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Linkage and LOD score

Linkage and LOD score. Manuel AR Ferreira. Massachusetts General Hospital. Harvard Medical School. Boston. Egmond, 2006. Outline. 1. Aim. 2. The Human Genome. 3. Principles of Linkage Analysis. 4. Parametric Linkage Analysis. Practical. 5. Nonparametric Linkage Analysis. 1. Aim.

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Linkage and LOD score

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  1. Linkage and LOD score Manuel AR Ferreira Massachusetts General Hospital Harvard Medical School Boston Egmond, 2006

  2. Outline 1. Aim 2. The Human Genome 3. Principles of Linkage Analysis 4. Parametric Linkage Analysis Practical 5. Nonparametric Linkage Analysis

  3. 1. Aim

  4. QTL mapping LOCALIZE and then IDENTIFY a locusthat regulates a trait (QTL) Nucleotide or sequence of nucleotides with variation in the population, with different variants associated with different trait levels.

  5. For a heritable trait... Linkage: localize region of the genome where a QTL that regulates the trait is likely to be harboured Family-specific phenomenon: Affected individuals in a family share the same ancestral predisposing DNA segment at a given QTL Association: identify a QTL that regulates the trait Population-specific phenomenon: Affected individuals in a population share the same ancestral predisposing DNA segment at a given QTL

  6. 2. Human Genome

  7. DNA structure A DNA molecule is a linear backbone of alternating sugar residues and phosphate groups Attached to carbon atom 1’ of each sugar is a nitrogenous base: A, C, G or T Two DNA molecules are held together in anti-parallel fashion by hydrogen bonds between bases [Watson-Crick rules] Antiparallel double helix A gene is a segment of DNA which is transcribed to give a protein or RNA product Only one strand is read during gene transcription Nucleotide: 1 phosphate group + 1 sugar + 1 base

  8. DNA polymorphisms Microsatellites >100,000 Many alleles, (CA)n, very informative, even, easily automated SNPs 11,961,761 (11 Sept ‘06) Most with 2 alleles (up to 4), not very informative, even, easily automated A B

  9. DNA organization 22 + 1 2 (22 + 1) 2 (22 + 1) 2 (22 + 1) ♂ ♁ ♂ A - A - A - ♁ B - ♂ ♁ ♁ ♂ Mitosis B - B - chr1 A - A - A - - A A - - A ♁ ♁ ♂ B - B - B - - B B - - B A - - A - A B - - B - B chr1 G1 phase S phase M phase Haploid gametes Diploid zygote 1 cell Diploid zygote >1 cell

  10. DNA recombination 22 + 1 22 + 1 A - NR (♂) B - A - - A chr1 2 (22 + 1) 2 (22 + 1) B - - B - A ♁ Meiosis R chr1 (♂) (♁) ♂ ♁ - B A - A - - A - A chr1 B - B - - B - B A - R chr1 chr1 chr1 chr1 (♁) A - - A B - chr1 Diploid gamete precursor cell B - - B - A chr1 NR - B Haploid gamete precursors chr1 Hap. gametes

  11. DNA recombination between linked loci 22 + 1 A - NR B - (♂) A - - A B - - B 2 (22 + 1) - A ♁ Meiosis NR - B (♂) (♁) ♂ ♁ A - A - - A - A B - B - - B - B A - NR B - (♁) A - - A B - - B Diploid gamete precursor - A - B NR Haploid gamete precursors Hap. gametes

  12. Human Genome - summary DNA is a linear sequence of nucleotides partitioned into 23 chromosomes Two copies of each chromosome (2x22 autosomes + XY), from paternal and maternal origins. During meiosis in gamete precursors, recombination can occur between maternal and paternal homologs Recombination fraction between loci A and B (θ) Proportion of gametes produced that are recombinant for A and B If A and B are very far apart: 50%R:50%NR - θ = 0.5 If A and B are very close together: <50%R - 0 ≤ θ < 0.5 Recombination fraction (θ) can be converted to genetic distance (cM) Haldane: eg. θ=0.17, cM=20.8 Kosambi: eg. θ=0.17, cM=17.7

  13. 3. Principles of Linkage Analysis

  14. Linkage Analysis requires genetic markers Q M1 Mn M2 .3 .4 .4 .3 0.5 0.5 θ 0.5 .15 M1 Mn M2 .35 .22 .35 .26 0.5 θ 0.5 0.5 .4 .3 .3 .4 .1 M1 Mn M2

  15. Linkage Analysis: Parametric vs. Nonparametric Gene Chromosome Recombination Genetic factors M Q A Mode of inheritance Correlation D Phe C E Environmental factors Adapted from Weiss & Terwilliger 2000

  16. 4. Parametric Linkage Analysis

  17. Linkage with informative phase known meiosis Gene Chromosome ♂ ♁ M1..6 Q1,2 Autosomal dominant, Q1 predisposing allele Estimate θ between M and Q M2M5Q2Q2 M1M6Q1Q? M1 Q1 Informative Phase known M1Q1/M2Q2 M3M4Q2Q2 M1M2Q1Q2 M2 Q2 M1Q1/M3Q2 M2Q2/M3Q2 M1Q1/M4Q2 M1Q1/M4Q2 M2Q2/M4Q2 M2Q1/M3Q2 NR: M1Q1 NR: M2Q2 (~20.8 cM) θMQ = 1/6 = 0.17 R: M1Q2 R: M2Q1

