A note on plating efficiency in fluctuation experiments

Methods for two nonstandard problems arising from the Luria-Delbrück experiment

The fluctuation experiment, devised by Luria and Delbrück in 1943, remains the method of choice for measuring microbial mutation rates in the laboratory. While most inference problems commonly encountered in a fluctuation experiment can be tackled by existing standard algorithms, investigators from time to time run into nonstandard problems not amenable to any existing algorithms. A major obstacle to solving these nonstandard problems is the construction of confidence intervals for mutation rates. This note describes methods for two important categories of nonstandard problems, namely, pooling data from separate experiments and analyzing grouped mutant count data, focusing on the construction of likelihood ratio confidence intervals. In addition to illustrative examples using real-world data, simulation results are presented to help assess the proposed methods.

Efficient, robust, and versatile fluctuation data analysis using MLE MUtation Rate calculator (mlemur)

The fluctuation assay remains an important tool for analyzing the levels of mutagenesis in microbial populations. The mutant counts originating from some average number of mutations are usually assumed to obey the Luria-Delbrück distribution. While several tools for estimating mutation rates are available, they sometimes lack accuracy or versatility under non-standard conditions. In this work, extensions to the Luria-Delbrück protocol to account for phenotypic lag and cellular death with either perfect or partial plating were developed. Hence, the novel MLE MUtation Rate calculator, or mlemur, is the first tool that provides a user-friendly graphical interface allowing the researchers to model their data with consideration for partial plating, differential growth of mutants and non-mutants, phenotypic lag, cellular death, variability of the final number of cells, post-exponential-phase mutations, and the size of the inoculum. Additionally, mlemur allows the users to incorporate most of these special conditions at the same time to obtain highly accurate estimates of mutation rates and P values, confidence intervals for an arbitrary function of data (such as fold), and perform power analysis and sample size determination for the likelihood ratio test. The accuracy of point and interval estimates produced by mlemur against historical and simulated fluctuation experiments are assessed. Both mlemur and the analyses in this work might be of great help when evaluating fluctuation experiments and increase the awareness of the limitations of the widely-used Lea-Coulson formulation of the Luria-Delbrück distribution in the more realistic biological contexts.

Ecological effects of stress drive bacterial evolvability under sub-inhibitory antibiotic treatments

Stress is thought to increase mutation rate and thus to accelerate evolution. In the context of antibiotic resistance, sub-inhibitory treatments could then lead to enhanced evolvability, thereby fuelling the adaptation of pathogens. Combining wet-lab experiments, stochastic simulations and a meta-analysis of the literature, we found that the increase in mutation rates triggered by antibiotic treatments is often cancelled out by reduced population size, resulting in no overall increase in genetic diversity. A careful analysis of the effect of ecological factors on genetic diversity showed that the potential for regrowth during recovery phase after treatment plays a crucial role in evolvability, being the main factor associated with increased genetic diversity in experimental data.

webSalvador: a Web Tool for the Luria-Delbrük Experiment

Existing Web tools for the Luria-Delbrück fluctuation experiment do not offer many desirable capabilities that are vital to mutation research. webSalvador offers these capabilities via a user interface that allows researchers to access most of the functions in the R package rSalvador without having to learn the R language.

Live-cell single-molecule tracking highlights requirements for stable Smc5/6 chromatin association in vivo

The essential Smc5/6 complex is required in response to replication stress and is best known for ensuring the fidelity of homologous recombination. Using single-molecule tracking in live fission yeast to investigate Smc5/6 chromatin association, we show that Smc5/6 is chromatin associated in unchallenged cells and this depends on the non-SMC protein Nse6. We define a minimum of two Nse6-dependent sub-pathways, one of which requires the BRCT-domain protein Brc1. Using defined mutants in genes encoding the core Smc5/6 complex subunits, we show that the Nse3 double-stranded DNA binding activity and the arginine fingers of the two Smc5/6 ATPase binding sites are critical for chromatin association. Interestingly, disrupting the single-stranded DNA (ssDNA) binding activity at the hinge region does not prevent chromatin association but leads to elevated levels of gross chromosomal rearrangements during replication restart. This is consistent with a downstream function for ssDNA binding in regulating homologous recombination.

New approaches to mutation rate fold change in Luria-Delbrück fluctuation experiments

For nearly eight decades the Luria-Delbrück protocol remains the preferred method for experimentally determining microbial mutation rates. However, earnest development and rigorous applications of statistical methods for mutation rate comparison using fluctuation assay data are a relatively recent phenomenon. While likelihood ratio tests tailored for the fluctuation protocol give investigators appropriate tools, researchers sometimes may prefer to view the comparison of two mutation rates through the lens of the ratio of the two mutation rates. The idea of using the bootstrap technique to construct intervals for mutation rate fold change was proposed nearly a decade ago, but it failed to gain traction partly due to a failure to incorporate likelihood-based estimation. In addition to extending the bootstrap method, this paper proposes two new methods of constructing intervals for mutation rate fold change: a profile likelihood method and a Bayesian method utilizing Monte Carlo Markov chain. All three methods are assessed by large-scale simulations.

