Mutation and selection in bacterial populations: alternatives to the hypothesis of directed mutation

Mutation and Selection in Bacteria: Modelling and Calibration

Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be explained by this model. The selection–mutation model has unobservable fitness parameters, and, to estimate them, we use an Approximate Bayesian Computation algorithm. The algorithms are illustrated using in vitro data for phase variable genes of Campylobacter jejuni.

Evolutionary scalpels for dissecting tumor ecosystems

Amidst the growing literature on cancer genomics and intratumor heterogeneity, essential principles in evolutionary biology recur time and time again. Here we use these principles to guide the reader through major advances in cancer research, highlighting issues of "hit hard, hit early" treatment strategies, drug resistance, and metastasis. We distinguish between two frameworks for understanding heterogeneous tumors, both of which can inform treatment strategies: (1) The tumor as diverse ecosystem, a Darwinian population of sometimes-competing, sometimes-cooperating cells; (2) The tumor as tightly integrated, self-regulating organ, which may hijack developmental signals to restore functional heterogeneity after treatment. While the first framework dominates literature on cancer evolution, the second framework enjoys support as well. Throughout this review, we illustrate how mathematical models inform understanding of tumor progression and treatment outcomes. Connecting models to genomic data faces computational and technical hurdles, but high-throughput single-cell technologies show promise to clear these hurdles. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.

Rates and mechanisms of bacterial mutagenesis from maximum-depth sequencing

In 1943, Luria and Delbrück used a phage resistance assay to establish spontaneous mutation as a driving force of microbial diversity¹. Mutation rates are still studied using such assays, but these can only examine the small minority of mutations conferring survival in a particular condition. Newer approaches, such as long-term evolution followed by whole-genome sequencing ^{2, 3}, may be skewed by mutational “hot” or “cold” spots ^{3, 4}. Both approaches are affected by numerous caveats ^{5, 6, 7} (see Supplemental Information). We devise a method, Maximum-Depth Sequencing (MDS), to detect extremely rare variants in a population of cells through error-corrected, high-throughput sequencing. We directly measure locus-specific mutation rates in E. coli and show that they vary across the genome by at least an order of magnitude. Our data suggest that certain types of nucleotide misincorporation occur 10⁴-fold more frequently than the basal rate of mutations, but are repaired in vivo. Our data also suggest specific mechanisms of antibiotic-induced mutagenesis, including downregulation of mismatch repair via oxidative stress; transcription-replication conflicts; and in the case of fluoroquinolones, direct damage to DNA.

Scaling solution in the large population limit of the general asymmetric stochastic Luria-Delbrück evolution process

One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size N is large and mutation rates are low, but not necessarily small compared to 1/N. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy α-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in shortened form [11].

Fitness of Outbreak and Environmental Strains of Escherichia coli O157:H7 in Aerosolizable Soil and Association of Clonal Variation in Stress Gene Regulation

Airborne dust from feedlots is a potential mechanism of contamination of nearby vegetable crops with Escherichia coli O157:H7 (EcO157). We compared the fitness of clinical and environmental strains of EcO157 in <45 µm soil from a spinach farm. Differences in survival were observed among the 35 strains with D-values (days for 90% decreases) ranging from 1–12 days. Strains that survived longer, generally, were from environmental sources and lacked expression of curli, a protein associated with attachment and virulence. Furthermore, the proportion of curli-positive (C⁺) variants of EcO157 strains decreased with repeated soil exposure and the strains that were curli-negative (C⁻) remained C⁻ post-soil exposure. Soil exposure altered expression of stress-response genes linked to fitness of EcO157, but significant clonal variation in expression was measured. Mutations were detected in the stress-related sigma factor, rpoS, with a greater percentage occurring in parental strains of clinical origin prior to soil exposure. We speculate that these mutations in rpoS may confer a differential expression of genes, associated with mechanisms of survival and/or virulence, and thus may influence the fitness of EcO157.

Large population solution of the stochastic Luria-Delbruck evolution model

Luria and Delbrück introduced a very useful and subsequently widely adopted framework for quantitatively understanding the emergence of new cellular lineages. Here, we provide an analytical treatment of the fully stochastic version of the model, enabled by the fact that population sizes at the time of measurement are invariably very large and mutation rates are low. We show that the Lea-Coulson generating function describes the "inner solution," where the number of mutants is much smaller than the total population. We find that the corresponding distribution function interpolates between a monotonic decrease at relatively small populations, (compared with the inverse of the mutation probability), whereas it goes over to a Lévy α-stable distribution in the very large population limit. The moments are completely determined by the outer solution, and so are devoid of practical significance. The key to our solution is focusing on the fixed population size ensemble, which we show is very different from the fixed time ensemble due to the extreme variability in the evolutionary process.

