How many genes? Mapping mouse traits

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How many genes? How many genes? Mapping mouse traitsMapping mouse traits

Lecture 1, Statistics 246

January 20, 2004

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Aim of today’s and Thursday’s lecture

To review basic Mendelian genetics, the basics of recombination, and go on to see how genes contributing to qualitative and quantitative traits are mapped using data from crosses of inbred strains of mice.

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2.1 Genetic background

2.1 Loci and markers

We need to know the following notions from Meldelian genetics: autosomes, sex chromosomes, genotypes, phenotypes, loci, alleles, homozygous, heterozygous, dominant, recessive, (fully) inbred, markers.

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Our markers are Microsatellites

..AGTCCACACACACACACATGT..



..AGTCCACACACACACACACACACATGT..



PCR andelectrophoresis

A

B

H

Desirable: to call the genotypes (A, H, or B) automatically Problems: stutters and noise, variability of the patterns, etc.

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Similarity Sortingunsorted correlation matrixsorted

This is a useful technique to enhance presentation of gel traces and assist manual examination.

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Genotype CallingThis is a statistical pattern recognition problem:• Fit mixture models• Discriminant analysis

A BH

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JnoTyper: software implementation in Java

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2.2 Inbred strains and their crosses

Our main players are the C57BL/6 (BL for black, abbreviated B6), a robust strain that has been around about 90 years, and the NOD (non-obese diabetic) mouse strain, a delicate diabetes-prone strain discovered in 1990.

Coat colours: agouti is standard, B6 is black, NOD is albino (i.e. white).

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Normal (wild-type) mouse coat: color = agoutia grizzled color of fur resulting from the barring of each hair in several alternate dark and light bands

10Black mouse: C57/BL6 strain

11Albino mouse: non-obese diabetic (NOD) strain

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Coat color loci in mice

Four main loci : A, B, C and D

• Locus A – agouti• Locus B – black• Locus C (known as Tyr) – albinism• Locus D – dilution gene

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Alleles at the Agouti (A) locus

• Ay, Lethal dominant yellow • Avy, Viable yellow • Aw, White-bellied Agouti • A, Agouti or Wild type • At, Black and Tan • Am, mottled agouti • a, Non-agouti • ae., Extreme non-agouti A and a are a dominant/recessive allele pair

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Alleles at the Albino (C) Locus

• C, full color gene • cch, chincilla• ch, himalayan• c, albino gene

C and c are a dominant/recessive pair of alleles

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Alleles at A and C interact (called epistasis in genetics))

• If the mouse is aaCx it is not agouti and not albino (in our case a black mouse)

• If the mouse is AxCx it is agouti and not albino

• If the mouse is xxcc it is albino no matter what the alleles at the agouti locus are because they are irrelevant

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Crosses

We will denote the NOD mice by A, and the B6 mice by B. This same notation will denote the two homozygotes at a polymorphic marker.

Two main crosses interest us, following the first filial generation or F1 , which we denote by AB H. Here H denotes heterozygote, which is the case for our F1s.

The backcross BC is arrived at via HB BC, or a variant, while the F2 intercross is given by HH F2.

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2.3 Data

• An F2 inter cross was performed starting with C57BL/6 and NOD parental lines.

• We have 133 female mice at the F2 generation, just females for the reason that males fight, and this influences other (quantitative blood) phenotypes of interest

• They were genotyped at 153 microsatellite markers spanning all 19 autosomes and the X chromosome. We also have coat color and a few white blood cell phenotypes.

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A small portion of the data (beginning)

data type f2 intercross .133 153 7*D10M106 BBABBBBBHBBABBBBAABBBB-BABABABBABBBBBBBBBBBBB-BBBBBBABBAAABBBBBBBBB-HBABABB-ABBBBAB-BBBABABBB-BBBBBCBCBCBHBBBHCBBHBHHBCBBBBBBBHBHBHCH*D10M14 AHHBHHHAHHABAHBHHBABAA-BHHAHAAHAHHHHHBAHHHAHHBAHBHABBBHAAHHHHAHBHHH--HHHHAHAHAHBHHHAHHABAHHHAHHHAHBHBBHHHAAHAAHHBHHAHAH-HBABAHAHBHHAH*D10M163 AHBBHHB-HHAB-HBH-BAHBA-BHHAHAAHAAHHAHBAHHHHHHHAHBHABBBHAAHBBHAHBBHHBBHBHHHH-HBHHHHHAHHAHABH-AHHHAHBABBBBAAAHAAHHBHHAHHHBHBAHAHABHHHAH*D10M20 HCBHAHBAHHAHAHBABAHHBH-HHHABAAHAAABHHBH-HAHBHAAHBCABABHAAABBHAHBHHBBBHBHAHH-HBHHHABAHHHHAHHBAAHHABHABHBHAAHBHAAHBHAAHBHBHBHHHHABAHAAH


D10M106 = a marker on chr 10 defined by MITIncompleteness code: C = B or H, D = A or H, - = missing

#individuals #loci #traits marker next column = data from mouse1

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A small portion of the raw data (end)


