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 ...

Originally developed to elucidate the mechanisms of natural selection in bacteria, the Luria-Delbrück model assumed that cells are intrinsically capable of dividing an unlimited number of times. This assumption however, is not true for human somatic cells which undergo replicative senescence. Replicative senescence is thought to act as a mechanism to protect against cancer and the escape from i...

The classical Luria-Delbrück model for fluctuation analysis is extended to the case where cells can either divide or die at the end of their generation time. This leads to a family of probability distributions generalizing the Luria-Delbrück family, and depending on three parameters: the expected number of mutations, the relative fitness of normal cells compared to mutants, and the death probab...

Concepts of infinitely divisible distributions are reviewed and applied to mutant number derived from the Lea-Coulson other models which describe Luria-Delbrück fluctuation test. A key finding is that arising a generalised model for normal cell growth non-decreasing unimodal. An integral criterion given separates cases mode at origin, or not.