Determining mutation rates in bacterial populations

Abstract

When properly determined, spontaneous mutation rates are a more accurate and biologically meaningful reflection of underlying mutagenic mechanisms than are mutant frequencies. Because bacteria grow exponentially and mutations arise stochastically, methods to estimate mutation rates depend on theoretical models that describe the distribution of mutant numbers among parallel cultures, as in the original Luria-Delbr]uck fluctuation analysis. An accurate determination of mutation rate depends on understanding the strengths and limitations of these methods, and how to design fluctuation assays to optimize a given method. In this paper we describe a number of methods to estimate mutation rates, give brief accounts of their derivations, and discuss how they behave under various experimental conditions.

Figure 1

The number of cultures required to achieve a theoretical precision of 20% using various estimators vs m, the number of mutations per culture. Precision is the coefficient of variation, (σ_m /m) × 100%, where σ was calculated from Eq. 35 and 41 of reference (4) for the p₀ method and the Lea-Coulson method of the median, respectively, and from Eq. 1 of reference (12) for the MSS-maximum-likelihood method. These equations were solved for C, the number of cultures, by setting σ_m /m = 0.2

Figure 1

The number of cultures required to achieve a theoretical precision of 20% using various estimators vs m, the number of mutations per culture. Precision is the coefficient of variation, (σ_m /m) × 100%, where σ was calculated from Eq. 35 and 41 of reference (4) for the p₀ method and the Lea-Coulson method of the median, respectively, and from Eq. 1 of reference (12) for the MSS-maximum-likelihood method. These equations were solved for C, the number of cultures, by setting σ_m /m = 0.2

Figure 2

Examples of methods to solve transcendental equations by iteration using a spreadsheet.