Genetic Theory - Overview

Pak ShamInternational Twin Workshop

Boulder, 2005

The Human Genome23 Chromosomes, each containing a DNA molecule (Watson and Crick, 1953)

3 × 109 base pairs, completely sequenced (Human Genome Project, 2003)

Approximately 24,000 genes, each coding for a polypeptide chain

Approximately 107 common polymorphisms (variable sites, documented in dbSNP database)

Genetic transmission

XY Zygote

Somatic cells

Germ cells Spermatozoa

XX Zygote

Somatic cells

Germ cells Ova Zygote

Mitosis Meiosis Fertilization

DIPLOID DIPLOID HAPLOID DIPLOID

Sources of Natural Variation

Genetic Differences Environmental Differences

Individual Phenotypic Differences

Genetic VariationChromosomal anomalies

Insertions / Deletions / Translocations

Variable sequence repeatsmicrosatellites (e.g. CACACA….)

Single nucleotide polymorphisms (SNPs)

Types of Genetic DiseaseMendelian diseases

e.g. Huntington’s disease, cystic fibrosisA genetic mutation causes the diseaseEnvironmental variation usually irrelevant Usually rareOccurs in isolated pedigrees

Multifactorial diseasese.g. Coronary heart disease, hypertension, schizophreniaA genetic variant increases the risk of diseaseEnvironmental variation usually importantOften commonOccurs in general population

Single-Gene DisordersHuman Genome Project completed in 2003Human Gene Mutation Database contains 44,090 mutations in 1,714 genesGene Test web site lists genetic tests for 1,093 diseasesdbSNP Database Build 123 contains 10,079,771 single nucleotide polymorphisms

Autosomal Dominant Disorders

Autosomal Dominant Disorders

Aa aa

Aaaa aa Aa aa

aa Aa Aa

Autosomal Recessive Disorders

Autosomal Recessive Disorders

Aa Aa

aa Aa Aa AA

X-linked Dominant Disorders

X-linked Dominant Disorders

a Aa

A a Aa aa

X-linked Recessive Disorders

X-linked Recessive Disorders

A Aa

a A AA Aa

Mendelian Segregation

Segregation Ratios

First discovered by Gregor Mendel in his experiments on the garden pea (published in 1866 and rediscovered in 1900)Form the basis of Mendel’s first law: “law of segregation”

Defined as the ratio of affected to normal individuals among the offspring of a particular type of mating.

Mendel’s Experiments

Pure Lines AA aa

F1 Aa Aa

AA Aa Aa aa

3:1 Segregation Ratio

Intercross

Mendel’s Experiments

Aa aa

Aa aa

F1 Pure line

Back cross

1:1 Segregation ratio

Segregation Ratios

Normal father x Carrier motherX-linked recessive

Normal father x Affected motherX-linked dominant

Carrier x CarrierAutosomal recessive

Affected x NormalAutosomal dominant

Segregation ratioAffected:Normal

Mating typeMode of inheritance

Segregation Ratios

Normal father x Carrier motherX-linked recessive

Normal father x Affected motherX-linked dominant

Carrier x CarrierAutosomal recessive

1:1Affected x NormalAutosomal dominant

Segregation ratioAffected:Normal

Mating typeMode of inheritance

Segregation Ratios

Normal father x Carrier motherX-linked recessive

Normal father x Affected motherX-linked dominant

1:3Carrier x CarrierAutosomal recessive

1:1Affected x NormalAutosomal dominant

Segregation ratioAffected:Normal

Mating typeMode of inheritance

Segregation Ratios

Normal father x Carrier motherX-linked recessive

1:1Normal father x Affected motherX-linked dominant

1:3Carrier x CarrierAutosomal recessive

1:1Affected x NormalAutosomal dominant

Segregation ratioAffected:Normal

Mating typeMode of inheritance

Segregation Ratios

1:1 in sonsNormal father x Carrier motherX-linked recessive

1:1Normal father x Affected motherX-linked dominant

1:3Carrier x CarrierAutosomal recessive

1:1Affected x NormalAutosomal dominant

Segregation ratioAffected:Normal

Mating typeMode of inheritance

Hardy-Weinberg Law

Parental Frequencies

Raa

QAa

PAA

FrequencyGenotype

R+Q/2a

P+Q/2A

FrequencyAllele

Mating Type Frequencies(Random Mating)

