Evolution of the genomic mutation rate: implications for ...
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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
Transcript of 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
A B
C
mu
tatio
n r
ate
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
Ara-
Ara-
Ara+
Daily growth in broth with 100-fold dilution
Daily transfer regime
100 ul into 9.9 mlfresh medium
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 2
Ara 4
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
Ara+3
insertion of G after position
521
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
Ara-2
Ara-4
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.
Fitn
ess
rela
tive
to
ance
stor
Generation
Ara-4 mutator substitution: Average fitnesses
Mut
ator
fre
quen
cy
0.8
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1
1.1
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1.8
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0
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1
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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
-0.1
-0.05
0
0.05
0.1
0.15
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0.25
0.3
Fitn
ess
gain r
elat
ive
to a
nces
tor
6500-90001500-35002000-3500
A+3
A-2
A-4
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
d
b eU
d < 1
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.
time
muta
tion r
ate
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,
iw
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.
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m m
0N cov( , )xμ
log( )Bf
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D E F
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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
0 0
0 0
( , , ) ( ) ( , , ) ( )
( , , ) ( ) ( , , ) ( )
y y y
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+
= + + +
+ +
M
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 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)
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m m
0N cov( , )xμ
log( )Bf
A B C
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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
Mutation-rate ratchet
Fitness collapse -rate catastrophe
Fitness collapse
H2H1
How it works: one possibility
H1: Fitness collapse first
time
mut
ation
rate
Fitness collapse
How it works: the otherpossibility
H2: Mutation-rate catastrophe
Fitness collapse
time
muta
tion r
ate
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
Mutation-rate ratchet
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
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1.E-06
Wild type Single mutator
(mutL13)
Double mutator
(dnaQ905 mutL13)
Muta
tion r
ate
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
Time
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.
So…
“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
Mutation-rate ratchet
Analytical predictions
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time (generations)
rate
of
mu
tati
on
-ra
te i
nc
rea
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predicted
observed
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of
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es
s i
nc
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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 ...
... ... ... ... ... ... ..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
time
Mutatormutation Beneficial mutation Deleterious mutation
Increase in population mutation ratethrough mutator hitchhiking
Mutator mutation Beneficial mutation Deleterious mutation
time
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
Muta
tion r
ate
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
2/
x D Dx t f m μ=
2/
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=
