Meiosis, recombination, and interference
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1 Meiosis, recombination, and interference Karl W Broman Department of Biostatistics Johns Hopkins University Baltimore, Maryland, USA kbroman
2 Outline Mitosis and meiosis Chiasmata, crossovers Genetic distance Genetic markers, recombination Chromatid and chiasma interference Mather s formula The count-location model The gamma model and the Data: humans and mice model
3 Mitosis: ordinary cell division
4 Mitosis: ordinary cell division Chromosomes duplicate
5 Mitosis: ordinary cell division Chromosomes duplicate Chromosomes line up
6 Mitosis: ordinary cell division Chromosomes duplicate Chr s pull apart and cell divides Chromosomes line up
7 Meiosis: production of sex cells
8 Meiosis: production of sex cells Chromosomes duplicate
9 Meiosis: production of sex cells Chromosomes duplicate Chromosomes pair up
10 Meiosis: production of sex cells Chr s exchange material and cell divides Chromosomes duplicate Chromosomes pair up
11 Meiosis: production of sex cells Chr s pull apart and cells divide Chr s exchange material and cell divides Chromosomes duplicate Chromosomes pair up
12 The exchange process Vocabulary Four-strand bundle Meiotic products Sister chromatids Non-sister chromatids Chiasma, chiasmata Crossovers Obligate chiasma
13 Genetic distance Two points are d Morgans apart if the average number of crossovers per meiotic product in the intervening interval is d. Usual units: centimorgan (cm); 100 cm = 1 Morgan Genetic distance Physical distance The intensity of the crossover process varies by Sex Individual Chromosome Position on chromosome Temperature
14
15 But we don t observe crossovers Crossover process Marker data Crossovers generally not observeable We instead observe the origin of DNA at marker loci. odd no. crossovers = recombination event even no. crossovers = no recombination Recombination fraction = Pr(recombination event in interval)
16 Microsatellite markers aka Short Tandem Repeat Polymorphisms (STRPs) GA T AGA T A C T A T C T A T GA T A C T A T Tandem repeat of something like GATA at a specific position in the genome. Number of repeats varies Use PCR to amplify region Use gel electrophoresis to determine length of region +
17 Map functions Connect genetic distance (average no. crossovers) to recombination fraction (chance of an odd no. crossovers). r M d d M-1 r We require a model for the crossover process.
18 Interference Chromatid interference: strand choice Chiasma interference: positions of chiasmata
19 Mather s formula Assuming no chromatid interference (NCI): Pr(no rec n in interval) = Pr(no chiasma in interval) [in random meiotic product] [on -strand bundle] Let n = no. chiasmata in interval on -strand bundle and m = no. crossovers in interval on random meiotic product Under NCI, m n Binomial(n, 1/2) Thus Pr(m is odd n) = 0 if n = 0 1/2 if n 1
20 Haldane map function Under no interference, the locations of chiasmata on the -strand bundle are according to a Poisson process (rate: 2 per Morgan). Thus n Poisson(2 d) where d is the genetic length of the interval (in Morgans) Thus Pr(n = 0) = exp(-2 d) Thus r = exp(-2 d)
21 Models for recombination Thin by 1/2 chiasmata on strand bundle XOs on random meiotic product Assuming NCI, thin -process by 1/2, independently, to get the XO-process. Models: Count-location model Gamma model, model
22 Count-location (CL) model Let n = no. chiasmata on -strand bundle Model: n p = (p 0, p 1, p 2,... ) locations n iid uniform(0,l) Note: p = Poisson(2L) no interference Under NCI, crossovers on random meiotic product will also follow a count-location model. Let m = no. crossovers on random meiotic product Then m n Binomial(n, 1/2) and Pr m i n 0 p n n i 1 2 n
23 The CL model stinks Advantage: Can easily incorporate obligate chiasma Disadvantage: Fits data poorly! Allows crossovers to be too close together.
