Download Mendelian Inheritance

2013-06-20
Genes — Mendelian Inheritance
Gregor Mendel, monk in a
monastery in Brünn (now
Brno in Czech Republic):
Breeding experiments with the
garden pea: Flower color and
seed shape (phenotypes) are
determined by “factors” (now
“genes”) that are passed
through generations. He
formulated two laws of
inheritance that he thought
were generally valid.
Lecture 1
Mendelian Inheritance
Jurg Ott
Mendel’s paper
Mendel’s Laws
Mendel GJ (1866)
Versuche über PflanzenHybriden. Verh Naturforsch Ver Brünn 4:3-47
• First Law, Segregation of Characteristics
•
Of a pair of characteristics (e.g. blue and
brown eye color) only one can be represented
in a gamete even though there are two genes in
ordinary cells.
Second Law, Independent Assortment
For two characteristics, the genes are inherited
independently. Today we make use of
deviations from this law for statistical gene
mapping.
Ironically, when Mendel’s
paper was published in
1866, it had little impact. It
wasn’t until the early 20th
century that the enormity
of his ideas was realized.
Mendelian Inheritance
Familial Hypercholesterolemia
• Trait due to a single gene
• Huntington disease (dominant). Mapped 1983
• Alaska kindred with many affected
by Gusella et al
• Cystic fibrosis (recessive). Mapped 1985 by
Lap-Chee Tsui et al
• LIPED computer program, Ott 1974
Dominant
Schrott et al (1972) Annals of Internal Medicine 76, 711-720
•
•
Recessive
•
D/N
N/N
N/N
D/N
D/N
D/N
D/D
D/N
D/N
N/N
•
individuals. Cholesterol level > 95th %ile of
normal → affected
Early analysis with LIPED program showed
mild evidence of linkage to C3
polymorphism (Ott et al, 1974).
Later confirmed by others. This
demonstrated existence of a disease gene in
the vicinity of C3 (chr. 19)
Work by Joe Goldstein and Michael Brown
(Nobel prize in 1985) identified disease as
defect in LDL receptor; located on
chromosome 19.
Now drugs have been developed (statins)
for lowering cholesterol level.
Alaska kindred
with familial
hypercholesterolemia
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X-Linked Inheritance
Genotype and Phenotype
• Female genotypes:
As for autosomal
genes
• Male genotypes: N/y
and D/y
(hemizygous)
XX
• Genotype = set of 2 alleles at a locus (gene) in an
XY
XX
individual. Examples: A/G (marker alleles), N/D (disease
alleles)
• Haplotype = set of alleles, one each at different loci,
inherited from one parent (on same chromosome).
• Diplotype = set of genotypes… (genotype pattern)
• Phenotype = “what you see”, expression of this genotype.
Examples: A/G (marker), “affected” (disease).
XY
• Examples (usually recessive; mutation-
selection!): hemophilia, red/green color
blindness, Duchenne muscular dystrophy
ABO Blood Types
Relation between Genotype
and Phenotype
Dominant, A > N
3 alleles: A, B, 0
Recessive
Genotype
Genotype
Phenotype
N/N
A/N
A/A
Phenotype
N/N
A/N
A/A
unaffected
1
0
0
unaffected
1
1
0
affected
0
1
1
affected
0
0
1
Table entries = penetrances. Usually, only 1 line needed (affected).
Penetrance = conditional probability of phenotype given genotype.
Penetrance = probability of being affected given genotype (diseases).
PhenoA/A
type
A
1
B
AB
0
0
0
0
Genotype
A/B
A/0
B/B
B/0
0/0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
Hardy-Weinberg Equilibrium, HWE
Parent 1
A (p)
T (1 – p)
Conditioning on blood type: Bottom sums =1
Parent 2
A (p)
T (1 – p)
p2
p(1 – p)
(1 – p)p
(1 – p)2
p = frequency
of A allele
AA
AT
TT
p2 2p(1 – p) (1 – p)2
Independently formulated ~100 years ago by Hardy (mathematician)
and Weinberg (physician). Earlier, people thought that dominant
diseases had to increase in frequency.
