Rise and Fall of Mutator Bacteria The Evolution of Mutation Rates in Bacteria Yoav Ram Hadany Evolutionary Theory Lab 29 May 2011
Bacteria Bacteria are unicellular, haploid and asexual Reproduce by binary fission No recombination (almost) No segregation Mutation is the ultimate source of adaptation
Mutation Considered to be a random event: Uniformly distributed over genomes Uniformly distributed over populations Poisson distributed over time Considered to be mostly deleterious or neutral and mostly with small effect (low variance, mean 0)
Symbols µ = the mutation rate: mutation probability / average mutations per genome per replication ω = individual fitness: some measure of reproductive success ω = the mean fitness of a population s = selection coefficient: the effect of a single mutation on the fitness
Mutation-Selection Balance - 1-locus One locus, two alleles: A and a f(a)=p, f(a)=1-p, ω(a)=1, ω(a)=1-s Assumptions: Only deleterious mutations (A->a) Infinite population no drift No recombination s>μ Population genetics: a concise guide / John H. Gillespie, 2004
Mutation-Selection Balance - 1-locus ω = p + (1 p) 1 s p = p 1 μ ω Equilibrium: p = p p[p + 1 p 1 s ] = p(1 μ) p sp + μ s = 0 p 0 f A = p = 1 μ s, f a = μ s ω = 1 μ
MSB - multiple loci μ i - mutation rate at locus i, ω i - fitness at locus i n n i=1 n ω i = 1 μ i ω = ω i ω = (1 μ i ) ln (ω) = ln 1 μ i i=1 i=1 n n ln ω = ln 1 μ i μ i = μ i=1 ω e μ i=1
Mutation-Selection Balance ω e μ This function has a maximum at μ=0 Evolution towards a physiological minimal mutation rate which balances: Reduction of mutation load Cost of fidelity
Problems In the model: Evolution in a constant environment In reality: Environments constantly change and organisms are forced to adapt
Environmental Challenges for Bacteria Starvation Carbon & energy sources Amino acids Oxidative stress DNA damage Host immune system Bacteriophages Antibiotics Shifting temperatures Competition with other microorganisms Biology graduate students Antibiotics test plate with S. aureus B. anthracis attacked by white blood cell Bacteriophages attached to bacterial cell
Mutators & Oscillating Environments Leigh, Egbert Giles Jr., Natural Selection and Mutability. The American Naturalist, 1970 Extension of the selection-mutation balance model to allow for a mutator allele and environmental changes
Leigh 1970 - Assumptions A and a are fitness alleles: f(a)=p, ω(a)=1 B and b are mutators, f(b)=q AB<->aB with rate µ Ab<->ab with rate µ Mutators ratio: R = f B = q f b 1 q At MSB: f A = 1 μ s 1, f a = μ s
Leigh 1970 - Derivation Frequency of a created by B is q μ s Frequency of a created by b is 1 q μ s The ratio of frequencies of the mutators among a alleles is f ab f ab = μ μ R
Leigh 1970 - Derivation Before environmental change: f B f b = R f ab f ab = μ μ R After an environmental change: f a 1 R = μ μ R
Leigh 1970 - Derivation If an environmental change occurs every n generations and n is larger than time needed to reach MSB, then after each environmental cycle: n R μ 1 μ μe nμ = μ R R 1 μ n μ e nμ 1 x n n n ex for x = 1 μ and a large n
Leigh 1970 - Result A mutator allele maximizing μe nμ will be favored by selection Find the maximum: d dμ μe nμ = e nμ nμe nμ = 0 μ = 1/n If n 1,000 then μ 10-3, much higher than 10-7* * Mutation rate per gene per replication 10-7 Drake, PNAS 1991
Leigh 1970 - Conclusions μ = 1/n Mutations per gene per generation Mutation rates are optimized not minimized but only in slowly oscillating environment and in MSB Mutators are selected for the variation they generate before environmental changes
Problems In the model: Evolution in MSB (slow changes) In reality: The Red Queen Hypothesis "It takes all the running you can do, to keep in the same place. - Lewis Carrol, Through the Looking Glass van Valen, 1973
Mutators & Adaptive Evolution Taddei, Radman, Maynard-Smith, Toupance, Gouyon & Godelle. Role of mutator alleles in adaptive evolution. Nature 1997 Simulations of adaptation to new environment In the same issue of Nature: Sniegowski, Gerrish & Lenski. Evolution of high mutation rates in experimental populations of E. coli.
