Fluctuation analysis: the probability distribution of the number of mutants under different conditions.
Abstract
In the 47 years since fluctuation analysis was introduced by Luria and Delbrück, it has been widely used to calculate mutation rates. Up to now, in spite of the importance of such calculations, the probability distribution of the number of mutants that will appear in a fluctuation experiment has been known only under the restrictive, and possibly unrealistic, assumptions: (1) that the mutation rate is exactly proportional to the growth rate and (2) that all mutants grow at a rate that is a constant multiple of the growth rate of the original cells. In this paper, we approach the distribution of the number of mutants from a new point of view that will enable researchers to calculate the distribution to be expected using assumptions that they believe to be closer to biological reality. The new idea is to classify mutations according to the number of observable mutants that derive from the mutation when the culture is selectively plated. This approach also simplifies the calculations in situations where two, or many, kinds of mutation may occur in a single culture.
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Investigators who were aware of the effects of partial plating often relied on an adjustment due to Stewart et al. (1990), as this was the only approach recommended on the FALCOR web site.
“Investigators who were aware of the effects of partial plating often relied on an adjustment due to Stewart et al. (1990), as this was the only approach recommended on the FALCOR web site.”
From rSalvador: An R Package for the Fluctuation Experiment (2017) · cites this paper as Stewart et al. (1990)
The section on plating efficiency (p. 8) explains how observing only a random fraction of mutants affects the distribution, and the discussion of Figure 3 (p. 10) relates the true and apparent mean numbers of mutations when only part of a culture is plated. This supports attributing a partial-plating adjustment to Stewart et al., but the paper does not establish how often investigators used it or what the FALCOR website recommended. (LLM, conf=0.88)
Experimental — accuracy not yet measuredDelayed phenotypic expression of a mutant phenotype has the biggest impact on the lower tail of the mutant distribution, as reflected in the shapes of empirical CDFs in Figure 4.
“Delayed phenotypic expression of a mutant phenotype has the biggest impact on the lower tail of mutant distribution [5,10,33], and this fact is reflected in the shapes of empirical CDFs in Figure 4.”
From Efficient, robust, and versatile fluctuation data analysis using MLE MUtation Rate calculator (mlemur) (2023) · cites this paper as [10]
The “Phenotypic lag” section (p. 5) describes delayed expression and how it can change the number of mutants counted. The Results discussion of lower and upper distribution curves (p. 10) concerns plating efficiency, not phenotypic lag. Our copy therefore does not establish that delayed expression has its biggest impact on the lower tail; Figure 4 belongs to the citing paper, not this source. (LLM, conf=0.76)
Experimental — accuracy not yet measuredThe resulting mutant distribution was further studied by Stewart et al. (1990).
“The resulting mutant distribution was further studied by Stewart et al. (1990).”
From rSalvador: An R Package for the Fluctuation Experiment (2017) · cites this paper as Stewart et al. 1990
In the Newcombe experiment, the extent of phenotypic delay has been estimated at 3-4 generations, in agreement with Armitage, and the adjusted mutation rate between 1.34×10^-8 and 2.72×10^-8.
“The extent of phenotypic delay has been estimated at 3-4 generations, in agreement with analysis by Armitage [10], and the adjusted mutation rate between 1.34×10 -8 and 2.72×10 -8 .”
From Efficient, robust, and versatile fluctuation data analysis using MLE MUtation Rate calculator (mlemur) (2023) · cites this paper as [10]
The ‘Phenotypic lag’ passage (Relation to Earlier Work, p. 5) explains the concept and discusses Armitage, but gives no estimate for the Newcombe experiment. Searches for Newcombe, 3–4 generations, and the stated mutation-rate bounds found no passage in our copy supporting those figures. (LLM, conf=0.75)
Experimental — accuracy not yet measured
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- Authors
- Stewart, F. M., Gordon, D. M., & Levin, B. R.
- Affiliations
- Brown University (US)
- University of Massachusetts Amherst (US)
- ORCID
- Levin, B R
- Venue
- Genetics
- Publisher
- Oxford University Press (OUP)
- Published
- 1990-01-01
- Volume
- 124
- Issue
- 1
- Pages
- 175-185
- ISSN
- 0016-6731 (ISSN-L)
- 1943-2631
- OpenAlex
- W1824301619
- Cited by
- 126
- References
- 10
- Citations by year
- 2025: 2 · 2024: 1 · 2023: 3 · 2022: 2 · 2021: 2 · 2019: 2 · 2018: 3 · 2017: 6 · 2016: 3 · 2015: 3 · 2014: 4 · 2013: 5 · 2012: 3
- FWCI
- 6.06
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Genetics (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Institute of General Medical Sciences (GM 33782, R01GM033782)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Evolution and Genetic Dynamics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Genetics › Bacterial Genetics and Biotechnology
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- fluctuation analysis, mutation rate estimation, mutant classification, selective plating, multiple mutations, growth rate
- MeSH terms
- Bacteria, Cell Division, Kinetics, Mathematics, Models, Genetic, Mutation, Phenotype, Probability, Selection, Genetic
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