True for large population, absence of mutation, selection, etc. Small
populations: Genetic drift (random walks).
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Generalized Mendelian Inheritance
Penetrance: Cystic fibrosis
p = frequency of disease alleles, 0.025
Genotype
NN
DN
DD
Frequency* (1 – p)2 2p(1 – p)
p2
Penetrance
f3
f1
f2
* HWE assumed
p = population frequency of D allele
Prevalence = (1 – p)2 f1 + 2p(1 – p) f2 + p2 f3
Age-dependent penetrance
Huntington disease
NN
DN
DD
Frequency
0.9506
0.0488
0.0006
Penetrance
0
0
1
Incidence = Prevalence at birth = 0.0006 = 1/1600
Carrier frequency = 0.0488  1/20
Familial Breast Cancer, BRCA1
Newman et al. (1988) PNAS 85, 3044
Easton et al. (1993) Am J Hum Genet 52, 678
Penetrance
100%
Age class Penetrance
0-15
0.02
16-30
0.33
31-45
0.58
46-60
0.71
61+
0.94
Genotype
Age
group
<30
30-39
40-49
50-59
60-69
70-79
80+
Age at onset
Penetrance = Proportion of susceptible individuals
affected by given age
Torsion Dystonia
Median age of onset  10 years
Penetrance at high age  30%
P(affected by given age)
dd
Dd
DD
.00009
.008
.008
.00146
.083
.083
.0083
.269
.269
.021
.469
.469
.039
.616
.616
.061
.724
.724
.082
.801
.801
Cystic fibrosis — 3 mating types
Breast Cancer Penetrances
t/n or r/n
1
0.9
Penetrance
0.8
Genetic cases
0.7
0.6
Non-genetic cases
0.5
0.4
t = tested CF mutations
cover 80% of mut.
0.3
0.2
0.1
0
<30
30-39
40-49
50-59
60-69
70-79
80+
Age
r = remaining mutations,
20%
Counselee =
t/n or r/n unaffected child,
negative for tested
mutations. Carrier?
No genetic marker
information.
Mother
t/n 0.8
r/n 0.2
Father
t/n 0.8 r/n 0.2
0.64
0.16
0.16
0.04
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Cystic fibrosis — Calculations
Mating types
Counselee’s genotype
¼
¼
¼
¼
t/n × t/n 0.64 t/t 0.16 t/n 0.16 t/n 0.16 n/n 0.16
t/n × r/n 0.32 t/r 0.08 t/n 0.08 r/n 0.08 n/n 0.08
r/n × r/n 0.04 r/r 0.01 r/n 0.01 r/n 0.01 n/n 0.01
Risk:
8 11
10 2

  29%
8  1  1  16  8  1 35 7
Distribution of CCR5Δ32 in Europe
Limborska et al. (2002) Hum Hered 53, 49-54
Heritability
• Linear model for phenotype:
• x = g + c + e. Heritability = Var(g)/Var(x)
• Gene-environment interactions:
• CCR5: No effect of mutation without infection
• Sickle cell anemia: heterozygote advantage in
malaria
• Pima Indians: Obesity, “thrifty gene” hypothesis
• Measure degree of genetic influence by how
consistently a trait runs in families
Framingham Study
http://www.nhlbi.nih.gov/about/framingham/policies/pagetwelve.htm
Blood Pressure Variable
Twin Concordance Rates
“Complex Diseases”
Plomin et al. (1994) Science 264, 1734
Families
Subjects
Systolic Blood Pressure, adjusted for age
238
2067
0.323 ± 0.043
Heritability
Systolic Blood Pressure, adjusted for age, BMI
238
2064
0.339 ± 0.043
Lipid Variable
Families
Subjects
Total Cholesterol, adjusted
1366
4527
Heritability
HDL Cholesterol, adjusted
1366
4527
0.433 ± 0.034
Log Lp(a), adjusted
902
1832
0.805 ± 0.064
0.462 ± 0.034
Log TG, adjusted
1366
4527
0.396 ± 0.033
TC / HDL Ratio, adjusted
1366
4527
0.410 ± 0.032
TG / HDL Ratio, adjusted
1366
4527
0.332 ± 0.031
Risch’s Lambda
Risch (1990) Am J Hum Genet 46, 222-228
• Risk, Rr = Prob(relative or type r has
trait given index case has trait)
• Risk ratio, r = Rr/Runrelated = Rr/K,
K = population prevalence
• Most common: s = risk ratio to a sib
• CF: s = ¼ / 0.0006 = 417
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Sib risk ratios for obesity
Penetrance ~ Risk Ratio
Price and Lee (2001) Hum Hered 51, 35-40
Ott J (1994) Choice of genetic models for linkage analysis of psychiatric
traits, in: Genetic approaches to mental disorders. E. S. Gershon and C.
