanics tools—in particular, by modeling the phenomenon resorting to methodologies borrowed from classical kinetic theory of rarefied gases. The aim is to construct a linear kinetic model that can reproduce the Luria–Delbrück distribution starting from the elementary interactions that qualitatively and quantitatively describe the variations in mutated cells. The kinetic description is easily adaptable to different situations and makes it possible to clearly identify the differences between the elementary variations, leading to the Luria–Delbrück, Lea–Coulson, and Kendall formulations, respectively. The kinetic approach additionally emphasizes basic principles which not only help to unify existing results but also allow for useful extensions.

Original languageEnglish
Article number265
Issue number3
Publication statusPublished - 3 Mar 2023


  • Fokker–Planck equations
  • kinetic theory
  • Luria–Delbrück distribution
  • mutation rates

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Mathematical Physics
  • Logic
  • Geometry and Topology

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