An algorithm accounting for plating efficiency in estimating spontaneous mutation rates

Efficient, robust, and versatile fluctuation data analysis using MLE MUtation Rate calculator (mlemur)

The fluctuation assay remains an important tool for analyzing the levels of mutagenesis in microbial populations. The mutant counts originating from some average number of mutations are usually assumed to obey the Luria-Delbrück distribution. While several tools for estimating mutation rates are available, they sometimes lack accuracy or versatility under non-standard conditions. In this work, extensions to the Luria-Delbrück protocol to account for phenotypic lag and cellular death with either perfect or partial plating were developed. Hence, the novel MLE MUtation Rate calculator, or mlemur, is the first tool that provides a user-friendly graphical interface allowing the researchers to model their data with consideration for partial plating, differential growth of mutants and non-mutants, phenotypic lag, cellular death, variability of the final number of cells, post-exponential-phase mutations, and the size of the inoculum. Additionally, mlemur allows the users to incorporate most of these special conditions at the same time to obtain highly accurate estimates of mutation rates and P values, confidence intervals for an arbitrary function of data (such as fold), and perform power analysis and sample size determination for the likelihood ratio test. The accuracy of point and interval estimates produced by mlemur against historical and simulated fluctuation experiments are assessed. Both mlemur and the analyses in this work might be of great help when evaluating fluctuation experiments and increase the awareness of the limitations of the widely-used Lea-Coulson formulation of the Luria-Delbrück distribution in the more realistic biological contexts.

A Bayesian approach for correcting for partial plating in fluctuation experiments

The fluctuation experiment is the preferred method for estimating microbial mutation rates. A difficult task facing the data analyst is to infer the mean number of mutations from the number of mutant cells that only indirectly reflects the number of mutations. Partial plating, commonly practised in the laboratory, renders this task even more challenging by allowing only a portion of the mutant cells to be counted. In this paper, we propose a Bayesian approach to correcting for partial plating in the analysis of fluctuation experiments.

Bootstrap estimation of confidence intervals on mutation rate ratios

The fluctuation test is a useful tool for estimating the mutation rate of cells. However, statistical methods for comparing mutation rate estimates between different strains or conditions have not yet been fully developed. Methods exist for placing confidence intervals on estimates of the number of mutational events in cultures for a given strain and set of conditions, but placing confidence intervals on mutation rate is complicated by differences in the final number of cells in culture between parallel cultures. Additionally, confidence intervals on individual mutation rate estimates are not always the most useful statistical tool when comparing two or more different strains or conditions. We present a bootstrap method for estimating confidence intervals on the quotient of two mutation rates determined from two fluctuation test experiments using experimental and control strains or conditions. We use Monte Carlo simulations to validate this method over a wide range of mutation rates and for empirically measured variation in the estimates of final number of cells in culture. Furthermore, we provide the computational tools to implement the bootstrap method described here on experimental fluctuation test data and to evaluate this method for experimental parameters other than those considered herein.

A simple formula for obtaining markedly improved mutation rate estimates

In previous work by M. E. Jones and colleagues, it was shown that mutation rate estimates can be improved and corresponding confidence intervals tightened by following a very easy modification of the standard fluctuation assay: cultures are grown to a larger-than-usual final density, and mutants are screened for in only a fraction of the culture. Surprisingly, this very promising development has received limited attention, perhaps because there has been no efficient way to generate the predicted mutant distribution to obtain non-moment-based estimates of the mutation rate. Here, the improved fluctuation assay discovered by Jones and colleagues is made amenable to quantile-based, likelihood, and other Bayesian methods by a simple recursion formula that efficiently generates the entire mutant distribution after growth and dilution. This formula makes possible a further protocol improvement: grow cultures as large as is experimentally possible and severely dilute before plating to obtain easily countable numbers of mutants. A preliminary look at likelihood surfaces suggests that this easy protocol adjustment gives markedly improved mutation rate estimates and confidence intervals.

A note on plating efficiency in fluctuation experiments

In estimating mutation rates using the Luria-Delbrück experimental protocol, it is often assumed that all mutant cells survive the plating procedure to form visible mutant colonies. This assumption of perfect plating efficiency may not hold in certain circumstances, but none of the existing estimation methods that adjust for plating efficiency is strictly based on the likelihood principle. To ameliorate this situation, we propose likelihood based algorithms for computing point and interval estimates of mutation rates.