Heredity GENETICS 160
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This 22 page Class Notes was uploaded by Ms. Kody Cremin on Thursday September 17, 2015. The Class Notes belongs to GENETICS 160 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 71 views. For similar materials see /class/205242/genetics-160-university-of-wisconsin-madison in Genetics (Graduate Group) at University of Wisconsin - Madison.
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Date Created: 09/17/15
Meiosis recombination and interference Karl W Broman Department of Biostatistics Johns Hopkins University Baltimore Maryland USA wwwbiostatjhsphedu kbroman Outline Mitosis and meiosis Chiasmata crossovers Genetic distance Genetic markers recombination Chromatid and chiasma interference Mather s formula The countlocation model The gamma model and the X2 model Data humans and mice Mitosis ordinary cell division Chromosomes Chr s pull apart duplicate and cell divides v 0 8 Chromosomes 8 A X line up 0 3 9 Meiosis production of sex cells Chr s pull apart and cells divide Chr s exchange material lt 8 and cell divides m iChromosomes lt duplicate mm 0 Chromosomes amp x 8 pair up The exchange process Vocabulary Fourstrand bundle Meiotic products i Sister chromatids Nonsister chromatids CD Q Chiasma chiasmata OQ Crossovers QC Obligate chiasma CDC Genetic distance Two points are d Morgans apart ifthe average number of crossovers per meiotic product in the intervening interval is d Usual units centiMorgan CM 100 cM 1 Morgan Genetic distance 7 Physical distance The intensity of the crossover process varies by 0 Sex 0 Individual o Chromosome o Position on chromosome o Temperature cM Mb cnvomocome 20 emscal lacalm my But we don t observe crossovers O O OO O Crossover process Marker data 0 Crossovers generally not observeable e We instead observe the origin of DNA at marker loci odd no crossovers recombination event even no crossovers no recombination Recombination fraction Prrecombination event in interval Microsatellite markers aka Short Tandem Repeat Polymorphisms STRPs gt GATAGATA GATA CTATCTAT CTAT lt o Tandem repeat of something like GATA at a specific position in the genome 0 Number of repeats varies 0 Use PCR to amplify region 0 Use gel electrophoresis to determine length of region Map functions Connect genetic distance average no crossovers to recombination fraction chance of an odd no crossovers r Md d M39lm We require a model for the crossover process Interference Chromatid interference strand choice i Chiasma interference positions of chiasmata CD Q o Q QC CDC Mather s formula Assuming no chromatid interference NCI Prno rec n in interval 1 Prno chiasma in interval in random meiotic product on 4strand bundle Let n no chiasmata in interval on 4strand bundle and m no crossovers in interval on random meiotic product Under NCI m n N Binomialn 12 0 ifn0 Thus Prmisoddn 12 ifngt1 Haldane map function Under no interference the locations of chiasmata on the 4strand bundle are according to a Poisson process rate 2 per Morgan Thus n Poisson2 d where dis the genetic length of the interval in Morgans Thus Prn 0 exp2 d Thus r1 exp2d Models for recombination 35 35 5E 55 55 35 I chiasmataon 4strand bundle i Thin by 12 I V V V V I XOs on random I meiotic product o Assuming NCI thin Xprocess by 12 independently to get the XOprocess o Models Countlocation model Gamma model X2 model Countlocation CL model Let n no chiasmata on 4strand bundle MOde3 7 NP p0 P1 P2 locations n N iid uniformOL Note p Poisson2L gt no interference Under NCI crossovers on random meiotic product will also follow a countlocation model Let m no crossovers on random meiotic product Then m n N Binomialn 12 and Wm i 2771010496 The CL model stinks Advantage Can easily incorporate obligate chiasma Disadvantage Fits data poorly gt Allows crossovers to be too close together Gamma model Locations of chiasmata according to a stationary gamma renewal process Increments are iid gammashape 12 rate 21 Constrained to have mean 12 Morgan 1 no interference V gt1 positive chiasma interference Locations of crossovers on random meiotic product also a stationary