genetic linkage and chromosome mapping. · chapter 5: genetic linkage and chromosome mapping....

Chapter 5:

Genetic linkage and chromosomechromosomemapping.mapping.

OverviewIntroductionLinkage and recombination of genes in a g gchromosomePrinciples of genetic mappingBuilding linkage mapsChromosome and chromatid interferenceGenetic mapping in human and animal pedigreesMapping by tetrad analysisSpecial features of recombination


IntroductionGenes located on the same chromosome might be expected to be in COMPLETE might be expected to be in COMPLETE linkage.As a result of crossing-over however As a result of crossing over, however, recombinant progeny with genotypes not observed in the parents are not observed in the parents are observed.

IntroductionThe probability of recombination increases with genetic distance. Thus increases with genetic distance. Thus recombination rate can be used as a unit of distance between loci and used unit of distance between loci and used to build maps.Linkage analysis is very important in Linkage analysis is very important in genetics. It is often the first step towards isolating genes underlying towards isolating genes underlying defined phenotypes including inherited diseasesdiseases.


Linkage and recombination of ggenes in a chromosome

Mendel’s second law: parental versus recombinant gametesSyntenic loci may be linked, i.e. F1’s produce more parental than recombinant gametesThe recombination rate is the same whether the mutant alleles are in cis or trans in the F1 parentparentThe chi-squared test for linkageE h i f li k d h h t i ti Each pair of linked genes has a characteristic frequency of recombinationRecombination in females versus malesRecombination in females versus males

Mendel’s second law: parental pversus recombinant gametes

Mendel’s second law: parental pversus recombinant gametes



Syntenic loci may be linked Syntenic loci may be linked

66.5% parentals

33.5% recombinants



Coupling versus repulsion of of p g psyntenic alleles

Repulsion Coupling

Coupling versus repulsion of of p g psyntenic alleles

62.3% parentals6 3% pa e ta s

37.7% recombinants



The chi-squared test for linkageLinkage and recombination of ggenes in a chromosome


Each pair of linked genes has a p gcharacteristic frequency of rec.

98 6% parentals98.6% parentals

1.4% recombinants



Recombination in females versus males

DrosophilaOther organisms (including Other organisms (including mammals)


Genetic mapping

Hypothesis (Sturtevant & Morgan)Test 1: recombination between genes Test 1: recombination between genes results from a physical exchange bet een ch omosomes (Ste n 1936)between chromosomes (Stern, 1936)Test 2: Crossing-over takes place at the 4-strand stage of meiosisFrequency of recombination versus Frequency of recombination versus map distance: Haldane’s mapping functionfunction

Hypothesis (Sturtevant & yp (Morgan)

Recombination is due to an exchange of segments between homologous segments between homologous chromosomes in the process called crossing-over , manifested physically as crossing over , manifested physically as a chiasmaThe likelihood of a crossing-over The likelihood of a crossing over between two loci depends on their distance on the chromosome thus distance on the chromosome, thus explaining variable recombination rates => should allow “mapping”=> should allow mapping

Hypothesis (Sturtevant & yp (Morgan) Genetic mapping


Recombination results from a physical Recombination results from a physical exchange between homologues Genetic mapping


Crossing-over takes place at 4-g pstrand stage of meiosis

Crossing-over takes place at 4-g pstrand stage of meiosis

Genetic mapping


Frequency of recombination q y(FR) versus map distance (MD)

FR (%): proportion of recombinant gametes (two proportion of recombinant gametes (two loci) Non-additive (see hereafter)Non-additive (see hereafter)

MD (centiMorgan = cM):½ average number of crossing-overs (m) / meiotic cell (between two loci)additive

Difference: multiple cross-overs p

Frequency of recombination q yversus map distance

Frequency of recombination q yversus map distance

Nota bene Haldane’s mapping function

Haldane’s mapping function0 crossing-over:

P0=e-m

R 0%Rec = 0%1 crossing-over:

P1= m1e-m/1!/Rec = 50%

2 crossing-over:P2

...!2

2!1

1021

+++=−−

−mm

m emxemxxemP2 = Rec = ?%

3 crossing-over:g……

1 crossing-overg=> 50% recombinant gametes


P0=e-m


P1= m1e-m/1!/Rec = 50%

2 crossing-over:P2 2 m/2!

...!2

2!1

1021

+++=−−

−mm

m emxemxxemP2 = m2e-m/2!Rec = ?%

3 crossing-over:g……

2 crossing-overg=> 50% rec. gam. !!


P0=e-m


P1= m1e-m/1!/Rec = 50%

2 crossing-over:P2 2 m/2!

