A kinetic description of mutation processes in bacteria

TheLuria–Delbru ̈ckmutationmodelhasbeenmathematicallyfor- mulated in a number of ways. Last, a mean field picture derived from a kinetic formulation has been derived by Kashdan and Pareschi. There, the Luria–Delbru ̈ck 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, as well as for the Kendall formulation, focusing on important modeling is- sues 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.