Determining Mutation Rates in Bacterial Populations

Abstract

When properly determined, spontaneous mutation rates are a more accurate and biologically meaningful reflection of the underlying mutagenic mechanism than are mutation 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-Delbrück 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.The purpose of this article is to provide experimental and mathematical methods for determining spontaneous mutation rates in bacterial cultures. Mutations are heritable changes in an organism's DNA (or RNA for RNA-based organisms). Spontaneous mutations are mutations that occur in the absence of an exogenous DNA damaging agent. These include DNA polymerase errors, mutations induced by endogenous agents, as well as deletions, duplications, and insertions. It is generally assumed that most spontaneous mutations that occur during growth are linked to DNA replication. Although we have not included mutations induced by DNA damaging agents in this article, the methods discussed also can be applied to mutations induced by DNA base analogues or by low, nonlethal doses of other mutagens. We assume that our readers are interested in the mechanism of mutation, in mutation rates among natural isolates of bacteria, and/or in the influence of genetic background or environment on the mutational process. The alternative to determining a mutation rate is to determine a mutant frequency, that is simply to average the fraction of mutant bacteria in a few replicate cultures. There are two reasons for making the effort to determine a mutation rate instead of a frequency.First, when properly determined, the mutation rate is more accurate and reproducible than the mutant frequency. This is, indeed, the fundamental fact that was exploited in the famous Luria and Delbrück experiment (1). During exponential growth every cell has a low but nonzero probability of sustaining a mutation during its lifetime, and this probability is what we call the mutation rate. After a cell sustains a mutation it produces a clone of mutants, and the size of this clone will depend on when during the growth of the population the mutation occurred. Thus, even though the growth of the population may be deterministic, the final number of mutants in the population reflects an underlying stochastic process. Because of the exponential growth of mutants, low probability events occurring early during the growth of a population have huge consequences. This makes mutant frequency, no matter how many cultures are Corresponding author: Patricia L. Foster, Ph.D., S107,...

Insights Into Mutagenesis Using Escherichia coli Chromosomal lacZ Strains That Enable Detection of a Wide Spectrum of Mutational Events

“…We calculated all mutation rates to two significant figures. To verify the results of our program, lacZ Mutational Reporters we also calculated by the method of the median by Lea and Coulson (1949) and/or by the p0 method (Rosche and Foster 2000). All three calculation methods gave nearly identical results (Table S1).…”

“…For those strains with high reversion rates (.0.3 reversions per 10 8 cell divisions), serial dilutions of cultures in 56/2 were plated on LacMinXI plates. For those data sets where only a fraction of the culture was plated, the following equation was used: (where actual mutation rate ¼ m act , observed mutation rate ¼ m obs , and fraction plated ¼ z) m act ¼ m obs *(z 2 1)/(z*ln(z)) as described previously (Rosche and Foster 2000). Ninety-five percent confidence intervals were also calculated (Rosche and Foster 2000).…”

“…For those data sets where only a fraction of the culture was plated, the following equation was used: (where actual mutation rate ¼ m act , observed mutation rate ¼ m obs , and fraction plated ¼ z) m act ¼ m obs *(z 2 1)/(z*ln(z)) as described previously (Rosche and Foster 2000). Ninety-five percent confidence intervals were also calculated (Rosche and Foster 2000). Calculation of mutation rate was performed using the Ma-Sandri-Sarkar (MSS) method (Sarkar et al 1992) as described in Rosche and Foster (2000).…”

“…Ninety-five percent confidence intervals were also calculated (Rosche and Foster 2000). Calculation of mutation rate was performed using the Ma-Sandri-Sarkar (MSS) method (Sarkar et al 1992) as described in Rosche and Foster (2000). We wrote a VB.net program (Table S1, K. Seier) that performs the recursive calculations necessary to determine the M value by the MSS.…”

Does age influence loss of heterozygosity?

“…In contrast to a mutation rate, a mutation frequency is limited in terms of the conclusions that can be made, which is especially relevant to our discussion of changes with age (reviewed in Rosche and Foster, 2000). As a cell grows and divides it has a low but nonzero probability to sustain a mutation during its lifetime, and this probability is its mutation rate.…”