  18. Linkage with informative phase unknown meiosis M1 Q1 M1 Q2 Q2Q2 Q1Q? M2 M2 Q2 Q1 Informative Phase unknown M1Q1/M2Q2 M1M2Q1Q2 M3M4Q2Q2 M1Q2/M2Q1 M1Q1/M3Q2 M2Q2/M3Q2 M1Q1/M4Q2 M1Q1/M4Q2 M2Q2/M4Q2 M2Q1/M3Q2 M1Q2/M2Q1 M1Q1/M2Q2 P P N N 3 3 R: M1Q1 NR: M1Q1 1-θ θ R: M2Q2 NR: M2Q2 2 2 NR: M1Q2 R: M1Q2 0 0 θ 1-θ NR: M2Q1 R: M2Q1 1 1 + +

  19. Parametric LOD score calculation R Overall LOD score for a given θ is the sum of all family LOD scores at θ eg. LOD=3 for θ=0.28

  20. Parametric Linkage Analysis - summary Q M1 Mn M2 .3 .4 .4 .3 θ 0.5 0.5 0.5 .1 For each marker, estimate the θ that yields highest LOD score across all families This θ (and the LOD) will depend upon the mode of inheritance assumed MOI determines the genotype at the trait locus Q and thus determines the number of meiosis which are recombinant or nonrecombinant. Limited to Mendelian diseases. Markers with a significant parametric LOD score (>3) are said to be linked to the trait locus with recombination fraction θ

  21. Practical: what is the most likely θ between M and Q? M1M2Q1Q1 M3M4Q1Q2 M2M3Q1Q1 M1M4Q1Q2 M1M4Q1Q1 M2M4Q1Q2 M2M4Q1Q2 1. Identify informative individual with offspring in the pedigree 2. Reconstruct possible phases of that individual and of all offspring 3. Classify the gametes that individual produces as R or NR 4. Count the number of R and NR gametes effectively produced 5. Express 6. Express LOD score

  22. Practical: answers 4. Count the number of R and NR gametes effectively produced 3. Classify the gametes that individual produces as R or NR 1. Identify informative individual with offspring in the pedigree 5. Express 6. Express LOD score 2. Reconstruct possible phases of that individual and all offspring M1M2Q1Q1 M3M4Q1Q2 M2M3Q1Q1 M1Q1/M4Q2 M1Q1/M4Q1 M2Q1/M4Q2 M2Q1/M3Q1 M2Q1/M4Q2 M1M4Q1Q2 M1M4Q1Q1 M2M4Q1Q2 M2M4Q1Q2 M3Q2/M4Q1 M3Q1/M4Q2 P P N N 1 1 R: M3Q1 NR: M3Q1 θ 1-θ R: M4Q2 NR: M4Q2 3 3 NR: M3Q2 R: M3Q2 0 0 1-θ θ NR: M4Q1 R: M4Q1 1 1 + +

  23. Outline 1. Aim 2. The Human Genome 3. Principles of Linkage Analysis 4. Parametric Linkage Analysis 5. Nonparametric Linkage Analysis

  24. 5. Nonparametric Linkage Analysis

  25. Approach Parametric: genotypes marker locus & genotypes trait locus (latter inferred from phenotype according to a specific disease model) Parameter of interest: θbetween marker and trait loci Nonparametric: genotypes marker locus & phenotype If a trait locus truly regulates the expression of a phenotype, then two relatives with similar phenotypes should have similar genotypes at a marker in the vicinity of the trait locus, and vice-versa. Interest: correlation between phenotypic similarity and marker genotypic similarity No need to specify mode of inheritance, allele frequencies, etc...

  26. Phenotypic similarity between relatives Squared trait differences Squared trait sums Trait cross-product Trait variance-covariance matrix Affection concordance T2 T1

  27. Genotypic similarity between relatives IBSAlleles shared Identical By State “look the same”, may have the same DNA sequence but they are not necessarily derived from a known common ancestor M3 M1 M2 M3 Q3 Q1 Q2 Q4 IBDAlleles shared Identical By Descent are a copy of the same ancestor allele M1 M2 M3 M3 Q1 Q2 Q3 Q4 IBD IBS M1 M3 M1 M3 2 1 Q1 Q4 Q1 Q3 0 0 1 0 1 Inheritance vector (M)

  28. Genotypic similarity between relatives - Inheritance vector (M) Number of alleles shared IBD Proportion of alleles shared IBD - M2 M3 M1 M3 0 0 0 1 1 0 Q2 Q4 Q1 Q3 M1 M3 M1 M3 0 0 1 0 0.5 1 Q1 Q4 Q1 Q3 M1 M3 M1 M3 0 0 0 0 2 1 Q1 Q3 Q1 Q3

  29. Genotypic similarity between relatives - D A B C 22n

  30. Statistics that incorporate both phenotypic and genotypic similarities Phenotypic similarity 0.5 1 0 Genotypic similarity ( )

  31. Haseman-Elston regression – Quantitative traits 0.5 1 0 Phenotypic (dis)similarity = b × Genotypic similarity + c

  32. VC ML – Quantitative & Categorical traits method 0.5 1 0 H1: H0: e.g. LOD=3

  33. Genome-wide linkage analysis (e.g. VC) Individual LOD scores can be expressed as P values (Pointwise) LOD Chi-sq (n-df) P value 2.1 9.67 0.0009 (x4.6) True positive Theoretical(Lander & Kruglyak 1995) k LOD LOD = 3.6, Chi-sq = 16.7, P = 0.000022 Type I error

  34. Nonparametric Linkage Analysis - summary No need to specify mode of inheritance Models phenotypic and genotypic similarity of relatives Expression of phenotypic similarity, calculation of IBD HE and VC are the most popular statistics used for linkage of quantitative traits Other statistics available, specially for affection traits

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