Taddei et al. 1997 Typical parameters for E. coli Mutator alleles: strong (x1,000), medium (x100), or weak (x10) Mutators generated at rate 5x10-7 by: Point mutation can be reversed at rate 5x10-10 Deletion irreversible Many possible deleterious mutations, s=0.05 15-39 possible beneficial, 0.005<s<0.03 Non-mutator mutation rate: deleterious 10-4, lethal 10-5, beneficial 10-8
Mutation-Selection Balance Adaptations not available yet A balance between generation of mutators and the decreased fitness caused by deleterious mutations Equilibrium frequency of mutators: 6x10-4 (x10), 6x10-5 (x100), 10-5 (x1,000)
Infinite Populations Easy to model deterministic behavior Only mutation and selection No extinctions
Infinite Populations An arrow symbolizes the time when population fitness has reached 0.99
Infinite Populations When reversion rate was zero, x1000 did not improve the rate of increase of the fitness
Finite Populations Stochastic events Mutation, selection, and random drift Colon of mammals: 10 6-10 8 cells/g of intestinal content Liquid culture: 10 9 cells/ml Simulations: 10 8-10 10 cells Drift modeled by random sampling of small classes E. coli
Finite Populations x10 mutator -> 100 replicates -> Summary: x10 > 50% in 19% x100 > 50% in 7% Drift is significant, as mutators are initially rare
Leigh 1970 vs. Taddei 1997 Population size, or presence of The Random Drift : L: only infinite, no drift T: infinite and finite, yes drift Environmental change: L: oscillations in a specific locus, can be extended T: a single event of adaptation at multiple loci Benefit to mutators: L: variation before change T: create variation faster after change Methods: L: analytic, deterministic T: numerical, deterministic and stochastic
Leigh 1970 vs. Taddei 1997 Leigh s Results: In oscillations between MSBs the mutation rate is optimized not minimized Taddei s Results: Moderate mutators temporary fix, strong mutators do not All mutators increase the population s rate of adaptation (when LD is not complete)
Rise of the Mutator Mutators generate more adaptations No recombination: mutator allele hitchhikes with generated adaptations to fixation If adaptation events are frequent (Red Queen), the mutation rate may increase with every adaptation event Probably relevant to pathogens and parasites If adaptation events are infrequent.
Fall of the Mutator Mutators have deleterious backgrounds Deleterious mutations are overproduced even when adaptation is complete Mutators suffer from decreased fitness at mutation-selection balance (ω e μ ) Transient Mutator decrease in frequency when competing with anti-mutator in MSB Causes: migration, mutation, recombination
The Stress-Induced Mutator Mutator allele regulates the mutation rate Induction of high mutation rate by different stress responses To formalize it: μ ω 1 or μ 1 ω
B. subtilis SIM Evidence Bacteria Out of 787 natural isolates of E. coli, 40% were SIM compared to 3% CM - Bjedov et al., Science 2003 Escherichia coli lab strains Pseudomonas putida Bacillus subtilis Listeria monocytogenes Staphylococcus aureus Helicobacter pylori Mycobacterium tuberculosis E. coli Reviewed by Foster, 2007 and Galhardo, 2007
SIM Evidence - Eukarya Chlamydomonas (green algae) Goho & Bell, 2000 S. cerevisiae Hall, 1992; Heidenreich, 2007 D. melanogaster Agrawal & Wang, 2008 Humans Bindra et al., 2005; Bindra & Glazer, 2007; Mihaylova et al., 2003; Koshiji et al., 2005 Humans D. melanogaster Chlamydomonas
SIM: Two Evolutionary Explanations Adaptive explanation: increases variation Non-adaptive: by-product of stress, cost of fidelity Lenski & Sniegowski, Science 1995; Saint-Ruf & Matic, 2006 This Study Selection for SIM Evolutionary advantage of SIM Individual level Population level Constant and changing environments
