Lecture 19 : Mutation

November 2, 2012

Last Time

Human origins

Human population structure

Signatures of selection in human populations

Neanderthals, Denisovans and Homo sapiens

Today

Mutation introduction

Mutation-reversion equilibrium

Mutation and selection

What Controls Genetic Diversity Within Populations?

4 major evolutionary forces

Diversity

Mutation+

Drift-

Selection

+/-

Migration

+

Mutation

Primary driver of genetic diversity

Main source of new variants within a reproductively isolated species

Mutation often ignored because rates assumed to be extremely low relative to magnitude of other effects

Accumulation of mutations in population primarily a function of drift and selection PLUS rate of back-mutation

Mutation rates are tough to estimate!

Spontaneous mutation rates Schlager and Dickie (1967) tracked

spontaneous mutation at 5 loci controlling coat color in 7.5 million house mice

Forward > Backward mutation

http://www.gsc.riken.go.jphttp://jaxmice.jax.org

Mutation Rates can Vary Tremendously Among Loci

Length mutations occur much more frequently than point mutations in repetitive regions

Microsatellite mutation rates as high as 10-2

Source: SilkSatDB

Question:

Do most mutations cause reduced fitness?

Relative Abundance of Mutation Types

Most mutations are neutral or ‘Nearly Neutral’

A smaller fraction are lethal or slightly deleterious (reducing fitness)

A small minority are advantageous

Types of Mutations (Polymorphisms)

First and second position SNP often changes amino acid

UCA, UCU, UCG, and UCC all code for Serine

Third position SNP often synonymous

Majority of positions are nonsynonymous

Not all amino acid changes affect fitness: allozymes

Synonymous versus Nonsynonymous SNP

Nuclear Genome Size Size of nuclear genomes

varies tremendously among organisms

Weak association with organismal complexity, especially within kingdoms

Arabidopsis thaliana 120 MbpPoplar 460 MbpRice 450 Mbp Maize 2,500

Mbp Barley 5,000

MbpHexaploid wheat 16,000

MbpFritillaria (lilly family) >87,000

Mbp

Noncoding DNA accounts for majority of genome in many

eukaryotes

Intergenic space is larger

Transposable element insertions (Alu in humans)

Noncoding DNA accounts for majority of genome in many

eukaryotesG

enic

Fra

ctio

n (%

)

Genome Size (x109 bp)

Intron Size Partly Accounts for Genome Size Differences

Fugu: 365 Mbp

Human: 3500 Mbp

log(

num

ber

of in

tron

s)

Intron Size (bp)

Aparicio et al. 2002, Science 297:1301

What is the probability of a mutation hitting a coding region?

Lynch (2007) Origins of Genome

Architecture

Composition of the Human Genome

Reverse Mutations

Most mutations are “reversible” such that original allele can be reconstituted

Probability of reversion is generally lower than probability of mutation to a new state

Possible States for Second Mutation at a LocusThr Tyr Leu LeuThr Tyr Leu LeuACC TACC TAAT TTG CTGT TTG CTG

Reversion ACC TACC TGGT TTG T TTG CTG CTG

Thr Thr PhePhe Leu Leu Leu LeuC GC GACC TACC TCCT TTG T TTG CTG Thr CTG Thr SerSer Leu Leu Leu Leu

A CA C

ACC TACC TTTT TTG CTG T TTG CTG Thr Thr CysCys Leu Leu Leu Leu

C TC T

Allele Frequency Change Through Time

001 ppp

With no back-mutation:

0)1( p

0)1( pp tt

How long would it take to reduce A1 allele frequency by 50% if μ=10-5?

Two-Allele System with Forward and Reverse Mutation

where μ is forward mutation rate, and ν is reverse mutation rate

A1 A2 µ

ν

qpq Expected change in mutant allele:

Allele Frequency Change Driven By Mutation

Equilibrium between forward and reverse mutations:

)( qq

)(

eq )(

ep

qpq

Allele Frequency Change Through Time with Reverse mutation

Forward Mutation (µ)

Reverse Mutation (ν)

Allele Frequency (p)

Mutant Alleles (q)

Equilibrium Occurs between Forward and Reverse Mutation

Forward mutation 10-5

Lower rate of reverse mutation means higher qeq

)(

eqIs this equilibrium stable or unstable?

μ=10-5

Mutation-Reversion Equilibrium

)(

ep

where µ=forward mutation rate (0.00001)and ν is reverse mutation rate (0.000005)

Mutation-Selection Balance

Equilibrium occurs when creation of mutant allele is balanced by selection against that allele

For a recessive mutation:

pqmu

0 smu qq

At equilibrium:

2

2

1 sq

psqp

sqeq

sqeq

2

2

2

1 sq

psqqs

assuming: 1-sq21

sqeq

What is the equilibrium allele frequency of a recessive lethal with no mutation in a large (but finite) population?

What happens with increased forward mutation rate from wild-type allele?

How about reduced selection?

Balance Between Mutation and Selection

Recessive lethal allele with s=0.2 and μ=10-5

Muller’s Ratchet

Deleterious mutations accumulate in haploid or asexual lineages

Driving force for evolution of recombination and sex

Mutation-Selection Balance with Dominance

Dominance exposes alleles to selection, and therefore acts to decrease equilibrium allele frequencies

hsqeq

for h>>0

Complete Dominance of A2:

sqeq

sqeq

Recessive Case:

Which qeq is larger?

Why?

Effect of dominance and selection on allele frequency in mutation-selection balance (μ=10-5)

Drastic effect of dominance on equilibrium frequencies of deleterious alleles

Exposure to selection in heterozygotes

recessive case

What if the population is not infinite?

Fate of Alleles in Mutation-Drift Balance

Time to fixation of a new mutation is much longer than time to loss

Npu

2

1)(

Nqu

2

11)(

u(p) is probability of fixationu(q) is probability of loss

An equilibrium occurs between creation of new mutants, and loss by drift

p=frequency of new mutant

allele in small population

Infinite Alleles Model (Crow and Kimura Model) Each mutation creates a completely new allele

Alleles are lost by drift and gained by mutation: a balance occurs

Is this realistic?

Average human protein contains about 300 amino acids (900 nucleotides)

Number of possible mutant forms of a gene:542900 1014.74 xn

If all mutations are equally probable, what is the chance of getting same

mutation twice?

Infinite Alleles Model (IAM: Crow and Kimura Model)

Homozygosity will be a function of mutation and probability of fixation of new mutants

21 )1()

2

11(

2

1

t

eet f

NNf

Probability of sampling same

allele twice

Probability of sampling two

alleles identical by descent due to

inbreeding in ancestors

Probability neither allele

mutates

Expected Heterozygosity with Mutation-Drift Equilibrium under IAM

At equilibrium ft = ft-1=feq

Previous equation reduces to:

214

21

e

eq Nf

Ignoring μ2

14

4

e

ee N

NH

Remembering that H=1-f:

4Neμ is called the population mutation

rate

21 )1()

2

11(

2

1

t

eet f

NNf

14

1

eeq Nf

Ignoring 2μ

Equilibrium Heterozygosity under IAM

Frequencies of individual alleles are constantly changing

Balance between loss and gain is maintained

14

4

e

ee N

NH

4Neμ>>1: mutation predominates, new mutants persist, H is high

4Neμ<<1: drift dominates: new mutants quickly eliminated, H is low

Effects of Population Size on Expected Heterozgyosity Under Infinite Alleles Model (μ=10-5)

Rapid approach to equilibrium in small populations

Higher heterozygosity with less drift