Discussion on research methods of bacterial resistant mutation mechanisms under selective culture—uncertainty analysis of data from the Luria-Delbrück fluctuation experiment

Whether bacterial drug-resistance is drug-induced or results from rapid propagation of random spontaneous mutations in the flora prior to exposure, remains a long-term key issue concerned and debated in both genetics and medicinal fields. In a pioneering study, Luria and Delbrück exposed E. coli to T1 phage, to investigate whether the number of resistant colonies followed the Poisson distribution. They deduced that the development of resistant colonies is independent of phage presence. Similar results have since been obtained on solid medium containing antibacterial agents. Luria and Delbrück??s conclusions were long considered a gold standard for analyzing drug resistance mutations. More recently, the concept of adaptive mutation has triggered controversy over this approach. Microbiological observation shows that, following exposure to drugs of various concentrations, drug-resistant cells emerge and multiply depending on the time course, and show a process function, inconsistent with the definition of Poisson distribution (which assumes not only that resistance is independent of drug quantity but follows no specific time course). At the same time, since cells tend to aggregate after division rather than separating, colonies growing on drug plates arise from the multiplication of resistant bacteria cells of various initial population sizes. Thus, statistical analysis based on equivalence of initial populations will yield erroneous results. In this paper, 310 data from the Luria-Delbrück fluctuation experiment were reanalyzed from this perspective. In most cases, a high-end abnormal value, resulting from the non-synchronous variation of the two above-mentioned time variables, was observed. Therefore, the mean value cannot be regarded as an unbiased expectation estimate. The ratio between mean value and variance was similarly incomparable, because two different sampling methods were used. In fact, the Luria-Delbrück data appear to follow an aggregated, rather than Poisson distribution. In summary, the statistical analysis of Luria and Delbrück is insufficient to describe rules of resistant mutant development and multiplication. Correction of this historical misunderstanding will enable new insight into bacterial resistance mechanisms.     

Mutations of Chinese Hamster Somatic Cells from 2-Deoxygalactose Sensitivity to Resistance

In Chinese hamster somatic cells, the spontaneous change of phenotype from 2-deoxygalactose sensitivity to resistance was studied using fluctuation test experiments à la Luria and Delbrück (1943) for four Chinese hamster cell strains derived from V79. The results are consistent with true mutational events. The mutation rates are in the range of 1 to 3.5 X 10(-5) per cell per generation. The relationship between the 2-deoxyglactose resistance and the galactokinase markers is discussed.     

Fluctuation Analysis: The Probability Distribution of the Number of Mutants under Different Conditions

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.     

A deterministic approach for the estimation of mutation rates in cultured mammalian cells

Unequal growth rates between mutant and wild-type cells in a large population constitute a problem for the estimation of mutation rate. Over a period of cell growth, a selective advantage of one cell type over the other might lead to considerable error in the estimation of mutation rate if equal growth rates are assumed. In this study, we propose a formula and apply it to the estimation of spontaneous mutation rate in a growing population of Chinese hamster V79 cells in which ouabain-resistant mutant cells exhibit a slower growth rate than the wild-type cells. The formula is a generalization of that previously presented by Armitage (1953), and this is the first attempt to apply the deterministic approach for mutation rate estimation to cultured mammalian cells. The value of the estimated rate is compared with that derived from a parallel experiment using the fluctuation test of Luria and Delbrück (1943). The limitations and advantages of taking the deterministic approach to mutation rate estimation in mammalian cell systems are discussed.     

Time Inhomogeneous Mutation Models with Birth Date Dependence

The classic Luria–Delbrück model for fluctuation analysis is extended to the case where the split instant distributions of cells are not i.i.d.: the lifetime of each cell is assumed to depend on its birth date. This model takes also into account cell deaths and non-exponentially distributed lifetimes. In particular, it is possible to consider subprobability distributions and to model non-exponential growth. The extended model leads to a family of probability distributions which depend on the expected number of mutations, the death probability of mutant cells, and the split instant distributions of normal and mutant cells. This is deduced from the Bellman–Harris integral equation, written for the birth date inhomogeneous case. A new theorem of convergence for the final mutant counts is proved, using an analytic method. Particular examples like the Haldane model or the case where hazard functions of the split-instant distributions are proportional are studied. The Luria–Delbrück distribution with cell deaths is recovered. A computation algorithm for the probabilities is provided.     

