Fluctuation analysis: the effect of plating efficiency

Fm, Stewart

doi:10.1007/bf00123984

Cited by 26 publications

(23 citation statements)

References 5 publications

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“…One can correct for this by fitting the data to a two-parameter model that accounts for postplating growth or largely eliminate it by increasing the concentration of canavanine. Other processes that introduce error into mutation rate estimates such as differential growth rates between mutants and nonmutants (Zheng 2005) and poor plating efficiency (Stewart et al 1990;Stewart 1991) will also produce deviations from the expected Luria-Delbrü ck distribution. Therefore, we suggest that fitting fluctuation data to the cumulative distribution and comparing the sum-ofsquares differences with simulated data should be used as a general method for assaying the quality of data resulting from fluctuation assays.…”

Section: Can1mentioning

confidence: 99%

Estimating the Per-Base-Pair Mutation Rate in the YeastSaccharomyces cerevisiae

2008

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Although mutation rates are a key determinant of the rate of evolution they are difficult to measure precisely and global mutations rates (mutations per genome per generation) are often extrapolated from the per-base-pair mutation rate assuming that mutation rate is uniform across the genome. Using budding yeast, we describe an improved method for the accurate calculation of mutation rates based on the fluctuation assay. Our analysis suggests that the per-base-pair mutation rates at two genes differ significantly (3.80 3 10 À10 at URA3 and 6.44 3 10 À10 at CAN1) and we propose a definition for the effective target size of genes (the probability that a mutation inactivates the gene) that acknowledges that the mutation rate is nonuniform across the genome.

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Section: Can1mentioning

confidence: 99%

Estimating the Per-Base-Pair Mutation Rate in the YeastSaccharomyces cerevisiae

2008

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Section: Introductionmentioning

confidence: 99%

“…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) form. The great utility of PGFs is that (1) distributions can be easier to derive in PGF form, (2) distributions can be expressed compactly in PGF form, even in cases where there is no way to write down a general (nonderivative) expression for the individual probabilities of the distribution itself, and (3) from a distribution expressed in PGF form, the zero class and the moments of the distribution are immediate.…”

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confidence: 99%

“…The fraction of plated mutants that do ultimately form observable colonies was originally called the ''plating efficiency,'' but it is mathematically equivalent to sampling the culture by any means, such as intentionally plating only a fraction of the final culture by either direct aliquot or dilution. To account for such sampling, Jones (1993Jones ( , 1994 and Stewart (1991) both model the LDD as an irreducible compound distribution: the total number of mutations that occur during the growth of a culture is a Poisson-distributed random variable, and the total number of mutant colonies that derive from each mutation event is an independent random variable whose distribution is the ''clone-size'' distribution derived by Lea and Coulson. Jones and Stewart both reworked the clone-size distribution with a sampling step added: they derived the probability that a mutation occurring during the growth of a culture gives rise to k visible colonies when only a fraction of mutants form visible colonies.…”

mentioning

confidence: 99%

“…Jones and Stewart both reworked the clone-size distribution with a sampling step added: they derived the probability that a mutation occurring during the growth of a culture gives rise to k visible colonies when only a fraction of mutants form visible colonies. To generate the probabilities of total numbers of mutant colonies on plates after growth and sampling, they both outlined different programming algorithms (Stewart et al 1990;Stewart 1991;Jones 1993;Crane et al 1996) to compose the primary Poisson distribution for numbers of mutations occurring during growth with their reworked clone-size distributions that take preplating sampling into account. Jones' algorithm is as follows.…”

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confidence: 99%

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A Simple Formula for Obtaining Markedly Improved Mutation Rate Estimates

Gerrish

2008

Genetics

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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...

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