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Lecture 4: When 2 or more genes are on the
same chromosomeor lets relax the assumption ofindependence, central to prediction in Classical
Mendelian Models.
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What is the probability of having two girls and a
boy ?
(GGB or GBG or BGG)
a) 1/2b) 1/4c) 1/8
d) 1/16e) 3/8
In genetics you often use both multiplicative and additive rules in oneproblem
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The chromosomal theory of inheritance: first proposed by W. Sutton, T. Boveri
1902, based on correlation between chromosome division into gametes and the
inheritance of sex. For example, W. Sutton wrote that the association of paternal
and maternal chromosomes (of the grasshopper Brachystoma magna) in pairs and
their subsequent separation during the reducing division (of meiosis) may explain
Mendelian segregation and that maternal and paternal pairs are indifferent to
their position relative to others when they assort and segregate in meiosis.
T.H. Morgan and his student C. Bridges experiments on Drosophila showed
phenotype ratios are informative even when they deviate from Mendels classic
ratio because they correlate with chromosome segregation.This work strongly suggested, that units of inheritance of different
phenotypic characters -genes- are in chromosomes
2
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Ifn is the basic number of chromosomes.
In humans 2n = 46
n = 23There are 22 autosomepairs
and a (1) sex chromosomepair
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Chromosomes differ in size and the position of their
centromere
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Prophase -Metaphase chromosome
Interphasechromosomes
Each diploid humancell contains about 2m
of DNA in nuclei with
an average diameter of
6 micrometers (10-6m)
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To represent the cellular behavior of chromosomes at the cytological
scalein meiosis we use the following model of chromosome structure, a
double stranded DNA molecule with associated histone proteins.
The centromere is part of a DNA molecule, it is hundreds of kilobases
long, with no functional genes. Count chromosomes by counting
centromeres.
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Figure 2-15
Key stages of meiosis and mitosis
Homologous
chromosomes
Sister chromatids
Sister Chromatids
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Synaptonemal complexes at meiosis
(3)Pachytene(synaptonemal complex,crossover, recombination).
Recombinationoccurswhere maternal &
paternalchromosomes
arms break, andrecombine with theirhomologue.
There aregeneticrepair mechanisms
associated with thepairing of chromosomesin Prophase1.
(3)Pachytene(synaptonemal complex,
crossover, recombination).
Recombination (1)
occurs where maternal &paternalchromosomes
arms break, and recombine
with their homologue.
There aregenetic repairmechanisms associatedwith the pairing ofchromosomes in Prophase1.
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Recombinants (1) are produced by crossovers thathappen in prophase 1 of meiosis
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Synaptonemal complex
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Crossover, recombination and
repair has finished
in (4)Diplotene, thechromosomes are beginning to
repel and the chiasmata (points
of recombination)are
beginning to migrate to thetelomeres.
In (5) Diakinesis, chiasmata
have migrated to the
chromosome ends (telomeres)
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Recombination 2: metaphase: paired homologues
orientrandomlyon the metaphase plate Mendel 2
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Understand This !
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Genes for
flower, leaf and
stem shape and
color
There is more than
one per
chromosome, or
they are linked andpotentially non-
independent
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Linked genes:genes are linked when they are on the same chromosome.
Nomenclature: AB/ab , you might see
AB//ab or, AB or ++/ ab, or
ab
Separate chromosomes?A/a ; C/c (known), A/a . C/c (unknown),
Key terms:Meiotic recombination, dyads, tetrads, crossover,
chiasma(ta), parentals, recombinants, recombinant frequency, map unit,
centimorgan.
Key Breeding designs-
Dihybrid Parental cross, eg. Ab/Ab X aB/aB
and F1testcross AB/ab X ab/ab
AB ab
ab X
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Gene linkage can be: very close, close or distant
A B
a b
(2) But, if they are far enough apart on a chromosome, they may
act as if they assort independently
A B
a b
Genes on the same chromosome are linked.