Viability of Escherichia coli ATCC 8739 in Nutrient Broth, Luria-Bertani Broth and Brain Heart Infusion over 11 Weeks

Background:

Escherichia coli is a widely studied prokaryotic system. A recent study had demonstrated that reduced growth of E. coli after extended culture in Luria-Bertani broth is a result of depletion of fermentable sugars but able to sustain extended cell culture due to the presence of amino acids, which can be utilized as a carbon source. However, this had not been demonstrated in other media. The study aimed to determine the growth and viability of E. coli ATCC 8739 in 3 different media, Nutrient Broth (NB), Brain Heart Infusion (BHI) and Luria-Bertani Broth (LB) over 11 weeks.

Methods:

Growth of E. coli ATCC 8739 was determined by optical density. Viability was determined by serial dilution/spread-plate enumeration. After 11 weeks, the media were exhausted by repeated culture. Glucose was added to the exhausted media to determine whether glucose is the growth-limiting factor.

Results:

Our results showed that cell density in all 3 media increased to about 1 × 10⁹ cells/ml by the end of week 1, from the inoculation density of 2.67 × 10⁵ cells/ml, peaked at about 1 × 10¹³ cells/ml at week 4, before declining to about 5 × 10⁷ cells/ml at week 7. Cell density is highly correlated to genomic DNA content (r² = 0.93) but poorly correlated to optical density (r²< 0.2). Our results also showed that the spent media were able to support further growth after glucose-supplementation.

Conclusion:

NB, LB and BHI are able to support extended periods of culture and glucose depletion is the likely reason for declining cell growth.

Dormancy in Stationary-Phase Cultures of Micrococcus luteus: Flow Cytometric Analysis of Starvation and Resuscitation

Cultures of the copiotrophic bacterium Micrococcus luteus were stored in spent growth medium for an extended period of time following batch culture. After an initial decrease, the total cell counts remained constant at approximately 60 to 70% of the counts at the beginning of storage. The level of viability, as judged by plate counts, decreased to less than 0.05%, while respiration and the ability to accumulate the lipophilic cation rhodamine 123 decreased to undetectable levels. However, using penicillin pretreatment (to remove viable cells) and flow cytometry and by monitoring both the total and viable counts, we found that at least 50% of the cells in populations of 75-day-old cultures were not dead but were dormant. Resuscitation in liquid medium was accompanied by the appearance of a population of larger cells, which could accumulate rhodamine 123 and reduce the dye 5-cyano-2,3-ditolyl tetrazolium chloride to a fluorescent formazan, while a similar fraction of the population was converted to colony-forming, viable cells. We surmise that dormancy may be far more common than death in starving microbial cultures.

Stress-induced mutagenesis in bacteria

Bacteria spend their lives buffeted by changing environmental conditions. To adapt to and survive these stresses, bacteria have global response systems that result in sweeping changes in gene expression and cellular metabolism. These responses are controlled by master regulators, which include: alternative sigma factors, such as RpoS and RpoH; small molecule effectors, such as ppGpp; gene repressors such as LexA; and, inorganic molecules, such as polyphosphate. The response pathways extensively overlap and are induced to various extents by the same environmental stresses. These stresses include nutritional deprivation, DNA damage, temperature shift, and exposure to antibiotics. All of these global stress responses include functions that can increase genetic variability. In particular, up-regulation and activation of error-prone DNA polymerases, down-regulation of error-correcting enzymes, and movement of mobile genetic elements are common features of several stress responses. The result is that under a variety of stressful conditions, bacteria are induced for genetic change. This transient mutator state may be important for adaptive evolution.

Amplification of lac cannot account for adaptive mutation to Lac+ in Escherichia coli

When the Lac- strain of Escherichia coli, FC40, is incubated with lactose as its sole carbon and energy source, Lac+ revertants arise at a constant rate, a phenomenon known as adaptive mutation. Two alternative models for adaptive mutation have been proposed: (i) recombination-dependent mutation, which specifies that recombination occurring in nongrowing cells stimulates error-prone DNA synthesis, and (ii) amplification-dependent mutation, which specifies that amplification of the lac region and growth of the amplifying cells creates enough DNA replication to produce mutations at the normal rate. Here, we examined several of the predictions of the amplification-dependent mutation model and found that they are not fulfilled. First, inhibition of adaptive mutation by a gene that is toxic when overexpressed does not depend on the proximity of the gene to lac. Second, mutation at a second locus during selection for Lac+ revertants is also independent of the proximity of the locus to lac. Third, mutation at a second locus on the episome occurs even when the lac allele under selection is on the chromosome. Our results support the hypothesis that most Lac+ mutants that appear during lactose selection are true revertants that arise in a single step from Lac- cells, not from a population of growing or amplifying precursor cells.

