Fluctuation analysis: can estimates be trusted?

TL;DR

This paper investigates the biases in fluctuation analysis caused by assumptions on cell division times, extending the model to general division time distributions and proposing more reliable estimation methods.

Contribution

It generalizes the classical fluctuation analysis model to arbitrary division time distributions and introduces empirical techniques for more accurate estimation of mutation rates and fitness.

Findings

Biases occur when using classical models outside their assumptions.

Generalized distribution depends on mutation count, fitness, and division times.

Empirical methods improve estimation accuracy even with limited division time information.

Abstract

The estimation of mutation probabilities and relative fitnesses in fluctuation analysis is based on the unrealistic hypothesis that the single-cell times to division are exponentially distributed. Using the classical Luria-Delbr\"{u}ck distribution outside its modelling hypotheses induces an important bias on the estimation of the relative fitness. The model is extended here to any division time distribution. Mutant counts follow a generalization of the Luria-Delbr\"{u}ck distribution, which depends on the mean number of mutations, the relative fitness of normal cells compared to mutants, and the division time distribution of mutant cells. Empirical probability generating function techniques yield precise estimates both of the mean number of mutations and the relative fitness of normal cells compared to mutants. In the case where no information is available on the division time distribution, it is shown that the estimation procedure using constant division times yields more reliable results. Numerical results both on observed and simulated data are reported.