The structure of mutations and the evolution of cooperation

Evolutionary game dynamics in finite populations assumes that all mutations are equally likely, i.e., if there are n strategies a single mutation can result in any strategy with probability 1/n. However, in biological systems it seems natural that not all mutations can arise from a given state. Certain mutations may be far away, or even be unreachable given the current composition of an evolving population. These distances between strategies (or genotypes) define a topology of mutations that so far has been neglected in evolutionary game theory. In this paper we re-evaluate classic results in the evolution of cooperation departing from the assumption of uniform mutations. We examine two cases: the evolution of reciprocal strategies in a repeated prisoner's dilemma, and the evolution of altruistic punishment in a public goods game. In both cases, alternative but reasonable mutation kernels shift known results in the direction of less cooperation. We therefore show that assuming uniform mutations has a substantial impact on the fate of an evolving population. Our results call for a reassessment of the "model-less" approach to mutations in evolutionary dynamics.     

One-third rules with equality: Second-order evolutionary stability conditions in finite populations

The one-third law of evolutionary dynamics [Nowak et al. 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650] describes a robustness criterion for evolution in a finite population: If at an A-frequency of 1/3, the fitness of an A player is greater (smaller) than the fitness of a B player, then a single A mutant that appears in a population of otherwise all B has a fixation probability greater (smaller) than the neutral threshold 1/N, the inverse population size. We examine the case where at an A-frequency of 1/3, the fitness of an A player is exactly equal to the fitness of a B player. We find that in this case the relative magnitude of the cross payoffs matters: If the payoff of A against B is larger (smaller) than the payoff of B against A, then a single A mutant has a fixation probability larger (smaller) than 1/N. If the cross payoffs coincide, we are in the special case of a partnership game, where the deviation cost from an inefficient equilibrium is exactly balanced by the potential gain of switching to the payoff dominant equilibrium. We show that in this case the fixation probability of A is lower than 1/N. Finally, we illustrate our findings by a language game with differentiated costs of signals.     

Stochastic evolutionary dynamics of bimatrix games

Evolutionary game dynamics of two-player asymmetric games in finite populations is studied. We consider two roles in the game, roles α and β. α-players and β-players interact and gain payoffs. The game is described by a pair of matrices, which is called bimatrix. One's payoff in the game is interpreted as its fecundity, thus strategies are subject to natural selection. In addition, strategies can randomly mutate to others. We formulate a stochastic evolutionary game dynamics of bimatrix games as a frequency-dependent Moran process with mutation. We analytically derive the stationary distribution of strategies under weak selection. Our result provides a criterion for equilibrium selection in general bimatrix games.     

Acquisition of rifabutin resistance by a rifampicin resistant mutant of Mycobacterium tuberculosis involves an unusual spectrum of mutations and elevated frequency

Background

Mutations in a small region of the rpoB gene are responsible for most rifamycin resistance in Mycobacterium tuberculosis. In this study we have sequentially generated resistant strains to first rifampicin and then rifabutin. Portions of the rpoB gene were sequenced from 131 randomly selected mutants. Second round selection resulted in a changed frequency of specific mutations.

Methods

Mycobacterium tuberculosis (strain Mtb72) rifamycin resistant mutants were selected in vitro with either rifampicin or rifabutin. One mutant R190 (rpoB S522L) selected with rifampicin had a rifampicin MIC of 32 μg/ml but remained sensitive to rifabutin (MIC<0.8 μg/ml). This mutant was subjected to a second round of selection with rifabutin.

Results

All 105 first round resistant mutants derived from the parent strain (Mtb72) screened acquired mutations within the 81 bp rpoB hotspot. When the rifampicin resistant but rifabutin sensitive S522L mutant was subjected to a second round of selection, single additional rpoB mutations were identified in 24 (92%) of 26 second round mutants studied, but 14 (54%) of these strains contained mutations outside the 81 bp hotspot (codons 144, 146, 148, 505). Additionally, spontaneous rifabutin resistant mutants were produced at >10 times the frequency by the S522L mutant than the parent strain.