(1) Closelylinked alleles assort into the same gametes and are more
frequently inherited togetherthan you would expect than if they
were on different chromosomes (not linked).
18Recombination 1
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(1a) Very closely linked allelesusually
assort into the same gametesor, they are
almostalways co-inherited.
A B
ab
A B
ab
A B
a b
A B
a b
A Prophase 1 tetrad-2 synapsed replicated chromosomes
tetrad
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AB ab
AB / ab ab / abab
(1) Dihybrid Parentals (AA BB & aa bb) cross
(2) F1testcross, showing parental, homozygous test
gametesand the expected F1 offspring genotypesfor
(a)very closely linked genes in
(b)
a small - sized sample.
ratios ?
20
tester
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Linked alleles are inherited together unless,
(2 )there is a cross-over between the locations (loci) of 2genes on homologous chromatids in prophase 1 of meiosis.
A B
a b
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Gene linkage Gene recombination in Pachytene, a sub-stage in
prophase 1 of meiosis.
Linked alleles are inherited together, except when there is across-over between linked loci on homologous chromatids
A B
a b
There may be a cross-over, but it cannot be detectedunless there are different alleles on each dyad(a pair
of sister chromatids joined at the centromere).
chiasma
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Gene linkage and recombination in Pachytene
(1) Linked alleles are inherited together except when there is a
cross-over between linked loci on homologous chromatids.A B
a b
Crossovers involve the breaking of at least one
chromatid on each dyad and the rejoining of maternalwith paternal fragments.
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Gene linkage and recombination:
Linked alleles are inherited together exceptwhen there
is a cross-over between homologous chromatids or
closely - linked genes sometimes recombine.
A B
a b
a B
A b
A B
a B
A b
a b
Parentals Recombinant
gametes
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In GENERAL
(1)There is always at least one chiasma(ta)-(a crossover point) per
chromosome, per meiosis, regardless of chromosome length.
(2)Thegreater the distancebetween two gene locations (loci)on a
chromosome the greater the chance of a cross over between them.
(3) The position of the crossover between two loci, is at first
approximationrandom.
A B C
a b c
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With CLOSE LINKAGE Parental types will be more frequent-
(in excess of 50 %)than recombinant types (less than 50%).
>1/4
>1/4
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Mapping closely linked genes
using their linkage relationship
Complete linkage between loci (absence of a chiasma in
meiosis) decreases with increasing distance between
markers (loci) on a chromosome, or, as the distance
increases between 2 loci on a chromosome, the probability
of a crossover and recombinant gametes increases.
AlfredSturtevantfirst suggested using % recombinants as a
linear measure of chromosomal map distance
One map unit = 1% recombinants
1 map unit= 1 centimorgan (cM)
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Crossover between 2 markers keeping it organized
Testing for linkage between genes for fruit shape (beaked bk)
and internal division number (1 locule Lc or many lc)
in tomatoes, and if linked, measuring the map distance between
them.
Bk bk lc Lc
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Measuring linkage between genes for beaked fruit and many
locules in tomatoes.
Bk bk lc Lc
P: Bk /Bk . Lc /Lc x bk /bk . lc/ lc
Test cross: Bk/ bk . Lc/ lc x bk /bk . lc /lc
Bk bk Lclc 170
Bk bk lc lc 26
bk bk Lc lc 30bk bk lc lc 168
400
The ratio of the 4 classes of
offspring is clearly not
1:1:1:1 suggesting
The two genes are closely
linked on the same
chromosome.29
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Measuring linkage between genes for beaked fruit and many
locules in tomatoes.
Bk bk lc Lc
P: Bk Lc / Bk Lc x bk lc / bk lc
F1
Bk bk Lc lc 170
bk bk lc lc 168
Bkbk lc lc 26
bkbkLclc 30
400
The % recombinant offspring is:
(26 + 30) / 400 = 56 / 400
= 14%
The distance between Bk and Lc is 14 map units
Bk Lc x bk lcbk lc bk lc
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Test cross:
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AB Ab aB ab
AB/ab Ab/ab aB/ab ab/abab
Dihybrid testcross, showing parental,
recombinant, homozygous testgametes and theexpected genotypesin the F2.
