Crossing over and map distance • Replicated chromosomes during meiosis are comprised of two sister chromatids. • Crossovers occur between non-sister chromatids from homologous chromosomes, thereby producing recombinant haplotypes. • Recombination frequencies between widely spaced genes tend towards 50%.
Crossing over and map distance. Replicated chromosomes during meiosis are comprised of two sister chromatids. Crossovers occur between non-sister chromatids from homologous chromosomes, thereby producing recombinant haplotypes. - PowerPoint PPT Presentation
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Crossing over and map distance
• Replicated chromosomes during meiosis are comprised of two sister chromatids.
• Crossovers occur between non-sister chromatids from homologous chromosomes, thereby producing recombinant haplotypes.
• Recombination frequencies between widely spaced genes tend towards 50%.
Crossing over and map distance
• We observe the frequency of recombinants, not the frequency of crossing over
• An odd number of crossovers between two loci produces recombinant haplotypes, whereas an even number of crossovers between two loci produces non-recombinant haplotypes.
– recombination frequency ≠ crossover frequency
• The presence of one crossover often suppresses crossover in the immediate vicinity, a phenomenon known as interference.
– recombination frequencies are not additive
Map distance• The genetic map distance between two genes, measured in centi-
Morgans (cM), is the expected number of crossovers that arise on a single chromatid.
• The mean number of crossovers per chromatid between A and C in the diagram shown below is one. (0 + 1 + 2 + 1)/4 = 1
A
B
C
A
B
C
12
a
b
c
a
b
c
34
A
b
c
A
B
C
12
a
b
C
a
B
c
34
A
b
c
A
B
C
21
a
b
C
a
B
c
43
Meiotic Post-Meiotic
Mapping functions
• Recombination frequency and map distance (r = d) are equal in the absence of multiple crossovers
• Mapping functions are used to transform recombination frequencies into additive map distances to better estimate map distance by counting single crossover events once and double crossover events twice.
Morgan mapping function (1928)
• With complete interference (C = 0) and absence of multiple crossovers
rd d = map distance in Mr = recombination frequency
• In most cases, this assumption only applies for very tighly linked loci (r< 0.1)
Haldane mapping function (1919)
• With no interference (C = 1), the distribution of crossovers is Poisson
)ˆ21ln(2
1rd
x = number of crossoversd = map distance in Mr = recombination frequency
Haldane map distance
Distances will be additive only when there is no interference
dx
ex
ddx
!);Pr(
BCABAC ddd
BCABBCABAC rrrrr ˆˆ2ˆˆ
Haldane mapping function (1919)
3.0ˆ
1.0ˆ
22.0ˆ
BC
AC
AB
r
r
r
2899.0)]22.0(21ln[2
1)ˆ21ln(
2
1 ABAB rd
4015.0)]276.0(21ln[2
1)ˆ21ln(
2
1 BCBC rd
Order BAC
1116.0)]10.0(21ln[2
1)ˆ21ln(
2
1 ACAC rd
276.0)1.0)(22.0(21.022.0ˆˆ2ˆˆ ACABACABBC rrrrr
276.032.010.022.0ˆˆ ACABBC rrr
4015.01116.02899.0 ACABBC ddd
Kosambi mapping function (1944)
• Condition: C = 2r
• Make sense biologically– C tends to 1 as r approaches 0.5– C tends to 0 as r approaches 0.0.
• Widely used
• For three linked loci ordered ABC
Kosambi’s addition formula for the recombination fractions of the loci
s = prob. of misclassifying recombinants as non- recombinants and vice versa
Aa misclassified as aa
aa misclassified as Aa
Incomplete Penetrance
prrfrprfprfprfL aaAa )1(
2
1lnˆ)1(
2
1lnˆ)1(
2
1lnˆ)1)(1(
2
1lnˆ 4321
)1(
2
1lnˆ
2
1lnˆ
2
1lnˆ)1(
2
1lnˆ 4321 rfrfrfrfL
)1)(1(
2
1lnˆ)1(
2
1lnˆ)1(
2
1lnˆ)1(
2
1lnˆ 4321 prfprfrprfprrfL Aaaa
Incomplete Penetrance
4321
32
ˆˆˆˆ
ˆˆˆ
ffff
ffr
)ˆˆ(ˆ)ˆˆ(ˆ)ˆˆ(ˆ
ˆ421312
312
ffffff
fffr
)ˆˆ)(ˆˆ(
ˆˆˆˆˆ
4231
2143
ffff
ffffp
)ˆˆ(ˆ)ˆˆ(ˆ)ˆˆ(ˆ
ˆ134243
243
ffffff
fffr
)ˆˆ)(ˆˆ(
ˆˆˆˆˆ
1324
3412
ffff
ffffp
Fully penetrant
Aa misclassified as aa
aa misclassified as Aa
Segregation Distortion
Genotypes Observed count
Exp. freq.
No diff. viability
Exp. freq. with diff. viability
for the A locus
AaBb f1 r r) r r
r
Aabb f2 r r r r r
aaBb f3 r r r r r r
aabb f4 r r r r
r
r
-viability coefficient for the A locus- Aa genotypes are less viable than aa when 0.0 < < 1.0- Aa and aa genotypes are equally viable when = 1.0- Aa genotypes are more viable than aa when 1.0 < < ∞