Mean field mutation dynamics and the continuous Luria-Delbrück distribution

Details Mean field mutation dynamics and the continuous Luria-Delbrück distribution Mean field mutation dynamics and the continuous Luria-Delbrück distribution

2011-12-13

arxiv.org/abs/1112.2836v1

Physics

Mathematical Physics

Scientific paper

The Luria-Delbr\"uck 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-Delbr\"uck distribution. Numerical results confirming the theoretical analysis are also presented.

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