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Linkage Mapping and Crossing-over
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Independent assortment vs linkage.
Independent assortment occurs when the genes for two different traits
or genetic markers are located on different chromosomes. Mendel was
lucky enough to have chosen such a configuration.
Assuming pea plants have approximately, !,!!! genes and seven
chromosomes, then each chromosome might carry around ,"!!genes. #hese genes are not expected to assort independently during
meiosis. In other words, there is a roughly "$ chance of the genes
%eing linked.
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Comparison of independent and linked genetic
markers.
&A
A
'
'
a
a
%
%( )
'
a %
A
Independent
#estcross*
a
a
%
%
'
a %
A
&a
a
%
%
a
A %
%a
a
'
%
+!$ parental
phenotypes
+!$ recom%inant
phenotypes
'
a %
A
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&A
A
a
a c
)
Linked genetic markers
#estcross*
cC
C
A C
a c
A C
a c
a
a c
c
&
A C
a c
A
a c
c
a c
Ca
reater than +!$
of progeny with parental
phenotype
less than +!$
of progeny with recom%inant
(henotype resulting from crossing over.
a
a c
c
#rans, or repulsion
Cis-configuration
or coupling
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&s/ s
)
#estcross*
In female flies
%%/
&
s/0 long wings
%/ 0gray %odies
s 0 short wings
% 0%lack %odies
s/ %/ s %
s/ %/
%
s/ %/
s/ %/
s
%s
%s
%s
%s
s/ %
%s %s
%s
%s
"$
"$
1$
1$
Long wing, gray %odies
Long wing, gray %odies short wing, %lack %odies
Long wing, gray %odies
short wing, %lack %odies
short wing, gray %odies
Long wing, %lack %odies
(arental
com%inations
2ecom%inant
com%inations
)ruit flies
%/s
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&s/ s
)
% %/
&
s/0 long wings
%/ 0gray %odies
s 0 short wings
% 0%lack %odies
s/ %/s%
s/ %
s/ %/
s
%s
%s
%s
%s
%s
1$
1$
Long wing, gray %odies
Long wing, gray %odies short wing, %lack %odies
Long wing, gray %odies
short wing, %lack %odies
(arental
com%inations
2ecom%inant
com%inations
%/
s/ %
s %/
%s
%s
s/ %
"$
"$ short wing, gray %odies
Long wing, %lack %odies
s %/
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A C
a c
a
a c
c
A
A
C
C
All even num%er of exchanges %etween two segregating loci will yield
parental com%inations and thus go undetected.
In general the maximum fre9uency of recom%ination for two genes located
8n the same chromosome is +!$.
Two stranded double crossover
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A B
#wo-stranded dou%le crossover
#hree stranded dou%le crossover
)our-stranded dou%le crossover
:ou%le crossovers occur in the following ways
All
parental
p
p
r
r
p
p
r
r
A '
a %a %A %
All
2ecom
%inant
a '
A %
5
; p
; rec
; p
; rec
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If one looks at all the different possibilities of double crossovers one
arrives
at a similar conclusion, again at most 50 will be recombinant. !see
ne"t slide#.
6ven if crossovers did not occur %y chance %ut all the time, +!$ would still
%e the limit. 7imilarly, if one went through all the possi%ilities of triple
crossovers, one would again arrive at a theoretical maximum of +!$.etc.
8nly if nature had some kind of %ias toward four-stranded dou%le
crossovers, would the ratio come out to more than +!$
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C$%C&'(I$%) If over 50 of the gametes produced b* a + cross contain
parentalcombinations of genetic markers, this is an indication that genes are
linked. 3hen a large num%er of genes is analy5 average
num%er of all cross-overs per interval in a meiotic cell.
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If one assumes proportionality %etween the distance %etween two loci and the
average num%er of crossovers per chromatid then*
%umber of crossovers / !distance#,
3here ? is a proportionality constant. In that case one would also predict that the
map distances would also %e additive.
A CB
&$
recom
%ination
@$ recom%ination
&/@$ recom%ination
3hen distances are large B! - 5! map units the results are less then the
additivity would predict.
In that case dou%le or even num%ered crossovers occur almost as fre9uently
as single or uneven num%ered crossover. 6ven num%ered crossovers are not
phenotypically detected as recom%inant events, as the second event
apparently cancels the first.
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If p is the fre9uency for
one crossover in interval I
and 9 the fre9uency
)or interval two, the
fre9uency for a dou%le
crossover is p9 >" or
; x. ;,
7ince p or 9 are ;
each.
#he a%ility to identify theparental and the two
reciprocal dou%le
crossover
classes also allows one to
determine the order of theD genetic markers.
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Three-factor crosses
.If one uses three markersto map a chromosome it %ecomes possi%le todetect and uantif* double crossovers, and it %ecomes possible to orderthe markers relative to each other. In diploid organisms three factor
crosses are used in analogous fashion to two-factor crosses. #hat is,homo
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In a three-factor cross for three linked genes* how are the gametes formed4
1 2 3
x y a%c +!
A'c>a%c 5a%C>a%c D
A%C>a%c F+
a'c>a%c F!
#otal !!!
