Evolution of the genomic mutation rate: implications for ...

Evolution of the genomic mutation rate:implications for asexual populations

Paul Sniegowski

University of Pennsylvania

Philip J. Gerrish

University of New Mexico

Presented at KITP, Santa Barbara November 2008

Outline

Evolution of mutation rate: equilibrium notions

How does the genomic mutation rate evolve?

Experimental studies of mutation rate evolution

The dangers of a high mutation rate for asexuals

Outline of the “mutation rate catastrophe” hypothesis

Some theoretical results on the mutation rate ratchet

Early experimental results

Implications and future directions

Comparative Data on Mutation Rates

mutational load

beneficial

mutationscost of

fidelity

Indirect

selection

Indirect

selection

Direct

selection

Natural selection and the mutation rate

linked

notlinked

Linkage and “mutator” hitchhiking

Comparative Data on Mutation Rates

Experimental studies

In vitro microbial evolution

Lenski’s long term evolution experiment in E. coli

Single ancestral colony of E. coli B

Daily growth in broth with 100-fold dilution

Daily transfer regime

100 ul into 9.9 mlfresh medium

10 ml 10 ml 10 ml

Day n Day n + 1 Day n + 2

Source: Lenski, R.E. and M. Travisano. 1994. PNAS 91, 6808-6814.

Ara 30 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Generation

Population

Mutator

Wildtype

Mutator sequence a nal ysis

Population Mutato r mut ation Ef fect Addit iona l c oding

changes a t

20,000

generations

insertion of G after position

frameshift in 1st

third of protein

I->V at a.a. 694,

assuming original

reading frame

Ara-2 insertion of two a.a. repeat

(LA) after a.a. position 68

see below G->E at a.a. 32

M->T at a.a. 135

V->A at a.a. 274

Ara-4 deletion of two a.a. repeat

(LA) after a.a. position 68

see below G->D at a.a. 281

A->V at a.a. 606

Note: An LALALA repeat makes up the end of the B a-helix of MutL. Immediately

following the repeat is a loop which leads to the C a-helix. This helix-loop-helix

structure is thought to form the lid of the ATP binding site for MutL, implying that

CTGGCGCTGGCGCTGGCG

68 KKDELALALARHATS

68 KKDELALALALARHATS

68 KKDELALARHATS

Ancestor

Repeat alterations in mutL

Possible causes of mutator allelesubstitution

1. Direct selection on mutator allele-Predicts advantage of mutator allele over wild type on

isogenic background.

2. Genetic drift-Predicts very slow, unsteady rise of allele.

3. Indirect selection (hitchhiking)-Predicts fitness gains greater than direct advantage (if

any) of allele while the allele is substituting inpopulation.

Generation

Ara-4 mutator substitution: Average fitnesses

6500 7000 7500 8000 8500 9000

mutator frequency

mutator fitness

wild type fitness

Shaver et al. 2002, Genetics 162, 557-566.

$64,000 QUESTION

Is there any adaptive advantage to evolving a highmutation rate?

Fixation interval (generations)

Fitness gains during mutator substitutions

gain r

6500-90001500-35002000-3500

Population substituting a mutator allele

Nine “normal” populations

$65,000 QUESTION

What is the ultimate implication of indirect selection onthe mutation rate for an asexual population?

(Hint: The answer might be something sinister…)

Source: Ridley, M.2004. Evolution, 3rd ed. Blackwell.

Asexuals are ephemeral

Four ways in which an elevated genomic mutation ratecan threaten population viability in asexuals

1. Muller’s ratchet is accelerated (stochastic).

2. Mutational meltdowns are accelerated (stochastic).

3. The lethal mutation rate is exceeded (deterministic).

4. The error threshold for fitness and/or mutationrate is exceeded (deterministic).

Figure source: Maynard Smith, J. Evolutionary Genetics, 2nd ed. Oxford U. Press

"…an asexual population incorporates akind of ratchet mechanism, such that itcan never get to contain, in any of itslines, a load of mutations smaller thanthat existing in its at present least-loaded lines."