New algorithms for Luria-Delbrück fluctuation analysis

Fluctuation analysis is the most widely used approach in estimating microbial mutation rates. Development of methods for point and interval estimation of mutation rates has long been hampered by lack of closed form expressions for the probability mass function of the number of mutants in a parallel culture. This paper uses sequence convolution to derive exact algorithms for computing the score function and observed Fisher information, leading to efficient computation of maximum likelihood estimates and profile likelihood based confidence intervals for the expected number of mutations occurring in a test tube. These algorithms and their implementation in SALVADOR 2.0 facilitate routine use of modern statistical techniques in fluctuation analysis by biologists engaged in mutation research.

Distinct signatures for mutator sensitivity of lacZ reversions and for the spectrum of lacI/lacO forward mutations on the chromosome of nondividing Escherichia coli

A conditional lethal galE(Ts)-based strategy was employed in Escherichia coli, first to eliminate all growth-associated chromosomal reversions in lacZ or forward mutations in lacI/lacO by incubation at the restrictive temperature and subsequently to recover (as papillae) spontaneous mutations that had arisen in the population of nondividing cells after shift to the permissive temperature. Data from lacZ reversion studies in mutator strains indicated that the products of all genes for mismatch repair (mutHLS, dam, uvrD), of some for oxidative damage repair (mutMT), and of that for polymerase proofreading (dnaQ) are required in dividing cells; some others for oxidative damage repair (mutY, nth nei) are required in both dividing and nondividing cells; and those for alkylation damage repair (ada ogt) are required in nondividing cells. The spectrum of lacI/lacO mutations in nondividing cells was distinguished both by lower frequencies of deletions and IS1 insertions and by the unique occurrence of GC-to-AT transitions at lacO +5. In the second approach to study mutations that had occurred in nondividing cells, lacI/lacO mutants were selected as late-arising papillae from the lawn of a galE+ strain; once again, transitions at lacO +5 were detected among the mutants that had been obtained from populations initially grown on poor carbon sources such as acetate, palmitate, or succinate. Our results indicate that the lacO +5 site is mutable only in nondividing cells, one possible mechanism for which might be that random endogenous alkylation (or oxidative) damage to DNA in these cells is efficiently corrected by the Ada Ogt (or Nth Nei) repair enzymes at most sites but not at lacO +5. Furthermore, the late-arising papillae from the second approach were composed almost exclusively of dominant lacI/lacO mutants. This finding lends support to "instantaneous gratification" models in which a spontaneous lesion, occurring at a random site in DNA of a nondividing cell, is most likely to be fixed as a mutation if it allows the cell to immediately exit the nondividing state.

The amplification model for adaptive mutation: simulations and analysis

It has been proposed that the lac revertants arising under selective conditions in the Cairns experiment do not arise by stress-induced mutagenesis of stationary phase cells as has been previously assumed. Instead, these revertants may arise within growing clones initiated by cells with a preexisting duplication of the weakly functional lac allele used in this experiment. It is proposed that spontaneous stepwise increases in lac copy number (amplification) allow a progressive improvement in growth. Reversion is made more likely primarily by the resultant increase in the number of mutational targets--more cells with more lac copies. The gene amplification model requires no stress-induced variation in the rate or target specificity of mutation and thus does not violate neo-Darwinian theory. However, it does require that a multistep process of amplification, reversion, and amplification segregation be completed within approximately 20 generations of growth. This work examines the proposed amplification model from a theoretical point of view, formalizing it into a mathematical framework and using this to determine what would be required for the process to occur within the specified period. The analysis assumes no stress-induced change in mutation rate and describes only the growth improvement occurring during the process of amplification and subsequent elimination of excess mutant lac copies. The dynamics of the system are described using Monte Carlo simulations and numerical integration of the deterministic equations governing the system. The results imply that the amplification model can account for the behavior of the system using biologically reasonable parameter values and thus can, in principle, explain Cairnsian adaptive mutation.

Catastrophe and what to do about it if you are a bacterium: the importance of frameshift mutants

Key problems that bacteria have historically faced are the challenges of the lack of essential nutrients and the presence of antibiotics produced naturally, but there are many other challenges. It appears that for many of these challenges the bacteria have mechanisms encoded in their genomes that are not usually functioning, but may be "turned on" when needed, even if the need only occurs once in hundreds of thousands of generations. Such mechanisms at other times somehow need to be "turned off" because they may cause a slight disadvantage, or even a grave disadvantage to the cell compared with wild-type cells during the time the population is not being challenged. On the other hand, a gene cannot simply be discarded because it might be needed again. How do microorganisms solve the problem of responding to challenges that only occur rarely? I suggest that in most cases, the mutation must occur by the existence of a readily reversible mutation. The mutation in likely the result of a frameshift mutation that caused the response and later another frameshift occurs to return the genome to its original state.

