accurate calculation of large map distances

1
LECTURE 07 EUKARYOTE CHROMOSOME MAPPING AND
RECOMBINATION II

• accurate calculation of large map distances
• mapping function
• analysis of single meioses
• ordered gene ? centromere
• unordered gene ? gene

2
CHAPTER 4 FURTHER IDEAS

• double higher multiple crossovers ?
  underestimates of map distances calculated from
  recombination
• specialized mapping formulae ? accurate map
  distance corrected for multiple crossovers
• analysis of single meioses (in Fungi) can...
• position centromeres on genetic maps ( genes)
• ? mechanisms of segregation and recombination
• crossovers occur occasionally in mitotic diploid
  cells

3
ACCURATE MAPPING

• mapping large distances is less accurate
• best estimate of map distance obtained by adding
  distances calculated for shorter intervals
• if possible, include more genes in the map

4
ACCURATE MAPPING

• problems occur when you have ...
• no intervening genes
• genes very close together

5
ACCURATE MAPPING

• account for multiple crossovers ?
• need mapping function to correct for multiple
  events and accurately relate recombination to map
  distance

6
POISSON DISTRIBUTION

• low s sampled from large population
• possible numbers obtainable are large, but most
  samples are small
• e.g. random distribution of 100 x 1 in class of
  100 students... few students receive many
  bills...

7
POISSON DISTRIBUTION

• e.g. random distribution of 100 x 1 in class of
  100 students

8
POISSON DISTRIBUTION

• here, average is 1 bill/student... m 1
• for a particular class... i 0, 1, 2... 100

9
POISSON DISTRIBUTION

• here, mean is 1 bill/student... m 1 because 100
  bills 100 students
• for a particular class... i 0, 1, 2... 100
• how many students are predicted to
  capture 3 bills?

10
POISSON DISTRIBUTION

• here, mean is 1 bill/student... m 1 because 100
  bills 100 students
• for a particular class... i 0, 1, 2... 100
• how many students are predicted to
  capture 3 bills?
• f(i)

e-m mi i !
11
POISSON DISTRIBUTION
12
POISSON DISTRIBUTION

• f(0) 0.368
• f(1) 0.368
• f(2) 0.184
• f(3) 0.061
• f(4) 0.015
• f(5) . . .

13
POISSON DISTRIBUTION

• proportion of class with i items
• different m values

14
MAPPING FUNCTION

• use Poisson to describe distribution of
  crossovers along chromosome
• if...
• crossovers are random,
• we know mean / region on chromosome
• then we can calculate distribution of meioses
  with 0, 1, 2... n multiple crossovers

15
MAPPING FUNCTION

• recombination frequency (RF) recombinants
• meiosis with 0 crossovers ? RF of 0

• meiosis with 1 crossover ? RF of 50

16
MAPPING FUNCTION

• meioses with 0 crossovers ? RF of 0
• meioses with gt 0 crossovers ? RF of 50

compare the non-recombinant chromatids recombina
nts shown darker
17
MAPPING FUNCTION

• recombinants make up half of the products of
  meioses with 1 or more crossovers
• 0 crossover class is the only critical one
• proportion of meioses with at least one crossover
  is 1 0 class the 0 class is...
• f(0) e-m

e-m m0 0 !
18
MAPPING FUNCTION

• proportion of meioses with at least one crossover
  is 1 0 class, which is...
• f(0) e-m
• so the mapping function can be stated as...
• RF ½ (1 e-m)

e-m m0 0 !
19
MAPPING FUNCTION

• for low m...
• m 0.05, RF ½ m
• m 0.1, RF ½ m
• m 1, RF 50
• ... RF m / 2 at the
• dashed line

RF ½ (1 e-m)
or use the equation...
20
MAPPING FUNCTION

• RF ½ (1 e-m)
• RF 27.5 cM ?
• 0.275 ½ (1 e-m)
• 0.55 1 e-m
• e-m 1 0.55 0.45

m ? 0.8 (mean of crossovers /
meiosis) corrected RF m/2 0.4 40 or 40 cM
21
MAPPING FUNCTION

• for low m...
• m 0.05, RF ½ m
• m 0.1, RF ½ m
• m 1, RF 50
• ... RF m / 2 at the
• dashed line

RF ½ (1 e-m) 40 cM
or use the equation...
22
MAPPING FUNCTION

• mapping large distances is less accurate
• best estimate of map distance obtained by adding
  distances calculated for shorter intervals
• if possible, include more genes in the map
• put RF values through a mapping function

23
ANALYSIS OF SINGLE MEIOSES

• products of meiosis remain together
• groups of haploid cells... either 4 (tetrads) or
  8 (octads)

24
ANALYSIS OF SINGLE MEIOSES

• Neurospora crassa (we use Sordaria fimicola in
  Lab 5)
• note pigment phenotypes of the ascospores

25
ANALYSIS OF SINGLE MEIOSES

• meiosis post-meiotic mitosis in linear tetrad /
  octad

26
ANALYSIS OF SINGLE MEIOSES

• 2 kinds of mapping with tetrads / octads
• ordered analysis to map gene ? centromere
• unordered analysis to map gene ? gene

27
ORDERED ANALYSIS

• no crossing over between gene A and centromere

MI segregation
28
ORDERED ANALYSIS

• crossing over between gene A and centromere

MII segregation
29
ORDERED ANALYSIS

• 4 types of MII patterns
• equal frequencies

30
ORDERED ANALYSIS
31
ORDERED ANALYSIS

• MI 126 132 258 86
• MII 9 11 10 12 42 14

32
ORDERED ANALYSIS

• ? divide by 2

33
ORDERED ANALYSIS
MII 9 11 10 12 42 14 ? A ?
centromere 14 / 2 7 cM
34
ORDERED ANALYSIS

• now consider 2 genes...