R. Cloninger. Washington, DC, American Psychiatric Press: 63-75
Risk ratios higher
when proband and
sibling have high
BMI  severe
obesity is more
heritable than mild
obesity.
• Let A = “affected” with disease,
G = risk genotype, g = non-risk genotype
• Epidemiology: P(A|G) = disease risk of gene
•
•
•
Quantitative Traits (QTLs)
Transformations
Hartl & Clark (1997) Principles of Population Genetics
• Many QTLs not normally distributed (lower limit
of 0).
• Suitable family of power transformations:
• Hallmark of mendelian
inheritance: Mixture of
distributions/bimodality
NN, DN
x = (yλ – 1)/λ + λ,
• Purely dominant trait:
Mean phenotype
elevated or reduced.
Examples: Cholesterol
level, bone mineral
density (osteoporosis)
DD
Analyzing Mixture of Distributions
0.16
0.14
Count
150
0.12
0.10
100
0.08
0.06
50
0.04
0.02
0
-1
0
1
2
LISI
3
0.00
4
Proportion per Bar
•
200
Use NOCOM (or other
suitable) program to estimate
mixture parameters.
Example with IRI (insulin
resistance index, low values
are indicative of disease):
•
•
•
•
λ = 1 for no transformation
λ = 0 for log-transformation
λ = ½ for square root transformation
y = original data, x = transformed (normalized)
data
Related Individuals
Ott J (1979) Hum Genet 51, 79-91
http://www.jurgott.org/linkage/util.htm
Thode et al (1988) Biometrics 44, 1195-1201
•
carriers, P(A|g) for non-gene carriers
Linkage analysis: P(A|G) = penetrance for genetic
cases, P(A|g) = penetrance for phenocopies
R = P(A|G)/P(A|g) = risk (penetrance) ratio
R = 1 → phenotype “unknown”
• Apply NOCOM program as if individuals
were unrelated
• Use resulting parameter estimates as input
to the ILINK program (LINKAGE package)
to obtain proper ML estimates
• Is relatively cumbersome
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The Polygenic Threshold Model
Hartl & Clark 1997
•
•
•
•
Liability = underlying QTL
T = threshold for disease
Bp = population prevalence
μ = mean liability, μs = f(T)/Bp
= mean liability of affecteds
• Lower panel: Liability
distribution of offspring with
one parent affected, Bo = proportion of affected offspring
Expression Level as Phenotype
Watts et al. (2002) Am J Hum Genet 71, 791-800
• Ataxia telangectesia (AT) = recessive trait
• Heterozygotes prone to other diseases
• Compare expression levels of 2880 genes
on each of 10 cases (heteroz. for AT) and
10 controls (no AT allele).
• Identified genes are likely to interact with
the AT gene.
Genes Influencing Variability of
Gene Expression
Morley…Cheung (2004) Nature 430, 743-747
• Used microarrays to measure gene expression
levels
• Genome-wide linkage analysis for expression
levels (= QTL) of 3,554 genes in 14 large families.
• For ~1,000 expression phenotypes, significant
linkage to specific chromosomal regions.
• These regions harbor determinants for variation in
human gene expression.
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