Fluctuation Analysis: Can Estimates Be Trusted?

The estimation of mutation rates and relative fitnesses in fluctuation analysis is based on the unrealistic hypothesis that the single-cell times to division are exponentially distributed. Using the classical Luria-Delbrück distribution outside its modelling hypotheses induces an important bias on the estimation of the relative fitness. The model is extended here to any division time distribution. Mutant counts follow a generalization of the Luria-Delbrück distribution, which depends on the mean number of mutations, the relative fitness of normal cells compared to mutants, and the division time distribution of mutant cells. Empirical probability generating function techniques yield precise estimates both of the mean number of mutations and the relative fitness of normal cells compared to mutants. In the case where no information is available on the division time distribution, it is shown that the estimation procedure using constant division times yields more reliable results. Numerical results both on observed and simulated data are reported.     

Analysis of distributions of mutants in clones of plant-cell aggregates

Summary The organization of plant cells (or any other genetic elements, such as organelles) into aggregates modifies the expected distribution of mutants in clones. The reason for the modification, and its effect on the use of the Luria-Delbrück fluctuation test, are discussed. The Luria-Delbriick test was used to show that the trait for chlorate resistance in cultured rose-cell aggregates appeared spontaneously and in the absence of chlorate ion.     

On fluctuation analysis: a new,simple and efficient method for computing the expected number of mutants

Fluctuation analysis, which is often used to demonstrate random mutagenesis in cell lines (and to estimate mutation rates), is based on the properties of a probability distribution known as the Luria-Delbrück distribution (and its generalizations). The two main new results reported in this paper are (i) a simple, completely general, and computationally efficient procedure for calculating probability distributions arising from fluctuation analysis and (ii) the formula for this procedure when cells in a colony have only grown for a finite number of generations after initial seeding. It is also shown that the procedure reduces to one that was developed earlier when an infinite number of generations is assumed. The derivation of the generating function of the distribution is also clarified. The results obtained should also be useful to experimentalists when only a relatively short time elapses between seeding and harvestint cultures for fluctuation analysis.     

Unbiased Estimation of Mutation Rates under Fluctuating Final Counts

Estimation methods for mutation rates (or probabilities) in Luria-Delbrück fluctuation analysis usually assume that the final number of cells remains constant from one culture to another. We show that this leads to systematically underestimate the mutation rate. Two levels of information on final numbers are considered: either the coefficient of variation has been independently estimated, or the final number of cells in each culture is known. In both cases, unbiased estimation methods are proposed. Their statistical properties are assessed both theoretically and through Monte-Carlo simulation. As an application, the data from two well known fluctuation analysis studies on Mycobacterium tuberculosis are reexamined.     

The axolotl mutants

The Mexican axolotl (Ambystoma mexicanum) has enjoyed wide use in experimental embryology for over 100 yr. Its usefulness has been extended into the area of developmental genetics largely due to the contributions of R. Briggs and R. R. Humphrey at Indiana University. To date over 30 mutants have been described, almost all of which affect development. Some of these have been discovered in inbred strains while others have been uncovered in recent Mexican imports. These mutants can be subdivided into several major classes. Maternal effect mutations lead to deficiencies in informational, structural, or metabolic components of the egg essential to early development prior to the time at which the embryo's own genome becomes active. In contrast, the developmental lethals affect later stages in embryogenesis when both morphogenetic and biochemical events are determined exclusively by the genotype of the embryo. Most lead to death at about feeding stage. Some, the cell lethals, are believed to suffer from fundamental metabolic defects affecting all parts of the embryo. Others affect the development of specific organs or tissues. The developmental nonlethals also affect specific systems, but ones that are not essential to survival. Some affect the development and survival of pigment cells and these, along with isozyme variants, are useful as markers in developmental experiments. A number of the mutants have been studied in detail, but others scarcely at all. The purpose of this review is to bring them to the attention of all developmental biologists in the hope that their potential will be even more widely recognized.     