24 Gamma model Locations of chiasmata according to a stationary gamma renewal process. Increments are iid gamma(shape =, rate = 2 (Constrained to have mean 1/2 Morgan.) ) 1 no interference 1 positive chiasma interference Locations of crossovers on random meiotic product also a stationary renewal process. Inter-arrival distribution is a mixture of gammas
25 Inter chiasma densities ν Distance (cm)
26 Inter crossover densities ν Distance (cm)
27 Chi-square model Special case of the gamma model when the parameter is a nonnegative integer (take m = 1). Computer simulations and many calculations are easier. Chiasmata on the -strand bundle: take every mth point from a Poisson process with rate 2m per Morgan. Inter-arrival distribution is a scaled version of a distribution. Example: (m = ) 0 L
28 The gamma model Advantage: Fits data reasonably well Disadvantage: Doesn t account for obligate chiasma
29 Human data 8 CEPH families three generations 11 to 15 progeny 92 meioses, total 8000 STRP markers ( 90% typed) Average spacing: Female: 0.6 Male: cm 1.0 cm Data cleaning Removed 76/95,25 ( double recombinants 0.08%) genotypes resulting in tight
30 CEPH pedigree (data on markers)
31 CEPH individual maternal chr 10 haplotype
32 Raw Data Clean Data No. markers between recombinations No. markers between recombinations No. markers between recombinations No. markers between recombinations
33 The data Progeny Location on female genetic map (cm)
34 MLEs of interference parameter 15 Female Male Interference parameter X Chromosome
35 Goodness of fit? Progeny Location on female genetic map (cm)
36 Maternal chromosome 1
37 Paternal chromosome 1
38 Maternal chromosome 2
39 Paternal chromosome 2
40 Mouse data Two interspecific backcrosses with common F 1 parent BSB: (C57BL/6J M. spretus) BSS: (C57BL/6J SPRET/Ei) 9 individuals from each cross High-density STRP markers BSB: 172 markers BSS: 91 markers Average spacing: BSB: 1.0 cm BSS: 0. cm C57BL/6J SPRET/Ei
41 Backcross pedigree B S F 1 S
42 Mouse data Backcross individuals Chromosome position (cm)
43 MLEs: mouse Interference parameter X Chromosome
44 Crossover locations: Chr 1
45 Crossover locations: Chr
46 Inter-XO distances: Chr 1
47 Inter-XO distances: Chr
48 Acknowledgements Terry Speed, University of California, Berkeley, and WEHI Hongyu Zhao, Yale University Mary Sara McPeek, University of Chicago Jim Weber, Marshfield Medical Research Foundation
49 References McPeek MS (1996) An introduction to recombination and linkage analysis. In: Speed TP, Waterman MS (eds) Genetic mapping and DNA sequencing. IMA volumes in mathematics and its applications. Vol 81. Springer-Verlag, New York, pp 1 1 McPeek MS, Speed TP (1995) Modeling interference in genetic recombination. Genetics 19: Zhao H, Speed TP, McPeek MS (1995) Statistical analysis of crossover interference using the chi-square model. Genetics 19: Zhao H, McPeek MS, Speed TP (1995) Statistical analysis of chromatid interference. Genetics 19: Speed TP (1996) What is a genetic map function? In: Speed TP, Waterman MS (eds) Genetic mapping and DNA sequencing. IMA volumes in mathematics and its applications. Vol 81. Springer-Verlag, New York, pp Zhao H, Speed TP (1996) On genetic map functions. Genetics 12:
50 Broman KW, Weber JL (2000) Characterization of human crossover interference. Am J Hum Genet 66: Broman KW, Rowe LB, Churchill GA, Paigen K (2002) Crossover interference in the mouse. Genetics 160:
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Chapter 6 DNA Replication Each strand of the DNA double helix contains a sequence of nucleotides that is exactly complementary to the nucleotide sequence of its partner strand. Each strand can therefore