1 How many genes? Mapping mouse traits Lecture 1, Statistics 246 January 20, 2004

2 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.

3 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.

4 Our markers are Microsatellites..AGTCCACACACACACACATGT....AGTCCACACACACACACACACACATGT.. PCR and electrophoresis A B H Desirable: to call the genotypes (A, H, or B) automatically Problems: stutters and noise, variability of the patterns, etc.

5 Similarity Sorting unsortedcorrelation matrixsorted This is a useful technique to enhance presentation of gel traces and assist manual examination.

6 Genotype Calling This is a statistical pattern recognition problem: Fit mixture models Discriminant analysis ABH

7 JnoTyper: software implementation in Java

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

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

10 Black mouse: C57/BL6 strain

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

12 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

13 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

14 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

15 ) 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

16 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 F 1, which we denote by A  B  H. Here H denotes heterozygote, which is the case for our F 1 s. The backcross BC is arrived at via H  B  BC, or a variant, while the F 2 intercross is given by H  H  F 2.

Data An F 2 inter cross was performed starting with C57BL/6 and NOD parental lines. We have 133 female mice at the F 2 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.

18 A small portion of the data (beginning) D10M106 = a marker on chr 10 defined by MIT Incompleteness code: C = B or H, D = A or H, - = missing #individuals #loci #traits marker next column = data from mouse1

19 A small portion of the raw data (end) Coat color code WBC traits

20 Snapshot of the genotype data

21 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)

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?

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.

24 Mating & Coat color outcomes in this cross Parental lines C57/BL6 males Black (aaBBCC) NOD females Albinos (AABBcc)  F1F1 All Agouti aABBCc F2F2 Agouti: 9 Black: 3 Albino 4 We need to check these last proportions following Mendel’s reasoning.

25 Punnett square depicting F 1 parental allele combinations passed on to F 2 offspring

26 It’s not always like that AH BTotal A H B Total locus genotypes at D12Mit51 and D12Mit132. If we pool A and H, we do not get 9:3:3:1.