Progress of a half century in the study of the Luria–Delbrück distribution

Zheng, Qi

doi:10.1016/s0025-5564(99)00045-0

Cited by 132 publications

(170 citation statements)

References 30 publications

Supporting

Mentioning

164

Contrasting

Order By: Relevance

“…The number of mutant stem cells and the degree of genetic mosaicism will therefore vary greatly between individuals according to a probability distribution called the Luria-Delbruck distribution (5). That distribution describes the number of mutant cells, M, in a population that grows exponentially from one cell to N cells (6,7).…”

Section: Genetic Mosaicismmentioning

confidence: 99%

“…Mutations during the exponential phase of cellular growth in development cause the average frequency of stem cells with mutations to be x ≈ u e ln(N) (6), where u e is the mutation rate during exponential cellular growth in development. Although the frequency of stem cells that start with a mutation may be small, those mutations can contribute substantially to the total risk of cancer.…”

Section: Risk Of Cancermentioning

confidence: 99%

See 1 more Smart Citation

Somatic evolutionary genomics: Mutations during development cause highly variable genetic mosaicism with risk of cancer and neurodegeneration

Frank

2010

Proc. Natl. Acad. Sci. U.S.A.

159

129

View full text Add to dashboard Cite

Somatic mutations must happen often during development because of the large number of cell divisions to expand from a single-cell zygote to a full organism. A mutation in development carries forward to all descendant cells, causing genetic mosaicism. Widespread genetic mosaicism may influence diseases that derive from a few genetically altered cells, such as cancer. I show how to predict the expected amount of mosaicism and the variation in mosaicism between individuals. I then calculate the predicted risk of cancer derived from developmental mutations. The calculations show that a significant fraction of cancer in later life likely arises from developmental mutations in early life. In addition, much of the variation in the risk of cancer between individuals may arise from variation in the degree of genetic mosaicism set in early life. I also suggest that certain types of neurodegeneration, such as amyotrophic lateral sclerosis (ALS), may derive from a small focus of genetically altered cells. If so, then the risk of ALS would be influenced by developmental mutations and the consequent variation in genetic mosaicism. New technologies promise the ability to measure genetic mosaicism by sampling a large number of cellular genomes within an individual. The sampling of many genomes within an individual will eventually allow one to reconstruct the cell lineage history of genetic change in a single body. Somatic evolutionary genomics will follow from this technology, providing new insight into the origin and progression of disease with increasing age.

show abstract

Section: Genetic Mosaicismmentioning

confidence: 99%

Section: Risk Of Cancermentioning

confidence: 99%

Somatic evolutionary genomics: Mutations during development cause highly variable genetic mosaicism with risk of cancer and neurodegeneration

Frank

2010

Proc. Natl. Acad. Sci. U.S.A.

159

129

View full text Add to dashboard Cite

show abstract

“…Apart from settling a controversy over one of the basic tenets of modern evolutionary theory, the Luria-Delbrück experiment became established as the standard method to estimate mutation rates (Foster 1999). For these reasons, a variety of alternate formulations, extensions, and analyses of their basic model have been proposed over the decades (Zheng 1999(Zheng , 2015Foster 2006).…”

mentioning

confidence: 99%

Determinants of Genetic Diversity of Spontaneous Drug Resistance in Bacteria

2016

View full text Add to dashboard Cite

Any pathogen population sufficiently large is expected to harbor spontaneous drug-resistant mutants, often responsible for disease relapse after antibiotic therapy. It is seldom appreciated, however, that while larger populations harbor more mutants, the abundance distribution of these mutants is expected to be markedly uneven. This is because a larger population size allows early mutants to expand for longer, exacerbating their predominance in the final mutant subpopulation. Here, we investigate the extent to which this reduction in evenness can constrain the genetic diversity of spontaneous drug resistance in bacteria. Combining theory and experiments, we show that even small variations in growth rate between resistant mutants and the wild type result in orders-ofmagnitude differences in genetic diversity. Indeed, only a slight fitness advantage for the mutant is enough to keep diversity low and independent of population size. These results have important clinical implications. Genetic diversity at antibiotic resistance loci can determine a population's capacity to cope with future challenges (i.e., second-line therapy). We thus revealed an unanticipated way in which the fitness effects of antibiotic resistance can affect the evolvability of pathogens surviving a drug-induced bottleneck. This insight will assist in the fight against multidrug-resistant microbes, as well as contribute to theories aimed at predicting cancer evolution.

show abstract

“…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.…”

mentioning

confidence: 99%

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

Progress of a half century in the study of the Luria–Delbrück distribution

Cited by 132 publications

References 30 publications

Somatic evolutionary genomics: Mutations during development cause highly variable genetic mosaicism with risk of cancer and neurodegeneration

Somatic evolutionary genomics: Mutations during development cause highly variable genetic mosaicism with risk of cancer and neurodegeneration

Determinants of Genetic Diversity of Spontaneous Drug Resistance in Bacteria

A Simple Formula for Obtaining Markedly Improved Mutation Rate Estimates

Contact Info

Product

Resources

About