Single-Gene Deletions Contributing to Loss of Heterozygosity in Saccharomyces cerevisiae: Genome-Wide Screens and Reproducibility

Loss of heterozygosity (LOH) is a phenomenon commonly observed in cancers; the loss of chromosomal regions can be both causal and indicative of underlying genome instability. Yeast has long been used as a model organism to study genetic mechanisms difficult to study in mammalian cells. Studying gene deletions leading to increased LOH in yeast aids our understanding of the processes involved, and guides exploration into the etiology of LOH in cancers. Yet, before in-depth mechanistic studies can occur, candidate genes of interest must be identified. Utilizing the heterozygous Saccharomyces cerevisiae deletion collection (≈ 6500 strains), 217 genes whose disruption leads to increased LOH events at the endogenously heterozygous mating type locus were identified. Our investigation to refine this list of genes to candidates with the most definite impact on LOH includes: secondary testing for LOH impact at an additional locus, gene ontology analysis to determine common gene characteristics, and positional gene enrichment studies to identify chromosomal regions important in LOH events. Further, we conducted extensive comparisons of our data to screens with similar, but distinct methodologies, to further distinguish genes that are more likely to be true contributors to instability due to their reproducibility, and not just identified due to the stochastic nature of LOH. Finally, we selected nine candidate genes and quantitatively measured their impact on LOH as a benchmark for the impact of genes identified in our study. Our data add to the existing body of work and strengthen the evidence of single-gene knockdowns contributing to genome instability.

Mutations in the S-Adenosylmethionine Synthetase Genes SAM1 and SAM2 Differentially Affect Genome Stability in Saccharomyces cerevisiae

Maintenance of genome integrity is a crucial cellular focus that involves a wide variety of proteins functioning in multiple processes. Defects in many different pathways can result in genome instability, a hallmark of cancer. Utilizing a diploid Saccharomyces cerevisiae model, we previously reported a collection of gene mutations that affect genome stability in a haploinsufficient state. In this work we explore the effect of gene dosage on genome instability for one of these genes and its paralog; SAM1 and SAM2 These genes encode S-Adenosylmethionine (AdoMet) synthetases, responsible for the creation of AdoMet from methionine and ATP. AdoMet is the universal methyl donor for methylation reactions and is essential for cell viability. It is the second most used cellular enzyme substrate and is exceptionally well-conserved through evolution. Mammalian cells express three genes, MAT1A, MAT2A, and MAT2B, with distinct expression profiles and functions. Alterations to these AdoMet synthetase genes, and AdoMet levels, are found in many cancers, making them a popular target for therapeutic intervention. However, significant variance in these alterations are found in different tumor types, with the cellular consequences of the variation still unknown. By studying this pathway in the yeast system, we demonstrate that losses of SAM1 and SAM2 have different effects on genome stability through distinctive effects on gene expression and AdoMet levels, and ultimately separate effects on the methyl cycle. Thus, this study provides insight into the mechanisms by which differential expression of the SAM genes have cellular consequences that affect genome instability.

Chromatin Modifiers Alter Recombination Between Divergent DNA Sequences

Recombination between divergent DNA sequences is actively prevented by heteroduplex rejection mechanisms. In baker's yeast, such antirecombination mechanisms can be initiated by the recognition of DNA mismatches in heteroduplex DNA by MSH proteins, followed by recruitment of the Sgs1-Top3-Rmi1 helicase-topoisomerase complex to unwind the recombination intermediate. We previously showed that the repair/rejection decision during single-strand annealing recombination is temporally regulated by MSH (MutShomolog) protein levels and by factors that excise nonhomologous single-stranded tails. These observations, coupled with recent studies indicating that mismatch repair (MMR) factors interact with components of the histone chaperone machinery, encouraged us to explore roles for epigenetic factors and chromatin conformation in regulating the decision to reject vs. repair recombination between divergent DNA substrates. This work involved the use of an inverted repeat recombination assay thought to measure sister chromatid repair during DNA replication. Our observations are consistent with the histone chaperones CAF-1 and Rtt106, and the histone deacetylase Sir2, acting to suppress heteroduplex rejection and the Rpd3, Hst3, and Hst4 deacetylases acting to promote heteroduplex rejection. These observations, and double-mutant analysis, have led to a model in which nucleosomes located at DNA lesions stabilize recombination intermediates and compete with MMR factors that mediate heteroduplex rejection.