Conclusion

First round selection of mutation S522L with rifampicin increased the frequency and changed the spectrum of mutations identified after selection with rifabutin.     

WRN mutations in Werner syndrome patients: genomic rearrangements, unusual intronic mutations and ethnic-specific alterations

Werner syndrome (WS) is an autosomal recessive segmental progeroid syndrome caused by null mutations at the WRN locus, which codes for a member of the RecQ family of DNA helicases. Since 1988, the International Registry of Werner syndrome had enrolled 130 molecularly confirmed WS cases from among 110 worldwide pedigrees. We now report 18 new mutations, including two genomic rearrangements, a deep intronic mutation resulting in a novel exon, a splice consensus mutation leading to utilization of the nearby splice site, and two rare missense mutations. We also review evidence for founder mutations among various ethnic/geographic groups. Founder WRN mutations had been previously reported in Japan and Northern Sardinia. Our Registry now suggests characteristic mutations originated in Morocco, Turkey, The Netherlands and elsewhere.     

A stochastic model of gene evolution with chaotic mutations

We develop here a new class of stochastic models of gene evolution in which the mutations are chaotic, i.e. a random subset of the 64 possible trinucleotides mutates at each evolutionary time t according to some substitution probabilities. Therefore, at each time t, the numbers and the types of mutable trinucleotides are unknown. Thus, the mutation matrix changes at each time t. The chaotic model developed generalizes the standard model in which all the trinucleotides mutate at each time t. It determines the occurrence probabilities at time t of trinucleotides which chaotically mutate according to three substitution parameters associated with the three trinucleotide sites. Two theorems prove that this chaotic model has a probability vector at each time t and that it converges to a uniform probability vector identical to that of the standard model. Furthermore, four applications of this chaotic model (with a uniform random strategy for the 64 trinucleotides and with a particular strategy for the three stop codons) allow an evolutionary study of the three circular codes identified in both eukaryotic and prokaryotic genes. A circular code is a particular set of trinucleotides whose main property is the retrieval of the frames in genes locally, i.e. anywhere in genes and particularly without start codons, and automatically with a window of a few nucleotides. After a certain evolutionary time and with particular values for the three substitution parameters, the chaotic models retrieve the main statistical properties of the three circular codes observed in genes. These applications also allow an evolutionary comparison between the standard and chaotic models.     

Mutation-selection equilibrium in games with mixed strategies

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an n×n payoff matrix. Players can use mixed strategies, which are given by the vector (p₁,…,p_n). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S_n. We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.     

Evolutionary Stability in the Asymmetric Volunteer's Dilemma

It is often assumed that in public goods games, contributors are either strong or weak players and each individual has an equal probability of exhibiting cooperation. It is difficult to explain why the public good is produced by strong individuals in some cooperation systems, and by weak individuals in others. Viewing the asymmetric volunteer''s dilemma game as an evolutionary game, we find that whether the strong or the weak players produce the public good depends on the initial condition (i.e., phenotype or initial strategy of individuals). These different evolutionarily stable strategies (ESS) associated with different initial conditions, can be interpreted as the production modes of public goods of different cooperation systems. A further analysis revealed that the strong player adopts a pure strategy but mixed strategies for the weak players to produce the public good, and that the probability of volunteering by weak players decreases with increasing group size or decreasing cost-benefit ratio. Our model shows that the defection probability of a “strong” player is greater than the “weak” players in the model of Diekmann (1993). This contradicts Selten''s (1980) model that public goods can only be produced by a strong player, is not an evolutionarily stable strategy, and will therefore disappear over evolutionary time. Our public good model with ESS has thus extended previous interpretations that the public good can only be produced by strong players in an asymmetric game.     