Physics and the origins of molecular biology

Bohr, Delbrück and Schrödinger were physicists who had important influences on biology in the second half of the twentieth century. They thought that future studies of the gene might reveal new principles or paradoxes, analogous to the wave/particle paradox of light propagation, or even new physical laws. This stimulated several physicists to enter the field of biology. Delbrück founded the bacteriophage group which provided one of the roots of molecular biology. Another was X-ray crystallography which led to the discovery of DNA structure. The strength and success of molecular biology came from the many interactions between geneticists, physicists, chemists and biochemists. It was also characterized by a powerful combination of theoretical and experimental approaches.     

Avoiding Dangerous Missense: Thermophiles Display Especially Low Mutation Rates

Rates of spontaneous mutation have been estimated under optimal growth conditions for a variety of DNA-based microbes, including viruses, bacteria, and eukaryotes. When expressed as genomic mutation rates, most of the values were in the vicinity of 0.003–0.004 with a range of less than two-fold. Because the genome sizes varied by roughly 10⁴-fold, the mutation rates per average base pair varied inversely by a similar factor. Even though the commonality of the observed genomic rates remains unexplained, it implies that mutation rates in unstressed microbes reach values that can be finely tuned by evolution. An insight originating in the 1920s and maturing in the 1960s proposed that the genomic mutation rate would reflect a balance between the deleterious effect of the average mutation and the cost of further reducing the mutation rate. If this view is correct, then increasing the deleterious impact of the average mutation should be countered by reducing the genomic mutation rate. It is a common observation that many neutral or nearly neutral mutations become strongly deleterious at higher temperatures, in which case they are called temperature-sensitive mutations. Recently, the kinds and rates of spontaneous mutations were described for two microbial thermophiles, a bacterium and an archaeon. Using an updated method to extrapolate from mutation-reporter genes to whole genomes reveals that the rate of base substitutions is substantially lower in these two thermophiles than in mesophiles. This result provides the first experimental support for the concept of an evolved balance between the total genomic impact of mutations and the cost of further reducing the basal mutation rate.     

Improved inference of mutation rates: I. An integral representation for the Luria-Delbrück distribution

The estimation of mutation rates is ordinarily performed using results based on the Luria-Delbrück distribution. There are certain difficulties associated with the use of this distribution in practice, some of which we address in this paper (others in the companion paper, Oprea and Kepler, Theor. Popul. Biol., 2001). The distribution is difficult to compute exactly, especially for large values of the random variable. To overcome this problem, we derive an integral representation of the Luria-Delbrück distribution that can be computed easily for large culture sizes. In addition, we introduce the usual assumption of very small probability of having a large proportion of mutants only after the generating function has been computed. Thus, we obtain information on the moments for the more general case. We examine the asymptotic behavior of this system. We find a scaling or "standardization" technique that reduces the family of distributions parameterized by three parameters (mutation rate, initial cell number, and final cell number) to a single distribution with no parameters, valid so long as the product of the mutation rate and the final culture is sufficiently large. We provide a pair of techniques for computing confidence intervals for the mutation rate. In the second paper of this series, we use the distribution derived here to find approximate distributions for the case where the cell cycle time is not well-described as an exponential random variable as is implicitly assumed by Luria-Delbrück distribution.     

Cell migration in development and disease

A recent meeting at the Max Delbrück Center in Berlin, Germany provided a forum to discuss the molecular mechanisms of cell migration in a broad range of contexts including chemotaxis, development, immunity, and cancer.     

Update on estimation of mutation rates using data from fluctuation experiments

This note discusses a minor mathematical error and a problematic mathematical assumption in Luria and Delbrück'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.     

The rate and character of spontaneous mutation in Thermus thermophilus

Selection of spontaneous, loss-of-function mutations at two chromosomal loci (pyrF and pyrE) enabled the first molecular-level analysis of replication fidelity in the extremely thermophilic bacterium Thermus thermophilus. Two different methods yielded similar mutation rates, and mutational spectra determined by sequencing of independent mutants revealed a variety of replication errors distributed throughout the target genes. The genomic mutation rate estimated from these targets, 0.00097 +/- 0.00052 per replication, was lower than corresponding estimates from mesophilic microorganisms, primarily because of a low rate of base substitution. However, both the rate and spectrum of spontaneous mutations in T. thermophilus resembled those of the thermoacidophilic archaeon Sulfolobus acidocaldarius, despite important molecular differences between these two thermophiles and their genomes.     

