Mean field mutation dynamics and the continuous Luria–Delbrück distribution

The Luria–Delbrück mutation model has a long history and has been mathematically formulated in several different ways. Here we tackle the problem in the case of a continuous distribution using some mathematical tools from nonlinear statistical physics. Starting from the classical formulations we derive the corresponding differential models and show that under a suitable mean field scaling they correspond to generalized Fokker–Planck equations for the mutants distribution whose solutions are given by the corresponding Luria–Delbrück distribution. Numerical results confirming the theoretical analysis are also presented.

► Kinetic and mean field modeling of the Luria–Delbrück mutation dynamic. ► Asymptotic mathematical analysis and generalized Fokker–Planck equations. ► Numerical simulations by Monte Carlo methods.