Pre-existing isoniazid resistance, but not the genotype of Mycobacterium tuberculosis drives rifampicin resistance codon preference in vitro

Both the probability of a mutation occurring and the ability of the mutant to persist will influence the distribution of mutants that arise in a population. We studied the interaction of these factors for the in vitro selection of rifampicin (RIF)-resistant mutants of Mycobacterium tuberculosis. We characterised two series of spontaneous RIF-resistant in vitro mutants from isoniazid (INH)-sensitive and -resistant laboratory strains and clinical isolates, representing various M. tuberculosis genotypes. The first series were selected from multiple parallel 1 ml cultures and the second from single 10 ml cultures. RIF-resistant mutants were screened by Multiplex Ligation-dependent Probe Amplification (MLPA) or by sequencing the rpoB gene. For all strains the mutation rate for RIF resistance was determined with a fluctuation assay. The most striking observation was a shift towards rpoB-S531L (TCG→TTG) mutations in a panel of laboratory-generated INH-resistant mutants selected from the 10-ml cultures (p<0.001). All tested strains showed similar mutation rates (1.33×10⁻⁸ to 2.49×10⁻⁷) except one of the laboratory-generated INH mutants with a mutation rate measured at 5.71×10⁻⁷, more than 10 times higher than that of the INH susceptible parental strain (5.46–7.44×10⁻⁸). No significant, systematic difference in the spectrum of rpoB-mutations between strains of different genotypes was observed. The dramatic shift towards rpoB-S531L in our INH-resistant laboratory mutants suggests that the relative fitness of resistant mutants can dramatically impact the distribution of (subsequent) mutations that accumulate in a M. tuberculosis population, at least in vitro. We conclude that, against specific genetic backgrounds, certain resistance mutations are particularly likely to spread. Molecular screening for these (combinations of) mutations in clinical isolates could rapidly identify these particular pathogenic strains. We therefore recommend that isolates are screened for the distribution of resistance mutations, especially in regions that are highly endemic for (multi)drug resistant tuberculosis.     

Population genetics, pleiotropy, and the preferential fixation of mutations during adaptive evolution

Ongoing debate centers on whether certain types of mutations are fixed preferentially during adaptive evolution. Although there has been much discussion, no quantitative framework currently exists to test for these biases. Here, we describe a method for distinguishing between the two processes that likely account for biased rates of substitution: variation in mutation rates and variation in the probability that a mutation becomes fixed once it arises. We then use this approach to examine the type and magnitude of these biases during evolutionary transitions across multiple scales: those involving repeated origins of individual traits (flower color change), and transitions involving broad suites of traits (morphological and physiological trait evolution in plants and animals). We show that fixation biases can be strong at both levels of comparison, likely due to differences in the magnitude of deleterious pleiotropy associated with alternative mutation categories. However, we also show that the scale at which these comparisons are made greatly influences the results, as broad comparisons that simultaneously analyze multiple traits obscure heterogeneity in the direction and magnitude of these biases. We conclude that preferential fixation of mutations likely is common in nature, but should be studied on a trait-by-trait basis.     

Studies of opal mutations in bacteriophage T4B

Hydroxylamine-induced amber and opal mutants are localized on the map of gene 47 of bacteriophage T4B. The matched map of amber and opal mutations showed the presence of four paired sites which seemed to have arisen in the triplet coding for tryptophan.In growth studies o opal mutants in gene 47 in a series of Su⁺ strains the number of strains bearing a gene-suppressor for amber or ochre mutations also had a weak suppressor activity for some opal mutants. This suppressor acitivity is supposedly due to a second mutation in gene Su_uga.A comparative study of the phage yield with amber and opal mutations located in the same (paired) triplet in gene 47 has shown that the suppressor activity depends on the location of the mutant site along the gene.Experiments dealing with the induction of reversions by nitrous acid in amber and opal mutants with mutational sites located in the same triplet of gene 47 (mutant pairs) have shown the essential influence of the nucleotide sequence in the triplet on the frequency of induced reverse mutations at the given site.     