Deterministic Models Infinite population 25 loci Selection Mutation max two mutations per replication Reproduction by cell division no recombination or segregation Constant environment Equilibrium
Population Equations f i - frequency of bacteria with i mutations ω i - fitness of bacteria with i mutations P i,j - probability to mutate from i to j ω = n i=0 ω i f i f i = ω i f ω i f i = j=0 P j,i f j Equilibrium: f i = n j=0 n P j,i ω j ω f j
Mutator Phenotypes P i,j WT = P i,j (γ, φ) P CM i,j = P i,j (τγ, τφ) WT SIM(π) i < π P i,j P i,j = CM i π P i,j π SIM threshold τ Mutation rate modifier
Results 2-locus Change in mutator frequency: p = 1 γ p + φ(1 s) 1 p At MSB: p = p sp 2 + γ + φ s sφ p 1 s φ = 0 Solving the quadratic equation for WT, CM, and SIM we get: p SIM > p WT > p CM And because ω = 1 s + sp increasing in p, we get ω SIM ω > ω WT > ω CM
Population Mean Fitness Results multiple loci Mean fitness at equilibrium for WT, CM, and SIM with different thresholds (using numerical iteration) A. 1 0.9998 0.9996 0.9994 B. 1 0.99 0.98 0.97 0.96 0.9992 0.95 0.999 0.9988 0.9986 0.94 0.93 0.92 0.91 0.9984 CM WT 0.9 CM s=0.01, τ=10, γ=0.01, ϕ=0.001.
Stochastic Models Agent-based simulations 10 5 individuals Stationary-phase constant size Asexual Haploid 1,000 loci Overlapping generations Multiplicative fitness Directional selection No mutation at mutator locus No recombination or segregation
Competitions Population in mutation-selection balance Invasion of mutator 50% of population Environmental change 4/1,000 genes Mean fitness decreases from 0.99 to 0.656
SIM vs. WT: π=4 µ=0.01 τ=10 400 generations
SIM and CM Competition with WT Mutator frequency at end of simulation 400 generations, SIM/CM and WT start at 50%, n>300, µ=0.01, τ=10, error bars: ±1 SE, P<0.0017
SIM Competition with CM SIM frequency at end of simulation 400 generations, SIM and CM start at 50%, n>100, µ=0.01, π=3, error bars: ±1 SE, P<0.003
Constant Environments
Mean Fitness Mean fitness of homogenous populations in changing environments 0.905 0.9 0.895 0.89 0.885 0.88 0.875 0.87 0.865 0.86 SIM 3 CM 2 CM 5 CM 10 WT π - SIM Threshold τ - CM Mutation Rate Modifier T change period, Change=4/1,000 genes, n>90, µ=0.01, Error bars: ±1 SE, P<10-25
Conclusions SIM can be selected for Selection for SIM stronger than for CM Evolves because beneficial to individuals Beneficial to the population, too In constant and changing environments No assumption on cost of fidelity Rise of Stress-Induced Mutator (No Fall!)
Some References Gillespie JH (2004) Population genetics: a concise guide. 2nd ed. Johns Hopkins University Press. Leigh EGJ (1970) Natural Selection and Mutability. Am Nat 104: 301-305. Taddei F, Radman M, Maynard-Smith J, Toupance B, Gouyon PH, Godelle, B. (1997) Role of mutator alleles in adaptive evolution. Nature 387: 700-2. Drake JW (1991) A constant rate of spontaneous mutation in DNA-based microbes. Proc Nat Acad Sci U S A 88: 7160-4. Van Valen, L. 1973. A new evolutionary law. Evol The 1: 1-30. Sniegowski PD, Gerrish PJ, Lenski RE (1997) Evolution of high mutation rates in experimental populations of E. coli. Nature 387: 703-5. doi:10.1038/42701 Foster PL (2007) Stress-induced mutagenesis in bacteria. Crit Rev Biochem Mol Bio 42: 373-97. Galhardo RS, Hastings PJ, Rosenberg SM (2007) Mutation as a stress response and the regulation of evolvability. Crit Rev Biochem Mol Bio 42: 399-435. Bjedov I, Tenaillon O, Gérard B, Souza V, Denamur E, Radman M, Taddei F, Matic I (2003) Stress-induced mutagenesis in bacteria. Science 300: 1404-9. Thanks For Listening!
Supplementary If time permits or questions rise
Mutation-selection balance μ=0.1, s=0.1.
Drake, PNAS 1991