8-Linkage and Gene Mapping Notes

Early Observations of Genetic Linkage in Sweet Peas

William Bateson and Reginald C. Punnett performed dihybrid cross experiments using sweet peas (Lathyrus odoratus) to evaluate Mendel's Law of Independent Assortment.

• Traits and Alleles:

  • Flower Color: Dominant allele $P$ (purple), recessive allele $p$ (red).

  • Pollen Shape: Dominant allele $L$ (long), recessive allele $l$ (round).

• Cross Setup:

  • Parental Generation ($P$): True-breeding purple, long crossed with true-breeding red, round ($PPLL \times ppll$).

  • First Filial Generation ($F_1$): Heterozygous purple, long ($PpLl$).

  • Second Filial Generation ($F_2$): Expected Mendelian dihybrid phenotypic ratio of $9:3:3:1$ if independent assortment holds.

• Observed vs. Expected Results in $F_2$ Progeny:

  • Purple, Long: Observed = $296$, Expected = $240.2$, $\frac{(O - E)^2}{E} = 13.1$

  • Purple, Round: Observed = $19$, Expected = $80.1$, $\frac{(O - E)^2}{E} = 46.5$

  • Red, Long: Observed = $27$, Expected = $80.1$, $\frac{(O - E)^2}{E} = 35.1$

  • Red, Round: Observed = $85$, Expected = $26.7$, $\frac{(O - E)^2}{E} = 127.3$

  • Total Counts: Observed Total = $427$, Expected Total = $427.1$

  • Chi-Square Statistic: $\chi^2 = 222.0$

• Key Allelic Configurations:

  • Coupling (Cis Configuration): Dominant alleles for both traits originate on the same parental chromosome ($PL$ and $pl$).

  • Repulsion (Trans Configuration): Dominant allele for one trait is linked with the recessive allele for the other trait on the same parental chromosome ($Pl$ and $pL$).

Morgan's Dihybrid Testcrosses in Drosophila melanogaster

Thomas Hunt Morgan analyzed diploid mapping in the fruit fly Drosophila melanogaster, establishing that linked genes do not assort independently because they reside on the same chromosome.

• Traits and Alleles in Drosophila:

  • Eye Color: Wild-type red ($pr^+$), mutant purple ($pr$).

  • Wing Phenotype: Wild-type normal ($vg^+$), mutant vestigial ($vg$).

• Morgan's First Testcross (Coupling / Cis Configuration):

  • Parental Cross ($P$): $pr^+ pr^+ vg^+ vg^+ \times pr pr vg vg$

  • $F_1$ Generation: Heterozygous females ($pr^+ pr vg^+ vg$).

  • Testcross: $F_1$ females ($pr^+ pr vg^+ vg$) crossed with homozygous recessive tester males ($pr pr vg vg$).

  • Tester Male Gametes: Always $pr\,vg$

  • Female Gametes and Phenotypic Progeny Breakdown ($N = 2839$):

  • Wild-type ($pr^+ vg^+$ gamete / $pr^+ pr vg^+ vg$ phenotype): Observed = $1339$, Expected = $709.75$, $\frac{(O - E)^2}{E} = 558$

  • Normal eye, Vestigial wing ($pr^+ vg$ gamete / $pr^+ pr vg vg$ phenotype): Observed = $151$, Expected = $709.75$, $\frac{(O - E)^2}{E} = 440$

  • Purple eye, Normal wing ($pr vg^+$ gamete / $pr pr vg^+ vg$ phenotype): Observed = $154$, Expected = $709.75$, $\frac{(O - E)^2}{E} = 435$

  • Purple eye, Vestigial wing ($pr vg$ gamete / $pr pr vg vg$ phenotype): Observed = $1195$, Expected = $709.75$, $\frac{(O - E)^2}{E} = 332$

  • Total Counts: Observed Total = $2839$, Expected Total = $2839.00$

  • Chi-Square Statistic: $\chi^2 = 1765$

• Morgan's Second Testcross (Repulsion / Trans Configuration):

  • Parental Cross ($P$): $pr^+ pr^+ vg vg \times pr pr vg^+ vg^+$

  • $F_1$ Generation: Heterozygous females ($pr^+ pr vg^+ vg$).

  • Testcross: $F_1$ females ($pr^+ pr vg^+ vg$) crossed with homozygous recessive tester males ($pr pr vg vg$).