R2QRPRaa

QRQ2PQAa

PRPQP2AA

aaAaAA

Offspring Segregation Ratios

aaAa:aa0.5:0.5

Aaaa

Aa:aa0.5:0.5

AA:Aa:aa0.25:0.5:0.25

AA:Aa0.5:0.5

Aa

AaAA:Aa0.5:0.5

AAAA

aaAaAA

Offspring Genotype Frequencies

R2+QR+Q2/4 = (R+Q/2)2aa

2PR+PQ+QR+Q2/2 = 2(P+Q/2)(R+Q/2)Aa

P2+PQ+Q2/4 = (P+Q/2)2AA

FrequencyGenotype

Offspring Allele Frequencies

(R+Q/2)2 + (P+Q/2)(R+Q/2) = R+Q/2a

(P+Q/2)2 + (P+Q/2)(R+Q/2) = P+Q/2A

FrequencyAllele

Hardy-Weinberg Equilibrium

In a large population under random mating:

Allele frequencies in the offspring, denoted asp and q, are the same as those in the parental generation. Genotype frequencies in the offspring will follow the ratios p2:2pq:q2, regardless of the genotype frequencies in the parents.

Hardy-Weinberg Equilibrium

qp

qq2pqa

ppqp2A

aA

Hardy-Weinberg Disequilibrium

qp

qq2+dpq-da

ppq-dp2+dA

aA

Genetic Linkage

Genetic Markers

ClassicalMendelian DisordersBlood groupsHLA Antigens

Molecular geneticMicrosatellites (e.g. CACACA… )Single-nucleotide polymorphisms (e.g. C/T)

High-Throughput GenotypingExtreme multiplexing (multiple markers)DNA Pooling (multiple samples)

Maximum throughput of SEQUENOM system at the HKU Genome Research Centre is 100,000 genotypes / day, at a cost of US$ 0.2 per genotype

Cost of genotyping set to decrease further – eventually enabling whole-genome association studies to be done.

Linkage = Co-segregation

A2A4

A3A4

A1A3

A1A2

A2A3

A1A2 A1A4 A3A4 A3A2

Marker allele A1cosegregates withdominant disease

Crossing-over in meiosis

Recombination

A1

A2

Q1

Q2

A1

A2

Q1

Q2

A1

A2 Q1

Q2

Likely gametes(Non-recombinants)

Unlikely gametes(Recombinants)

Parental genotypes

Recombination fraction

Recombination fraction between two loci

= Proportion of gametes that are recombinant with respect to the two loci

Double Backcross :Fully Informative Gametes

AaBb aabb

AABB aabb

AaBb aabb Aabb aaBb

Non-recombinant Recombinant

Haplotypes

Haplotypes

Paternalhaplotype

Maternalhaplotype

Genotype

RecombinationParental haplotypes

Non-recombinants Single recombinants Double recombinants

Possible transmitted haplotypes

Linkage Equilibrium

sr

qqsqra

ppsprA

bB

Linkage Disequilibrium (LD)

Sr

qqs+dqr-da

pps-dpr+dA

bB

Decay of LD

Gametes

1-θ θ

Non-recombinant Recombinant

pr+d 1-pr-d pr 1-pr

AB Others AB Others

Frequency of AB gametes = (1-θ)(pr+d)+θpr = pr+(1-θ)d

Single-Gene Disorders: Some Historical Landmarks

1902: First identified single-gene disorder -alkaptonuria1956: First identified disease-causing amino acid change: sickle-cell anaemia1961: First screening program: phenylketonuria1983: First mapped to chromosomal location: Huntington’s disease1986: First positionally cloned - chronic granulomatous disease, Duchenne muscular dystrophy1987: First autosomal recessive disease cloned –cystic fibrosis

