The Application of a Linear Algebra to the Analysis of Mutation Rates

Jones, Michael E.; Thomas, Susan M.; Clarke, Kieran

doi:10.1006/jtbi.1999.0933

Cited by 8 publications

(7 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Obviously, the final m also has to be small enough so that the number of colonies on the selective plates is countable. However, if there are a few outlier high counts, they can be truncated at 150 with little loss of precision (Asteris and Sarkar, 1996;Jones et al, 1999).…”

Section: Fluctuation Analysis Experimental Designmentioning

confidence: 99%

“…However, if several mutant phenotypes are to be assayed in the same cultures, sampling is unavoidable. In addition, because a large culture contains more "information" than a small culture, it is better to plate a small aliquot from a large culture than all of a small culture if a proper correction can be applied (Jones et al, 1999). Some, but not all, of the methods for calculate mutation rates discussed below are amenable to such corrections.…”

Section: Fluctuation Analysis Experimental Designmentioning

confidence: 99%

“…Most experiments have 10 to 100 parallel cultures, with about 40 being most common. There is little gain in precision if C is larger unless m is less than about 0.3 (Jones et al, 1999;Rosche and Foster, 2000).…”

Section: Fluctuation Analysis Experimental Designmentioning

confidence: 99%

See 2 more Smart Citations

Methods for Determining Spontaneous Mutation Rates

Foster

2006

Methods in Enzymology

274

333

View full text Add to dashboard Cite

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 and extended by Lea and Coulson. 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.

show abstract

Section: Fluctuation Analysis Experimental Designmentioning

confidence: 99%

Section: Fluctuation Analysis Experimental Designmentioning

confidence: 99%

See 1 more Smart Citation

Methods for Determining Spontaneous Mutation Rates

Foster

2006

Methods in Enzymology

274

333

View full text Add to dashboard Cite

show abstract

“…Put differently, quantile and zero-class methods have some advantage when there is some uncertainty about the underlying model or when there are known simplifying assumptions that can introduce error. The formula presented here derives from the simplest model for the LDD (Lea and Coulson 1949), which makes a number of simplifying assumptions, such as exponentially distributed times between replication events (a Markovian birth process) ( Jones et al 1999;Kepler and Oprea 2001), probabilities expressed in infinite (nontruncated) series thereby assigning nonzero (albeit miniscule) probabilities to unrealistically large mutant numbers (Armitage 1952;Bailey 1964;Stewart et al 1990;Ma et al 1992;Zheng 1999), and no difference in growth rates between wild-type and mutant subpopulations ( Jones 1994;Jaeger and Sarkar 1995;Zheng 1999). In light of these simplifying assumptions, whose impact can sometimes be significant, it might ultimately be desirable to use the less accurate but more robust quantile or zero-class methods to complement the more accurate but less robust likelihood methods.…”

Section: Discussionmentioning

confidence: 99%

“…Jones truncates the sum at 100, which is adequate for values L # 70, but thus limits applicability of his tabulated median method results to protocols for which plating efficiency is greater than $5%. A more elegant solution to the problem of infinite summation appears in Ma et al (1992) and Jones et al (1999).…”

mentioning

confidence: 99%

A Simple Formula for Obtaining Markedly Improved Mutation Rate Estimates

Gerrish

2008

Genetics

View full text Add to dashboard Cite

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...

show abstract