Evolution of resistance during clonal expansion

Acquired drug resistance is a major limitation for cancer therapy. Often, one genetic alteration suffices to confer resistance to an otherwise successful therapy. However, little is known about the dynamics of the emergence of resistant tumor cells. In this article, we consider an exponentially growing population starting from one cancer cell that is sensitive to therapy. Sensitive cancer cells can mutate into resistant ones, which have relative fitness alpha prior to therapy. In the special case of no cell death, our model converges to the one investigated by Luria and Delbrück. We calculate the probability of resistance and the mean number of resistant cells once the cancer has reached detection size M. The probability of resistance is an increasing function of the detection size M times the mutation rate u. If Mu < 1, then the expected number of resistant cells in cancers with resistance is independent of the mutation rate u and increases with M in proportion to M(1-1/alpha) for advantageous mutants with relative fitness alpha>1, to l nM for neutral mutants (alpha = 1), but converges to an upper limit for deleterious mutants (alpha<1). Further, the probability of resistance and the average number of resistant cells increase with the number of cell divisions in the history of the tumor. Hence a tumor subject to high rates of apoptosis will show a higher incidence of resistance than expected on its detection size only.     

Improved inference of mutation rates: II. Generalization of the Luria-Delbrück distribution for realistic cell-cycle time distributions

In the first paper of this series (Kepler and Oprea, Theor. Popul. Biol. 2001) we found a continuum approximation of the Luria-Delbrück distribution in terms of a scaled variable related to the proportion of mutants in the culture. Here we show that the Luria-Delbrück distribution is inaccurate when realistic division processes are being considered due to the non-Markovian character of the cell cycle. We derive the expectation of the proportion of mutants in the culture for arbitrary cell-cycle time distributions. We then introduce a two-parameter generalization of the continuum Luria-Delbrück distribution for two of the more commonly used cell-cycle time distributions: gamma and shifted exponential. We obtain the generalized distribution by defining a map from the actual parameters to "effective" parameters. The effective mutation rate is obtained analytically, while the effective population size is obtained by fitting simulation data. Our simulations show that the second parameter depend mostly on the coefficient of variation of the cell-cycle time distribution.     

Selection against hypermutability in Escherichia coli during long term evolution

Summary A population of a mutT strain of E. coli was maintained in a chemostat for 2,200 generations. Afterwards the rate, of mutation to resistance to three antibiotics was determined by the Luria-Delbrück fluctuation test. It was found that the strain had a distinctly reduced mutability after the long-term cultivation compared with the original strain. Nevertheless the mutability was still much higher than that of a wild-type strain. After transduction of the mutT gene into another genetic backgroud the transductants showed the same mutability as the original strain indicating that the mutT allele itself had not changed. Our results support the hypothesis that under new environmental conditions mutator strains have an advantage due to their more efficient production of beneficial mutations. After optimal adaptation there is selection against high mutation rates due to the increased mutational load in the mutator population.     

Alcohol-resistant sporulation mutants of Bacillus subtilis.

About 80% of Bacillus subtilis cells form spores when grown in nutrient broth. In medium containing various short-chain aliphatic alcohols, the frequency of sporulation was reduced to 0.5%. Mutants sporulated in the presence of alcohols at a frequency of 30 to 40%. Sporulation in the wild-type cells was sensitive to alcohol at the beginning of sporulation (stage zero). Sensitivity to alcohol in the mutants was also at stage zero, even though the sensitivity was considerably reduced. This sensitivity of sporulation to alcohol is the phenotypic expression of a genetic locus designated ssa. Mutations at this locus lead to a decreased sensitivity of sporulation to alcohol without modifying the sensitivity of growth. Genetic analysis by transduction was bacteriophage PBS1 revealed that ssa mutations are near the previously described spo0A locus. ssa mutants also differ from wild-type cells in the composition of membrane phospholipids. The relative amount of phosphatidylglycerol increased, whereas the relative amount of phosphatidylethanolamine and lysylphosphatidylglycerol decreased relative to the proportions in the wild type. The distribution of fatty acids in membrane lipids is the same as in the wild type. No differential sensitivity of phospholipid metabolism to alcohol could be detected in the mutant. This work therefore reveals that the extensive, pleiotropic changes in the membranes of ssa mutants are the phenotypic reflection of alterations at a specific gene locus.     