Types of Genetic DiseaseMendelian diseases

e.g. Huntington’s disease, cystic fibrosisA genetic mutation causes the diseaseEnvironmental variation usually irrelevant Usually rareOccurs in isolated pedigrees

Multifactorial diseasese.g. Coronary heart disease, hypertension, schizophreniaA genetic variant increases the risk of diseaseEnvironmental variation usually importantOften commonOccurs in general population

Genetic Study Designs

Family StudiesCase – Control Family Design

Compares risk in relatives of case and controls

Some terminologyProbandSecondary caseLifetime risk / expectancy (morbid risk)

Problem: Familial aggregation can be due to shared family environment as well as shared genes

Family Studies: Schizophrenia

13Children

9Siblings

6Parents

6Half siblings

5Grandchildren

4Nephews/Nieces

2Uncles/Aunts

2First cousins

1Unrelated

Lifetime Risk of Schizophrenia (%)Relationship to Proband

From: Psychiatric Genetics and Genomics. MuGuffin, Owen & Gottesman, 2002

Twin StudiesStudies risk of disease (concordance rates) in cotwins of

affected MZ and DZ Twin

Under the equal environment assumption, higher MZ than DZ concordance rate implies genetic factors

Problems:Validity of equal environment assumptionGeneralizability of twins to singletons

Twin Studies: Schizophrenia

48Monozygotic (MZ)

17Dizygotic (DZ)

Concordance (%)Zygosity

From: Psychiatric Genetics and Genomics. MuGuffin, Owen & Gottesman, 2002

Adoption StudiesAdoptees’ method compares

Adoptees with an affected parentAdoptees with normal parents

Adoptee’s family method comparesBiological relatives of adopteesAdoptive relatives of adoptees

Problems:Adoption correlated with ill-health/psychopathology in parentsAdoptive parents often rigorously screened

Adoption Studies: Schizophrenia

2Control parents

8Schizophrenic parents

Risk of Schizophrenia (%)Adoptees of

From: Finnish Adoption Study, as summarised in Psychiatric Genetics and Genomics. MuGuffin, Owen & Gottesman, 2002

Biometrical Genetic Model

Biometrical Genetic Model

0 d a-a

Trait Means

AA

Aa

aa

a

d

-a

aa Aa AA

Fisher’s convention: the midpoint between the trait means of the two homozygous genotypes is designated as 0

Biometrical Model: Mean

Genotype AA Aa aaFrequency p2 2pq q2

Trait (x) a d -a

Mean m = p2(a) + 2pq(d) + q2(-a)= (p-q)a + 2pqd

Biometrical Model: Variance

Genotype AA Aa aaFrequency p2 2pq q2

(x-m)2 (a-m)2 (d-m)2 (-a-m)2

Variance = (a-m)2p2 + (d-m)22pq + (-a-m)2q2

= 2pq[a+(q-p)d]2 + (2pqd)2

= VA + VD

Average Allelic EffectEffect of gene substitution: a → A

If background allele is a, then effect is (a+d)If background allele is A, then effect is (a-d)

Average effect of gene substitution is therefore

α= q(a+d) + p(a-d) = a + (q-p)d

Additive genetic variance is therefore

VA = 2pqα2

Additive and Dominance Variance

aa Aa AA

m

-a

ad

α

α

Cross-Products of Deviations for Pairs of Relatives

AA Aa aaAA (a-m)2

Aa (a-m)(d-m) (d-m)2

aa (a-m)(-a-m) (-a-m)(d-m) (-a-m)2

The covariance between relatives of a certain class is the weighted average of these cross-products, where each cross-product is weighted by its frequency in that class.