Program and Abstracts of the 9th Transgenic Technology Meeting (TT2010)

Abstracts

Program and Abstracts of the 9th Transgenic Technology Meeting (TT2010) 22–24 March 2010, Conference Centre, Max Delbrück Center for Molecular Medicine [MDC], Robert-R?ssle-Str. 10, 13125 Berlin, Germany     

GENETIC ADAPTATION AND ACCLIMATION OF PHYTOPLANKTON ALONG A STRESS GRADIENT IN THE EXTREME WATERS OF THE AGRIO RIVER–CAVIAHUE LAKE (ARGENTINA)1

We tested if different adaptation strategies were linked to a stress gradient in phytoplankton cells. For this purpose, we studied the adaptation and acclimation of Dictyosphaerium chlorelloides (Naumann) Komárek et Perman (Chlorophyta) and Microcystis aeruginosa (Kütz.) Kütz. (Cyanobacteria) to different water samples (from extremely acid, metal‐rich water to moderate stressful conditions) of the Agrio River–Caviahue Lake system (Neuquén, Argentina). Both experimental strains were isolated from pristine, slightly alkaline waters. To distinguish between physiological acclimation and genetic adaptation (an adaptive evolution event), a modified Luria‐Delbrück fluctuation analysis was carried out with both species by using as selective agent sample waters from different points along the stress gradient. M. aeruginosa did not acclimate to any of the waters tested from different points along the stress gradient nor did D. chlorelloides to the two most acidic and metal‐rich waters. However, D. chlorelloides proliferated by rapid genetic adaptation, as the consequence of a single mutation (5.4 × 10^?7 resistant mutants per cell per division) at one locus, in less extreme water and also by acclimation in the least extreme water. It is hypothesized that the stress gradient resulted in different strategies of adaptation in phytoplankton cells from nonextreme waters. Thus, very extreme conditions were lethal for both organisms, but as stressful conditions decreased, adaptation of D. chlorelloides cells was possible by the selection of resistant mutants, and in less extreme conditions, by acclimation.     

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.     

The mutagenic action of nitroimidazoles. II. Tinidazole, ipronidazole, panidazole and ornidazole.

The 5-nitroimidazoles tinidazole (Fasigyn), ipronidazole (Ro-7-1554), panidazole and ornidazole (Tiberal, Ro-7-0207) in concentrations of 0.02--1 mM per liter increased the mutation frequency of Klebsiella pneumoniae. Escherichia coli K12 and Citrobacter freundii to streptomycin resistance, including streptomycin dependence, in Luria and Delbrück's fluctuation test. At low concentration (0.1 mM), the increase of the mutation frequency caused by each compound was nearly the same, i.e. 3--4 times the spontaneous mutation frequency. At higher concentrations, considerable differences between the mutagenic activities of the compounds occurred.     

Reviews

Book reviewed in this article: South African perspectives on species: an evaluation of the recognition concept: Species and Speciation .—E. S. Vrba (ed.). Mind from Matter?-an essay on evolutionary epistemology .—Max Delbrück. The structure and affinities of the Hedyloidea: a new concept of the butterflies .—M. J. Scoble.     

The frequency of mutators in populations of Escherichia coli

Owing to occasional spontaneous mutations in genes encoding DNA repair, any population of a reasonable size is expected to harbor a sub-population of genetic mutators. Using a genetically modified strain of Escherichia coli K-12, we have estimated the frequency of mutators to be about 3x10(-5). By and large, this corresponds to a mutation rate from non-mutators to mutators of 5x10(-6) per bacterium per generation. Using a mutS∷Tn10 derivative as representative for mutators, we estimated the increase in mutation rates in mutators to be 19- to 82-fold, depending on the test-mutation under consideration. The load associated with this increase in mutation rate resulted in a growth inhibition of 1%. From these data, we estimated that the rate of detrimental mutations in the non-mutators to be 2x10(-4)-8x10(-4). The situations where adaptive mutations may result in an increase in the frequency of mutators are discussed.     