If a & b loci are so far apart that there is always a
crossover between them,then the ratios will be the
same as independent assortment of A & B loci.
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If they are close, then recombinants < parentals
If they are very close then all you see is parentals
F1:AB/ab
SUMMARY
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Double crossover between two markers (gene loci), in this
case there will not appear to be a crossover between v and cv.
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So all you will see are the genotypes of the F1
and the testers- no recombinants.
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Double crossover between v and cv will appear the same
as no crossover, but a third, intermediate markerhas
recombined. Use the third intermediate marker toestimate double frequency crossover.
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The outside markers are still the same as theparental, but the inside marker changes
chromosome association (switches).
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Three markers or loci on the same arm of a
chromosome allows you to:
(1)
detecting double crossovers between theoutside markers (loci)
(2)estimate the distance between loci
(3) determine the order of loci
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The three point cross is used, if they are linked, to map the
distance between three genes and determine their order.
F faciated, ff - two fasciaA purple stem, aa green stem
Hl hairless stems hl hl hairy stems
Parents F A Hl / F A Hl x f a hl / f a hl
F1 Test Cross: F A Hl// f a hl x f a hl // f a hl
Three genes controlling locule form, stem color and stem
hairiness in tomato are linked .
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The three point crossF fasciated ff - two fascia
A purple stem aa green stem
Hl hairless stems hl hl hairy stems
P: F A Hl//F A Hl x f a hl // f a hl
Test X: F A Hl// f a hl x f a hl // f a hl
F A Hl 302
f a hl 308
F a hl 101
f A Hl 109
F A hl 82f a Hl 77
F a Hl 10
f A hl 11
1000
Parental types
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Double crossover gametes
Single recombinants
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The three point crossF fasciated (many locules) ff - two locules
A purple stem X aa green stem
Hl hairless stems hl hl hairy stems
P: F A Hl//F A Hl x f a hl // f a hl
Test X: F A Hl // f a hl x f a hl // f a hl
Parental types
F A recombinants are unlike
parental configuration.
% recombination =
101 + 109 + 10 + 11 / 1000 =
231/ 1000 = 23.1 %
F-A-find recombinants
Work 2 loci at a time
F A Hl 302
f a hl 308
F a hl 101
f AHl 109
F A hl 82f a Hl 77
F a Hl 10
f Ahl 11
100037
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The three point crossF many locules ff - two locules
A purple stem X aa green stem
Hl hairless stems hl hl hairy stems
Parental types
F A recombinants 23.1 %
A Hl recombinants
82 + 77 + 10 + 11 / 1000 =180 / 1000 = 18%
Work 2 loci at a time A, Hl
F A Hl 302f a hl 308
F a hl 101
f AHl 109
FA hl 82
f a Hl 77
F a Hl 10
f A hl 11
100038
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The three point crossF many locules ff - two locules
A purple stem X aa green stem
Hl hairless stems hl hl hairy stems
Parental types
F Hl , % recombinants =
101 + 109 + 82 + 77 / 1000 =369 / 1000
= 36.9%
P: F A Hl / F A HlX f a hl /f a hl
Test X: F A Hl / f a hl X f a hl /f a hl
Work 2 loci at a time F-Hl
F A Hl 302
f a hl 308
Fa hl 101
f AHl 109
FAhl 82
f a Hl 77
F a Hl 10
f A hl 11
1000
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The three point crossF many locules ff - two locules
A purple stem X aa green stem
Hl hairless stems hl hl hairy stems
F A recombinants 23.1 %
A Hl recombinants 18%
F Hl recombinants 36.9%
? Outside loci (markers)
F A Hl 302
f a hl 308
F a hl 101
f AHl 109F A hl 82
f a Hl 77
F a Hl 10
f A hl 11
1000
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The three point crossF many locules ff - two locules
A purple stem X aa green stem
Hl hairless stems hl hl hairy stems
F A Hl 302f a hl 308
F a hl 101
f A Hl 109
F A hl 82
f a Hl 77
F a Hl 10
f A hl 11
1000
Distance between the outside loci =36.9 or 23.1+18= 41.1 ?
