Statistical methods for mapping imprinted QTL

1. Statistical methods for mapping imprinted QTL Yuehua Cui, Ph.D. Department of Statistics and Probability Michigan State University http://www.stt.msu.edu/~cui Email: cuiy@msu.edu The First Summer International Workshop on Statistical & Computational Genetics August 6, 2009

2. Genomic Imprinting (or parent-of-origin effect) The same allele is expressed differently, depending on its parental origin Female Male Female Male AAxaaaaxAA F1AaaA Epigenetic phenomenon (modifications to the structure of the DNA rather than the sequence). Battle (or tug of war) between sexes

3. A carton view The “– “ allele effect for the next generation depends on the gender of these mice.

4. Epigenetic modification Fig. 1. Imprinting switching in female and male germ lines. The expressed maternal allele is shown in red, whereas the silenced paternal allele is shown in blue. The maternal and paternal imprints are erased in premature germ cells (gray bars) and are subsequently replaced by new parent-specific imprints that result in allele-specific expression in the offspring. Parent-of-origin imprints must be re-set at each generation Maternal imprinting: allele from mother is silent. Paternal imprinting: allele from father is silent. (Figure from Walter and Paulsen Seminars in Cell & Developmental Biology 14:101-110)

5. Imprinted Genes • Increasing evidence has been observed from mouse, pig, sheep, chicken and human studies that imprinted genes may influence cancer, obesity, diabetes and behavior and cognitive functioning. • In plants, imprinted genes have also been detected to regulate embryonic development. Any essential role of imprinted genes in plants has until recently been inferred from inter-ploidy crosses. • More than 600 imprinted genes have been predicted in mouse genome (Luedi et al., 2005) . • The majority of imprinted genes in mammals have roles in the control of embryonic growth and development.

6. Example 1 Amaf amAf Amaf amAf The callipygous animals 1 and 3 compared to normal animals 2 and 4 (Cockett et al. (1996) Science 273: 236-238)

7. Example 2 • Prader-Willi Syndrome (PWS): caused by genetic deletions on Chromosome 15 (expressed gene is deleted). • Embryonal rhabdomyosarcoma– kidney cancer • Osteosarcoma– bone cancer • Angelman syndrome– delayed development, mental retardation and severe speech impairment

8. Example 3 • In maize endosperm, endoreduplication is a commonly observed phenomenon which shows a maternally controlled parent-of-origin effect (Dilkes et al., 2002). Cells undergo endoreduplication are typically larger than other cells, which consequently results in larger fruits or seeds beneficial to human beings (Grime and Mowforth, 1982). • R gene in the regulation of anthocyanin (Kermicle 1970), the seed storage protein regulatory gene dsrl (Chaudhuri and Messing 1994), the MEA gene affecting seed development (Kinoshita et al. 1999). • More examples in flowering plants (Nowack et al., 2007, Nature).

9. The cause of imprinting • DNA methylation is considered as one of the major causes of genomic imprinting.

10. Why Are the Epigenetic Changes Critical for the Disease’s (like cancer) Onset? In normal genome, even with a mutation on one allele, the other allele can still be transcribed and compensate the loss from the mutated one X If the epigenetic events happened  No more healthy genome = disease X Therefore, the epigenetic changes could provide the second hit for the disease’s onset and, without changing the genomic sequences physically

11. Quantitative genetics of genomic imprinting Genotype aa Aa aA AA Genotypic value G0 G10 G01 G2 Net genotypic value -a d-i d+i a a = additive genotypic value d = dominant genotypic value i = imprinting effect Genotype frequency P0 P10 P01 P2 at HWE =q2 =pq =pq =p2 Deviation from population -a -  d-i -  d+i -  a -  mean  =-2p[a+(q-p)d] = (q-p)[a+(q-p)d] = (q-p)[a+(q-p)d] = 2q[a+(q-p)d] -2p2d +2pqd-i +2pqd+i -2q2d Letting =a+(q-p)d =-2p-2p2d = (q-p)+2pqd-i =(q-p)+2pqd+i =2q-2q2d Population mean  = q2(-a) + pq(d-i) +pq(d+i) + p2a = (p-q)a+2pqd Genetic variance with no imprinting: 2g = q2(-2p-2p2d)2 + 2pq[(q-p)+2pqd]2 + p2(2q-2q2d)2 = 2pq2 + (2pqd)2 = 2a (or VA) + 2d (or VD) Genetic variance with imprinting: 2g = q2(-2p-2p2d)2 + 2pq[(q-p)+2pqd]2 + 2pqi2 + p2(2q-2q2d)2 = 2pq2+(2pqd)2+2pqi2 = 2a+2d+2i

12. Genomic imprinting results from (imbalanced) natural selection. • It does increase total genetic variance for a quantitative trait from a quantitative genetics point of view. • Thus, it is evolutionarily favorable.

