title: Mean field mutation dynamics and the continuous Luria-Delbrück distribution.
abstract: 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.
authors.affiliation: Applied Mathematics Department, Tel Aviv University, Israel. ekashdan@post.tau.ac.il
authors.forename: Eugene
authors.initials: E
authors.lastname: Kashdan
authors.forename: Lorenzo
authors.initials: L
authors.lastname: Pareschi
mesh_terms: D003198:Computer Simulation; D007700:Kinetics; D008957:Models, Genetic; D009010:Monte Carlo Method; D009154:Mutation; D016008:Statistical Distributions