F HlA
F A recombinants 23.1 %
A Hl recombinants 18%
F Hl recombinants 36.9%
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The three point crossF many locules ff - two locules
A purple stem X aa green stem
Hl hairless stems hl hl hairy stems
F A Hl 302f a hl 308
F a hl 101
f AHl 109
F A hl 82
f a Hl 77
F a Hl 10
f A hl 11
1000
F A recombinants 23.1 %
A Hl recombinants 18%
F Hl recombinants 36.9%
F A
23.1 18
36.9 + 4.2 = 41.1 map units
Hl
2.1% These classes are double cross-overs
for F and Hl and must be counted twice.
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F A Hl
f a hl
F A Hl302
f a hl 308F a hl 101
f AHl 109
F Ahl 82
f aHl 77
Fa Hl 10
f Ahl 11
(1)
Why calculate all 3 distances to get the order ?
(2) For the order, identify the double recombinant class,
look at which locus has flipped, relative to the parentalorder - this one is in the middle.
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F A Hl
f a hl
There are two ways to calculate the F to Hl distance. The answer
should beidentical.
1. Add the distances between the outside and middle markers or
loci:F to A distance, and A to Hl distance.
2. Identify the middle locus or marker(A), estimate the distance
between the 2 outside markers(F - Hl recombinants), and add 2times the number of double recombinants- because double
recombinants have single crossovers in each outside region.44
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F A Hl
f a hl
Mapping and recombination - the 4 step method when you do not have a data table
(1)Pair gametic types by complement & frequency
(2) ID parental chromosomes: F A Hl & f a hl (a) # highest ?
(b) complementary pairs ?(c)# similar ?
(3) Organize a table with the 2 or 3 mutant symbol headingthe column tops,
corresponding parentals at the top, below each heading.Remember, you are
always organizing & comparing recombinants with parentals.
(4)If the problem involves 3 markers (loci), identify the double recombinant
chromosomes F aHl (a) # lowest ?
(c) complementary pairs? f AHl (c) # similar ?
Then you can ID the middle marker(pair that has flipped to parentals)
Then you have the gene order. Put the double -X -over pair at the bottom
(5) Table the single recombinant classes (middle): (a) # similar ?
Estimate the required distances (b) complementary pairs ?
Parental F A Hl
Parental f a hl
recombinant
recombinant
2
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Interference between chiasmamay decrease the
observed crossover frequency and the apparentgenetic distance.
1. The coefficient of coincidenceis the observed frequency of
double recombinants divided by (standardized by) the expected
number of double recombinants.
2. The expected number of recombinants is the productof the
expectation of a crossover in each region (outside to middle).
3. Interference = 1- coefficient of coincidence
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P cn c px 296R1 cn c + 63
R2 cn + + 119
D cn + px 10
R2 + c px 86
D + c + 15P + + + 329
R1 + + px 82
1000
1. Calculate the individual distances make the map.
ORCompare double cross-overs with parental lines, the one gene
that is different is in the middle (order) then estimate the other distances.
C- curved wings, px - extra wing veins, cn - cinnabar eyes
In the lab, the numbers will not be pre - paired - Look at
magnitudes, check by locus complements (+ + + / cn c px)
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Recombination Mapping in General
As map distance increases over 10 map units, multiple crossovers
cause recombination frequency to underestimate crossover
frequency or the actual recombination map distance. For example,
when the recombination frequency is 30% the actual map distance is
50 mu in Drosophila.
Mapping functions help(p=1/2 (1-e-2d) d=crossover frequency
Or, map closely linked genes and add the distances.
Very Closely linked = ? Closely Linked = ? Distantly linked = ?
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