Distinct Signatures for Mutator Sensitivity of lacZ Reversions and for the Spectrum of lacI/lacO Forward Mutations on the Chromosome of Nondividing Escherichia coli

A conditional lethal galE(Ts)-based strategy was employed in Escherichia coli, first to eliminate all growth-associated chromosomal reversions in lacZ or forward mutations in lacI/lacO by incubation at the restrictive temperature and subsequently to recover (as papillae) spontaneous mutations that had arisen in the population of nondividing cells after shift to the permissive temperature. Data from lacZ reversion studies in mutator strains indicated that the products of all genes for mismatch repair (mutHLS, dam, uvrD), of some for oxidative damage repair (mutMT), and of that for polymerase proofreading (dnaQ) are required in dividing cells; some others for oxidative damage repair (mutY, nth nei) are required in both dividing and nondividing cells; and those for alkylation damage repair (ada ogt) are required in nondividing cells. The spectrum of lacI/lacO mutations in nondividing cells was distinguished both by lower frequencies of deletions and IS1 insertions and by the unique occurrence of GC-to-AT transitions at lacO +5. In the second approach to study mutations that had occurred in nondividing cells, lacI/lacO mutants were selected as late-arising papillae from the lawn of a galE+ strain; once again, transitions at lacO +5 were detected among the mutants that had been obtained from populations initially grown on poor carbon sources such as acetate, palmitate, or succinate. Our results indicate that the lacO +5 site is mutable only in nondividing cells, one possible mechanism for which might be that random endogenous alkylation (or oxidative) damage to DNA in these cells is efficiently corrected by the Ada Ogt (or Nth Nei) repair enzymes at most sites but not at lacO +5. Furthermore, the late-arising papillae from the second approach were composed almost exclusively of dominant lacI/lacO mutants. This finding lends support to “instantaneous gratification” models in which a spontaneous lesion, occurring at a random site in DNA of a nondividing cell, is most likely to be fixed as a mutation if it allows the cell to immediately exit the nondividing state.

Adaptive mutation: general mutagenesis is not a programmed response to stress but results from rare coamplification of dinB with lac

In a particular genetic system, selection stimulates reversion of a lac mutation and causes genome-wide mutagenesis (adaptive mutation). Selection allows rare plated cells with a duplication of the leaky lac allele to initiate clones within which further lac amplification improves growth rate. Growth and amplification add mutational targets to each clone and thereby increase the likelihood of reversion. We suggest that general mutagenesis occurs only in clones whose lac amplification includes the nearby dinB+ gene (for error-prone DNA polymerase IV). Thus mutagenesis is not a programmed response to stress but a side effect of amplification in a few clones; it is not central to the effect of selection on reversion.

Mathematical issues arising from the directed mutation controversy

During the past 14 years or so a large body of new evidence that supposedly supports the directed mutation hypothesis has accumulated. Interpretation of some of the evidence depends on mathematical reasoning, which can be subtler than it appears at first sight. This article attempts to clarify some of the mathematical issues arising from the directed mutation controversy, thereby offering alternative interpretations of some of the evidence.

Regulating general mutation rates: examination of the hypermutable state model for Cairnsian adaptive mutation

In the lac adaptive mutation system of Cairns, selected mutant colonies but not unselected mutant types appear to arise from a nongrowing population of Escherichia coli. The general mutagenesis suffered by the selected mutants has been interpreted as support for the idea that E. coli possesses an evolved (and therefore beneficial) mechanism that increases the mutation rate in response to stress (the hypermutable state model, HSM). This mechanism is proposed to allow faster genetic adaptation to stressful conditions and to explain why mutations appear directed to useful sites. Analysis of the HSM reveals that it requires implausibly intense mutagenesis (10(5) times the unselected rate) and even then cannot account for the behavior of the Cairns system. The assumptions of the HSM predict that selected revertants will carry an average of eight deleterious null mutations and thus seem unlikely to be successful in long-term evolution. The experimentally observed 35-fold increase in the level of general mutagenesis cannot account for even one Lac(+) revertant from a mutagenized subpopulation of 10(5) cells (the number proposed to enter the hypermutable state). We conclude that temporary general mutagenesis during stress is unlikely to provide a long-term selective advantage in this or any similar genetic system.

Statistical and algorithmic methods for fluctuation analysis with SALVADOR as an implementation

This paper aims at removing certain long-standing impediments to more effective and widespread use of fluctuation analysis. The paper presents a method of constructing confidence intervals for mutation rates using data from fluctuation experiments. The method was inspired by a rediscovery of a little-known, not fully developed method of Lea and Coulson; substantial modifications have been made both to enhance computational efficiency and to widen the scope of the original method's applicability. A computer package named SALVADOR is presented that can be used for Monte Carlo simulation, for point and interval estimation of mutation rates, and for exploration of various hypotheses spawned by the directed mutation controversy. In addition to the maximum likelihood method, methods of considerable historical interest are also examined and included in SALVADOR to help the reader compare and assess some of the most popular methods for estimating mutation rates.

