Context dependence in the distribution of mutation effects on fitness Guillaume MARTIN Equipe Metapop, ISEM, CNRS Montpellier.

Présentation au sujet: "Context dependence in the distribution of mutation effects on fitness Guillaume MARTIN Equipe Metapop, ISEM, CNRS Montpellier."— Transcription de la présentation:

1 Context dependence in the distribution of mutation effects on fitness Guillaume MARTIN Equipe Metapop, ISEM, CNRS Montpellier

2 Importance of the distribution of mutation effects on fitness s determines the change in frequency Adaptation or maladaptation depends on available s The ‘cause’ of s need not be known sometimes… Mutation is the ultimate source of new variation = what drives adaptation on the long run Cost of mutations determines their frequency at equilibrium = source for adaptation to future changes

3 « The » distribution of fitness among mutants (accumulated ~ randomly) At some genomic rate U beneficial (s > 0) deleterious (s < 0) Measured in drosophila, C. elegans, bacteria, yeast, viruses etc. 0% 5% 10% 15% 20% 25% 30% 35% Fitness of the mutant lines Wild – type + neutral (s = 0) U pbU pb U pdU pd E(s) = mean effect of all random mutations V(s) = variance of these effects U = rate of (expressed and non neutral) mutations p b, p d = proportion of beneficial vs. deleterious Characterisitcs of the distribution Importance of the distribution of mutation effects on fitness

4 Outline (hopefully…) 1. How to estimate s 2. How to create random mutations 3. Context dependence in s: effect of the environemnt 4.Beneficial mutations: data vs theory 5.Conclusions 6.Bonus: effect of background (epistasis, dominance)…if we have time

5 1/ How to measure a given mutation’s effects on fitness

6 Time (generations) s = 0.3 s = 0.1 s = 0.05 Exact solution Logistique Dynamique de la fréquence allélique sous sélection

7 Observation au laboratoire: évolution expérimentale Test de la logistique Mesures de s pour différents allèles Exemple chez espèces modèles de microbes (bacteries, levures, chlamydomonas...) -temps de génération court - petite taille - facile à élever - marquage possible de ≠ génotypes Il y a d’autres espèces (C. elegans, drosophile …)

8 Observations au laboratoire: évolution experimentale ~ 37°C Sucre (miam) Chemostat cultures UV (sterilisation) Temps (h) Nb de cellules 10 9 10 3 Chemostat Exemple avec E. coli Méthode d’élevage à long terme (plusieurs centaines de générations) Renouvellement d’un % du milieu

9 Observations au laboratoire: évolution experimentale Batch cultures batch Ou en milieu liquide.. ~ 37°C Renouvellement d’un % du milieu Chemostat cultures UV (sterilization) Temps (h) Nb de cellules 10 9 10 3 Chemostat Exemple avec E. coli Méthode d’élevage à long terme (plusieurs centaines de générations) Sucre (miam)

10 Observations au laboratoire: évolution experimentale Chemostat cultures Exemple: effet de la délétion d’un gène 50% type sauvage 50% mutant délété + Marqueur du mutant : - résistance antibiotique - coloration de colonie - marqueur fluorescent (suivi automatisé) ~ 37°C Sucre Renouvellement d’un % du milieu UV (sterilisation) À quoi faut-il faire attention pour le choix du marqueur ?

11 Ici pour trois délétions différentes: un perte de fonction peut être avantageuse… Selon l’environnement Observations au laboratoire: évolution experimentale

12 DFE: empirical measurement Measuring mutant fitnesses: 1 clone or isogenic line: Fitness components (clonal growth rate, lifetime reproductive sucess, survival, fecundity) 2 clones: Competitive index (marked genotypes: ara+, FP etc.) 2 sexual lines: isogenic lines and balancer chromosomes (+ marker: red eye etc.) Many clones (gene deletion sets, DFE in one gene): molecular tags/deep sequencing => growth of all mutants in a single culture. Several viruses, E.coli, yeast, drosophila, C. elegans, arabidopsis  What generalization : across environments, backgrounds, species

13 2/ How to create a set of random mutants

14 DFE: empirical measurement Generating mutants: Single random mutations in the genome (ex. transposon inserts) Gene deletion sets (covers ~ all genes) Single random mutations in a gene (site directed mutagenesis etc. several methods now) Naturally occuring mutations in mutation-accumulation experiments