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:etermining the order of three linked markers.
#he dou%le crossover results in an interchange of the center marker. #hus,
#he recom%inant class with the lowest fre9uency indicates the identity of
central marker.
enotype Eum%er of progeny
A'C>a%c DF!
a%c>a%c DG+
A%c>a%c "+
a'C>a%c +!
A'c>a%c 5a%C>a%c D
A%C>a%c F+
a'c>a%c F!
(arental configuration all cis
7ingle crossover in interval I
7ingle crossover in interval II
:ou%le crossover* one in interval I
and one in interval II
#otal !!!
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7ince the recom%ination class A'c, a%C occurs with the lowest fre9uency
it must %e marker C>c that is located in the center, since marker C is
recom%inant in that class. #hat is the order of the markers must %e AC'.
#he linkage distances can now %e calculated as follows*
:istance %etween A and C* add fre9uencies of single and dou%le crossover
in
interval AC* A%c, a'C, is "+/+!/ 5/D>!!! 0 !. or !$.
Linkage distance in interval II, i.e. 'C* F+/F!/5/D>!!! 0 !.+ or +$.
#he dou%le crossovers are included in the calculation %ecause one of the 5
crossovers occurred in the interval.
! map units + map units
A,a C,c ',%
I t f
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Interference*
In a three factor testcross the o%served fre9uency of a
dou%le crossover was + out of a thousand or !.!!+. If the two crossovers
in a dou%le crossover had %een completely independent, the expected
fre9uency would have %een !.+ & !.0 !.!+. #he o%servation thatactually fewer dou%le crossovers occur than expected was called chromosome
interference or chiasma interference. #his is o%served in most dou%le crossovers. #his
is not to %e confused with chromatid interference.
#he degree of interference is measured %y the coefficient of coincidence*
Coefficient of coincidence 0 o%served dou%le crossover fre9uency
expected dou%le crossover fre9uency
Coefficient of interference 0 - coefficient of coincidence.
6xample one gives a coefficient of coincidence of !.!!+>!.!+0.DDD
Coeff. of interference 0 H !.DDD 0 !.F
A positive coefficient of interference %etween ! and indicates that the first crossover
interferes with a second.
In %acteria the coefficient of coincidence can %e greater than one negative interference
indicating that the occurrence of one crossover increases thero%a%ilit of a second.
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4ore reasons wh* recombination freuencies are not linearand additive over all
distances* ecombination freuencies differs between male and femaleindividuals,
the reason is not clear. (e"es can have different map distances for the same
chromosomeswith the same primary :EA se9uence. In :rosophila males there is
practically no crossing over occuring.
#he correlation %etween physical distance and genetic map distance can %reak down
within a chromosome as a result of changing chromatin structure, from euchromatin to
hetero chromatin. enetic distances appears much shorter in heterochromatin than in
euchromatin. 2emem%er, the closer the genes are the less recom%ination. Ksually
there is more heterochromatin in the vicinity of the centromere.
)or example in euchromatin the map distance may %e !" map units, the same stretch
of :EA will give rise to a recom%ination fre9uency of D map units in the heterochromatin
state.
=owever, generally in euchromatin the correlation %etween physical distance andgenetic map distance is relatively good.
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6xample II
:. melanogaster, curled> straight wings cu>cu/, e%ony>gray %ody
color e>e/ and scarlet> red eyes st>st/
enotype Eum%er of progeny
cu e st/> cu e st D
cu/e/ st> cu e st DG!
cu e st> cu e st 5"
cu/e/st/> cu e st D!
cu/e st> cu e st G1
cu e/st/> cu e st !+
cu e/st> cu e st 5cu/e st/> cu e st "
parental
7ingle crossover interval I
7ingle crossover interval II
dou%le crossover, per interval
!!!
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#he advantage of working in Neurospora.Neurosporacrassaspends a significant part of its life cycle the in haploidstate. 2ight after meiosis N.crassaundergoes one more mitotic division,su%se9uently spores can germinate and reproduce asexually %y mitotic
division of haploid cells to form mycelia. #hus the phenotype of thespores can %e assessed after meiosis, without any test crosses, since therecessive genes are not masked in the haploid state. )urthermore, in N.crassa the haploid products of meiosis ascospores are kept in linearorder within the tu%e like structure called ascus. #his order reflects theorder in which they were formed during meiosis.
In Neurosporathe products of meiosis can %e phenotypically analy
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If crossing over occurs %efore chromosome
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If crossing over occurs %efore chromosome
replication*
A '
a %
A %
a '
A %
A %
a '
a '
!!$ recom%inant
A '
a %
A '
a %
a '
A %
A '
a %
5+$(arental
5+$ parental
+! $recom%inant
If crossing over occurs after chromosomereplication*
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)irst divisional segregation pattern
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A
a
a
A
a
A
a
tedrad
Meiosis I
A
Meiosis II MitosisA
A
a
a
All A
All a
A
a
A
a
)irst divisional segregation pattern
Alleles are segregated into different nuclei
In first division
second division segregation pattern
Alleles are segregated into different nuclei in 5nddiv.