...!2

2!1

1021

+++=−−

−mm

m emxemxxemP2 = m2e-m/2!Rec = 50%

3 crossing-over:g…Rec = 50%

Haldane’s mapping function

( ) ( )MDmFR 211 11 −−( ) ( )MDm eeFR 221

21 11 −=−=


=Haldane’s MF


Non-syntenic loci are characterized by a RF of 50%a RF of 50%Syntenic loci are characterized by a RF ≤ 50%RF ≤ 50%


Building linkage mapsg g pMultiple two-point crosses

Building linkage mapsg g pThree-point crosses

Parental (most frequent) genotypes


Double recombinant (DR) (rarest) genotypes


Identification of parental genotypes + double-recombinants unambiguously double recombinants unambiguously determines locus order => Lz-Su-Gl


Lz_Su_GlLzxSu GlLzxSu_GlLz_SuxGlLzxSuxGlLzxSuxGlLzxSuxGlLz SuxGlLz_SuxGlLzxSu_GlLz Su GlLz_Su_Gl


RFLzxSu = FLzxSu_Gl + FLzxSuxGl

RF = F + FRFSuxGl = FLz_SuxGl + FLzxSuxGl

RFLzxGl = FLz_SuxGl + FLzxSu_Gl

RFLzxGl < RFLzxSu + RFSuxGl

Building linkage mapsg g pExamples

m

Chr

ng a

rm

r. 10

–lo

n

–sho

r. 10

ort ar

Ch

rm

Building linkage mapsg g pGenetic vs physical map distance

Building linkage mapsg g pGenetic vs physical map distance


Chromosome interference

Lz_Su_GlLzxSu GlLzxSu_GlLz_SuxGlLzxSuxGlLzxSuxGlLzxSuxGlLz SuxGlLz_SuxGlLzxSu_GlLz Su GlLz_Su_Gl

Chromosome interference

I(nterference) = 1 – coefficient of coincidencecoincidenceCoefficient of coincidence = Observed DR / E pected DRDR / Expected DRObserved DR = FLzxSuxGlu

Expected DR = RFLzxSu x RFSuxGl

Chromosome interferencePositive interference

first crossing-over reduces probability to have a second one in the vicinity=> fewer observed than expected DRThe rule in many genomes (at low resolution) => The rule in many genomes (at low resolution) => Kosambi’s mapping function

Negative interferencegFirst crossing-over increases probability to have second one in the vicinity

> b d th t d DR=> more observed than expected DRObserved as a result of gene conversion at very high resolution

Kosambi’s mapping function Chromosome interferencePositive interference

first crossing-over reduces probability to have a second one in the vicinity=> fewer observed than expected DRThe rule in many genomes (at low resolution) => The rule in many genomes (at low resolution) => Kosambi’s mapping function

Negative interferencegFirst crossing-over increases probability to have second one in the vicinity

> b d th t d DR=> more observed than expected DRObserved as a result of gene conversion at very high resolution

Chromatid interference

Positive:First crossing-over involving specific non-First crossing-over involving specific non-sister chromatids decreases probability for their involvement in second onefor their involvement in second oneWould increase 4-strand DCWould push FR > 50%Would push FR > 50%Never observed


The lod scoreDefinition

Compute likelihood of the observations under H1 i e FR ≤ 50% observations under H1, i.e. FR ≤ 50%. (Find value of FR that maximizes likelihood of the data) => L1likelihood of the data) => L1Compute likelihood of the b ti d H0 i FR 50% observations under H0, i.e. FR = 50%

=> L0Lod score = log10 L1/L0

Mapping in human and animal pp gpedigrees

Maximum likelihood and lod scores

The lod scoreProperties

Can be added across pedigrees ( log of product of prob = sum of logs)Sequential test:

> 3: reject H0< -2: accept H0-2 < z < 3: collect more data

Baysian justification of very stringent threshold Baysian justification of very stringent threshold of 3 (prior probability of linkage is low ∼ 1/50)Allows for unknown phase incomplete Allows for unknown phase, incomplete penetrance, …

Mapping in human and animal pp gpedigrees

Maximum likelihood and lod scores

The lod scoreProperties

Can be added across pedigrees ( log of product of prob = sum of logs)Sequential test:

> 3: reject H0< -2: accept H0-2 < z < 3: collect more data

Baysian justification of very stringent threshold Baysian justification of very stringent threshold of 3 (prior probability of linkage is low ∼ 1/50)Allows for unknown phase incomplete Allows for unknown phase, incomplete penetrance, …


Mapping by tetrad analysispp g y yUnordered tetrads


Non-syntenic lociPD = NPDPD NPD


Syntenic lociloci

PD >> NPD


( ) [ ] [ ]( ) [ ] 1004221 NPDNPDTTMD +−( ) [ ] [ ]( ) [ ] 100__

xtetradsNTotal

MD°

=

Gene centromere mapping inpp gordered tetrads


First vs second-division division segregation


FRC_G = ½ (% 2nd div. segr.) (% 2nd div segr ) ≤ 66 7% (2/3)(% 2nd div. segr.) ≤ 66,7% (2/3)

Gene centromere mapping in pp gmammals: teratocarcinoma


Special featurespRecombination within genes

Special featurespMitotic recombination

Somatic mosaics (cancer !)

genetic linkage and chromosome mapping. · chapter 5: genetic linkage and chromosome mapping....

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