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

The Luria-Delbrück mutation model has been mathematically formulated in a number of ways. This review article examines four most important formulations, focusing on important practical issues closely linked with the distribution of the number of mutants. These issues include the probability generating functions, moments (cumulants), computational methods and asymptotics. This review emphasizes basic principles which not only help to unify existing results but also allow for a few useful extensions. In addition, the review offers a historical perspective and some new explanations of divergent moments.

The physiological contribution of Acinetobacter PcaK, a transport system that acts upon protocatechuate, can be masked by the overlapping specificity of VanK

VanK is the fourth member of the ubiquitous major facilitator superfamily of transport proteins to be identified that, together with PcaK, BenK, and MucK, contributes to aromatic catabolism in Acinetobacter sp. strain ADP1. VanK and PcaK have overlapping specificity for p-hydroxybenzoate and, most clearly, for protocatechuate: inactivation of both proteins severely impairs growth with protocatechuate, and the activity of either protein alone can mask the phenotype associated with inactivation of its homolog. Furthermore, vanK pcaK double-knockout mutants appear completely unable to grow in liquid culture with the hydroaromatic compound quinate, although such cells on plates convert quinate to protocatechuate, which then accumulates extracellularly and is readily visible as purple staining. This provides genetic evidence that quinate is converted to protocatechuate in the periplasm and is in line with the early argument that quinate catabolism should be physically separated from aromatic amino acid biosynthesis in the cytoplasm so as to avoid potential competition for intermediates common to both pathways. Previous studies of aromatic catabolism in Acinetobacter have taken advantage of the ability to select directly strains that contain a spontaneous mutation blocking the beta-ketoadipate pathway and preventing the toxic accumulation of carboxymuconate. By using this procedure, strains with a mutation in structural or regulatory genes blocking degradation of vanillate, p-hydroxybenzoate, or protocatechuate were selected. In this study, the overlapping specificity of the VanK and PcaK permeases was exploited to directly select strains with a mutation in either vanK or pcaK. Spontaneous mutations identified in vanK include a hot spot for frameshift mutation due to contraction of a G6 mononucleotide repeat as well as point mutations producing amino acid substitutions useful for analysis of VanK structure and function. Preliminary second-site suppression analysis using transformation-facilitated PCR mutagenesis in one VanK mutant gave results similar to those using LacY, the prototypic member of the major facilitator superfamily, consistent with the two proteins having a similar mechanism of action. The selection for transport mutants described here for Acinetobacter may also be applicable to Pseudomonas putida, where the PcaK permease has an additional role in chemotaxis.

Adaptive mutation: a general phenomenon or special case?

A recent article by Galitski and Roth characterizes adaptive reversion of chromosomal lac- mutations in Salmonella typhimurium LT2. Using a classical genetic approach they show that adaptive reversion, as characterized by the appearance of late revertant colonies, is an exception rather than a general phenomenon for reversion of nonsense, missense, frameshift and insertion mutations. For certain mutations, however, the number of late revertants exceeds the predicted number. These excess revertants suggest that adaptive mutability is applicable to chromosomal genes as well as to genetic changes involving F plasmids and lysogenic phages.

A search for a general phenomenon of adaptive mutability

The most prominent systems for the study of adaptive mutability depend on the specialized activities of genetic elements like bacteriophage Mu and the F plasmid. Searching for general adaptive mutability, we have investigated the behavior of Salmonella typhimurium strains with chromosomal lacZ mutations. We have studied 30 revertible nonsense, missense, frameshift, and insertion alleles. One-third of the mutants produced > or = 10 late revertant colonies (appearing three to seven days after plating on selective medium). For the prolific mutants, the number of late revertants showed rank correlation with the residual beta-galactosidase activity; for the same mutants, revertant number showed no correlation with the nonselective reversion rate (from fluctuation tests). Leaky mutants, which grew slowly on selective medium, produced late revertants whereas tight nongrowing mutants generally did not produce late revertants. However, the number of late revertants was not proportional to residual growth. Using total residual growth and the nonselective reversion rate, the expected number of late revertants was calculated. For several leaky mutants, the observed revertant number exceeded the expected number. We suggest that excess late revertants from these mutants arise from general adaptive mutability available to any chromosomal gene.

Evolutionary consequences of mutation and selection within an individual

Whether in sexual or asexual organisms, selection among cell lineages during development is an effective way of eliminating deleterious mutations. Using a mathematical analysis, we find that relatively small differences in cell replication rates during development can translate into large differences in the proportion of mutant cells within the adult, especially when development involves a large number of cell divisions. Consequently, intraorganismal selection can substantially reduce the deleterious mutation rate observed among offspring as well as the mutation load within a population, because cells rather than individuals provide the selective "deaths" necessary to stem the tide of deleterious mutations. The reduction in mutation rate among offspring is more pronounced in organisms with plastic development than in those with structured development. It is also more pronounced in asexual organisms that produce multicellular rather than unicellular offspring. By effecting the mutation rate, intraorganismal selection may have broad evolutionary implications; as an example, we consider its influence on the evolution of ploidy levels, finding that cell-lineage selection is more effective in haploids and tends to favor their evolution.