Muller 1964

Muller's Ratchet: A cost of asexuality

Note: Muller’s ratchet and mutational meltdowns can be slowed and even stopped by large population size and/or beneficial mutations.

The idea of “lethal mutagenesis” in asexuals(interesting recent papers by Jim Bull, Claus Wilke et al.)

Assume:-mutations per genome are Poisson-distributed-all mutations deleterious or neutral-deleterious mutations arise at genomic rate Ud-population infinite

Then mean fitness at equilibrium is the Poisson fraction of mutation-free genotypes:

Let b represent the number of offspring that would reproduce in theabsence of mutation.

Then extinction in the largest population is assured if equilibriumabsolute fitness is less than one:

w = eU

Lethal mutagenesis, contd.

Consider a simple model for a bacterial population that in the absenceof mutation would be growing exponentially by binary fission (and ignoring absolute generation time). For this situation, b = 2 and extinction is assured if

Ud > 0.69.

Under more realistic circumstances, a lower genomic rate can cause extinction.

Notes:

--The process is deterministic and does not depend on population size.

--Approach to equilibrium fitness may take many generations and depends ondistribution of effects of deleterious mutations. (Equilibrium occurs in 1 generationif all mutations are lethal…) This point about the approach to equilibrium fitness will become important later in a different context.

--Beneficial mutations are not considered in the model but can slow or even prevent extinction.

The idea of the “error threshold”

This concept comes from the quasispecies theory of Eigen and Schuster,which considers the evolution of polynucleotide sequences of infinite lengthin an infinite population under mutation and selection.

For a simple fitness landscape with a single peak, adaptation of the population(by which is meant localization around the peak in sequence space) is impossible if u > 1/L, where u is per site mutation rate and L is sequence length. Beyond this threshold the population undergoes a sharp transition to a state in which all sequences become equally likely.

Notes: The significance of the error threshold for extinction is controversial. Its original formulation is for an infinite population, so extinction cannot occur, strictlyspeaking. The concept has been liberally invoked in the viral mutagenesis literature, but it may be that the theory of lethal mutagenesis is more relevant there. Nonetheless, the error threshold may be an important part of extinction under the mutation rate ratchet process (to be described next), because it is insensitive to the presenceof beneficial mutations.

IMPOSSIBLE!

A sinister simulation result

The mutation rate ratchet idea: elements

1. The mutation rate in any organism--even viruses--is a polygenic trait. There aremany potential mutator loci, and their effects can act cumulatively to produceextremely high mutation rates.

2. Any antimutator allele that arises in a population is most likely to arise on theaverage loaded background and thus to have no immediate advantage over a mutatorallele. Only its future advantage--a decreased accumulation of deleterious mutationsover time--is likely to give an antimutator a selective edge. Although the equilibriumcost of a mutator allele in an asexual population is easily calculated and can besubstantial, theory indicates that this equilibrium will be approached slowly if thereare many mildly deleterious mutations.

3. In the meantime, additional mutator hitchhiking events may occur in associationwith beneficial mutations, driving the genomic mutation rate even higher.

4. Above a certain genomic mutation rate, the accumulation of deleterious mutationscauses the extinction of an asexual population in the relatively short term.

tion r

Mutation-rate ratchet

Rate of fixation of

mutators due to

hitchhiking

Rate of fixation of

anti-mutators>>

The mutation rate catastrophe hypothesis

Our hypothesis is that recurrent mutator hitchhiking(the mutation rate ratchet) can take an asexualpopulation beyond the tolerable mutation rate, causingextinction.

We will show two kinds of results that support thispossibility: Individual-based simulations and numericalsolution of a PDE model.

