Instructor: Julia N. Bailey, Ph.D. Lecture: 1:00 – 2:50 Thursdays, Public Health 61262

Instructor: Julia N. Bailey, Ph.D.

Lecture: 1:00 – 2:50 Thursdays, Public Health 61262

Office: West LA VA, Building 500, Suite 3405Office Hours: By appointment

Email: [email protected]

EPIDEMIOLOGY 249 • GENETIC EPIDEMIOLOGY

Linkage:

•Basic principles (revisiting Mendelian segregation)

•Hardy Weinberg Equilibrium (HWE)

•Inbreeding

•Mendel segregation of traits - Linkage

•genetic markers and maps

•model-based linkage models

•discrete trait linkage

•pedigrees

•LOD scores

• Segregation ratio is ½ and parental transmissions are independent– A heterozygous parent (Aa) is equally likely to

transmit either of the two alleles– What one parent transmits has no effect on

the other parent

Mendel’s First Law

If a trait is recessive does that mean that one in four people will have that trait?

Question?

Hint - we have to think in terms of allele frequencies and genotype frequencies in the population.

Allele frequency

• Definition:– The probability that a gene selected at

random will be of a specific type

• Frequency of ‘A’ is p

• Frequency of ‘a’ is q

Genotype Frequencies

Three types of genotypes – AA, Aa, AA

p= f(AA) + ½ f(Aa)

q= f(aa) + ½ f(Aa)

f(AA)+f(Aa)+f(aa)=1=p+q

Calculating p&q by gene counting

Population has the following individuals:AA, Aa, AA, Aa, aa, AA, AA, AA, Aa, Aa(10 individuals = 20 alleles)

f(AA)=p=(2+1+2+1+0+2+2+2+1+1)/20 =14/20=0.7f(aa) = q = (0+1+0+1+2+0+0+0+1+1)/20 =6/20=0.3(q=1-p)

Godfrey Harold Hardy (1877 – 1947) was a prominent English mathematician who left his mark in the field of population genetics in addition to mathematics. He played cricket with the geneticist Reginald Punnett who introduced the problem to him.

Dr Wilhelm Weinberg (1862 — 1937) was a German physician who in 1908 independently formulated the Hardy-Weinberg principle.

The Hardy–Weinberg principle states that both allele and genotype frequencies in a population remain constant or are in equilibrium from generation to generation unless specific disturbing influences are introduced.

Hardy-Weinberg Equilibrium

• Predicts genotype frequencies from allele frequencies

AA = p2 Aa = 2pq aa = q2

• Populations will be in HWE in one generation unless specific disrupting influences are introduced.

Test of H-W equilibrium

• Simple chi-square test (goodness of fit)

• Compare observed to expected allele frequencies

Calculating HWEAA, Aa, AA, Aa, aa, AA, AA, AA, Aa, Aap=0.7, q=0.3

AA Aa aa

Observed 5 4 1

Expected p2 N 2pqN q2N

(.7) 210

=4.9

2(.3)(.7) 10

=4.2

(.3) 210

=0.9

2 = 0.01, p=0.99

Causes of Deviations from Hardy-Weinberg Genotype Frequencies

• Assortative (non-random) mating– Ethnic/racial/regional groups, endogamy– Inbreeding or consanguineous mating

• Changing allele frequencies– Genetic drift (small populations only)– Selection, mortality, mutation, migration

• Genotyping error– Tends to increase homozygosity

• Predicted genotype frequencies:

PAA = p2 (1-f) + pf

PAa = 2pq(1-f)

Paa = q2(1-f)+qf

Effect of Inbreeding

f is the ‘inbreeding coefficient’

Bennett et al. (2002)

• Consanguineous matings increase rates of recessive genetic disease, but most such diseases are rare such that a large relative risk may still imply a small absolute risk

• Current laws prohibiting first-cousin marriages are overly restrictive

King Charles II of Spain, the product of generations of inbreeding by the Hapsburg family. This is a man whose face and chin were so distorted by the "Hapsburg Lip" that he could not eat without assistance. He also had cognitive issues.

Matings VS populations

• Mendel’s peas again…

Going from segregation to linkage…

• Study transmission of two traits simultaneously• Start with plants that are purebred for two traits• e.g., round yellow seeds and wrinkled green

seeds• Yellow is dominant over green• Round is dominant over wrinkled• Cross these to produce round yellow ‘dihybrids’• Cross the dihybrid plants to produce a variety of

combinations of traits

Dihybrid Cross

F0

F1

F2

Takes 2 generations to see results

AA X aa

F0 X F0 produces F1 (Filial 1)

Aa X Aa

F1 X F1 produces F2

AA, Aa, aa (1/4, ½, ¼)

Mendelian Genetics

• Independent Assortment– Segregations for two traits are independent

• Mendel was wrong on this one!– He studied pairs of traits that showed

independence• e.g., color and shape of seeds

– Some traits that he studied separately would not have shown independence if he had studied them jointly because THEY WERE LINKED ON THE CHROMOSOME

Mendel’s Second Law

Patterns of Recombination

Thomas Hunt Morgan

• amount of crossing over between linked genes differs led to the idea that crossover frequency might indicate the distance separating genes on the chromosome.

Alfred Sturtevant (1913). J. Exper. Zool.

– showed genes have a "linear arrangement" – ordered

– developed recombination fraction

– Centimorgan (cM) is defined as the distance between genes (DNA) for which one product of meiosis in 100 is recombinant.