The effect of adaptive mutagenesis on genetic variation at a linked, neutral locus

Based on recent studies in single-celled organisms, it has been argued that a fitness benefit associated with a mutation will increase the probability of that mutation occurring. This increase is independent of mutation rates at other loci and is called adaptive mutagenesis. We modeled the effect of adaptive mutagenesis on populations of haploid organisms with adaptive mutation rates ranging from 0 to 1 x 10(-5). Allele frequencies at the selected locus and a neutral linked locus were tracked. We also observed the amount of linkage disequilibrium during the selective sweep and the final heterozygosity after the sweep. The presence of adaptive mutagenesis increases the number of genetic backgrounds carrying the new fitter allele, making the outcomes more representative of the population before the selection. Therefore, more neutral genetic variation is preserved in simulations with adaptive mutagenesis than in those without it due to hitchhiking. Since adaptive mutagenesis is time-dependent, it can generate mutants when other mechanisms of mutation cannot. In addition, adaptive mutagenesis has the potential to confound both phylogeny construction and the detection of natural selection from patterns of nucleotide variation.

Multiple trait analysis of genetic mapping for quantitative trait loci

We present in this paper models and statistical methods for performing multiple trait analysis on mapping quantitative trait loci (QTL) based on the composite interval mapping method. By taking into account the correlated structure of multiple traits, this joint analysis has several advantages, compared with separate analyses, for mapping QTL, including the expected improvement on the statistical power of the test for QTL and on the precision of parameter estimation. Also this joint analysis provides formal procedures to test a number of biologically interesting hypotheses concerning the nature of genetic correlations between different traits. Among the testing procedures considered are those for joint mapping, pleiotropy, QTL by environment interaction, and pleiotropy vs. close linkage. The test of pleiotropy (one pleiotropic QTL at a genome position) vs. close linkage (multiple nearby nonpleiotropic QTL) can have important implications for our understanding of the nature of genetic correlations between different traits in certain regions of a genome and also for practical applications in animal and plant breeding because one of the major goals in breeding is to break unfavorable linkage. Results of extensive simulation studies are presented to illustrate various properties of the analyses.

Evidence that F plasmid transfer replication underlies apparent adaptive mutation

An Escherichia coli K12 strain, FC40, has been used extensively in the analysis of adaptive mutability. This strain carries a revertible mutant lac allele on an F plasmid and accumulates Lac+ (lactose utilizing) revertants, but not unselected mutants, when placed on selective medium. These adaptive mutations are a subset of spontaneous types and their formation depends on the RecABC functions. Data presented here suggest that this phenomenon depends on transfer functions of the F factor. Fertility inhibition eliminates RecA-dependent adaptive reversion. Thus, "adaptive" revertants may form during replication from the transfer origin, whereas loci in the nonreplicating chromosome show little mutation.

Population dynamics of a Lac- strain of Escherichia coli during selection for lactose utilization

During selection for lactose utilization, Lac+ revertants of FC40, a Lac- strain of Escherichia coli, appear at a high rate. Yet, no Lac+ revertants appear in the absence of lactose, or in its presence if the cells have another, unfulfilled requirement for growth. This study investigates more fully the population dynamics of FC40 when incubated in the absence of a carbon source or when undergoing selection for lactose utilization. In the absence of a carbon source, the viable cell numbers do not change over 6 days. When incubated in liquid lactose medium, Lac- cells do not undergo any measurable increase in numbers or in turbidity for at least 2 days. When FC40 is plated on lactose minimum medium in the presence of scavenger cells, the upper limit to the amount of growth of Lac- cells during 5 days is one doubling, and there is no evidence for turnover (i.e., a balance between growth and death). The presence of a minority population that could form microcolonies was not detected. The implications of these results, plus the fact that the appearance of Lac+ revertants during lactose selection is nearly constant with time, are discussed in reference to several models that have been postulated to account for adaptive mutations.