Covariance of MZ Twins

AA Aa aaAA p2

Aa 0 2pqaa 0 0 q2

Covariance = (a-m)2p2 + (d-m)22pq + (-a-m)2q2

= 2pq[a+(q-p)d]2 + (2pqd)2

= VA + VD

Covariance for Parent-offspring (P-O)

AA Aa aaAA p3

Aa p2q pqaa 0 pq2 q3

Covariance = (a-m)2p3 + (d-m)2pq + (-a-m)2q3

+ (a-m)(d-m)2p2q + (-a-m)(d-m)2pq2

= pq[a+(q-p)d]2

= VA / 2

Covariance for Unrelated Pairs (U)

AA Aa aaAA p4

Aa 2p3q 4p2q2

aa p2q2 2pq3 q4

Covariance = (a-m)2p4 + (d-m)24p2q2 + (-a-m)2q4

+ (a-m)(d-m)4p3q + (-a-m)(d-m)4pq3

+ (a-m)(-a-m)2p2q2

= 0

Covariance for DZ twins

Genotype frequencies are weighted averages:

¼ MZ twins (when π=1)½ Parent-offspring (when π =1)¼ Unrelated (when π =0)

Covariance = ¼(VA+VD) + ½(VA/2) + ¼ (0)= ½VA + ¼VD

Covariance: General Relative Pair

Covariance = Prob(π=1)(VA+VD)+ Prob(π=1/2)(VA/2)+ Prob(π=0)(0)

= (Prob(π =1)+Prob(IBD=1/2)/2)VA

+ Prob(π =1) VD

= E(π)VA + Prob(π=1)VD

= 2ΦVA + ∆VD

Total Genetic Variance

Heritability is the combined effect of all locitotal component = sum of individual loci

components

VA = VA1 + VA2 + … + VAN

VD = VD1 + VD2 + … + VDN

Correlations MZ DZ P-O UVA (2Φ) 1 0.5 0.5 0VD (∆) 1 0.25 0 0

Quantitative Genetics

Quantitative Genetics

Examples of quantitative traitsBlood Pressure (BP)Body Mass Index (BMI)Blood Cholesterol LevelGeneral Intelligence (G)

Many quantitative traits are relevant to health and disease

Quantitative Traits

0

1

2

3

1 Gene 3 Genotypes 3 Phenotypes

0

1

2

3

2 Genes 9 Genotypes 5 Phenotypes

01234567

3 Genes27 Genotypes 7 Phenotypes

05

1015

20

4 Genes81 Genotypes 9 Phenotypes

Central Limit Theorem → Normal Distribution

Continuous Variation

µ µ +1.96σµ -1.96σ

2.5%2.5%

95% probability

),(~ 2σµNX

Normal distributionMean µ, variance σ2

Bivariate normal

-3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3

0.30.40.5

Familial Covariation

Relative 1

Relative 2

),(~ ΣµNXBivariate normal disttribution

⎥⎦

⎤⎢⎣

⎡=

2

1

µµ

µ

⎥⎦

⎤⎢⎣

⎡= 2

221

1221

σσσσ

Σ

Correlation due to Shared Factors

Francis Galton: Two Journeys starting at same time

Denmark Hill VictoriaPaddington

Brixton

A B

C

Journey Times: A+B and A+C

Shared A Covariance Correlation

Shared Genes

AB CD

AC AD

Gene A is shared:= Identity-By-Descent (IBD)

⇒ Shared Phenotypic Effects

At any chromosomal location, two individuals can share 0, 1 or 2 alleles.

Identity by Descent (IBD)Two alleles are IBD if they are descended from and replicates of the same ancestral allele

7

Aa

Aa Aa

AA

aa

AA

Aa

Aa

1 2

3 4 5 6

8

IBD: Parent-Offspring

AB CD

AC

If the parents are unrelated, then parent-offspring pairs always share 1 allele IBD

IBD: MZ Twins

AB CD

AC

MZ twins always share 2 alleles IBD

AC

IBD: Half Sibs

AB CD

AC

EE

CE/DE

IBD Sharing Probability

0 ½

1 ½

IBD: Full Sibs

21

10

IBD of paternal alleles

IBD of maternal alleles

0 1

0

1

IBD: Full Sibs

IBD Sharing Probability

0 1/4

1 1/2

2 1/4

Average IBD sharing = 1

Genetic Relationships

Φ (kinship coefficient): Probability of IBD between two alleles drawnat random, one from each individual, at the same locus.