The required linkage

Loci that affectmutation rate:replication, repair,proofreading, etc…

Loci that affect fitness:use your imagination…

Simulations

genome

fitness (w) - rate entropy: w,

entropy: w,

Poissonw

Replication:

Simulating mutation rate evolution in asexuals-Simulations keep track of every individual and every replication event in thepopulation.

-Populations are haploid and asexual.

-Offspring can differ from parents in fitness, in mutation rate, or both.

-Offspring number is Poisson distributed for each individual; the mean is set by thefitness of the individual relative to the population mean.

-Offspring acquire XD new deleterious mutations that are either lethal or decreasefitness by a factor (1 - MD) and XB new beneficial mutations that increase fitness bya factor (1 + MB).

-Offspring acquire XM new mutator mutations that increase log mutation rate byMM and XA new antimutator mutations that decrease log mutation rate byMA.

-XD, XB, XM, and XA are all Poisson random variables with means μD, μB, μM, and μAthat depend on the genomic mutation rate, the relative genomic mutation rate of anindividual (which mutates and evolves…), and the fractions of deleterious, beneficial,mutator, and antimutator mutations fD, fB, fM, and fA, which are set by the user.

-MD, MB, MM, and MA are continuous random variables with means mD, mB, mM, and mA;a wide variety of distributions of these mutational effects was explored.

100000

-9 -7 -5 -3

100000

120000

0.001 0.01 0.1 1 10

100000

0.001 0.01 0.1 1 10 100 1000

100000

0.001 0.01 0.1 1

100000

0.001 0.01 0.1

100000

0.1 1 10

100000

M Af f

0N cov( , )xμ

log( )Bf

100000

1000000

1000 10000 100000 1000000

100000

1E-09 1E-07 0.00001 0.001 0.1 10

G HDefault parameter values

μ = 0.1fB = 0.0003fD = 0.1fM = 0.001fA = 0.0001mB = md = mM = mA = 0.03N = 10,000

( )( )yux x u e u

t= + M

u = u(x,y,t) , the probability density of genotypes withfitness x and mutation rate y at time t.

M is the mutation operator and models mutation to and fromother genotypes.

( ) yux x u e u

t= + M

Analytical theory

Model 1

Model 2

( , , ) ( ) ( , , ) ( )

B B D D

y y y y y y

M M AM AM

e u f e u x x y t g x d x u f e u x x y t g x d x u

f e u x y y t g y d y e u f e u x y y t g y d y e u+

= + + +

fB = fraction of mutations that increase fitness (beneficial)

fD = fraction of mutations that decrease fitness (deleterious)

fM = fraction of mutations that increase mutation rate (mutator)

fAM = fraction of mutations that decrease mutation rate (antimutator)

gB = distribution of effects for beneficial mutations

gD = distribution of effects for deleterious mutations

gM = distribution of effects for mutator mutations

gAM = distribution of effects for antimutator mutations

2 2(2 ) ( )x x y y y y y

u u u uu D d D D d D d u

x yx y+ + + + + +M

2 2 2 21 12 2

( ) ( )x D D D B B B

D f m f m= + + +x D D B B

d f m f m=

2 2 2 21 12 2

( ) ( )y A A A M M MD f m f m= + + + y A A M Md f m f m=

Numerical solution of Model 1

μ = 0.003fB = 1e-6fD = 0.1fM = 0.001fA = 0.0001mB = mD = mM = mA = 0.003

contour plot on a logscale.

fitness increase “pulls”mutation rate up.

eventual “phasetransition”

final state: highestmutation rate, lowestfitness.

