Genotypes, Phenotypes and Hardy Weinberg Equilibrium. Biostatistics 666 Lecture II

Transcription

1 Genotyes, Phenotyes and Hardy Weinberg Equilibrium Biostatistics 666 Lecture II

2 Previously: Refresher on Genetics DNA sequence Human Genome Inheritance of genetic information Sequence variation VNTRs, microsatellites and SNPs Common Tyes of Genetic Study

3 Gregor Johann Mendel Discovered basic rinciles of genetics The Father of Genetics Monk, lived Crosses between strains of eas Garden ea (Pisum sativum) Each strain has articular characters Height, flower color, seed shae

4 Mendel s Exeriment Crossed different truebreeding strains Identical results for recirocal crosses F 1 resembled one of the arental strains In F generation, the other arental trait reaears

5 Mendel s Numbers Seeds: Yellow vs. Green F 1 : All yellow F : 60 yellow, 001 green 75.1% yellow, 4.9% green Seeds: Smooth vs. Wrinkled F 1 : All smooth F : 5474 smooth, 1850 wrinkled 74.7% yellow, 5.3% wrinkled

6 Phenotye vs. Genotye Genotye Underlying genetic constitution Phenotye Observed manifestation of a henotye The yellow eas in the arental and F 1 generations are not the same

7 Mendel s Interretation Each trait determined by articulate factors (genes) E.g.: Seed colour Alternative forms for each factor (alleles) E.g.: Yellow seeds or green seeds Each lant carried two alleles Identical for true breeding arental strains Different for F 1 generation

8 The Princile of Segregation Mendel s First Law The two alleles of a gene air segregate from each other in the formation of gametes (gametes are reroductive cells that fuse to form a new organism in sexual reroduction)

9 Genotyes Each individual carries two alleles If there are n alternative alleles there will be n(n+1)/ ossible genotyes Homozygotes The two alleles are the same E.g.: Green/Green or Yellow/Yellow Heterozygotes The two alleles are different E.g.: Green/Yellow

10 Penetrance Describes the relationshi between henotyes and genotyes Comlete Penetrance Each genotye corresonds to only one henotye Incomlete Penetrance Link between henotye and genotye is only robabilistic

11 The ABO blood grou Imortant for blood transfusions Determined by alleles of the ABO gene 3 alternative alleles A, B and O 6 ossible genotyes, n (n + 1) / A/A, A/B, A/O, B/B, B/O, O/O

12 ABO Blood Grou II Phenotye Antigen Antibody A B A B A B O AB

13 Relationshis between alleles Relation between alleles A and B are dominant over O O is recessive in relation to A and B A and B are codominant In this case all genotyes are fully enetrant Genotye A/A A/B A/O B/B B/O O/O Phenotye A AB A B B O

14 BRCA1 and Breast Cancer BRCA1 mutations redisose to breast cancer About 0.1% of the oulation carries mutations in the BRCA1 gene Disease Risk Age Carriers 40% 70% 80% Non-carriers 0.4% 3% 8%

15 Alleles, Genotyes and Phenotyes Classifying genotyes Homozygous Heterozygous Penetrance Relationshis between alleles Dominant, Recessive, Co-Dominant

16 Genes in Poulations Genotye Frequencies Halotye Frequencies Allele Frequencies Penetrance Function Derived measures of marker informativeness

17 Notation ij i frequency of genotye i/j in the oulation n(n+1)/ of these frequency of allele i in the gene ool n of these Write allele frequencies as function of genotye frequencies

18 Hardy-Weinberg Equilibrium Random union of games Relationshi discovered it in 1908 Hardy, British mathematician Weinberg, German hysician Shows n allele frequencies determine n(n+1)/ genotye frequencies Large oulations

19 Required Assumtions Diloid, sexual organism Non-overlaing generations Autosome Large oulation Random mating Equal genotye frequencies among sexes Selection

20 Random Mating: Mating Tye Frequencies Mating Frequency A 1 A 1 *A 1 A 1 11 ² A 1 A 1 *A 1 A 11 1 A 1 A 1 *A A 11 A 1 A *A 1 A 1 ² A 1 A *A A 1 A A *A A ² Total 1.0

21 Mendelian Segregation: Offsring Genotye Frequencies Offsring Mating Frequency A 1 A 1 A 1 A A A A 1 A 1 *A 1 A 1 11 ² 11 ² A 1 A 1 *A 1 A A 1 A 1 *A A A 1 A *A 1 A 1 ² ¼ 1 ² ½ 1 ² ¼ 1 ² A 1 A *A A A A *A A ² ²

22 And now ) )( ( ' ) ( ' ) ( '

23 Conclusion Genotye frequencies are function of allele frequencies Equilibrium reached in one generation Indeendent of initial genotye frequencies Random mating, etc. required Conform to binomial exansion ( 1 + ) =

24 A few more notes Can be exanded to multile alleles Exand ( k ) Holds in almost all human oulations Little inbreeding (tyical F = ~0.005) Deviations can suggest: Problems with exerimental assays Non-indeendence of observations Selection Disease locus

25 Heterozigosity Probability that two alleles will differ H 1 i For a equally frequent alleles 1 a 1 H 1 a a Sometimes called gene diversity

26 PIC Probability that alleles of arent can be distinguished in offsring Botstein et al, Markers that could track dominant alleles Probability that arent will heterozygous and informative in relation to souse

27 PIC Definition In general: PIC 1 n n n i i1 i1 ji1 ( i j ) For a equally frequent alleles a PIC PIC <= H a 1 a 1 a 3

28 Exercise ABO locus allele frequencies A frequency 0.3 B frequency 0.1 O frequency 0.6 Calculate genotye frequencies Calculate heterozygosity and PIC Calculate henotye frequencies

29 NOD and Bowel Disease Leu1007fs Frame shift mutation at osition 1007 Frequency of about 5% Disruts gene Penetrance Genotye +/+ -/+ -/- P(Crohn s G) 0.1% 0.% 3% Calculate frequency of -/- genotye in oulation and among atients