Microalgal adaptation to a stressful environment (acidic,metal-rich mine waters) could be due to selection of pre-selective mutants originating in non-extreme environments

At least six species of eukaryotic microalgae inhabit the acidic (pH 2.4–2.7), metal-rich mine waters from ponds in the copper mine district of Mynydd Parys (N Wales, UK). Consequently, these ponds constitute interesting natural laboratories for analysis of adaptation by microalgae to extremely stressful conditions. To distinguish between the pre-selective and post-selective origin of adaptation processes that allow the existence of microalgae in these ponds, a Luria-Delbrück fluctuation analysis was performed with the chlorophycean Dictyosphaerium chlorelloides isolated from non-acidic waters. In this analysis, natural Mynydd Parys pond water (MPW) was used as selective factor. Pre-selective, resistant D. chlorelloides cells appeared with a frequency of 1.6 × 10^?6 per cell per generation. MPW-resistant mutants, with a diminished Malthusian fitness, are maintained in non-extreme waters as the result of a balance between new MPW-resistant cells arising by mutation and MPW-resistant mutants eliminated by natural selection (equilibrium at ca. 19 MPW-resistant per 10⁷ wild-type cells). We propose that the microalgae inhabiting these stressful ponds could be the descendents of chance mutants that arrived in the past or are even arriving at the present.     

Direct detection of deletion mutations in the yeast DEL assay using quantitative PCR (TaqMan)

Established mutagenesis assays measure mutant frequencies at selectable loci. These assays work by encouraging the growth of mutants to form visible colonies while suppressing the growth of non-mutants. An alternative strategy is to detect DNA alterations directly. We present an example of this latter strategy using TaqMan to quantify deletion mutants in mixed cultures of Saccharomyces cerevisiae strain RS112. The RS112 strain contains two heteroallelic his3 sequences that share approximately 400bp homology and are separated by approximately 7 kb of plasmid DNA. Spontaneous and chemical-induced strand breaks that occur in this region are repaired by intrachromosomal recombination, resulting in the loss of the plasmid DNA and creation of a His prototroph. Ordinarily, these prototrophs are detected by growth on His- medium over 2-3 days. In this case, we used TaqMan to selectively detect the DNA of deletion mutants in the presence of a large excess of DNA from non-mutants. This was accomplished using primers whose annealing sites were outside the region of DNA lost due to recombination. Thus, the primers were too far apart to produce PCR products using DNA from non-mutants, but produced a robust TaqMan signal using DNA from deletion mutants. Spontaneous and chemical-induced recombination frequencies (RF) were measured in a series of time-course and dose-response experiments with direct-acting mutagens. Interestingly, chemical-induced increases in RF were observed within a few hours of initiation of exposure, demonstrating that deletion mutations in RS112 can be fixed soon after DNA damage occurs. The ability to measure RF at any time during treatment will be useful for additional mechanistic studies. Chemical-induced increases in RF were also observed in the absence of selective growth conditions. As such, detection of deletion mutations with TaqMan may be applicable to measurements of RFs at non-selectable loci in yeast and other species. Finally, chemical-induced RFs after 17 h exposure were similar to those observed after 3 days growth on selective medium. The TaqMan assay may therefore be used to screen compounds more quickly for their ability to cause deletion mutations than is currently done by plating on selective medium.     

Characteristics of detection of mutants on selective media

The regularities of formation and appearance of mutants after transfer or plating yeast cells on selective media are analysed. The knowledge of these patterns is necessary for quantitative evaluation of mutants' content in the culture. Mutants formed in a cell culture, prior to transfer onto selective medium, are revealed on this medium as colonies and form a wave in time that is being observed during several days. Due to residual growth of cells, new mutants are formed and revealed as the second wave. Following two waves, an increasing front may approach which is formed from mutants of unknown origin. For evaluation of the number of mutants in the culture, prior to transfer onto selective medium, it is necessary to count up only the "first wave" of mutant colonies' appearance.     

Fitness alteration of foot-and-mouth disease virus mutants: measurement of adaptability of viral quasispecies.

