A kinetic description of mutation  processes in bacteria

Giuseppe Toscani

doi:10.3934/krm.2013.6.1043

Article Contents

2013, Volume 6, Issue 4: 1043-1055. Doi: 10.3934/krm.2013.6.1043

This issue Previous Article Local existence with mild regularity for the Boltzmann equation Next Article

A kinetic description of mutation processes in bacteria

Giuseppe Toscani^1,

1.
University of Pavia, Department of Mathematics, Via Ferrata 1, 27100 Pavia

Received: August 31, 2013

Revised: August 31, 2013

Published: November 2013

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Abstract

The Luria--Delbrück mutation model has been mathematically formulated in a number of ways. Last, a mean field picture derived from a kinetic formulation has been derived by Kashdan and Pareschi in [18]. There, the Luria--Delbrück distribution appears as the solution of a Fokker-Planck like equation obtained as the quasi-invariant asymptotics of a linear Boltzmann equation for the number density of the number of mutated cells. This paper addresses the kinetic description for the Lea--Coulson formulation [21], as well as for the Kendall formulation [19], focusing on important modeling issues closely linked with the distribution of the number of mutants. The paper additionally emphasizes basic principles which not only help to unify existing results but also allow for a useful extensions.

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Mathematics Subject Classification: Primary: 92D25, 60K35; Secondary: 76P05.

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