tedrad
Meiosis IMeiosis II
5A ascospores
5A
5a
5a
As well as opposite
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A
A
A
A
A
A
A
A
a
a
a
a
a
a
a
a
#hese four second-division segregation ascus patterns are e9uivalent.
they all reflect the same event, that is a single crossover relative to the
centromere .
ascospores
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a %
Meiosis I
A '
Meiosis IIMitosisA '
A '
a %
a %
All A'
All a%
A '
A '
a %
a %
A '
A '
a %
a %
(arental ditype ascus pattern, no crossover
a '
A %
A '
a %
Meiosis I
Meiosis II5A'
5a'
5a%
5A%
a %
A '
A '
A %
a '
a %
A '
A %
a '
a %
#etratype ascus pattern* single crossover
ascospores
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If tedrads are ordered in the ascus and recovered> dissected without
distur%ing the order, as in E crassa, %ut not in 7. cerevisiae
it %ecomes possi%le to order the two markers relative to the centromere.
#he recombination freuenc* from a gene to the centeromere is 6 the
freuenc* of asci that e"hibit second7division segeragation patterns
for the alleles of the gene%ecause only half of the chromatids are involved in
the crossover.
#he map distance from centromere to gene A 0
!.+xnum%er of asci with second division segregation pattern&!!
total num%er of asci
some %ooks say !.+ %ecause only half of the single crossovers are productive.
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a '
A %
A %
a '
Eon-parental ditype, four strand dou%le crossover
#his ditype will %e rare in the case of linked genes %ut
will %e as fre9uent as parental ditype for independently
assorting genes.
"A%
"a'
A '
a %
#he pattern for a two stranded dou%le crossover %etween the two loci looks
again like the parental ditype. #he relative fre9uencies of parental ditype ,tetratype and nonparental ditype asci can %e used to calculate the linkage
distance %etween the two loci.
In ordered tetrad data, the centromere can %e used as a marker. #his is done
%y determining whether each ascus is the result of first or second division
segregation.
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#ype of ascus pattern
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7pore pair 5 D "
#ype of ascus pattern
A' A' A' A' A%
5 A' A% a% a' A%
D a% a' A' A% a'
" a% a% a% a% a'
#otal num%er of asci* 5 "G DG 5 !
(: ## ## E(:
):A ):A 7:A 7:A
):' 7:' 7:' ):'
#ype*
:ivision segregation pattern*
(:, parental ditype
##, tetratype, single cross over %etween two of the markers.
7: second division segregation pattern* cross-over %etween centromere and the two
markers,
):* first division segregation pattern, no crossover %etween that marker and the
centromere. E(:, non parental ditype, four-stranded dou%le cross-over.
#ype of ascus pattern
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7pore pair 5 D "
#ype of ascus pattern
A' A' A' A'
5 A' A% a% a'
D a% a' A' A%
" a% a% a% a%
#otal num%er of asci* 5 "G DG 5
I Eot alll patterns are e9ual in their fre9euncy, so genes A and ' are
linked. i.e. on the same chromosome.
II Ascus pattern t*pe oneis most fre9uent and represent the parental ditype, and first division
segregation, no crossover occurred.
III Ascus pattern t*pe fouris least fre9uent* therefore a two stranded dou%le crossover gives rise
to that pattern.
I udging %y there intermediate fre9uency, ascus pattern type 5 and D are
most likely the result of a single crossover.
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Map distance 0 !!x!.+x N of asci w> 5nd
div. segr patterns> total N of asci*
=ence, distance A,' 0 !! x !.+"G/5>5!!05.+ map units
:istance cetromere, A* 0!!x!.+DG/5>5!!0! map units.
7pore pair 5 D "
#ype of ascus pattern
A' A' A' A'
5 A' A% a% a'
D a% a' A' A%
" a% a% a% a%
#otal num%er of asci* 5 "G DG 5
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I #ype 5 displays a second division segregation patter with respect to allele
', and first division segreg. pattern with respect to A alleles, indicating that
a crossover occurred %etween markers A and ', %ut not %etween the markers
and the centromere. #hus the fre9uency represents interval A'.
I #ype D represents a second division segregation for %oth A and
' loci, indicating a single crossover %etween %oth , A and ' loci, and the
centromere, %ut not %etween A and ', since that would have re9uired a
dou%le crossover. #hus the centromere has to %e one the side of either A, or '.
II udging %y the fre9uency, #ype " must result from a two stranded dou%le
Crossover. If the centromere were in the middle, the pattern would
have to %e parental, having a second division segregation %etween the
centromere and A, %ut not %etween the centromere and ', indicates that
the dou%le crossover happened in intervals centromere and A, and A'.#hus the order must %e centromere, A,'
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89
%89
TT
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TT
(9(
TT
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3hen taking all the different crossover patterns into account, including multiplecrossovers then the formula %ecomes
map distance 0.5 !single crossovers#:total ; < " 0.5 !doubles#:total ;
= " 0.5 !triples#:total ; > " 0.5!uadruples#:totaletc.
#he factors !.+, , .+ is a matter of how many times does the crossover type affect
the given interval in a tetrad. 6g. A single exchange affects half of the strands in that
interval , a dou%le exchange affects
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is parental
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