  • Progeny Phenotypic Breakdown ($N = 2335$):

  • Wild-type ($pr^+ vg^+$ gamete): Observed = $157$, Expected = $583.75$, $\frac{(O - E)^2}{E} = 312$

  • Normal eye, Vestigial wing ($pr^+ vg$ gamete): Observed = $965$, Expected = $583.75$, $\frac{(O - E)^2}{E} = 249$

  • Purple eye, Normal wing ($pr vg^+$ gamete): Observed = $1067$, Expected = $583.75$, $\frac{(O - E)^2}{E} = 400$

  • Purple eye, Vestigial wing ($pr vg$ gamete): Observed = $146$, Expected = $583.75$, $\frac{(O - E)^2}{E} = 328$

  • Total Counts: Observed Total = $2335$, Expected Total = $2335.00$

  • Chi-Square Statistic: $\chi^2 = 1289$

Principles of Genetic Linkage and Recombination

• Characteristics of Two-Point Crosses:

  • Involves crossing a dihybrid heterozygote with a homozygous recessive tester organism.

  • Unlinked genes assorting independently produce an expected phenotypic ratio of $1:1:1:1$

  • Linked genes fail to display a $1:1:1:1$ ratio. There is no single fixed ratio for linked genes; proportions vary based on physical distance between loci.

  • Linked dihybrid testcrosses display two nearly equally frequent majority classes (parental / nonrecombinant types) and two nearly equally frequent minority classes (recombinant types).

• Physical Basis of Recombination:

  • Linked genes reside on the same physical chromosome.

  • Recombinant genotypes arise through physical crossing over—the breaking and rejoining of homologous nonsister chromatids during meiosis.

  • Meiotic crossover events swap genetic material between homologues, generating recombinant gametic combinations ($bn\,det$ and $bn^+\,det^+$) alongside nonrecombinant parental combinations ($bn\,det^+$ and $bn^+\,det$).

• Gene Mapping Concepts:

  • Recombination Frequency Equation:     $\text{Recombination Frequency} = \left( \frac{\text{Number of Recombinants}}{\text{Total Progeny}} \right) \times 100$

  • Map Unit / Centimorgan ($cM$): Defined as the physical distance along a chromosome that yields a $1\%$ recombination rate.

  • Proximity Rule: Recombination frequency measures the closeness of two loci; smaller frequencies reflect closer proximity on the chromosome.

Gene Mapping Examples and Calculations

• Example 1: Mapping Banded ($bn$) and Detached ($det$) Genes in Drosophila:

  • Traits: Abdomen shape (wild-type vs. Banded $bn$) and wing vein morphology (wild-type vs. Detached $det$).

  • Parental Cross ($P_1$): Banded ($bn\,bn\,det^+\,det^+$) crossed with Detached ($bn^+\,bn^+\,det\,det$).

  • Testcross: $F_1$ females ($bn\,det^+ / bn^+\,det$) crossed with tester males ($bn\,bn\,det\,det$).

  • Progeny Phenotypes and Counts ($N = 1000$):

  • Banded ($bn\,det^+$ gamete): $483$ (Nonrecombinant / Parental)

  • Detached ($bn^+\,det$ gamete): $512$ (Nonrecombinant / Parental)

  • Banded, Detached ($bn\,det$ gamete): $2$ (Recombinant)

  • Wild-type ($bn^+\,det^+$ gamete): $3$ (Recombinant)

  • Classification Totals:

  • Nonrecombinants = $483 + 512 = 995$ ($99.5\%$

  • Recombinants = $2 + 3 = 5$ ($0.5\%$

  • Map Distance Calculation:     $\text{Distance} = \left( \frac{5}{1000} \right) \times 100 = 0.5\% = 0.5\,cM$

• Example 2: Generic Two-Point Linkage Mapping:

  • Parental Cross ($P_1$): $AABB \times aabb$

  • Testcross Setup: $F_1$ dihybrid ($AaBb$) crossed with tester ($aabb$).

  • $F_2$ Progeny Phenotypic Distribution:

  • $AaBb$: $250$ (Parental / Nonrecombinant)

  • $aabb$: $262$ (Parental / Nonrecombinant)

  • $Aabb$: $94$ (Recombinant)

  • $aaBb$: $86$ (Recombinant)

  • Total Progeny ($N$): $250 + 262 + 94 + 86 = 692$

  • Total Recombinants: $94 + 86 = 180$

  • Recombination Frequency Calculation:     $\text{Recombination Frequency} = \left( \frac{180}{692} \right) \times 100 \approx 26.01\% = 26.01\,cM$