Numerical solution

fB = 1e-10fD = 1e-2fM = 1e-4fA = 1e-5mB = mD = mM = mA = 0.03

Conditions for extinction under the mutation rateratchet (mutation rate catastrophe): Extinctionoccurs

IF: fM > fAM

(mutator mutations more common than antimutatormutations)

IFF: fD > fB > 0

(deleterious mutations more common than beneficialmutations)

100000

-9 -7 -5 -3

100000

120000

0.001 0.01 0.1 1 10

100000

0.001 0.01 0.1 1 10 100 1000

100000

0.001 0.01 0.1 1

100000

0.001 0.01 0.1

100000

0.1 1 10

100000

M Af f

0N cov( , )xμ

log( )Bf

100000

1000000

1000 10000 100000 1000000

100000

1E-09 1E-07 0.00001 0.001 0.1 10

G HDefault parameter values

μ = 0.1fB = 0.0003fD = 0.1fM = 0.001fA = 0.0001mB = md = mM = mA = 0.03N = 10,000

How it might work

Mutator hitchhiking

Fitness collapse -rate catastrophe

Fitness collapse

How it works: one possibility

H1: Fitness collapse first

Fitness collapse

How it works: the otherpossibility

H2: Mutation-rate catastrophe

Fitness collapse

tion r

Mutation-rate catastrophe

Fitness collapse

H1 or H2?

What the simulation evidence seems tosupport.

Fitness peaks first, and mutation rate keeps rising

The emerging picture: H1

Fitness collapse

Reinforced by-rate catastrophe?

Why it works (in simulations, at least)

Why does natural selection, a processthat operates through the avoidance ofextinction, drive a population extinct?

Natural selection is short-sighted

Mutational load takes

time to accumulate.

Natural selection does

not anticipate the

realization of excess

mutational load.

Can’t wait for whole process: too long.

However, mutator hitchhiking is predictable inshort run (to be addressed in a minute).

A possible approach:Create strains with one and two mutator defects. (Done.)

Test for hitchhiking of double mutator over single; this isone click of the mutator ratchet. (Done.)

Establish condition under which double-mutator (but notsingle!) has intolerable mutation rate. See if double-mutator genotype hitchhikes to fixation, then thepopulation goes extinct.

How to test it experimentally?

Source: Chao, L. and E.C. Cox. 1983. Evolution 37, 125-134

Figure 5. Mutation rates to nalidixic acid resistance measured in the constructed strains. Error bars give 95% confidence limits.

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

Wild type Single mutator

(mutL13)

Double mutator

(dnaQ905 mutL13)

tion r

Single and double-mutator strains: mutation rates

Note: Lynch and Kibota used a mutation accumulation assay to estimate Ud > 0.0002 for E. coli under experimental conditions similar to ours. Thus the 4,000-fold increase in mutation rate in our double-mutator strain suggests Ud > 0.8.

A double- vs single-mutator hitchhiking experiment

Day 0:Six separatepopulations ofa double (2M)and a single(1M) mutatorstrain areestablished inminimalmedium.(Ne 50,000)

Everyday:Eachpopulationdiluted1:1000000 andused toinoculate afresh culture,givingabout 20generations ofgrowth per day

Day 93:2M population #2 goesextinctDay 97:2M population #6 goesextinctDay 98: 2M populations#1,3,4,5 go extinctAll 1M populations extant

“Burndown” of double-mutator populations in ~1800 generations (!?)

Preliminary assays suggest that fitness increased sharply early in the 2Mpopulations, then declined sharply at the end. Mutation rate also appears to have increased greatly near the end, but more work is needed to confirm this.

Adaptation by Darwinian selection is ultimatelyself-destructive.

Most organisms in nature have to adapt now andthen to survive changes in biotic and abioticenvironments.

Under Darwinian evolution, therefore, mostorganisms should have gone extinct.

“Conclusions”

“Conclusion”

Darwin was wrong!!

“Conclusion”

Darwin was wrong!!

Extending the error threshold approach to

incorporate finite, varying population size and

effects of mutations on mutation rate itself.

Exploring effects of recombination, diploidy.

Extending simulations to very large (>1e6)

population sizes.

Further work: theory

Detailed characterization of mutation rate, fitness

and their covariance in existing “burndown”

populations. (Relies on novel methods.)