rSalvador: An R Package for the Fluctuation Experiment

The past few years have seen a surge of novel applications of the Luria-Delbrück fluctuation assay protocol in bacterial research. Appropriate analysis of fluctuation assay data often requires computational methods that are unavailable in the popular web tool FALCOR. This paper introduces an R package named rSalvador to bring improvements to the field. The paper focuses on rSalvador’s capabilities to alleviate three kinds of problems found in recent investigations: (i) resorting to partial plating without properly accounting for the effects of partial plating; (ii) conducting attendant fitness assays without incorporating mutants’ relative fitness in subsequent data analysis; and (iii) comparing mutation rates using methods that are in general inapplicable to fluctuation assay data. In addition, the paper touches on rSalvador’s capabilities to estimate sample size and the difficulties related to parameter nonidentifiability.

Sample size determination for the fluctuation experiment

The Luria-Delbrück fluctuation experiment protocol is increasingly employed to determine microbial mutation rates in the laboratory. An important question raised at the planning stage is "How many cultures are needed?" For over 70 years sample sizes have been determined either by intuition or by following published examples where sample sizes were chosen intuitively. This paper proposes a practical method for determining the sample size. The proposed method relies on existing algorithms for computing the expected Fisher information under two commonly used mutant distributions. The role of partial plating in reducing sample size is discussed.

The Luria-Delbrück protocol is still the most practical

It is theoretically appealing to determine microbial mutation rates by counting mutant cells in two successive generations. However, major experimental difficulties have been largely ignored, causing unreliable estimates of mutation rates to be unwittingly accepted. Counting mutant cells twice in the same liquid culture incurs appreciable errors that are difficult to quantify; maintaining synchronous cell growth for 25 or more generations is an equally daunting laboratory feat.

A new practical guide to the Luria-Delbrück protocol

Since 2000 several review papers have been published about the analysis of experimental data obtained using the Luria-Delbrück protocol. These timely papers cleared much of the confusion surrounding various methods for estimating or comparing mutation rates. As a result, today the fluctuation test is more widely applied with much improved accuracy. The present paper provides guidelines on a few remaining problems that continue to baffle mutation researchers. Among the issues addressed are incomplete plating, relative fitness, and comparison of experiments where average final cell population sizes differ. It also offers a fresh view on the estimation methods that are based on the sample median.

bz-rates: A Web Tool to Estimate Mutation Rates from Fluctuation Analysis

Fluctuation analysis is the standard experimental method for measuring mutation rates in micro-organisms. The appearance of mutants is classically described by a Luria-Delbrück distribution composed of two parameters: the number of mutations per culture (m) and the differential growth rate between mutant and wild-type cells (b). A precise estimation of these two parameters is a prerequisite to the calculation of the mutation rate. Here, we developed bz-rates, a Web tool to calculate mutation rates that provides three useful advances over existing Web tools. First, it allows taking into account b, the differential growth rate between mutant and wild-type cells, in the estimation of m with the generating function. Second, bz-rates allows the user to take into account a deviation from the Luria-Delbrück distribution called z, the plating efficiency, in the estimation of m. Finally, the Web site provides a graphical visualization of the goodness-of-fit between the experimental data and the model. bz-rates is accessible at http://www.lcqb.upmc.fr/bzrates.

Volatility of Mutator Phenotypes at Single Cell Resolution

Mutator phenotypes accelerate the evolutionary process of neoplastic transformation. Historically, the measurement of mutation rates has relied on scoring the occurrence of rare mutations in target genes in large populations of cells. Averaging mutation rates over large cell populations assumes that new mutations arise at a constant rate during each cell division. If the mutation rate is not constant, an expanding mutator population may contain subclones with widely divergent rates of evolution. Here, we report mutation rate measurements of individual cell divisions of mutator yeast deficient in DNA polymerase ε proofreading and base-base mismatch repair. Our data are best fit by a model in which cells can assume one of two distinct mutator states, with mutation rates that differ by an order of magnitude. In error-prone cell divisions, mutations occurred on the same chromosome more frequently than expected by chance, often in DNA with similar predicted replication timing, consistent with a spatiotemporal dimension to the hypermutator state. Mapping of mutations onto predicted replicons revealed that mutations were enriched in the first half of the replicon as well as near termination zones. Taken together, our findings show that individual genome replication events exhibit an unexpected volatility that may deepen our understanding of the evolution of mutator-driven malignancies.