15 Construction de mutants aléatoires Méthode 1: fabriquer des mutants « à la main » et mesurer leur s relativement au parent 1. site - directed mutagenesis = un nucleotide modifié (virus), 2. insertion de mini transposon + marqueur (resistance antibio) pour vérifier l’insertion 3. gene knock-outs avec des marqueurs (mini-séquences) associés 4. Analyse de tétrades (levures): mutations « naturelles » héterozygotes Le pb: les variants que l’on récupère en population naturelle (ou dans le tube) sont passées sous le filtre de la sélection 1 mutation = différences de croissance 2:2 Diploïde portant une mutation Méiose 4 cellules filles haploides Croissance sur plaque

16 VSVTEV Carrasco et al 2007 J. Virol.Sanjuan & Elena PNAS 2004  X174 Domingo-Calap 2009 PLoS Genetics E. coli Elena et al 1998 Genetica yeast Szafraniec et al 2003 Genetics DFE : beneficial deleterious lethal Special issue: Phil. Trans. R. Soc. Lond. B. Biol. Sci. (2010) The Good, the Badand the Ugly

17 Majorité d’effets délétères Il semble qu’il y ait souvent une forte classe de létaux Skewness vers les valeurs < 0 Possible présence de bénéfique, parfois 50% (c’est rare à ce jour, arabidospsis) Moyenne (par génération) négative typiquement entre ~ 1 % et 20 % Typiquement distribution gamma ou beta La méthode ne semble pas trop affecter la mesure de E(s) (levure & coli) Mais attention: on peut rater certains effets faibles peut être, pourquoi ? Distributions des effets de mutations aléatoires Le Bon, La Brute, et le Truand

18 Accumulation de mutations Méthode 2: On évite la compétition entre descendants mutants vs type sauvage. = Eliminer la sélection en augmentant la dérive (Terumi Mukai, 1968) x x x Etc.. Mesure des fitness moyennes de chaque lignée (idealement à differents temps) x Lignée isogénique de départ: Un évènement mutationnel x Nb de mutations:002011 ~ hors compétition Microbes: repiquage d’un nombre très petit d’individus dès que colonie visible Pluricellulaires: autofécondations ou croisements frère - sœur et on isole les descendants très jeunes

19 Phyloxera Accumulation de mutations Méthode 2: On évite la compétition entre descendants mutants vs type sauvage. = Eliminer la sélection en augmentant la dérive (N e s << 1) = Accumulation de mutations aléatoires à un taux U Caenorhabditis Drosophile Décroissance de la fitness moyenne Augmentation de la variance en fitness entre lignées Tobacco Etch Virus Malthusian fitness Darwinian fitness Fitenss in competition

20 Analyse: estimer le taux et l’effet des mutations Hypothèse: mutations arrivent suivant une loi de Poisson de taux U Décroissance linéaire de la fitness moyenne au taux Augmentation linéaire de la variance entre lignées au taux generations Variance entre lignées Fitness moyenne des lignées On néglige var(s) : CV(s) = 0 On fixe var(s): exponentiel => CV(s) = 1 Effet s moyen Taux de mutation (-) Estimateur biaisé (+) Peut s’appliquer à toute espèce « élevable » au laboratoire (+) permet aussi d’estimer le t x U (+/-) ne mesure que les mutations ayant un effet sur la fitness

21 4/ Context dependance of f(s): data and theory

22 Theories of the distribution of s among beneficial mutations Dealing with context dependence… Many mutations are only beneficial or deleterious in a given environment and genetic background (genomic environment) Some are always deleterious: e.g. a mutation that destroys the glycolysis pathway (that is why some genes of this pathway are very conserved across species)

23 Adaptation to glucose minimal medium in E. coli Lenski & Travisano (1994). Courbes saturantes: pourquoi ?? Adaptation to captivity in drosophila cages of size N = 1000 Gilligan & Frankham (2003) 02000600010000 0.0 0.2 0.4 0.6 generations Mean Malthusian relative fitness Evolution expérimentale: cas 3/ trajectoires de fitness à « long » terme Des exemples au labo