We document the rapid alteration of fitness of two foot-and-mouth disease virus (FMDV) mutants resistant to a neutralizing monoclonal antibody. Both mutants showed a selective disadvantage in BHK-21 cells when passaged in competition with their parental FMDV. Upon repeated replication of the mutants alone, they acquired a selective advantage over the parental FMDV and fixed additional genomic substitutions without reversion of the monoclonal antibody-resistant phenotype. Thus, variants that were previously kept at low frequency in the mutant spectrum of a viral quasispecies rapidly became the master sequence of a new genomic distribution and dominated the viral population.     

Mutability and importance of a hypermutable cell subpopulation that produces stress-induced mutants in Escherichia coli

In bacterial, yeast, and human cells, stress-induced mutation mechanisms are induced in growth-limiting environments and produce non-adaptive and adaptive mutations. These mechanisms may accelerate evolution specifically when cells are maladapted to their environments, i.e., when they are are stressed. One mechanism of stress-induced mutagenesis in Escherichia coli occurs by error-prone DNA double-strand break (DSB) repair. This mechanism was linked previously to a differentiated subpopulation of cells with a transiently elevated mutation rate, a hypermutable cell subpopulation (HMS). The HMS could be important, producing essentially all stress-induced mutants. Alternatively, the HMS was proposed to produce only a minority of stress-induced mutants, i.e., it was proposed to be peripheral. We characterize three aspects of the HMS. First, using improved mutation-detection methods, we estimate the number of mutations per genome of HMS-derived cells and find that it is compatible with fitness after the HMS state. This implies that these mutants are not necessarily an evolutionary dead end, and could contribute to adaptive evolution. Second, we show that stress-induced Lac⁺ mutants, with and without evidence of descent from the HMS, have similar Lac⁺ mutation sequences. This provides evidence that HMS-descended and most stress-induced mutants form via a common mechanism. Third, mutation-stimulating DSBs introduced via I-SceI endonuclease in vivo do not promote Lac⁺ mutation independently of the HMS. This and the previous finding support the hypothesis that the HMS underlies most stress-induced mutants, not just a minority of them, i.e., it is important. We consider a model in which HMS differentiation is controlled by stress responses. Differentiation of an HMS potentially limits the risks of mutagenesis in cell clones.     

Biochemical characteristics of new thermosensitive secretory mutants of yeasts

New thermosensitive mutants of the yeast Saccharomyces cerevisiae which block the secretion of periplasmic enzymes at restriction temperature have been obtained. These mutants accumulate active low molecular weight and mature invertase species in the cell; the buoyant density of the cells in a Percoll gradient is higher than that in the wild strain cells. The mutant cells transferred to permissive temperature (25 degrees C) in the absence of protein synthesis can secrete some amount of accumulated invertase. It was found that the secretory defects of conditional mutants do not affect the activity of cytoplasmic enzymes (e.g., alcohol dehydrogenase) or the level of total protein synthesis and glycosylation and do not induce non-specific disturbances in energy metabolism and plasma membrane functions at restriction temperature. Some strains of new secretory mutants revealed uncoupled defective secretion of periplasmic enzymes and intrinsic membrane proteins (proline permease). The possibility of branching of the secretory pathway for periplasmic enzymes and cytoplasmic membrane proteins is discussed.     

A novel approach to improve specificity of algal biosensors using wild-type and resistant mutants: an application to detect TNT

A new genetic approach was developed for increasing specificity of microalgal biosensors. This method is based on the use of two different genotypes jointly to detect a given pollutant: (i) a sensitive genotype to obtain sensitivity; and (ii) a resistant mutant to obtain specificity. The method was tested by the development of a microalgal biosensor for the detection of the explosive 2,4,6-trinitrotoluene (TNT) using a wild-type strain (DcG1wt) of Dictyosphaerium chlorelloides (Chlorophyceae) as the sensitive organism, and a TNT-resistant mutant, obtained from DcG1wt strain by a modified Luria-Delbrück fluctuation analysis. The inhibition of chlorophyll a fluorescence of PSII by TNT was used as the biological signal. Significant differences in maximal fluorescence of light-adapted algae (F'(m)) between wild-type DcG1wt cells and TNT-resistant mutants, were observed in all the TNT concentrations tested (from 0.5 to 31.3 mg l(-1)) after only 3 min of exposure. Resistant mutants always exhibited significant higher F'(m) values in the presence of TNT than wild-type cells. These results suggest that the use of two different genotypes (sensitive and resistant to a given pollutant) jointly is a useful method to improve microalgal biosensors specificity.     