Further hitchhiking/extinction experiments at

different population sizes, mutation rates.

Sequence analysis of burndown populations.

Incorporate recombination into system somehow?

Further work: experiments

Treatment of viral infections

Age of asexual lineages

Antiquity of recombination

Genome structure

Possible implications, if true, for

Alan Perelson, Los Alamos National Lab

Alexandre Colato, Instituto de Fisica de Sao Paolo

Szi-Chieh Yu, U. Illinois Chicago

Chris Gentile, U. Pennsylvania

Ruy Ribiero, Los Alamos National Lab

Rob De Boer, Utrecht University

Valeria Souza, Universidad Nacional Autonoma de Mexico

The Alfred P. Sloan Foundation, NSF, NIH, LANL, the UNAM,

and FAPESP.

Many thanksto...

Reference

How it works - 1

Mutator hitchhiking

How it works - 2

Analytical predictions

-0.004

-0.002

0 20000 40000 60000

time (generations)

predicted

observed

-0.004

-0.002

0 20000 40000 60000

time (generations)

predicted

observed

Analytical predictions

2/ cov( , )M M

t x f mμ μ μ= +

Hitchhiking

dominates

Generation ~40000

Mutation dominates

3D plot on an

arithmetic scale.

can’t see the

accumulation of

mutators.

but the sharpness of

the “phase transition”

is seen.

Numerical solution

Growth of lineages in excess of fitness error-threshold

source frequency of mutators

Jyssum, 1960 ~2% of samples of hospital E. coli

Gross and Siegel, 1981 <1% of samples of coliform bacteria

Suárez et al., 1992 7 of 60 samples of influenza virus

Leclerc et al., 1996 ~3% of samples from pathogenic populations of E. coliand Salmonella enterica

Matic et al., 1997 up to 15% of samples from commensal and pathogenicpopulations of E. coli

Oliver et al., 2000 20% of Pseudomonas aeruginosa isolates from cysticfibrosis patients

Mutators in natural populations

GAG CTG GCG CTG GCG CTG GCG CGT

... ... ... ... ... ... ... ...

... ... ... ... ... ... ..T ...

... ... ... ... ... ... ..C ...

... ... ... ... ... ... ..T ...

..T T.. ..A ... ... T.. ..C ..C

..C ... C.. ... ..C ... ..T ..C

..T TGC AA. .GA ..T T.C CG. ..C

..C A.C .AA ..C ... ..C CAC ..C

E. coli B

E. coli O157:H7

E. coli K-12

S. typhimurium

S. enterica

S. flexneri

Y. pestis

P. aeruginosa

B. subtilis

N. meningitidis

The CTG GCG repeat array is not well conserved

Mutatormutation Beneficial mutation Deleterious mutation

Increase in population mutation ratethrough mutator hitchhiking

Mutator mutation Beneficial mutation Deleterious mutation

Antimutatormutation Beneficial mutation Deleterious mutation

Failure to decrease populationmutation rate due to anti-mutator’s

failure to hitchhike

Beneficial mutationAntimutator mutation Deleterious mutation

Source: Ban, C. and W. Yang. 1998. Cell 95, 541-552.

location of LALA repeat

ATP-binding pocket

1.0E-10

1.0E-09

1.0E-08

1.0E-07

PS2348 PS2350 PS2353 PS2355 PS2358 PS2360

Strain

tion r

Allele replacement experiments confirm mutL repeatmutations as cause of mutator phenotype in

Ara-2 and Ara-4 populations

deoxyribosyl-dihydropyrimido[4,5-c][1,2]oxazin-7-one

(dP nucleoside): a powerful base analogue mutagen

Setting up an intolerable mutation rate

(work in progress…)

Source: Negishi et al. 2002. Genetics 161: 1363-1371

Putting the hypothesis in context

Many disadvantages of asexuality are indeed already

known or have been hypothesized in theoretical work,

but these are generally subtle evolutionary impairments

that put asexual lineages at a disadvantage relative to

their sexual counterpart. These subtle impairments do

not present any real threat to an adapting asexual

population by itself. In contrast to established theory,

our findings would suggest that asexual systems are not

only at a disadvantage when compared to sexual

systems but that, by themselves, asexual systems are

fundamentally flawed.