24 Environment (abiotic mainly a priori) How to study it? Which effect is most important How to predict the effect? But in fact this is context dependent: E(s) = mean effect of all random mutations V(s) = variance of these effects U = rate of (expressed and non neutral) mutations p b, p d = proportion of beneficial vs. deleterious Characterisitcs of the distribution Non neutral mutation rate U (e.g. stress => repair system + expression) Phenotypic effects (plasticity) Phenotype – fitness map (same phenotype = more or less fit) Environmental variation affects the distribution of mutation effects on fitness: causes and a priori

25 Landscape models to describe context dependenace Data vs. theory: Effect of simple abiotic stresses on mutation fitness effects among all mutations Data vs. theory: Effect of a beneficial mutation in another environment (cost of resistance) A project of experimental test

26 fitness phenotype (phenotypic space) Trait 2 Trait 1 Wild type optimal phenotype mutant phenotypes Qualitative assumptions: Fitness is determined by (unknown) underlying traits Mutations makes random displacement on these traits with symetric effects Typical quantitative assumptions: gaussian w(z) gaussian mutant distribution around wild type Dealing with context dependence: Fisher’s landscape model

27 Allows to predict : How stress changes the whole distribution of s The distribution in Environment 2 of mutations with effect s > 0 in Environment 1 (cost of adaptation) phenotype (phenotypic space) Trait 2 Trait 1 Environment 2: « non stressful », or « permissive » = Wild type close to optimum Environment 1: « stressful », or « selective » = Wild type far from optimum

28 Data vs. theory: Effect of simple abiotic stresses on mutation fitness effects among all mutations

29 fitness Trait 2 Trait 1 Effect of stress on the proportion of beneficial mutations p b 1. Proportion of beneficial mutations increases in stressful environments / in less adapted genotypes Beneficial mutations Deleterious mutations fitness Trait 2 Trait 1 Environment / background 1 Environment / background 2

30 Effect of stress on the proportion of beneficial mutations p b 1. Proportion of beneficial mutations increases in stressful environments / in less adapted genotypes Adaptation to glucose minimal medium in E. coli Lenski & Travisano (1994). 02000600010000 0.0 0.2 0.4 0.6 generations Mean Malthusian relative fitness An indirect proof: Saturation of fitness trajectories = p b decreases Effect of background adaptation : direct empirical confirmation (C. Burch unpublished) Adaptation to captivity in drosophila cages of size N = 1000 Gilligan & Frankham (2003)

31 E(s) Quadratic fitness V(s) standard W(z)W(z) zo  0zo  0 At the optimum (standard conditions to which the wild type is adapted) What is the effect of stress on the mean E(s) and variance V(s) of f(s) Phenotype z « standard » conditions Effect of stress on U, E(s), V(s): predictions

32 Phenotype z Quadratic fitness W(z)W(z) zo  0zo  0 What is the effect of stress on the mean E(s) and variance V(s) of f(s) E(s) V(s) stress Away from the optimum (stressful conditions: e.g. increased T° etc.) « stressful » conditions Effect of stress on U, E(s), V(s): predictions

33 Stress + quadratic fitness function = > What is the effect of stress on the mean E(s) and variance V(s) of f(s) Phenotype z Quadratic fitness W(z)W(z) V(s) stress V(s) standard B. The variance in mutant fitness increases A. The average deleterious effect remains approximately constant stressfulstandard Effect of stress on U, E(s), V(s): predictions

34 Stress + quadratic fitness function = > What is the effect of stress on the mean E(s) and variance V(s) of f(s) Effect of stress on U, E(s), V(s): predictions V(s) = V(s*) (1+ 2 q s o / |E(s)|) Fitness distance to optimum relative to mean step size Variance in fitness at the optimum Directionnality effect B. The variance in mutant fitness increases A. E(s) approximately constant

35 Mutation accumulation experiments Fitness of the mutant lines in different environments standard vs. stressful (e.g. increased T°, osmolarity etc.) most studies = S. cerevisiae, E. coli, D. melanogaster Effect of stress on U, E(s), V(s): Test