The origin of phage virology.

The history of bacteriophage (phage) had its start in 1915, when Twort isolated an unusual filterable and infectious agent from excrete of patients struck by diarrhoea; this discovery was followed by an analogous, and probably independent, finding of d'Hérelle in 1917. For several years phage research made scant progress but great attention was paid to the question of phage nature, which saw the contrast between d'Hérelle and Bordet's views (living against chemical nature, respectively). This situation changed with the independent discovery of lysogeny, in 1925, thanks to Bordet and Bail: this phenomenon was considered of genetical origin, a view that Wollman interpreted by assimilating the properties of phage to those of gene (according to a previous idea of Muller). In the 1930s, Burnet's work opened a new era by demonstrating the occurrence of several species of phages and their antigenic property. In the same period, the physical and chemical characteristics of these viruses were disclosed thanks, in particular, to the work of Schlesinger, who first demonstrated that a virus (phage) was constituted of nucleoproteins. The peculiarity of phage was finally shown after the invention of electron microscope: H. Ruska, in 1940, and Anderson and Luria in the next years, obtained the first images of tailed phages, a finding that strongly helped the investigation on the first steps of the infection process. The decisive impulse to phage virology came from Delbrück, a physicist who entered biology giving it a new arrangement. The so-called "phage group" assembled brilliant minds (Luria, Hershey and Delbrück himself, and later a dozen of other scientists): this group faced three fundamental questions of phage virology, i.e., the mechanisms of attack, multiplication and lysis. In ten years' time, phage virology became an integrant part of molecular biology, also thanks to the discovery of the genetical properties of DNA: in such scientific context, Delbrück, Luria and Hershey's works emerged for the absolute excellence of their results, which led such scientists to Nobel prize. Lysogeny was however neglected by the phage group: this singular property shared by bacteria and phages was instead investigated by Lwoff's group, in Paris, and explained in its fundamental features during the 1950s. The "phage's saga" has gone on being an important division of molecular biology till today, and its history is far from being over.     

The Distribution of Mutation Effects on Viability in Drosophila Melanogaster

Parameters of continuous distributions of effects and rates of spontaneous mutation for relative viability in Drosophila are estimated by maximum likelihood from data of two published experiments on accumulation of mutations on protected second chromosomes. A model of equal mutant effects gives a poor fit to the data of the two experiments; higher likelihoods are obtained with leptokurtic distributions or for models in which there is more than one class of mutation effect. Minimum estimates of mutation rates (events per generation) at polygenes affecting viability on chromosome 2 are 0.14 and 0.068, but estimates are strongly confounded with other parameters in the model. Separate information on rates of molecular divergence between Drosophila species and from rates of movement of transposable elements is used to infer the overall genomic mutation rate in Drosophila, and the viability data are analyzed with mutation rate as a known parameter. If, for example, a mutation rate for chromosome 2 of 0.4 is assumed, maximum likelihood estimates of mean mutant effect on relative viability are 0.4% and 1%, but the majority of mutations have very much smaller effects than these values as distributions are highly leptokurtic. The methodology is applied to estimate viability effects of single P element insertional mutations. The mean effect per insertion is found to be higher, and their distribution is found to be less leptokurtic than for spontaneous mutations. The equilibrium genetic variance of viability predicted by a mutation-selection balance model with parameters estimated from the mutation accumulation experiments is similar to laboratory estimates of genetic variance of viability from natural populations of Drosophila.     

Dynamic interactions of Sup35p and PrP prion protein domains modulate aggregate nucleation and seeding

The mouse monoclonal antibody POM2 directed against the PrP octapeptide region was a generous gift of Dr. Polymenidou and Dr. A. Aguzzi (Institute of Neuropathology, University of Zürich). The plasmid pEGFP-HD72Q was kindly provided by Dr. E. Wanker (Max Delbrück Center of Molecular Medicine, Berlin). We thank members of the Vorberg and Schätzl laboratories for constructive comments on this work. Financial support for this work was provided by the Deutsche Forschungsgemeinschaft SFB 596 B14, VO 1277/1-2, the European Commission (grant TSEUR LSHB-CT-2005-018805) and by the EU NoE Neuroprion.