∆: Probability that both alleles at the same locus are IBD

Relationship Φ ∆

MZ twins 0.5 1Parent-offspring 0.25 0Full sibs 0.25 0.25Half sibs 0.125 0

Proportion of Alleles IBD (π)

Relatiobship Φ E(π) Var(π)

MZ 0.5 1 0Parent-Offspring 0.25 0.5 0Full sibs 0.25 0.5 0.125Half sibs 0.125 0.25 0.0625

Most relationships demonstrate variation in π across the chromosomes

Proportion of alleles IBD = Number of alleles IBD / 2

Classical Twin AnalysisMZ Twins DZ Twins

Average genetic sharing 100% 50%

Phenotypic correlation

=

> ⇒

⇒

Geneticinfluences

No genetic influences

Note: Equal Environment Assumption

P1

A1C1E1

P2

A2 C2 E2

1

[0.5/1]

e ac eca

ACE Model for twin data

Implied covariance matrices

⎥⎦

⎤⎢⎣

⎡

+++++

=Σ22222

222

ecacaeca

MZ

⎥⎦

⎤⎢⎣

⎡

+++++

=Σ 2222221

222

ecacaeca

DZ

⇒ Difference between MZ and DZ covariance ~ Genetic Variance / 2

Heritability

Is proportion of phenotypic variance due to genetic factorsIs population-specificMay change with changes in the environmentA high heritability does not preclude effective prevention or interventionMost human traits have heritability of 30% –90%

Liability-Threshold Models

Single Major Locus (SML) Model

Genotype Phenotypef2AA

aa

Aa

Disease

Normal

f1

f0

1- f2

1- f1

1- f0

“Penetrance parameters”

Liability-Threshold Model

Affected individuals

Threshold Liability

Normal individuals

Population distribution of liability to disease

Liability-threshold model

0

0.1

0.2

0.3

0.4

-3 -2 -1 0 1 2 3

General population

Relatives of probands

Threshold Model with SML

f(X)

X

AA

Aa

aa

Quantitative Trait Linkage

QTL Linkage Analysis

Local genetic sharing 2 1

Phenotypic correlation

Linkage

No linkage

0

DZ Twins / Sibling Pairs

P1

Q1A1E1

P2

Q2 A2 E2

0.5

e qa eaq

π̂

QTL linkage model for sib pairs

Exercise

From the path diagram write down the implied covariance matrices for sib pairs with proportion IBD sharing of 0, 0.5 and 1.

Quantitative Association

Allelic Association

disease susceptibility allele is more frequent in cases than in controls

Controls Cases

Example: Apolipoprotein E ε4 allele increases susceptibility to Alzheimer’s disease

Analysis of Means

AA Aa aa

No association

Association

Phenotype

Genotype

Causes of association

Direct: allele increases risk of disease

Indirect: allele associated with a risk-increasing allele through tight linkage

“Spurious”: allele associated with disease through confounding variable (e.g. population substructure).

Haplotype associationMutational event on ancestral chromosome

Multiple generations

Present mutation-bearing chromosomes with variable preserved region

Complex Disorders:Some Historical Landmarks

1875: Use of twins to disentangle nature from nurture (Galton)1918: Polygenic model proposed to reconcile quantitative and Mendelian genetics (Fisher)1965: Liability-threshold model postulated for common congenital malformations (Carter)1960’s: Association between blood groups and HLA antigens with disease1990’s: Identification of APOE-e4 as a susceptibility allele for dementia 2000’s: International HapMap Project

of the Behavior Genetic Association.