36 Mutations = Poisson process rate U: Mean fitness among lines decreases at rate Variance in fitness among lines increases at rate generations Fitness Variance Mean fitness Effect of stress on U, E(s), V(s): Test Variance in stressful resp. permissive environment Mean in stressful resp. permissive environment

37 -0.500.511.522.5-0.624.22 Relative effect of stress 0% 20% 40% 60% Proportion of MA studies increasedecrease No trend in the effect of stress on the average effect 50% increases (14/28 studies), small variation sign test p = 0.37 A. The average deleterious effect remains approximately constant Effect of stress on U, E(s), V(s): Test Effect on E(s)

38 -0.500.511.522.5-0.624.22 Relative effect of stress 0% 20% 40% 60% Proportion of MA studies increasedecrease Strong trend toward increased variance under stress 25/30 studies, large variation sign test p = 0.0012 B. The variance in mutant fitness increases Effect of stress on U, E(s), V(s): Test Effect on E(s) Effect on V(s)

39 Mutations = Poisson process rate U: Mean fitness among lines decreases at rate Variance in fitness among lines increases at rate generations Fitness Variance Mean fitness Effect of stress on U, E(s), V(s): Test Effect of stress on U (expression not repair) Mean of s Variance of s Variance in stressful resp. permissive environment Mean in stressful resp. permissive environment

40 Effect of stress on U, E(s), V(s): Test Data from Yeast,droso, coli, C. elegans Fisher model: Stress only affects the variance of s y = x. Simulations of Fisher model Martin & Lenormand, 2006 Evolution

41 The prediction based on a quadratic fitness approximation is consistent with the data ( review across different environments and model species) Stress = > The variance of mutant fitness increases The average effect is little affected The nb of expressed mutations is little affected Suggests: Valid assumption, even in the stressful conditions considerred A simple model can account for the observed change in f(s) across environments Explains why: Increased adaptation to stressful conditions Increased advantage to sex under stress Etc. Effect of stress on U, E(s), V(s): summary

42 3/ How to study beneficial mutations

43 1/ Mutants aléatoires: peu sont avantageuses dans le milieu standard du laboratoire => changer le contexte (stress, background) 3/ aller à la pêche: les mutations qui ont augmenté en fréquence en fin d’expérience Données séquences en nature: il faut scanner le génome (voir cours Nicolas Bierne) 4/ Suivi de mutations qui montrent une augmentation en fréquence (asexués) 2/ Screen de résistances, résistances naturelles en nature (insecticides, antibiotiques etc.) Single nucleotide substitutions (rpoS, E.coli : perte de fonction) Gene duplications (Ester locus moustique resistance aux insecticides) Transposon inserts (ex. levure) Tous les types Observations de mutations avantageuses

44 4/ Suivi de mutations nouvelles Observations de mutations avantageuses Soupe initiale: 50% type sauvage + marqueur YFP 50% type sauvage + marqueur CFP CFP (YFP): Cyan(Yellow) Fluorescent Protein Souches modifiées génétiquement pour exprimer ces protéines Suivi de la fréquence du marqueur au cours du temps (e.g. automatisé par fluorescence) (Hegreness et al., Science 2006)

45 Observations de mutations avantageuses Quelle distribution on obtient? (Rozen et al. Current Biol., 2002) (Perfeito et al. Science, 2002) selective advantage, s Tous les exemples à ce jour Par cette méthode

46 Mutations avantageuses « Fait main » chez un virus (méthode 1/) Mutations échappant à la dérive chez E.coli Récupéré par méthode 4/ Observations de mutations avantageuses selective advantage, s Density 00.010.02 (Sanjuan et al. PNAS, 2004) P(fixation) ~ 2s Dérive = filtre On le voit empiriquement: les mutations avantageuses « fixées » ≠ sous échantillon aléatoire des s >0 selective advantage, s (Rozen et al. Current Biol., 2002)

47 Theories of the distribution of s among beneficial mutations Extreme value theory Extreme value theory (Gillespie) Assumption: beneficial mutations are a subsample of all mutations at the extreme right tail Then we can apply extreme value theory which gives us the distribution of this right tail 0 Distribution of s beneficialsdeleterious Three « domains of attraction » according to the type of distribution Gumbel: distribution which decay exponentially (gaussian gamma etc.): s b ~ Exponential Weibull: distributions with a maximum positive value (e.g. with an optimum): s b ~ Beta Fréchet: distributions with a fatter tail than exponential Paysage avec un optimum + WT près de l’optiumum : s benefiques ~ Beta (1,m/2) s fixés ~ Beta (2,m/2)