Ascertainment of the effect of differential growth rates of mutants on observed mutant frequencies in X-irradiated mammalian cells An indication for the occurrence of X-ray-induced untargeted mutagenesis

As it is not known to what extent differential growth rates of induced mutants lead to over- and under-representation of mutants in treated populations and thereby affect the determination of mutant frequencies, the mutation induction in X-irradiated L5178Y mouse lymphoma cells was determined via two methods. The first method involves the standard protocol which may suffer from the effect of differential growth rates, while the second method is based upon the fluctuation test in which the differential growth rates can be actually measured. It appeared that the standard protocol led to a mutant frequency that was similar to the mutant frequency determined in the fluctuation test. Therefore, the standard protocol appears to lead to only a minor under-estimation if any. Substantial heterogeneity in growth rates of induced mutants was observed, but the mutants with a selective advantage appear largely to compensate for the mutants that are lost because of selective disadvantage. It was calculated that the chance for isolating the same mutant twice from a treated population had been increased 2.2-fold because of the observed differential growth rates. Therefore, our data indicate that the standard protocol does not lead to serious errors in the determination of mutant frequencies and in the sampling of mutants. The fluctuation tests were also used to determine the spontaneous mutation frequency per cell per generation. The mutation rate appeared more than 10-fold enhanced in X-irradiated cells which may be attributed to the induction of a process of untargeted mutagenesis in mammalian cells.     

Genetic control of somatic cell differentiation in Volvox analysis of somatic regenerator mutants

The somatic regenerator (reg) mutants of Volvox carteri affect the ability of the normally terminally differentiated somatic cells to establish and/or maintain the differentiated state. Thirty-nine reg mutants of four phenotypic classes have been mapped to two, unlinked genes, regA and regB. Mutants at the regA locus have one of three phenotypes: All somatic cells regenerate new spheroids, somatic cells in the spheroid posterior region regenerate while those in the anterior region differentiate as somatic cells, or regenerating and nonregenerating cells are randomly intermixed. The regB mutant has a random intermixture of regenerating and nonregenerating cells. Somatic cells regenerate new Volvox spheroids in two ways; the cells lose their characteristic shape, become immotile, enlarge and undergo cleavage similar to that of normal reproductive cells or undergo cell division without prior enlargement or loss of cell shape. Temperature shift experiments on a cold-sensitive reg mutant suggest that the gene product acts after the somatic cell initials are formed at the end of cleavage.     

Isolation and characterization of TMPD-oxidase mutants of Pseudomonas aeruginosa

Mutants showing negative oxidase-reaction have been isolated from Pseudomonas aeruginosa following mutagenesis with N-methyl-N-nitro-N-nitrosoguanidine. These mutants were compared to the wild type cells with respect to their respiratory activities and cytochrome contents. They exhibit lower respiration rates and contain much less cytochrome c's which are responsible for their weak or negative oxidase-reaction in these mutants. This is supported in part from an initial linear relationship observed between the measured oxidase activities and the lower cytochrome c contents in these mutants. Further evidence comes from analyzing oxidase-negative cells of P. syringae, in which low cytochrome c contents similar to these oxidase mutants account for negative oxidase activities. Cytochrome o was the sole oxidase found among these mutants as well as in the wild type cell, suggesting that cytochrome c+o complex is responsible for the tetramethyl-p-phenylenediamine-oxidase activity in these mutants as the case in the wild-type cells. From the spectral characteristics it seems that all mutants contain about the same amount and type of terminal oxidase as that of the wild-type cells. The mutation occurred which altered the oxidase activities in these mutants appears to affect cytochrome c gene(s), but not the terminal oxidase gene(s).Abbreviations TMPD Tetramethyl-p-phenylenediamine - MD minimal Davis