– A recombinant frequency (RF) of 1 % is equivalent to 1 genetic map unit. (mu)

Recombination Fraction

• The proportion of meioses that produced a recombinant between the two loci will always range between 0 and 0.5. This proportion is called the recombination fraction and is usually denoted (theta).

is a measure of distance

T

U

t

uT t

U u

Here, there will be fewrecombinaints, and will be near zero.

Here, there will be many recombinants and will be greater than zero.

The number of recombinants is directly related to the distance between the loci.

Exercise: Estimate

Exercise: Estimate

# recombinants

(# recombinants+ # non-recombinants)

= 1/(1+5) = 0.17

gene 1 gene 2 recombination frequency

yellow white 0.010

yellow vermilion 0.322

white vermilion 0.297

vermilion miniature 0.030

white miniature 0.337

white rudimentary 0.452

vermilion rudimentary 0.269

As a very rough rule of thumb, 1 cM on a chromosome encompasses 1 megabase (1 Mb = 100 bp) of DNA.

•this relationship is only approximate.

Genetic maps of human females average 90% longer than the same maps in males, their chromosomes contain the same number of base pairs. So their physical maps are identical.

Genetic Map Physical MapRecombination fraction base pairs (bp, or Mb)

• Linkage Analyses (Finally!)

– Two point Linkage analyses• Disease & Marker • Marker & Marker

(that’s how they made the map).

Ex Calculating by HandABO Blood Group

• Blood types: A, B, AB and O

• Alleles: IA, IB and i

• Genotypes:– A is either IA i or IA IA

– B is either IB i or IB IB

– AB is always IA IB

– O is always i i

Exercise:Computing by Hand

Exercise:Computing by Hand

# Recombinants = 2

# Non Recombinants = ?

Problems

• Assumed phase (need to consider both)

• Assumed complete dominant penetrance

• Assumed complete genotype data (no missing data).

• Direct method may be biased.

• Maximum likelihood estimator of recombination

– Extracts all linkage information (e.g. phase)

• Measure evidence for linkage• Logarithm of the Odds (odds for linkage vs odds against linkage)

• z is used directly as the indicator of significance.– z greater than 3.0 (3.3) is taken as significant

evidence for linkage.– z less than –2.0 is taken as significant evidence

against linkage.

LOD scores

)5.()free (

log

LL

Z

Z()=log10[L]- log10[L(=0.5)]

)5.()free (

log

LL

Z

• Various are estimated – usually at 0, 0.1, 0.2, 0.3, 0.4

• Lodscores are computed for each family• Lodscores of multiple families are just summed

across families.

– Maximum Lods are the highest lod obtained (maximizing )

• Likelihood of the pedigree, given specific parameters– Distance between disease & marker is – Disease is modeled with specific

inheritance patterns, e.g. dominant/recessive/additive, gene frequency, autosomal or X linked

– Can incorporate parameters for missing data,

Benefits

Typical two-point analyses

Test Disease – Marker at various values of

Genome Scan

• Assume a genetic model – either a guess or based on data

• We want to know where that gene is in the genome.

• Assume we have genetic markers evenly spaced throughout the genome (genome scan – 10-20 cM spaced markers ~400 microsatellite markers, SNP genome scans may have 100,000+ markers)

• Assess likelihood of linkage of each marker with disease status.

DISEASE GENE

Is this a good family for Linkage Analyses?

Multipoint Linkage Analysis

• The classical lodscore method is often called two-point because we test two loci (trait and marker) for linkage.

• It is possible to combine information from multiple markers in the same area. This increases the power to detect linkage and improves localization.

• This combined information can be used to estimate the inheritance (recombination information) at each point on the chromosome (no longer need an explicit estimate of q).

• Combining marker information in this way is called multipoint linkage analysis.

Disease Gene (DG) Marker 1 Marker 2 Marker 3

Marker 1 DG Marker 2 Marker 3

Marker 1 Marker 2 DG Marker 3

Marker 1 Marker 2 Marker 3 DG

Marker 1 Marker 2 Marker 3





0.4, 0.13, 0.27

0.3, 0.13, 0.27

0.2, 0.13, 0.27

0.1, 0.13, 0.27

0.05, 0.13, 0.27

0, 0.13, 0.27

.13 .27

tested





0.05, 0.08, 0.0.27

0.06, 0.09, 0.27

0.08, 0.05, 0.27

0.13, 0, 0.27

.13 .27

tested





0.13, 0.1, 0.17

0.13, 0.2, 0.07

0.13, 0.27, 0

.13 .27

tested





0.13, 0.27, 0.1

0.13, 0.27, 0.2

0.13, 0.27, 0.3

0.13, 0.27, 0.4

.13 .27

tested

Pedigree

• Seems to have originated in French– Pied de Grue = foot of the crane

• A pedigree is a chart showing a “family tree”• Old pedigrees may have looked like a bird’s foot• Modern charts are very sophisticated and can

display a tremendous amount of information about a family. – Standard rules– Computer programs can draw them for us

Rules for Drawing Pedigrees

• Most of the following rules are widely accepted

• These rules were developed by Robin L. Bennett et al. (1995) American Journal of Human Genetics, 56, 745-752.

Instructor: Julia N. Bailey, Ph.D. Lecture: 1:00 – 2:50 Thursdays, Public Health 61262

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Transcript of Instructor: Julia N. Bailey, Ph.D. Lecture: 1:00 – 2:50 Thursdays, Public Health 61262