Introduction of cytochrome b mutations in Saccharomyces cerevisiae by a method that allows selection for both functional and non-functional cytochrome b proteins

We have previously used inhibitors interacting with the Qn site of the yeast cytochrome bc₁ complex to obtain yeast strains with resistance-conferring mutations in cytochrome b as a means to investigate the effects of amino acid substitutions on Qn site enzymatic activity [M.G. Ding, J.-P. di Rago, B.L. Trumpower, Investigating the Qn site of the cytochrome bc1 complex in Saccharomyces cerevisiae with mutants resistant to ilicicolin H, a novel Qn site inhibitor, J. Biol. Chem. 281 (2006) 36036-36043.]. Although the screening produced various interesting cytochrome b mutations, it depends on the availability of inhibitors and can only reveal a very limited number of mutations. Furthermore, mutations leading to a respiratory deficient phenotype remain undetected. We therefore devised an approach where any type of mutation can be efficiently introduced in the cytochrome b gene. In this method ARG8, a gene that is normally encoded by nuclear DNA, replaces the naturally occurring mitochondrial cytochrome b gene, resulting in ARG8 expressed from the mitochondrial genome (ARG8^m). Subsequently replacing ARG8^m with mutated versions of cytochrome b results in arginine auxotrophy. Respiratory competent cytochrome b mutants can be selected directly by virtue of their ability to restore growth on non-fermentable substrates. If the mutated cytochrome b is non-functional, the presence of the COX2 respiratory gene marker on the mitochondrial transforming plasmid enables screening for cytochrome b mutants with a stringent respiratory deficiency (mit⁻). With this system, we created eight different yeast strains containing point mutations at three different codons in cytochrome b affecting center N. In addition, we created three point mutations affecting arginine 79 in center P. This is the first time mutations have been created for three of the loci presented here, and nine of the resulting mutants have never been described before.     

Point mutations in firefly luciferase C-domain demonstrate its significance in green color of bioluminescence

Firefly luciferase is a two-domain enzyme that catalyzes the bioluminescent reaction of firefly luciferin oxidation. Color of the emitted light depends on the structure of the enzyme, yet the exact color-tuning mechanism remains unknown by now, and the role of the C-domain in it is rarely discussed, because a very few color-shifting mutations in the C-domain were described. Recently we reported a strong red-shifting mutation E457K in the C-domain; the bioluminescence spectra of this enzyme were independent of temperature or pH. In the present study we investigated the role of the residue E457 in the enzyme using the Luciola mingrelica luciferase with a thermostabilized N-domain as a parent enzyme for site-directed mutagenesis. We obtained a set of mutants and studied their catalytic properties, thermal stability and bioluminescence spectra. Experimental spectra were represented as a sum of two components (bioluminescence spectra of putative “red” and “green” emitters); λ_max of these components were constant for all the mutants, but the ratio of these emitters was defined by temperature and mutations in the C-domain. We suggest that each emitter is stabilized by a specific conformation of the active site; thus, enzymes with two forms of the active site coexist in the reactive media. The rigid structure of the C-domain is crucial for maintaining the conformation corresponding to the “green” emitter. We presume that the emitters are the keto- and enol forms of oxyluciferin.     

New Escherichia coli gyrA and gyrB mutations which have a graded effect on DNA supercoiling

Summary We isolated new gyrA and gyrB mutations in Escherichia coli which have a graded effect on DNA supercoiling. The mutants, selected respectively for resistance to nalidixic acid and coumermycin, were sorted by means of a rapid in vivo assay of DNA gyrase activity (Aleixandre and Blanco 1987). Cells carrying a gyrB (Cou^r) mutation usually showed a decrease in DNA supercoiling, which would indicate a reduction in gyrase activity. In contrast, most of the gyrA (Nal^r) mutations had no significant effect on DNA supercoiling. Moreover, they conferred a high level of resistance to nalidixic acid and other quinolones, thus being similar to the gyrA(Nal^r) mutants currently used. We also detected rare gyrA mutants showing a reduction in DNA gyrase activity. These mutants were, in addition, resistant to only low concentrations of quinolones, which allowed us to use the phenotype of partial quinolone resistance as an indicator to score gyrA mutations affecting DNA supercoiling. When gyrB mutations were introduced into the gyrA mutants, these became more sensitive to quinolones and a decrease in supercoiling was observed. Moreover, the topA10 mutation sensitized gyrA(Nal^r) cells to quinolones. We conclude therefore that the GyrA-dependent quinolone resistance is diminished as a consequence of the reduction either in topoisomerase I or gyrase activities.     

