Mutations Mutations de novode novoIntroduction to genetics

Department of Medical GeneticsMedical University of Warsaw

De novo mutations

- importance

• so far omitted from our course –

to make things simpler

• very rare indeed, BUT ...

• historical necessity

(population size vs allele heterogeneity vs

consequences of homozygosity)

• suprising frequency in diseases with genetic

background (today’s topic)

• causes of mutations?

Mutations vs allele frequency

(mutation-retromutation equilibrium)

p → q

Generation 0: p0=1; q0=0

Generation 1: q1=

Generation n: qn=qn-1+µpn-1; pn=(1-µ)n

Generation 2: q2=

(mutation rate)

with frequency µµµµ

µp0=µ; p1=(1-µ)

q1 p2=(1-µ)2+µp1;

p ← q

qn=qn-1+µpn-1

(retromutation rate)

with frequency νννν

-νqn-1

���� µpn-1 – νqn-1 = 0

since p+q=1 ���� p=(1-q)

equilibrium: qn=qn-1 ���� µpn-1 = νqn-1

q = µ / (µ+ν)

p = ν / (µ+ν)

���� µ(1-q)=vq���� µ-µq=νq ���� µ=νq+µq=q(µ+ν)

For a mutation with a strong phenotypic effect the frequency of a mutated allele

is determined by selectionrather than retromutation

selection coefficient (S) –

denotes a degree of reproductive deficiency

of a given genotype in relation to a genotype

with the highest reproductive rate in a population

S jest dopełnieniem wartości przystosowawczej (W) genotypu do jedności (S = 1 – W).

Selection & allele frequency

(selection in medical genetics)

S=1/3

Selection & allele frequency

(selection in medical genetics)

N=9×3=27 N=4×2=8 (50%->23%)

N=27×3=81 N=8×2=16 (50%->16%)

N=81×3=243 N=16×2=32 (50%->12%)

N=9 N=4 (50%->31%)

S=1/3

Selection & allele frequency

(selection in medical genetics)

S=1

Genetically lethal disease

either

• kills before puberty

or

• causes sterility

2

Fq 1p

2p

Fq ≈→≅∩=

Autosomal dominant inheritance

Disease frequency F

Mutated allele frequency q

Autosomal recesive inheritance

X-linked recessive inheritance

males: Fm=

Fq =

Hardy & Weinberg

principle

p2+2pq+q2=1

p+q=1

Disease frequency vs

allele frequency

F =

F =

2pq

q2

q q = Fm

All defective alleles

are being lost in each generation

and must be replaced via mutations

All cases of disease are due to new mutations !!! Very low recurrence risk apart from germline mosaicism

de novo mutation

selection

q = µ

p – wild-type allele frequency

q – mutated allele frequency

µ – mutation frequency

Autosomal dominant diseases

(genetically lethal)

Some defective allelesare being lost in each generationand must be replaced via mutations

S×q = µ

p – wild-type allele frequency

q – mutated allele frequency

S – selection coefficient

µ – mutation frequency

Autosomal dominant diseases

(all)

de novo mutation

selection

• population: N

• disease frequency: q2

• No of individuals not passing their alleles: q2×N

(only q are lost)

• No of alleles lost: 2 × q2×N

• No of all alleles: 2 × N

• frequency of alleles being lost: 2 × q2×N / 2 × N = q2

• only q are lost

• lost alleles replaced due to de novo mutations: µ=q2

All homozygotes are sterile,

their alleles are lost in each generation

and must be replaced via mutations

Autosomal recessive diseases

(genetically lethal)

de novo mutation

selection

Practically in autosomal recessive diseases

mutations de novo need not be considered !

Autosomal recessive diseases

(genetically lethal)

example: q=0.01 => µ=0.0001 (µ is very small, ≈0)

q2 = µ

de novo mutation

selection

All homozygotes are sterile,

their alleles are lost in each generation

and must be replaced via mutations

p – wild-type allele frequency

q – mutated allele frequency

µ – mutation frequency

All homozygotes are less fertile, some

of their alleles are lost in each generation

and must be replaced via mutations

Autosomal recessive diseases

(all)

de novo mutation

selection

• population: N

• disease frequency: q2

• No of individuals not passing their alleles: q2×N

(only q are lost)

• No of alleles lost: 2 × S × q2×N

• No of all alleles: 2 × N

• frequency of alleles being lost: 2 × S×q2×N / 2 × N = S×q2

• only q are lost

• lost alleles replaced due to de novo mutations: µ=S×q2

If an autosomal recessive disease is not genetically lethal,

de novo mutations play even lesser role !

p – wild-type allele frequency

q – mutated allele frequency

S – selection coefficient

µ – mutation frequency

Autosomal recessive diseases

(all)

example: q=0.01 & S=0.25 => µ=0.000025=2.5×10-5

µ = S×q2

All homozygotes are less fertile, some

of their alleles are lost in each generation

and must be replaced via mutations

de novo mutation

selection

XY XX

X-linked recessive diseases

(genetically lethal)

If the disease is genetically lethal,

all mutated alleles

carried by hemizygotic males

are lost in each generation

achieving equilibrium is

more complex

de novo mutation

selection

H/2

A H

H/2+µ

A

µ

H=½H+2µ

H-½H=2µ

½H=2µ //×2

H=4µ

H/2+

µ+µH=4µH/2+µA=3µ

A=½H+µA=½(4µ)+µA=2µ+µA=3µ Częstość:

A – chorych mężczyzn

H – kobiet nosicielek

µ – mutacji

X-linked recessive diseases Frequency of mutations (µ), sicked males (A) and female carriers (H)

2µ

3µ 4µ

2µ+µ

3µ

µ

2µ+

µ+µ4µ2µ+µ3µ

Częstość:

