Matched asymptotic analysis of the Luria–Delbrück distribution in a reversible fluctuation assay

PavolBokes

Comenius University

"Matched asymptotic analysis of the Luria–Delbrück distribution in a reversible fluctuation assay"

We study a fluctuation test where cell colonies grow from a single cell to a specified population size before being treated. During growth, cells may acquire resistance to treatment and pass it to offspring, with a small probability. Unlike the classical Luria–Delbrück test, we allow the resistant state to revert to a drug-sensitive state, motivated by recent research on drug tolerance in cancer and microbes. This modification does not change the central part of the Luria–Delbrück distribution, where the Landau probability density function approximation still applies. However, the right tail of the distribution deviates from the power law of the Landau distribution, with the correction factor equal to the Landau cumulative distribution function. We use singular perturbation theory and asymptotic matching to derive uniformly valid approximations and describe tail corrections for populations with different initial cell states.
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