Link to classical theory

x D Dx t f m μ=

xx t =

Fisher’s fundamental theorem:

Modification due to linkage:

Link to classical theory

Price equation:

Modification due to linkage:

2/ cov( , )M M

t x f mμ μ μ= +

/ cov( , )t xμ μ=

Evolution of the genomic mutation rate: implications for ...

Documents

Transcript of Evolution of the genomic mutation rate: implications for ...

Review of cellular division , mutation and law of inheritance, human genome project, the genomic era …………………..

Genomic Organization of Plants Terpene Synthases and Molecular Evolutionary Implications

Genomic investigations of evolutionary dynamics and ...a mutation in a particular pathway, either beneﬁcial or deleterious,may potentiate beneﬁcial mutationsin this pathway.Bycontrast,withinasinglegene,onemutation

Evolutionary Considerations in Sexual Reproduction Implications for Genomic Structure

Home | Genetics - Genomic Organization of Plant …Genomic Organization of Plant Terpene Synthases and Molecular Evolutionary Implications Susan C. Trapp and Rodney B. Croteau Institute

a+ --> a- mutation (forward mutation)

for Medical Students Review - Universidad de Navarradadun.unav.edu/bitstream/10171/39289/1/198-7122-3-PB.pdf · The hallmarks are: genomic instability and mutation, tumor promoting

Potential implications of new synthetic biology and ...This scoping report focuses on the potential implications of new synthetic biology and genomic research trajectories on the International

Low Copy Repeats in the Human Genome Implications for Genomic Structure

RISK REDUCTION STRATEGIESgbcc.kr/upload/gbc2019 RRS 2.pdf · Genomic medicine 2nd edition, Oxford, p149 Point Mutation Small Insertion/ Deletion Larger Duplication/ Deletion MLPA

eXtasy: variant prioritization by genomic data fusion€¦ · Mutation Taster 0.7659 0.8774 0.3433 0.7350 Carol score 0.7627 0.8476 0.3199 0.6956 Supplementary Table 3 – Number

Evolutionary Considerations in Sexual Reproduction Implications for Genomic Structure MI615 Andrew J. Pierce Microbiology, Immunology and Molecular Genetics.

What Should Physician Assistants Know about Genetics ... · 4/5/2001 · Cancer • familial • sporadic. ... Genomic Analysis. EGFr Mutation and Gefitinib Sensitivity in NSC Lung

Genomic complexity of multiple myeloma and its clinical ... · Genomic complexity of multiple myeloma and its clinical implications Salomon Manier 1,2, Karma Z. Salem , Jihye Park

Analyzing the genomic integrity of stem cells...Analyzing the genomic integrity of stem cells Figure 1. Implications of genomic aberrations on stem cell applications. Genomic aberrations

Genomic (Precision) Medicine for the Hospitalist · Precision Genomics at Population Level • 1-3.5 % of everyone has a well-defined actionable mutation • Most ‘actionable’

mutation breeding in pre & post genomic era

Mechanism of Homologous Recombination and Implications for … · Mechanism of Homologous Recombination and Implications for ... mutation rate than the nuclear genome (10, 11). The

Genomic and non-genomic effects of ... - Clinical Science · the cardiovascular system: clinical implications ... Through the classic pathway with androgens crossing the plasma mem-brane

LUNG ADENOCARCINOMAS. CLINICOPATHOLOGICAL STUDY WITH RESPECT TO THE UPCOMING NEW CLASSIFICATION AND EGFR-KRAS MUTATION ANALYSIS IMPLICATIONS. First author: