2. Linkage and Mapping Irapuato, 18th October 2011

1. 2. Linkage and Mapping Irapuato, 18th October 2011

2. Lecture 2: Linkage and Mapping 1. Revision of basic terminology 2. Exceptions to Mendel’s 2nd law 3. Linkage mapping 4. The Poisson mapping function Ruairidh Sawers, Oct 2011

3. Revision of basic terminology 1 Locus: The chromosomal location linked to a heritable phenotype; the chromosomal location of a gene Recombination: Any process in a diploid cell that creates gene combinations not present in the progenitors; Generation of a haploid product at meiosis not present in the meiotic diploid Linkage: The physical association of genes on a chromosome Coupling: Linked heterozygous gene pairs in the confirmation AB/ab Repulsion: Linked heterozygous gene pairs in the confirmation Ab/aB Crossover: The exchange of portions of the chromosome between homologues Ruairidh Sawers, Oct 2011

4. Revision of basic terminology 2 Recombination frequency (RF): The proportion of non-parental (recombinant) progeny of a meiosis Genetic map unit (or cM): The distance between two linked markers such that 1% of the products of a meiosis are recombinant Coefficient of coincidence: The ratio of the observed number of double recombinants to the expected number Interference: A independence of crossover events, calculated as 1 - coincidence Mapping function: A formula expressing the relationship between genetic distance and recombination frequency Ruairidh Sawers, Oct 2011

5. Recombination During meiosis, recombination generates haploid genotypes differing for the haploid parental genotypes The recombination frequency is the proportion of recombinant genotypes Ruairidh Sawers, Oct 2011

6. Mendel’s 2nd law and recombination “the hybrid produces just so many kinds of egg and pollen cells as there are possible constant combination forms” Mendel’s 2nd Law During gamete formation the segregation of alleles of one gene is independent of the segregation of alleles of another gene The frequency of recombination between any two loci is 50% Ruairidh Sawers, Oct 2011

7. Sutton-Boveri Theory of Chromosome Inheritance “The association of paternal and maternal chromosomes in pairs and their subsequent separation during the reducing division [meiosis] … may constitute the physical basis of the Mendelian law of heredity” Walter Sutton, 1902 “Since the number of chromosomes is relatively small and the characters of the individual are very numerous it follows on the theory that many characters must mendelize together. Do the facts confirm to this requisite of the hypothesis? It seems to me that they do not.” Thomas Hunt Morgan, 1904 i.e. the chromosome theory predicts RF=50% for genes on different chromosomes, but for genes on the same chromosome the RF should be 0% Ruairidh Sawers, Oct 2011

8. Coupling and Repulsion in Sweet Pea (Bateson and Punnett) Flower colour and pollen grain shape Parents: Purple/Long and red/round Recombinants = 42/381 = 0.11 (11%) ≠ 50%! Ruairidh Sawers, Oct 2011

9. Revisiting Mendel’s 2nd law Mendel’s second law states an expected RF of 50% “the hybrid produces just so many kinds of egg and pollen cells as there are possible constant combination forms” Simple chromosomal inheritance predicts RF 50% (loci on same chromosome) or 0% (loci on different chromosomes) Empirical observation of linkage finds RF values in the range from 0% to 50% • Recombination of alleles through meiotic crossover Recombination ≠ Crossing over Ruairidh Sawers, Oct 2011

10. Chromosome crossover during meiosis Ruairidh Sawers, Oct 2011

11. Morgan, Sturtevant and linkage mapping (1911) T. H. Morgan Ruairidh Sawers, Oct 2011

12. Linkage in a test cross: Coupling pr+pr+ vg+ vg+ X prpr vg vg Red/purple Normal/vestigial pr+pr vg+ vg X prpr vg vg Parent Recombinant Testcross directly reveals allelic combinations in the gametes from females in the F1: the coupling inferred in the F2 Ruairidh Sawers, Oct 2011

13. Linkage in a test cross: Repulsion pr+pr+ vg vg X prpr vg+ vg+ pr+pr vg+ vg X prpr vg vg Recombinant Parent Ruairidh Sawers, Oct 2011

14. Linked loci on the chromosome vg+ vg pr+ pr+ pr vg pr vg + Ruairidh Sawers, Oct 2011

15. “In the latter part of 1911, in conversation with Morgan, I suddenly realized that variations in the strength of linkage, already attributed by Morgan to differences in the spatial separation of genes, offered the possibility of determining sequences in the linear dimension of a chromosome. I went home and spent most of the night (to the neglect of my undergraduate homework) in producing the first chromosome map” Alfred Sturtevant

16. Basic Principles of Linkage Mapping The greater the distance between linked genes, the greater the proportion of recombinants produced Recombination frequency (RF): The proportion of non-parental (recombinant) progeny of a meiosis # Recombinants RF = # Parents + Recombinants Genetic map unit (or cM): The distance between two linked markers such that 1% of the products of a meiosis are recombinant i.e. an RF of 0.01 (1%) is defined as 1 map unit (or cM) Ruairidh Sawers, Oct 2011

17. Linkage mapping based on Morgan’s testcross (coupling) pr+pr vg+ vg X prpr vg vg vg+ pr+ RF = 44/400 = 0.11 Map distance = 11cM 11cM Ruairidh Sawers, Oct 2011

18. Where was linkage in Mendel’s experiments? “the behavior of each pair of differentiating characters in hybrid union is independent of the other differences between the two original plants, and, further, that the hybrid produces just so many kinds of egg and pollen cells as there are possible constant combination forms.” Gregor Mendel, 1865 Ruairidh Sawers, Oct 2011

19. Three Point Testcross Red/vermilion Crossveins/crossveinless Normal wings/cut wings v+ v+ cv cvctct X v v cv+ cv+ct+ct+ v+ v cv+ cv ct+ct X v v cv cvctct Parent Ruairidh Sawers, Oct 2011

20. Three point testcross: v and cv RF = (134 + 134)/1448 = 0.185; Map distance = 18.5cM Ruairidh Sawers, Oct 2011

21. Three point testcross: v and ct RF = (99 + 92)/1448 = 0.132; Map distance = 13.2cM Ruairidh Sawers, Oct 2011

22. Three point testcross: cvand ct RF = (43 + 50)/1448 = 0.064; Map distance = 6.4cM Ruairidh Sawers, Oct 2011

23. Three point testcross: Linkage map ct cv v 13.2cM 6.4cM ? ? 13.2 + 6.4 = 19.6 ≠ 18.5 Ruairidh Sawers, Oct 2011

24. Double crossovers ct cv v+ Parental Meiotic product ct+ cv+ v ? ? ct cv v+ v+ ct cv ct+ cv+ v v ct+ cv+ ct cv v+ ct+ cv+ v With respect to loci v and cv, the double-crossover product is indistinguishable from the parental class ct cv v+ ct+ cv+ v v and cv RF = (134 + 134)+(2x(5+3))/1448 = 284/1448=0.196 Map distance = 19.6cM Ruairidh Sawers, Oct 2011

25. Recalculation of the v-cv interval Parent Single Double RF = (134 + 134)+(2x(5+3))/1448 = 284/1448=0.196 Map distance = 19.6cM v and cv Ruairidh Sawers, Oct 2011

26. Problem of multiple crossovers in estimating map distance Without ctdata, we would have incorrectly (under)estimated the size of the v-cv interval ? …and what about double crossovers between v and ct, or ct and cv? The larger the RF between two loci (i.e. the larger the mapping distance) the greater will be the problem of undetected multiple crossovers (remember the maximum value of RF = 0.5, independent assortment as Mendel’s second law) Ruairidh Sawers, Oct 2011

27. Haldane’s mapping function A mapping function relates RF to map distance RF in an experimental cross is the mean of all meioses In any individual meiosis, the number of crossovers may be 0, 1, 2, 3 or more If we know the mean number of crossovers in a given interval (m), the Poisson distribution can be used to describe the frequency of meiosis in which no crossovers occur, in which 1 occurs, in which 2 occur etc Ruairidh Sawers, Oct 2011

