Cellular replication limits in the Luria-Delbr\"uck mutation model

TL;DR

This paper extends the classical Luria-Delbr"uck mutation model to include cellular replication limits, providing a more realistic framework for understanding mutation dynamics in human somatic cells and their role in cancer development.

Contribution

It introduces a novel Luria-Delbr"uck model that explicitly accounts for replicative senescence and mutant escape, broadening the model's applicability to human cell biology.

Findings

Derived mean, variance, and distribution of mutant populations with replication limits.

Analyzed asymptotic behavior of mutants in the extended model.

Provided guidelines for applying the model to telomere crisis and fluctuation analysis.

Abstract

Originally developed to elucidate the mechanisms of natural selection in bacteria, the Luria-Delbr\"uck 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 it is a rate-limiting step in cancer progression. Here we introduce a Luria-Delbr\"uck model that explicitly takes into account cellular replication limits in the wild type cell population and models the emergence of mutants that escape replicative senescence. We present results on the mean, variance, distribution, and asymptotic behavior of the mutant population in terms of three classical formulations of the problem. More broadly the paper introduces the concept of incorporating replicative limits as part of the Luria-Delbr\"uck mutational framework. Guidelines to extend the theory to include other types of mutations and possible applications to the modeling of telomere crisis and fluctuation analysis are also discussed.