13. Statistical models for mapping imprinted quantitative trait loci (iQTL) in experimental crosses • Fixed effects model – estimate the fixed effects of an iQTL (Cui et al. 2006; Cui 2007; Li et al. 2008) • Random effects model – estimate the genetic variances contributed by an iQTL (IBD-based variance components linkage analysis) (Liu et al. 2007; Li and Cui, 2009)

14. The mapping principle • Considering the parental origin for an allele. Use subscript letters m and f to denote an allele inherited from mother and father, respectively. • For homozygous genotype AA or aa, there is no way we can distinguish the parent-of-origin of the two alleles. • For heterozygous Aa, testing imprinting is equivalent to test the mean difference between Amaf and amAf . • Thus, it is essential to construct a mapping population that we can distinguish the allelic parent-of-origin and further estimate and test the mean difference between the two reciprocal heterozygous.

15. QQ(P1) x qq(P2) F1Qq x qq BC1 Qqqq Reverse backcross qq x Qq BC2 qQqq Genetic design (experimental cross) • A backcross design • Similarly, we can get offsprings from QQ×Qq and Qq×QQ • It is very easy to generate the above segregation populations initiated with two inbreeding parents.

16. Quantitative genetic model • If a gene is completely maternal imprinting, the genotypic value is given as • If a gene is completely paternal imprinting, the genotypic value is given as

17. Quantitative genetic model • Define p as the probability that a gene is maternally imprinted. Then the genotypic value for • p=1: completely maternal imprinting • p=0: completely paternal imprinting • p=0.5: the model reduces to Mendelian model • p>/<0.5: partially maternal/paternal imprinting

18. Genetic design

19. Maximum likelihood estimation • The joint log-likelihood function combing the two backcross designs together is given as where is the component log-likelihood • Estimation: EM algorithm (see Cui 2007, J. Theo. Biol.)

20. Hypothesis tests The presence of QTL: The presence of iQTL: LR test and permutation for threshold determination

21. Simulation • Complete maternal imprinting:

22. Simulation • Complete paternal imprinting:

23. Simulation • No imprinting:

24. Imprinting power plot as a function of p

25. Model extension • Cytoplasmic maternal effect is another indirectgenetic source for offspring genetic variation (Wade, 1998). • With the proposed genetic design, we can also dissect the cytoplasmic maternal effect. • Define be the maternal genetic effects.

26. iQTL mapping for an inbreed F2 design (Cui et al. 2006 Genomics) • Genetic design: F2. AA x aa F1 Aa x Aa F2 AA Aa aA aa

27. The quantitative genetics model • Four types of alleles Am, am, Ap and apwith 4 possible imprinted genotypic means in F2: where m= additive effect from the maternal allele p= additive effect from the paternal allele  = dominant effect between the maternal and paternal alleles

28. Mapping procedure • Assume normality, a finite mixture model can be applied • The likelihood of the mixture model: • Test QTL effect: H0: m=p= =0 • Test imprinting effect: H01: m=p • Test completely maternal imprinting: H02: m= 0 or completely paternal imprinting: H03: p= 0 • Likelihood ratio test can be applied at each mapping position. • Traditional interval mapping procedure with EM algorithm can be applied.

29. Question: how to distinguish Aa and aA in an inbreed F2 population? • Empirical studies indicate that male and female chromosomes differ in length and recombination rate. Evans and Swezy, 1928)

30. Ratio of average recombination rate (female: male) • Mouse 1.25:1 (Dietrich et al. 1996). • Human 1.6:1 (Dib et al., 1996) • Dog 1.4:1 (Neffet al., 1999) • Pig 1.4:1 (Marklund et al., 1996). • With these information, we can derive the conditional QTL probability (four) given on the flanking markers, and can distinguish the four QTL genotypic means.

31. rM1 rP1 rP2 rM2 Mixture proportions (’s)

32. Application F2 mouse phenotype data (510 individuals) It is postulated that mouse growth may be controlled by imprinted genes. But little is known about the number, location and effect of these imprinted genes.

33. Linkage scan Out of four QTL identified, three are imprinted as indicated by the arrow sign (chrom 6, 10 and 15). (Cui et al., 2006, Genomics)

34. Inference of imprinting

35. Thank you! Questions?