28. The Poisson distribution The Poisson distribution is a description of randomness in time or space Classic Poisson phenomenainclude radioactive decay and passing traffic For our purposes, we can use the Poisson distribution to describe crossover in a given genetic interval Poisson probabilities are completely defined by the mean (λ) Ruairidh Sawers, Oct 2011

29. Recombinants in the v-cv interval In the test cross, 268/1448 = 18.5% flies were scored recombinants cv v 18.5cM What is the predicted distribution of crossovers in the 1448 flies? Recombinants ≠ Crossovers A Meiosis with 0 crossovers parental parental Mean RF = 0% parental parental Ruairidh Sawers, Oct 2011

30. Crossovers and recombination in an interval The mean RF of all meioses in any non-zero crossover class is 0.5, i.e. recombinants represent half of the total products of all meioses in which at least one crossover occurs. The frequency of meioses in which at least one crossover occurs = 1 – frequency of meioses in which no crossovers occur Therefore, the frequency of recombinants RF = ½(1-e-m) Zero class = e-mm0/0! = e-m Ruairidh Sawers, Oct 2011

31. The Poisson model of crossovers/RF relationship The frequency of recombinants RF = ½(1-e-m) Therefore, m = -ln(1-2RF) For small m, m ≈ 2RF;by analogy to Sturtevant, we can define m = 0.1 (i.e. 5% RF) as 5 corrected map units. Ruairidh Sawers, Oct 2011

32. Estimate of crossovers in the v-cv interval 268/1448 = 18.5% flies were phenotypic recombinants (RF=0.185) m = -ln(1-2RF) = -ln(1-2x0.185) = 0.462; = 0.462 x 50 = 23.1 CMU In 37% of meioses, 50% of the products are recombinant; i.e. 18.5% Ruairidh Sawers, Oct 2011

33. Corrected map of the v-cv interval Ruairidh Sawers, Oct 2011

34. Interference: non-independence of crossovers Poisson model assumes crossovers to be independent random events If crossovers independent, the frequency of double crossovers is expected to be the product of the frequency of single crossovers in two adjacent intervals ct cv v 13.2cM 6.4cM E(freq of double crossovers v and cv) = 0.132 x 0.064 = 0.0084 E(number of double crossovers) = 0.0084 x 1448 = 12 Observed number of double crossovers between v and cv = 8 Coefficient of coincidence (c.o.c.) = Obs/Exp = 8/12 = 0.666 Interference = 1 - c.o.c. = 0.333 Ruairidh Sawers, Oct 2011

35. Summary

36. Revision of basic terminology 1 Locus: The chromosomal location linked to a heritable phenotype; the chromosomal location of a gene Recombination: Any process in a diploid cell that creates gene combinations not present in the progenitors; Generation of a haploid product at meiosis not present in the meiotic diploid Linkage: The physical association of genes on a chromosome Coupling: Linked heterozygous gene pairs in the confirmation AB/ab Repulsion: Linked heterozygous gene pairs in the confirmation Ab/aB Crossover: The exchange of portions of the chromosome between homologues Ruairidh Sawers, Oct 2011

37. Revision of basic terminology 2 Recombination frequency (RF): The proportion of non-parental (recombinant) progeny of a meiosis Genetic map unit (or cM): The distance between two linked markers such that 1% of the products of a meiosis are recombinant Coefficient of coincidence: The ratio of the observed number of double recombinants to the expected number Interference: A independence of crossover events, calculated as 1 - coincidence Mapping function: A formula expressing the relationship between genetic distance and recombination frequency Ruairidh Sawers, Oct 2011

38. Linkage and genetic mapping Genes physically close together on a chromosome do not segregate independently at meiosis Crossover can produce recombination between linked genes; the greater the distance between genes, the greater the proportion of recombinants produced The frequency of recombination can be used to estimate physical distance: 1 genetic map unit (or cM) is defined such that 1% of the products of a meiosis are recombinant Multiple-crossovers can confound estimates of genetic distance over large intervals Ruairidh Sawers, Oct 2011

39. “an ordinary corn-field is a series of very complex hybrids produced by the combination of numerous elementary species [alleles]” George Schull, 1908