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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* ecombi

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