Mutations fuel microbial evolution and cancer. Cells with an increased rate of mutation are said to have a “mutator phenotype” and adapt more rapidly than non-mutator cells. Our study utilizes a novel way of measuring mutation rates of individual cell divisions to show that mutator cells can adopt one of two mutation rates that differ tenfold in magnitude. This mutator volatility suggests that the rates of mutation accumulation may vary widely within the same clone of mutator cells. Understanding how to modulate the mutator state may provide an avenue to treat certain cancers.

dNTP pool levels modulate mutator phenotypes of error-prone DNA polymerase ε variants

Mutator phenotypes create genetic diversity that fuels tumor evolution. DNA polymerase (Pol) ε mediates leading strand DNA replication. Proofreading defects in this enzyme drive a number of human malignancies. Here, using budding yeast, we show that mutator variants of Pol ε depend on damage uninducible (Dun)1, an S-phase checkpoint kinase that maintains dNTP levels during a normal cell cycle and up-regulates dNTP synthesis upon checkpoint activation. Deletion of DUN1 (dun1Δ) suppresses the mutator phenotype of pol2-4 (encoding Pol ε proofreading deficiency) and is synthetically lethal with pol2-M644G (encoding altered Pol ε base selectivity). Although pol2-4 cells cycle normally, pol2-M644G cells progress slowly through S-phase. The pol2-M644G cells tolerate deletions of mediator of the replication checkpoint (MRC) 1 (mrc1Δ) and radiation sensitive (Rad) 9 (rad9Δ), which encode mediators of checkpoint responses to replication stress and DNA damage, respectively. The pol2-M644G mutator phenotype is partially suppressed by mrc1Δ but not rad9Δ; neither deletion suppresses the pol2-4 mutator phenotype. Thus, checkpoint activation augments the Dun1 effect on replication fidelity but is not required for it. Deletions of genes encoding key Dun1 targets that negatively regulate dNTP synthesis, suppress the dun1Δ pol2-M644G synthetic lethality and restore the mutator phenotype of pol2-4 in dun1Δ cells. DUN1 pol2-M644G cells have constitutively high dNTP levels, consistent with checkpoint activation. In contrast, pol2-4 and POL2 cells have similar dNTP levels, which decline in the absence of Dun1 and rise in the absence of the negative regulators of dNTP synthesis. Thus, dNTP pool levels correlate with Pol ε mutator severity, suggesting that treatments targeting dNTP pools could modulate mutator phenotypes for therapy.

DNA replication error-induced extinction of diploid yeast

Genetic defects in DNA polymerase accuracy, proofreading, or mismatch repair (MMR) induce mutator phenotypes that accelerate adaptation of microbes and tumor cells. Certain combinations of mutator alleles synergistically increase mutation rates to levels that drive extinction of haploid cells. The maximum tolerated mutation rate of diploid cells is unknown. Here, we define the threshold for replication error-induced extinction (EEX) of diploid Saccharomyces cerevisiae. Double-mutant pol3 alleles that carry mutations for defective DNA polymerase-δ proofreading (pol3-01) and accuracy (pol3-L612M or pol3-L612G) induce strong mutator phenotypes in heterozygous diploids (POL3/pol3-01,L612M or POL3/pol3-01,L612G). Both pol3-01,L612M and pol3-01,L612G alleles are lethal in the homozygous state; cells with pol3-01,L612M divide up to 10 times before arresting at random stages in the cell cycle. Antimutator eex mutations in the pol3 alleles suppress this lethality (pol3-01,L612M,eex or pol3-01,L612G,eex). MMR defects synergize with pol3-01,L612M,eex and pol3-01,L612G,eex alleles, increasing mutation rates and impairing growth. Conversely, inactivation of the Dun1 S-phase checkpoint kinase suppresses strong pol3-01,L612M,eex and pol3-01,L612G,eex mutator phenotypes as well as the lethal pol3-01,L612M phenotype. Our results reveal that the lethal error threshold in diploids is 10 times higher than in haploids and likely determined by homozygous inactivation of essential genes. Pronounced loss of fitness occurs at mutation rates well below the lethal threshold, suggesting that mutator-driven cancers may be susceptible to drugs that exacerbate replication errors.

Decoding cell lineage from acquired mutations using arbitrary deep sequencing

Because mutations are inevitable, the genome of each cell in a multicellular organism becomes unique and therefore encodes a record of its ancestry. Here we coupled arbitrary single primer PCR with next-generation DNA sequencing to catalog mutations and deconvolve the phylogeny of cultured mouse cells. This study helps pave the way toward construction of retrospective cell-fate maps based on mutations accumulating in genomes of somatic cells.

A Bayesian approach for correcting for partial plating in fluctuation experiments

The fluctuation experiment is the preferred method for estimating microbial mutation rates. A difficult task facing the data analyst is to infer the mean number of mutations from the number of mutant cells that only indirectly reflects the number of mutations. Partial plating, commonly practised in the laboratory, renders this task even more challenging by allowing only a portion of the mutant cells to be counted. In this paper, we propose a Bayesian approach to correcting for partial plating in the analysis of fluctuation experiments.