Poisson-like fluctuation patterns of revertants of leucine auxotrophy (leu-500) in Salmonella typhimurium caused by delay in mutant cell division

Leu+ mutants from Salmonella typhimurium leu-500 strain MA412 arise at high frequencies and mutant colonies appear over a broad range of time on selective plates. This observation suggested that these Leu+ mutants might be induced or "directed."= If such a mechanism was responsible, mutants should originate on selective plates rather than in the preceding culture in nonselective conditions and should give rise to Poisson-like fluctuation curves upon plating of sister cultures on selective medium. Poisson-like distribution profiles were indeed observed for Leu+ mutants of S. typhimurium MA412. However, an explanation for the observed Poisson-like fluctuation patterns without a need for selection-induced mutations was found. Microscopical analysis and cell mass/viable count measurements showed that the size of Leu+ mutant cells was often much larger than those of nonmutants. This size difference was a stable characteristic of a large proportion of Leu+ mutants, was observed both in stationary and growing culture and did not measurably affect the division rates of the cells in nutrient broth. As the transition from normal-sized nonmutant to oversized mutant cells during the nonselective culture phase of the fluctuation experiment may have been accompanied by a period with no or few completed cell division cycles, the number of mutant offspring may have been smaller than that of sibling nonmutants. Such underrepresentation of mutants in the final culture is expected to give rise to Poisson-like fluctuation patterns without invoking "directed" mutations.

Time-dependent mitotic recombination in Saccharomyces cerevisiae

The time-dependent appearance of prototrophic recombinants between heterologously located artificial repeats has been studied in Saccharomyces cerevisiae. While initial prototrophic colony numbers from independent cultures were highly variable, additional recombinants were found to arise daily at roughly constant rates irrespective of culture. These late-appearing recombinants could be accounted for neither by detectable growth on the selective media nor by delayed appearance of recombinants present at the time of selective plating. Significantly, at no time did the distributions of recombinants fully match those expected according to the Luria-Delbruck model and, in fact, after the first day, the distributions much more closely approximated a Poisson distribution. Prototrophic recombinants accumulated not only on the relevant selective medium, but also on media unrelated to the acquired prototrophy.

The directed mutation controversy and neo-Darwinism

According to neo-Darwinian theory, random mutation produces genetic differences among organisms whereas natural selection tends to increase the frequency of advantageous alleles. However, several recent papers claim that certain mutations in bacteria and yeast occur at much higher rates specifically when the mutant phenotypes are advantageous. Various molecular models have been proposed that might explain these directed mutations, but the models have not been confirmed. Critics contend that studies purporting to demonstrate directed mutation lack certain controls and fail to account adequately for population dynamics. Further experiments that address these criticisms do not support the existence of directed mutations.

Adaptive mutation: the uses of adversity

When populations of microorganisms are subjected to certain nonlethal selections, useful mutants arise among the nongrowing cells whereas useless mutants do not. This phenomenon, known as adaptive, directed, or selection-induced mutation, challenges the long-held belief that mutations only arise at random and without regard for utility. In recent years a growing number of studies have examined adaptive mutation in both bacteria and yeast. Although conflicts and controversies remain, the weight of the evidence indicates that adaptive mutation cannot be explained by trivial artifacts and that nondividing cells accumulate mutations in the absence of genomic replication. Because this process tends to produce only useful mutations, the cells appear to have a mechanism for preventing useless genetic changes from occurring or for eliminating them after they occur. The model that most readily explains the evidence is that cells under stress produce genetic variants continuously and at random, but these variants are immortalized as mutations only if they allow the cell to grow.

An examination of adaptive reversion in Saccharomyces cerevisiae

Reversion to Lys+ prototrophy in a haploid yeast strain containing a defined lys2 frameshift mutation has been examined. When cells were plated on synthetic complete medium lacking only lysine, the numbers of Lys+ revertant colonies accumulated in a time-dependent manner in the absence of any detectable increase in cell number. An examination of the distribution of the numbers of early appearing Lys+ colonies from independent cultures suggests that the mutations to prototrophy occurred randomly during nonselective growth. In contrast, an examination of the distribution of late appearing Lys+ colonies indicates that the underlying reversion events occurred after selective plating. No accumulation of Lys+ revertants occurred when cells were starved for tryptophan, leucine or both lysine and tryptophan prior to plating selectively for Lys+ revertants. These results indicate that mutations accumulate more frequently when they confer a selective advantage, and are thus consistent with the occurrence of adaptive mutations in yeast.

Selection-induced mutations occur in yeast

Selection-induced mutations are nonrandom mutations that occur as specific and direct responses to environmental challenges and primarily in nondividing cells under conditions of intense prolonged selection. Selection-induced mutations have been shown to occur at six loci in Escherichia coli, but their existence has not previously been demonstrated in any eukaryotic organism. Here it is shown that selection-induced mutations occur at the HIS4 locus in the eukaryotic microorganism Saccharomyces cerevisiae.