• 3 possibilities
• 1. the genes are on separate chromosomes
• 2. the genes are linked but on opposite sides of
  the centromere
• 3. the genes are linked and on the same side of
  the centromere

35
ORDERED ANALYSIS

• crossover between centromere and both genes...

36
ANALYSIS OF SINGLE MEIOSES

• 2 kinds of mapping with tetrads / octads
• ordered analysis to map gene ? centromere
• unordered analysis to map gene ? gene

37
ORDERED ANALYSIS

• lots of crossovers between gene centromere...
  appear to be unlinked

38
ORDERED ANALYSIS

• MII frequency never reaches 100
• theoretical maximum RF 2/3 or 66.7
• theoretical maximum calculated map distance
  33.3
• gt1 crossovers ? with distance...
• especially, DCO look like SCO

39
ORDERED ANALYSIS

• second allele determines pattern
• maximum MII 2/3 33.3 33.3 cM
• multiple crossovers !

40
UNORDERED ANALYSIS

• meioses with 0 crossovers ? RF of 0
• meioses with gt 0 crossovers ? RF of 50

41
UNORDERED ANALYSIS
NCO 1/4 DCO 1/4 DCO SCO 1/2 DCO

• parental ditypes
• non-parenal ditypes
• tetratypes

42
UNORDERED ANALYSIS

• NCO PD NPD

PD but not NCO ?
P ? score 1x ?
43
UNORDERED ANALYSIS

• SCO TT 2NPD

T but not SCO ?
2P ? score 2x ?
44
UNORDERED ANALYSIS

• DCO 4NPD

DCO but not NPD ?
4P ? score 4x ?
45
UNORDERED ANALYSIS

• corrected map distance (cM) between genes
• RF 100 cM
• ½ single events double events /
  total 100 cM
• ½ ( TT 2NPD ) 4NPD / total 100
  cM
• ½ TT 6NPD / total 100 cM

46
ANALYSIS OF SINGLE MEIOSES

• 2 kinds of mapping with tetrads / octads
• ordered analysis to map gene ? centromere
• unordered analysis to map gene ? gene

47
e.g., ORDERED UNORDERED ANALYSIS
or
48
e.g., ORDERED UNORDERED ANALYSIS
49
e.g., ORDERED UNORDERED ANALYSIS
50
ORDERED UNORDERED ANALYSIS
51
ORDERED UNORDERED ANALYSIS

• ordered analysis to map gene ? centromere
• MI ... no recombination
• MII ... recombination

52
ORDERED UNORDERED ANALYSIS

• ordered analysis to map gene ? centromere
• MI ... no recombination
• MII ... recombination
• RF ½ (MII / TOTAL)

53
ORDERED UNORDERED ANALYSIS

• ordered analysis to map gene ? centromere
• MI ... no recombination
• MII ... recombination
• RF ½ (MII / TOTAL)
• RF x 100 map distance (cM)

54
ORDERED UNORDERED ANALYSIS
RF ½ (MII / TOTAL) RF x 100 map distance
(cM) r ? cent. ½ (12121)/200 x 100
1.75 cM t ? cent. ½ (1211513171)/200
x 100 16.75 cM
55
ORDERED UNORDERED ANALYSIS
56
ORDERED UNORDERED ANALYSIS

• unordered analysis to map gene ? gene
• consider all possible gene pairs (here only 1)
• PD ? NPD?, unlinked or PD gtgt NPD, linked
• PD NCO 2-strand DCO
• TT SCO 3-strand DCO (x2)
• NPD 4-strand DC) (¼ of all DC0)

57
ORDERED UNORDERED ANALYSIS

• unordered analysis to map gene ? gene
• RF ½ TT 6NPD / TOTAL

58
ORDERED UNORDERED ANALYSIS

• unordered analysis to map gene ? gene
• RF ½ TT 6NPD / TOTAL
• RF x 100 map distance (cM)

59
ORDERED UNORDERED ANALYSIS

• unordered analysis to map gene ? gene
• RF ½ TT 6NPD / TOTAL
• RF x 100 map distance (cM)
• PD (133) gtgt NPD (2) ? linked
• r ? t ½ 65 6(2) / 200 x 100 19.25 cM

60
ORDERED UNORDERED ANALYSIS
61
ORDERED UNORDERED ANALYSIS
but... 1.75 16.75 18.5 ??
62
ORDERED UNORDERED ANALYSIS
more accurate... calculation includes DCOs
63
EUKARYOTE CHROMOSOME MAPPING AND RECOMBINATION
PROBLEMS

• in Griffiths chapter 4, beginning on page 141,
  you should be able to do questions 1-30
• begin with the solved problems on page 138 if you
  are having difficulty
• look at the way Schaums Outline discusses
  linkage and mapping for alternative explanations
  - especially tetrad analyses
• try Schaums Outline questions in chapter 4,
  beginning on page 208