A – chorych mężczyzn

H – kobiet nosicielek

µ – mutacji

X-linked recessive diseases Frequency of mutations (µ), sicked males (A) and female carriers (H)

3/1000

3/1000

1/1000

2µ+

µ+µ2µ+µ3/1000

X-linked recessive diseases Frequency of mutations (µ), sicked males (A) and female carriers (H)

N = 1000M+1000K

µ = 1/10004/1000

4/2000(2/1000)

2/1000

+

1/1000

4/1000

X-linked recessive diseases Frequency of mutations (µ), sicked males (A) and female carriers (H)

A=½H+µ

H=½H+µ+µH=4µ

A=3µ

The frequency of female carriers

The frequency of sick males

µ - mutation rate

Sporadic

case 1

Probability of

I2 is

a carrier

I2 isn’t

a carrier

initial 4µ 1

conditional

(sick son)1/2 µ

odds 2 µ µ

final risk 2/3 1/3

Sex-linked recessive disease –mutation de novo (µf=µm) or inheritance? [Bayes theorem]

L1: I2 jest nosicielką

L2: mutacja de novo

LR=L1/L2=2 (2:1):

Every third sporadic case is due to de novo mutation!!!

Sex-linked recessive disease –mutation de novo (µf=µm) or inheritance? [LR]

~4µ

1/2

L1 = 4µ×0,5 = 2µ

L2 = 1×µ = µ

µ

~1

L1: I2 is a carrier

L2: mutation de novo

Results of dystrophin gene mutation in DMD:

a sample of a muscle of the healthy person (upper)

and the affected one (lower) stained with HE (left) or

immunostained with antibody against dystrophin (right)

Calves pseudohypertrophy

muscles are replaced with

fat and connective tissue

in 8-years old boy with

Duchenne muscular dystrophy

Duchenne muscular dystrophy myopathy due to DMD mutations (1/3500 M)

Gowers maneuver: boy with DMD rises from the ground

Duchenne muscular dystrophy

myopathy due to DMD mutations

• A third of mothers who have

a single son affected will not themselves be

carriers of a mutation in the DMD gene !!!

• Thus they have very low risk (µ)

of subsequent problems

α - male/female ratio of mutations)

Is evolution male-driven?

De novo mutation rates of male & female

origin in the diseases studied so far

Nat Rev Gen 2001

Meiosis in females

and in males

H/2

A H

H/2

+µF

A

µM

H=½H+µM+µF

H-½H=µM+µF

½H=µM+µF /×2

H=2µM+2µF

H/2+

µF+µM

H=

2µF+

2µM

H/2+µF

A=

2µF+µM

A=½H+µF

A=½(µM+µF)+µF

A=2µF+µM

Częstość:

A – chorych mężczyzn

H – kobiet nosicielek

µ – mutacji

X-linked recessive diseases Frequency of mutations (µ), sicked males (A) and female carriers (H)

when µF≠µM

2µf +µmµf +µm

µm

2µf +µm

µf +µm

+µf +µm

2µf +µm2(µf +µm)

µf +µm+µf

=2µf +µm

X linked recessive inheritance: relationship between µµµµ,

H, and A (cntd.), µµµµ differes between sexes (µf =µm) cntd.

gametes

chromosomes

people

people

4/1000 6/2000

X: 2/1000

Y: 0/ 1000

X: 4/1000

4/1000 6/1000

Relationship between µµµµ, H, and A (cntd.), µµµµ differs between sexes

Nfem.=Nmale.=1000, µµµµm=2/1000, µµµµf=1/1000

Y: 0/1000

X: 4/1000

X: 2/1000

X: (3+1)/1000

X: (3+1)/1000gametes

chromosomes

people

people

Sporadic

case 2

LR= (µf +µm) / µf.

X-linked recessive disease –

mutation de novo (µf≠µm) or inherited?

~2×(µf+µm)

1/2

L1= µf+µm

L2=1×µf=µf

µf

~1

L1: I2 is a carrier

L2: de novo mutation

if µf=0.2µm, then LR=1.2/0.2=6, tzn.:

Only 1/7 of sporadic cases are due to de novo mutations

P m

oth

er

as a

carr

ier

µµµµm

/µµµµf

0,67

0,72

0,77

0,82

0,87

0,92

2 3 4 5 6 7 8 9 101

X-linked recessive disease –

mutation de novo (µf≠µm) or inherited?

� Hemophilia A and hemophilia B are X-linked disorders of coagulation caused by mutations in the F8 and F9 genes, respectively. Mutations of F8 cause deficiency or dysfunction of clotting factor VIII; mutations of F9 cause deficiency or dysfunction of clotting factor IX.

� Hemophilia A has an incidence of 1 in 5000 to 10,000 newborn males.

� Hemophilia B is far rarer, with an incidence of 1 in 100,000.

Subcutaneous hematoma of the forehead

in a young heophiliac boy, days after a minor contusion.

The appearance of the forehead returned to normal in 6 months

Hemophilia B Factor IX α ~4 Sommer 2001.

Hemophilia A Factor VIII α ~3 Rosendaal 1990.

Hemophilia

� De novo mutations arise with comparable frequency during oogenesis and spermatogenesis

� The dystrophin gene is a very large (>2mB) and contains many repetitive regions. Furthermore, a greater than 30-fold(!) reduction in dystrophin activity must occur before the DMD phenotype is observed Sommer 2001.

� High frequency of large deletions (60% to 65%), large duplications (5% to 10%), and small deletions, insertions, or nucleotide changes (25% to 30%).

� Most de novo large deletions arise during oogenesis, whereas most de novo nucleotide changes arise during spermatogenesis

Duchenne muscular dystrophy

an exception to the rule?