Experimental evidence for an alternative to directed mutation in the bgl operon

The directed mutation hypothesis suggests that some mutations occur more often when selectively advantageous than when neutral or disadvantageous, challenging the principle that the selective value of a mutation does not affect the rate of its occurrence. Mutations in the bgl operon of Escherichia coli have been reported to be a case of directed mutation. E. coli K12 strains chi342LD cannot grow on salicin but derivatives with two mutations in the bgl operon, an excision of IS150 (formally called IS103) from bglF and a point mutation or insertion in bflR, grow rapidly on this sugar. When chi342LD is grown on a medium containing salicin, bglF excision mutants accumulate to a frequency of greater than 1%, even though these mutants are reportedly unable to grown on salicin, and Sal+ double mutants subsequently attain a high frequency. Comparable accumulations of excision mutants and Sal+ double mutants are not observed in the absence of salicin. As salicin is not mutagenic, it has been suggested that excision mutations in bglF might serve only to create the potential for a secondary selectively advantageous mutation. We show here, however, that these double mutants can be accounted for by spontaneous mutation to intermediate genotypes in non-growing populations, coupled with slow growth of some of these intermediates on salicin, which enables their populations to reach a size where secondary mutations allowing rapid growth on salicin become common.

Role of plasmid multimers in mutation to tetracycline resistance

As an additional system for analysing mutations that appear to be specifically induced or directed, we have used a plasmid that contains the mnt repressor gene inserted as an operon fusion with the tet gene of the plasmid pBR322. Thus, the mnt gene product acts as a negative transcriptional regulator of tet gene expression. Mutations inactivating the Mnt repressor are recessive while those destroying operator recognition (Oc) are dominant in conferring tetracycline resistance on the host. When resistance mutations were isolated on plates with high levels of tetracycline they were preferentially mnt- and the plasmids were monomers. Pre-exposure to low concentrations increased the frequency of resistant mutants by 100- to 1000-fold, and the mutations were now mostly Oc, located on one unit of a plasmid multimer. Recessive repressor mutations on one unit would not have been selected. We suggest that the high frequency of mutation in tandem multimeric plasmids may be caused by the formation of single-stranded and hence highly mutable regions by homologous pairing out of register. The role of tetracycline in promoting mutations is discussed.

Properties of plasmids responsible for production of extended-spectrum beta-lactamases

The extended-spectrum beta-lactamases are believed to arise by mutations which alter the configuration around the active site of TEM- and SHV-type enzymes so as to increase their efficiency with otherwise nonhydrolyzable cephalosporins and monobactams. This hypothesis predicts that the genes for these new enzymes should be found on the same wide variety of plasmids that encode TEM-1, TEM-2, and SHV-1 beta-lactamases and that at least some of them should be mediated by transposons. Fifteen plasmids, each encoding an extended-spectrum beta-lactamase, were examined. Unlike the average TEM plasmid, all were large, ranging in size from 80 to 300 kb. All determined resistance to multiple antimicrobial agents, ranging from 5 to 11, and some conferred resistance to heavy metals and UV radiation as well. The plasmids belonged to a limited number of incompatibility (Inc) groups, including IncC, IncFI, IncHI2, and IncM. Because most of the mutations giving rise to extended-spectrum activity are G.C----A.T transitions and some of the mutant genes have as many as four base substitutions, a plasmid-determined mutator gene was searched for, but no such property was found. Several techniques were used to detect transposition of the extended-spectrum beta-lactamase genes, but a mobile genetic element could not be demonstrated even though eight of the plasmids hybridized with a DNA probe derived from the tnpR gene of Tn3. The genesis of extended-spectrum beta-lactamases may not be as simple as has been supposed.

Spontaneous point mutations that occur more often when advantageous than when neutral

Recent reports have called into question the widespread belief "that mutations arise continuously and without any consideration for their utility" (in the words of J. Cairns) and have suggested that some mutations (which Cairns called "directed" mutations) may occur as specific responses to environmental challenges, i.e., they may occur more often when advantageous than when neutral. In this paper it is shown that point mutations in the trp operon reverted to trp+ more frequently under conditions of prolonged tryptophan deprivation when the reversions were advantageous, than in the presence of tryptophan when the reversions were neutral. The overall mutation rate, as determined from the rates of mutation to valine resistance and to constitutive expression of the lac operon, did not increase during tryptophan starvation. The trp reversion rate did not increase when the cells were starved for cysteine for a similar period, indicating that the increased reversion rate was specific to conditions where the reversions were advantageous. Two artifactual explanations for the observations, delayed growth of some preexisting revertants and cryptic growth by some cells at the expense of dying cells within aged colonies, were tested and rejected as unlikely. The trp+ reversions that occurred while trp- colonies aged in the absence of tryptophan were shown to be time-dependent rather than replication-dependent, and it is suggested that they occur by mechanisms different from those that have been studied in growing cells. A heuristic model for the molecular basis of such mutations is proposed and evidence consistent with that model is discussed. It is suggested that the results in this and previous studies can be explained on the basis of underlying random mechanisms that act during prolonged periods of physiological stress, and that "directed" mutations are not necessarily the basis of those observations.

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.