A Simple Formula for Obtaining Markedly Improved Mutation Rate Estimates

Abstract

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 nonmoment-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 common method for estimating mutation rates is the ''fluctuation assay,'' in which several bacterial cultures are grown from small, presumably mutant-free, inoculums to high-density cultures and subsequently screened for mutants by plating on selective media (Rosche and Foster 2000;Pope et al. 2008). On selective media, only selected mutants are able to form colonies, and the numbers of mutants counted on plates are an indicator of the mutation rate. To make an estimate of the mutation rate from these numbers, a priori knowledge of their distribution is required. The fundamental assumption upon which this distribution is derived is that no Lamarckian-like processes exist: mutations are assumed to occur spontaneously during cell division in a way that is completely independent of any detriment or benefit that the mutations might subsequently incur. Such mutations can occur at any time during the growth of a culture. If a mutation happens to occur early in the growth of a culture, it will leave a large number of mutant descendants in the culture at the time of plating. The nonnegligible probability of a mutation occurring early thus translates to nonnegligible probabilities in the right tail of the mutant distribution. The resulting heavy-tailed mutant distribution was first proposed by Luria and Delbrü ck (1943) and has since been dubbed the ''Luria-Delbrü ck distribution'' (LDD) in their honor. Its first rigorous derivation was given by Lea and Coulson (1949), and many subsequent derivations account for different biological and experimental details (Armitage 1952;Bailey 1964;Mandelbrot 1974;Bartlett 1978;Stewart et al. 1990;Stewart 1991;Pakes 1993;Zheng 1999;Kepler and Oprea 2001;Oprea and Kepler 2001;Dewanji et al. 2005).Each of these derivations culminates in a version of the LDD expressed in probability-generating function (PGF...

Teaching the fluctuation test in silico by using mutate: A program to distinguish between the adaptive and spontaneous mutation hypotheses

“…Because of this, the student is asked to perform several instances and asked to interpret the results not only in the context of the spontaneous and adaptive hypotheses, but also in terms of the power of the tests. Some example cases can be found at the following link: http://webs.uvigo.es/acraaj/MutateWeb/MutateExercises.html Furthermore, consideration of presampling factors such as mutant fitness and plating efficiency introduces important experimentally noisy effects that could affect the success of the fluctuation test [2,3]. In fact, we can check that, at least under our implementation, plating efficiency seems to only have a minor effect on the fluctuation test despite causing a clear decrease in the number of detected mutations.…”

“…Finally, it is worth commenting that nowadays the fluctuation test and its variants continue to be the reference for developing sophisticated mutation rate estimation methods [3,13,14]. In this context, the program Mutate can also be considered as an easy-to-use generator of data for testing mutation rate estimation algorithms.…”

“…It is equivalent to sampling the culture [3]. If we express plating efficiency as a fraction p from the number m' of mutants before plating, m' tþ1 ¼ 2bm t þ n then we can sample each mutant for platting with probability p to get an expected final number of m tþ1 ¼ pm' tþ1 .…”

“…1). Nevertheless, the variance will also be dependent on factors such as the mutation rate, the number of bacteria per plate, the number of plates, and still other pre-plating factors such as mutant fitness [2] and plating efficiency [3]. The Mutate software package performs both kinds of experiments allowing the user to set different values for the aforementioned parameters.…”

Luria-Delbrück Estimation of Turnip Mosaic Virus Mutation Rate In Vivo

“…From this vector of counts, R, a mutation rate was estimated using the following procedure. The number of mutants after growth and extraction from wild-type plants has a distribution whose probability generating function is (12):…”