48 E. coli Perfeito et al. (2007) Theories of the distribution of s among beneficial mutations Extreme value theory Empirical examples in viruses / qualitative test of the theory Beneficial mutations in VSV Data from (Sanjuan & Elena, 2004) Site directed mutagenesis subsample with s>0 Mutations that escaped extinction Fixed mutations in phage ID11 Rokyta et al. (2007) sbsb Density 0.0000.0100.020 0 40 80 120 s b ~ Exp s b / s o ~ Beta ( , m/2) s f / max(s f ) ) Density 0.00.20.40.60.81.0 0.0 0.5 1.0 1.5 s b ~ Exp s b / s o ~ Beta ( , m/2)

49 Pb with extreme value theory Does not tell us the frequency of those beneficial mutations just their effect distribution Does not account for changes of this distributions with the environment or the genetic background Landscape: (+) allows to predict the whole f(s) (+) with context dependence : environment and genotype (epistasis/dominance) How would you do that? Summary Martin & al. (2008) Nature Genetics.

50 Pb with extreme value theory Does not tell us the frequency of those beneficial mutations just their effect distribution Does not account for changes of this distributions with the environment or the genetic background Landscapes: (+) allows to predict the whole f(s) (+) with context dependence : environment and genotype (epistasis/dominance) (+) can be parameterized empirically (-) requires one estimate of f(s) in one environment (-) has to make assumptions on a fitness vs unknown traits relationship To be continued…

51 Merci de votre attention ! pour en savoir plus (entre autres références) … - Elena & Lenski (nat rev genetics 2003) evolution experimentale et adaptation dynamics - Orr, 2001, 2002 2005: paysages, dynamique adaptation, theorie des valeurs extremes (EVT) -Martin & Lenormand (2006, 2008): EVT, contexte dependance (environnement epistasie, dominance)+ tests empiriques

52 Epistasis, dominance Martin & al. (2008) Nature Genetics.

53 Dominance for random mutations : average h = 1/4 Epistasis among random mutants = Gaussian : e ij ~ N(0,2V(s*)) Independent of the wild type ‘position’ ( = environment or background) Confirmed by test on : - VSV (virus) (not optimally adapted) and - E.coli (optimally adapted) Epistasis, dominance Manna & al. (2011) Genetics.

54 Non costly resistance Selective environment (screening) Costly resistance Permissive environment (WT far from optimum) Permissive environment (WT close to optimum) costly + non costly all costly

55 Cost of adaptation: summary Theory can describe beneficial and fixed mutations With limited number of possible mutations => discretize = more noisy a. Effect of beneficial mutations b. Effect of fixed mutations c. Fixed and beneficial mutations Wild-type ill-adapted to permissiveWild-type well adapted to permissive    cos     cos  Simulations: Theory:

56 Evolution of the cost of adaptation in a constant permissive environment How  evolves determines the evolution of the cost distribution Constant permissive environment, as the population adapts to it:  All mutations become costly, fitness correlation becomes zero

57 Evolution of the cost of adaptation in a mosaic environment How  evolves determines the evolution of the cost distribution All mutations become costly, fitness correlation becomes negative Mosaic of selective/permissive environments,  becomes negative

58 Evolution of the cost of adaptation in a constant permissive environment A project to test this: All mutations become costly, fitness correlation becomes zero glucose - minimal medium E.coli (Lenski & Travisano, PNAS 1994) Wild types at different levels of adaptation 1.Screen for resistant mutants 2.Measure fitness with and w/o drugs 3.Measure the evolution of  and cost Distribution of s among single mutants at optimum = known in this system

59 Il ne peut en rester qu’un… sexués asexués A B 0 1 générations A B 0 1 ptpt ptpt Parce qu’il n’y a pas de recombinaison, seule la mutation courante d’effet s le plus fort se fixe Mutations avantageuses Échappant à la deriveMutations fixées Dérive Interference clonale L’interférence clonale