*DXM210 --HAAAAHHHAHAAAAAHAH-HAHHAHAHHH-HHH-H-H-AHH-AAHAA-HHAAAAAHH-AHHAAHHHAHAAH-HAHA-HAAHAHAA-A-HH-AAHHHAHAAHAAAAAHHHHAAAHAAHHAHHHHHHAHAAHA*DXM222 HAAHHAA-HHAAHAAHHAAAHH-HAAHAAHHHHHAHHHH-AAHHAHHAAHHHHHHAAHHAHHHHAAH-AHHHAHHAAAHHHAAAHAHAAHHAAHA-HAA--HHAHHA-AAHAAAAA-HH-AHAAAH-HHAAHA*DXM39 HAAAHAA-HHAH-AAA-HAAHH-HAAAAHHHHHHAHHHHAAHHAAAHAAHHHHAAAAHHHHHHAAHH--HAAAHH-AAHHAAHAHAHAAHH-AAAHHAAHAHAHAAAAHH-AAAAAAAH-AHAAHHAAAAAHA

*trait1 1 1 2 3 1 1 2 3 1 2 2 2 1 1 1 1 3 1 1 1 1 1 1 1 2 1 1 3 1 1 2 1 1 1 2 1 2 3 1 1 2 3 1 1 2 3 1 2 2 1 1 2 3 1 3 3 1 3 1 1 1 1 3 1 1 3 1 2 3 3 1 1 1 2 2 3 1 1 2 2 1 1 1 1 1 3 1 1 2 2 3 3 3 1 1 1 1 1 1 1 1 1 2 2 2 2 1 3 1 1 1 1 1 2 3 1 1 3 3 1 1 2 2 3*trait2 8.90472059883773 8.62455170973674 8.45460831622462 8.43453595773523 8.58360495693549 8.35936910622267 9.09754487783084 8.3999100308015 8.46379241468912 8.69506039786081 8.1840487448877 8.89745444516111 8.40886531453061 9.03400088685978 8.948542613*trait3 16.0508869012649 16.1080453151048 16.1678377428531 16.1130831091348 16.0999316803306 16.1941303372343 16.1773075105902 16.0347140420193 16.0917516756187 16.1524970776757 13.1806322855283 16.1240777226359 16.095850042011 16.1130831091348 16.1050104*trait4 16.0138456295845 16.0907244541622 16.1250712646947 16.1324915312421 16.0819502043220 16.1735303578464 16.1673618922612 16.1383883542261 16.1215895402126 16.1432759494886 16.0938029583893 16.1175955259166 16.1324915312421 16.1447375819047 16.150562*trait5 13.8887610197039 14.1288603771646 13.9863778758242 13.8489453340505 13.8806738838707 14.1443345737472 14.1776041279299 13.6876771864544 13.9578777992512 13.9682316449819 13.8188383480569 13.9645051106422 13.9086972726904 14.1572072187223 14.219196*trait6 7.1066061377273 6.52209279817015 6.63331843328038 6.53184897311552 6.73340189183736 6.45099687648642 6.82437367004309 6.40797949140273 6.18070654674651 6.555830937802 6.64639051484773 7.00910777324243 6.2079191102714 6.7761268365037 6.688769737816*trait7 8.65927129000923 8.41405243249672 8.15861166920692 8.19973896063079 8.32603268595508 8.13739583005665 8.91103545969641 8.16432053342724 8.22326945804098 8.47428569040496 7.8146688490437 8.59291890194437 8.2033952718339 8.87440132651663 8.786201998

Coat color code

WBC traits

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Snapshot of the genotype data

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Error Detection

calc.genoprob, calc.errorlod, plot.errorlod

Using the LOD_error statistic. Based on close recombn events which indicate possible presence of genotyping error

(see later)

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2.4 Mendel’s laws for one locus

We can (and should) check Mendel with data from our 133 offspring at each of our 153 loci.

For example, at D7Mit126, we have 24 A, 29 B and 67 H genotypes, adding to 120, indicating 12 incomplete or missing genotypes.

What do we expect according to Mendel? How would we test whether the data agree with our expectations?

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2.5 Mendel’s law for 2 loci

Mendel inferred from his data on peas the independent segregation of different factors.

Here we check that this holds for our two coat color loci, but not generally. We then go on to understand the more general situation.

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Mating & Coat color outcomes in this cross

Parental lines

C57/BL6 males

Black (aaBBCC)

NOD females

Albinos

(AABBcc)

F1

All Agouti

aABBCc

F2

Agouti :

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Black :

3

Albino

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We need to check these last proportions following Mendel’s reasoning.

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Punnett square depicting F1 parental allele combinations passed on to F2 offspring

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It’s not always like thatIt’s not always like that

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A H B Total

A 26 10

0 36

H 10 46 9 65B 0 5 23 28Total 36 61 32 129

2-locus genotypes at D12Mit51 and D12Mit132.If we pool A and H, we do not get 9:3:3:1.

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How many genes? Mapping mouse traits