renewal process Interarrival distribution is a mixture of gammas lnter chiasma densities Distance cM Inter crossover densities l l l o 50 100 150 200 Distance cM Chisquare model Special case of the gamma model when the parameter is a non negative integer take m 1 1 Computer simulations and many calculations are easier Chiasmata on the 4strand bundle take every mth point from a Poisson process with rate 2m per Morgan Interarrival distribution is a scaled version of a X2 distribution Example m 4 The gamma model Advantage Fits data reasonably well Disadvantage Doesn t account for obligate chiasma Human data 0 http researchmarshfieldclinic orggenetics o 8 CEPH families three generations 11 to 15 progeny 92 meioses total o 8000 STRP markers 90 typed o Average spacing Female 06 l 12 cM Male 04 l 10 cM o Data cleaning Removed 764954425 008 genotypes resulting in tight double recombinants CEPH pedigree data on 3 markers CEPH individual 1331 11 maternal chr 1O haplotype lllllll llllll l ll llllll O OOO OOO OOOO OOOOO l l l l l llll lll lllll ll l ll l ll l ll l O OOOO ll lll ll ll llll ll lll llll l 0000 00000 OOO O O llll l ll llllll lll lllllll l lll ll l l lllll lll 00000 0000 ll llll lllll ll llllllllll OOOO OOOO O ll ll lllll llll llll lll lllllll ll l l l l ll llllll OO OOO l ll ll llll lllll lOOOO O OO OOOO OOOO lllllll l lll lllll ll lllllll ll llllll ll lllllll llll lllll Raw Data Clean Data 800 800 600 600 400 400 200 200 0 0 M 0 100 200 300 400 500 600 0 100 200 300 400 500 600 No markers between recombinations No markers between recombinations 760 D 100 80 60 60 40 40 20 20 0 0 AI l 0 5 10 15 20 0 5 10 15 20 No markers between recombinations No markers between recombinations gt C D O O L D 0 50 100 Location on female genetic map CM 150 200 250 300 MLEs of interference parameter Interference parameter 5 HIM Milli i WW Him it i i i i i i i i i i i i i i i i i i i i i 12 3 4 5 6 7 8 910111213141516171819202122X Chromosome Goodness of fit Progeny 0 50 100 150 200 250 300 Location on female genetic map CM Maternal chromosome 1 0 100 200 300 Intercrossover distance cM Paternal chromosome 1 0 50 1 00 1 50 200 Inter crossover distance CM Maternal chromosome 2 0 100 200 300 Intercrossover distance CM Paternal chromosome 2 Intercrossover distance cM Mouse data 0 http www j ax orgresourcesdocumentscmdataftp html 0 Two interspecific backcrosses with common F1 parent BSB C57BL6J x M spretus gtlt C57BL6J BSS C57BL6J gtlt SPRETEi gtlt SPRETEi 94 individuals from each cross o Highdensity STRP markers BSB 1372 markers BSS 4913 markers o Average spacing BSB 10 CM BSS 03 CM Backcross pedigree 9 HH HH 0 UH DEEDS UH UH UH UH UH UH O L GEM l I IZEEI l Mouse data Backcross individuals FLLLLLHHLLI39IJJJJJLLquJJLl LLLIILLmULL L39ILLl Jl 0 20 40 60 80 1 00 Chromosome position CM MLEs mouse 256 128 Interference parameter IIIIIIIIIIIIIIIIIIII 12345678910111213141516171819X Chromosome Crossover locations Chr 1 x x um run o a 0039 0 on u 3 o o3 9o o quota u a mumquotmmquot l Crossover locations Chr 4 x x x I mnmlmnumlnIu I qu mumI Inn 4 mun my I InterXO distances Chr 1 Count Chr 1 n 46 i i 0 20 60 1 00 Inter crossover distance InterXO distances Chr 4 Count Chr 4 n 33 8 i 6 4 2 O i O 20 60 100 Intercrossover distance 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 References o 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 SpringerVerlag New York pp 1 14 0 McPeek MS Speed TP 1995 Modeling interference in genetic recombination Genetics 1391031 1044 0 Zhao H Speed TP McPeek MS 1995 Statistical analysis of crossover interfer ence using the chisquare model Genetics 1391045 1056 0 Zhao H McPeek MS Speed TP 1995 Statistical analysis of chromatid inter ference Genetics 1391057 1065 0 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 SpringerVerlag New York pp 65 88 0 Zhao H Speed TP 1996 On genetic map functions Genetics 1421367 1377 o Broman KW Weber JL 2000 Characterization of human crossover interfer ence Am J Hum Genet 66191 1 1926 0 Broman KW Rowe LB Churchill GA Paigen K 2002 Crossover interference in the mouse Genetics 1601123 1131
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