Fixation of beneficial mutations in the presence of epistatic interactions

We investigate the effect of deleterious mutations on the process of fixation of new advantageous mutants in an asexual population. In particular we wish to study the dependence of the process on the strength of the deleterious mutations. We suppose the existence of epistatic interaction between the genes. We study the model by means of branching process theory and also by numerical simulations. Our results show the occurrence of two distinct regimes of behavior for the probability of fixation of these variants. The occurrence of either regime depends on the ratio between the selective advantage of the beneficial mutation s _b and on the selective parameter for deleterious mutations s _b . In the former, which takes place for s _b /s _d ≲ 1, the probability of fixation increases with the epistasis parameter α, whereas for s _b /s _d ≫ 1 the probability of fixation is a complex function of α and the mutation rate U. Surprisingly, we find that for the multiplicative landscape (α = 1) the probability of fixation P _fix is given by where π (s _b ) is the probability of fixation for the two-allele model in the absence of mutations as calculated by Haldane (1927, Proc. Camb. Phil. Soc., 26, 220–230) and Kimura (1962, Genetics, 47, 713–719).     

Functional studies on twenty novel naturally occurring melanocortin-4 receptor mutations

The melanocortin-4 receptor (MC4R) is a G protein-coupled receptor critically involved in regulating energy balance. MC4R activation results in decreased food intake and increased energy expenditure. Genetic and pharmacological studies demonstrated that the MC4R regulation of energy balance is conserved from fish to mammals. In humans, more than 150 naturally occurring mutations in the MC4R gene have been identified. Functional study of mutant MC4Rs is an important component in proving the causal link between MC4R mutation and obesity as well as the basis of personalized medicine. In this article, we studied 20 MC4R mutations that were either not characterized or not fully characterized. We showed that 11 mutants had decreased or absent cell surface expression. D126Y was defective in ligand binding. Three mutants were constitutively active but had decreased cell surface expression. Eleven mutants had decreased basal signaling, with two mutants defective only in this parameter, suggesting that impaired basal signaling might also be a cause of obesity. Five mutants had normal functions. In summary, we provided detailed functional data for further studies on identifying therapeutic approaches for personalized medicine to treat patients harboring these mutations.     

Four novel GALC gene mutations in two Chinese patients with Krabbe disease

Krabbe disease (OMIM #245200) is a rare autosomal recessive leukodystrophy caused by deficiency of galactocerebrosidase (GALC) activity. We identified four novel mutations of the GALC gene in two unrelated Chinese families with Krabbe disease: one insertion mutation, c.1836_1837insT, and one nonsense mutation, c.599C>A (p.S200X), in an infantile patient, and one deletion mutation, c.1911+1_1911+5delGTAAG, and one missense mutation, c.2041G>A, in an adult late-onset patient. This is the first identification of GALC mutations in the Chinese population.     

Actin gene mutations in Drosophila; heat shock activation in the indirect flight muscles

We have identified four mutations affecting the actin III isoform in the indirect flight muscles (IFM) of Drosophila. One mutation does not produce any protein product, and three direct the synthesis of electrophoretic variants of actin. Complementation tests and recombination mapping indicate that all mutations are alleles of an actin gene at chromosomal band 88F (act88F gene). The effect of these mutations is restricted to the IFM. We conclude that the act88F gene is expressed only in the IFM to encode actin III, which is its major isoform. In two of the actin mutants, heat shock proteins are constitutively expressed in the IFM. Genetic evidence strongly suggest that this anomaly is primarily caused by the mutations in the act88F structural gene.