Update on Estimation of Mutation Rates Using Data From Fluctuation Experiments

Abstract

This note discusses a minor mathematical error and a problematic mathematical assumption in Luria and Delbrü ck 's (1943) classic article on fluctuation analysis. In addition to suggesting remedial measures, the note provides information on the latest development of techniques for estimating mutation rates using data from fluctuation experiments. T HE fluctuation test protocol devised by Luria andDelbrü ck (1943) still serves as the basis for estimating microbial mutation rates today, although later developments have resulted in much improved methods. Among the later contributions that enhanced our ability to analyze fluctuation experiments are those made by Lea and Coulson (1949), Armitage (1952), Crump and Hoel (1974), Mandelbrot (1974), Koch (1982), Stewart et al. (1990), Ma et al. (1992), Jones et al. (1994), and many others found in a recent review (Zheng 1999). Rosche and Foster's (2000) critical comparison of the then existing methods is a useful guide for biologists. One goal of this note is to notify the reader of the latest developments that can further help biologists improve their ability to measure mutation rates. Another goal is to discuss a minor mathematical error and a problematic mathematical assumption in Luria and Delbrü ck's (1943) article that have caused lingering confusion. Previous attempts to clarify the confusion were scarce and to a large extent failed to resolve some relevant practical issues. As a result, the genetics literature is increasingly fraught with mutation rates that were computed using either incorrect or unreliable methods. It appears helpful that the minor error and the problematic assumption are explained and remedial measures are provided. I begin with a paradox that has puzzled many.In a fluctuation experiment, each of n parallel cultures is seeded at time zero with N 0 nonmutant cells for incubation. At a later time T each culture has about N T nonmutant cells and the contents of each culture are plated to facilitate counting of mutants existing at time T in the n cultures. This process results in experimental data in the form of X 1 , X 2 , . . . , X n , the numbers of mutants existing in the n cultures immediately before plating. If z of the n cultures still remain devoid of mutant cells at time T, Luria and Delbrü ck's (1943) P 0 method estimates the mutation rate bŷwithp 0 ¼ z=n. Although Luria and Delbrü ck did not give the above equation, their numerical example on page 507 clearly indicates that they used (1) to estimate mutation rates defined as ''mutations per bacterium per division cycle.'' This definition of mutation rates has been widely accepted, and throughout this note the term ''mutation rate'' is used in that sense. In other words, a mutation rate is the probability that a cell undergoes a mutation during the cell's life cycle. Using the same definition, Lederberg (1951, p. 99) argued that mutation rates should be estimated bŷLederberg's reasoning runs as follows. In each culture N T ÿ N 0 cellular divisions have happened. If m 0 is the mut...

Disparate contributions of the Fanconi anemia pathway and homologous recombination in preventing spontaneous mutagenesis

“…For hprt mutants, replica cultures were seeded with 500 cells and grown in suspension to 1–2 × 10 6 cells/replica, plated and incubated under 6S-Gua selection (41). Hprt, dhfr and CAD mutation rates were calculated using the Poisson P 0 term (42), the maximum likelihood method (43) and the method of the mean (44). To recover cells having amplified dhfr or CAD genes, selection was done in 300 nM methotrexate or in 360 µM N -(phosphonacetyl)- L -aspartate (PALA) and 1 µM dipyridimole, respectively.…”

Branching Processes in Biology

“…An alternative method of calculating mutation rates is to use data observed at two successive generations (Niccum et al 2012). Zheng (1999Zheng ( , 2005 has reviewed practical issues in estimating mutation rates resulting from the unique distribution of mutants per culture.…”

“…Somewhat idiosyncratically, we will discuss mathematical models by Angerer (2001), estimation approaches by Zheng (1999Zheng ( , 2002Zheng ( , 2005 and applications to genomic mutation rates in bacteria by Foster (2006). Angerer (2001) developed a theory of FA which relaxed some of the Luria-Delbrück hypotheses regarding proliferation and mutation models.…”

“…Another essential problem has been tackled by Zheng (2005). When inferring the mutation rate from an experiment, it is frequently assumed that the number of mutants in each test tube follows a common distribution.…”

Effect of mutations induced by N-methyl-N′-nitro-N-nitrosoguanidine on expression of penicillin G acylase and β-lactamase in wild-type Escherichia coli strains

“…Random mutations that are produced independently of selection are important for the survival of an organism. We used the P 0 method to better estimate the mutation rate, which is the method required when the number of mutants in a culture is difficult to ascertain but the presence or absence of mutants in a culture can be determined (Zheng 2005). Our estimates of the number of mutations per cell division in wild-type and mutant cells under similar growth conditions indicate that mutants may grow faster than their parent.…”