2022/11/30 by Lorenzo Pareschi, Giuseppe Toscani, Pareschi, Lorenzo +1
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Social Sciences · #Advanced Thermodynamics and Statistical Mechanics #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Populations and Evolution (q-bio.PE) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2212.00146
openalex publication_date 2022/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 variation of 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 formulations of Luria--Delbrück, Lea--Coulson, and Kendall, respectively. The kinetic approach additionally emphasizes basic principles which not only help to unify existing results but also allow for useful extensions.