Accounting for plating efficiency when estimating spontaneous mutation rates

Competition for nutritional resources masks the true frequency of bacterial mutants

Background

It is widely assumed that all mutant microorganisms present in a culture are able to grow and form colonies, provided that they express the features required for selection. Unlike wild-type Escherichia coli, PHO-constitutive mutants overexpress alkaline phosphatase and hence can hydrolyze glycerol-2-phosphate (G2P) to glycerol and form colonies on plates having G2P as the sole carbon source. These mutations mostly occur in the pst operon. However, the frequency of PHO-constitutive colonies on the G2P selective plate is exceptionally low.

Results

We show that the rate in which spontaneous PHO-constitutive mutations emerge is about 8.0 × 10⁻⁶/generation, a relatively high rate, but the growth of most existing mutants is inhibited by their neighboring wild-type cells. This inhibition is elicited only by non-mutant viable bacteria that can take up and metabolize glycerol formed by the mutants. Evidence indicates that the few mutants that do form colonies derive from microclusters of mutants on the selective plate. A mathematical model that describes the fate of the wild-type and mutant populations under these circumstances supports these results.

Conclusion

This scenario in which neither the wild-type nor the majority of the mutants are able to grow resembles an unavoidable “tragedy of the commons” case which results in the collapse of the majority of the population. Cooperation between rare adjacent mutants enables them to overcome the competition and eventually form mutant colonies. The inhibition of PHO-constitutive mutants provides an example of mutant frequency masked by orders of magnitude due to a competition between mutants and their ancestral wild-type cells. Similar “tragedy of the commons-like” cases may occur in other settings and should be taken into consideration while estimating true mutant frequencies and mutation rates.

Supplementary Information

The online version contains supplementary material available at (doi:10.1186/s12915-020-00913-1).

bz-rates: A Web Tool to Estimate Mutation Rates from Fluctuation Analysis

Fluctuation analysis is the standard experimental method for measuring mutation rates in micro-organisms. The appearance of mutants is classically described by a Luria-Delbrück distribution composed of two parameters: the number of mutations per culture (m) and the differential growth rate between mutant and wild-type cells (b). A precise estimation of these two parameters is a prerequisite to the calculation of the mutation rate. Here, we developed bz-rates, a Web tool to calculate mutation rates that provides three useful advances over existing Web tools. First, it allows taking into account b, the differential growth rate between mutant and wild-type cells, in the estimation of m with the generating function. Second, bz-rates allows the user to take into account a deviation from the Luria-Delbrück distribution called z, the plating efficiency, in the estimation of m. Finally, the Web site provides a graphical visualization of the goodness-of-fit between the experimental data and the model. bz-rates is accessible at http://www.lcqb.upmc.fr/bzrates.

Frequency, spectrum, and nonzero fitness costs of resistance to myxopyronin in Staphylococcus aureus

The antibiotic myxopyronin (Myx) functions by inhibiting bacterial RNA polymerase (RNAP). The binding site on RNAP for Myx-the RNAP "switch region SW1/SW2 subregion"-is different from the binding site on RNAP for the RNAP inhibitor currently used in broad-spectrum antibacterial therapy, rifampin (Rif). Here, we report the frequency, spectrum, and fitness costs of Myx resistance in Staphylococcus aureus. The resistance rate for Myx is 4 × 10(-8) to 7 × 10(-8) per generation, which is equal within error to the resistance rate for Rif (3 × 10(-8) to 10 × 10(-8) per generation). Substitutions conferring Myx resistance were obtained in the RNAP β subunit [six substitutions: V1080(1275)I, V1080(1275)L, E1084(1279)K, D1101(1296)E, S1127(1322)L, and S1127(1322)P] and the RNAP β' subunit [five substitutions: K334(345)N, T925(917)K, T925(917)R, G1172(1354)C, and G1172(1354)D] (residues numbered as in Staphylococcus aureus RNAP and, in parentheses, as in Escherichia coli RNAP). Sites of substitutions conferring Myx resistance map to the RNAP switch region SW1/SW2 subregion and do not overlap the binding site on RNAP for Rif, and, correspondingly, Myx-resistant mutants exhibit no cross-resistance to Rif. All substitutions conferring Myx resistance exhibit significant fitness costs (4 to 15% per generation). In contrast, at least three substitutions conferring Rif resistance exhibit no fitness costs (≤0% per generation). The observation that all Myx-resistant mutants have significant fitness costs whereas at least three Rif-resistant mutants have no fitness costs, together with the previously established inverse correlation between fitness cost and clinical prevalence, suggests that Myx resistance is likely to have lower clinical prevalence than Rif resistance.

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.

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.

Methods for determining spontaneous mutation rates

Spontaneous mutations arise as a result of cellular processes that act upon or damage DNA. Accurate determination of spontaneous mutation rates can contribute to our understanding of these processes and the enzymatic pathways that deal with them. The methods that are used to calculate mutation rates are based on the model for the expansion of mutant clones originally described by Luria and Delbrück (1943) and extended by Lea and Coulson (1949). The accurate determination of mutation rates depends on understanding the strengths and limitations of these methods and how to optimize a fluctuation assay for a given method. This chapter describes the proper design of a fluctuation assay, several of the methods used to calculate mutation rates, and ways to evaluate the results statistically.

A new method for estimating high mutation rates in cultured cells

Fluctuation analysis allows for the determination of mutation rates in cell cultures in vitro. As originally described by Luria and Delbruck and extended by Lea and Coulson and by Capizzi and Jameson, this analysis has been useful in estimating mutation rates in cultured cells where the frequency of mutational events is low. However. in cultures where high mutation rates and multiple independent mutation events occur, leading to the accumulation of many mutant cells, these standard methods may not apply. Here, we present a new method for the estimation of mutation rates based on the assumption that multiple events may contribute to the accumulation of mutant cells. We compared mutation rates determined by Lea and Coulson's and by Capizzi and Jameson's methods with those determined by our method using experimental and stimulated data from our studies of immunoglobulin gene mutation and isotype switching in B lymphocyte cultures. The three methods resulted in very different calculated rates when many mutants were present in the culture, such as when mutation rates were high, while only small differences in calculated rates were found when mutants were rare. Unlike previous fluctuation analysis calculations, our method is applicable for the estimation of both low and high rates.