Linkage and Recombination in Genetics: The Sweet Peas Example, Study notes of Law

Download Linkage and Recombination in Genetics: The Sweet Peas Example and more Study notes Law in PDF only on Docsity!

Introduction to Linkage

Law of Independent Assortment

Mendel’s Second Law (Law of Independent Assortment) : The segregation of the genes for one trait is independent of the segregation of genes for another trait, i.e., when genes segregate, they do so independently This law essentially states that during gamete formation, the segregation of one gene is independent of the other gene This ”law” is frequently violated and is only true for loci/genes that are unlinked.

Recombination Fraction

Two loci that are unlinked follow Mendel’s Second Law, and all possible gametes for a parent are produced with equal frequency. When loci are physically located close to one another on a chromosome, there is a deviation from this relationship. This deviation is summarized by the recombination fraction. The recombination fraction is often denoted by θ where 0 ≤ θ ≤ (^12) P(recombinant gamete)= θ If θ < 12 , the loci are said to be linked or in genetic linkage When loci are completely linked, θ = 0 Two loci are said to be unlinked if θ = 12. Note that if two loci are on different chromosome, then θ = 12.

Linkage in a simple genetic cross

In the early 1900’s, Bateson and Punnet conducted genetic studies using sweet peas. They studied two characters: Petal color which has two alleles: P (purple) and p (red), where P is dominant. Pollen grain shape has two alleles: L (elongated) and l (disc-shaped), where L is dominant PPLL × ppll ↓ PpLl F Plants in the F1 generation were intercrossed: PpLl X PpLl. According to Mendel’s Second Law, during gamete formation, the segregation of one gene pair is independent of another gene pair. If this genetic model is correct, what segregation ratios of the phenotypes in the F2 generation would we expect?

Sweet Peas Linkage Example

The expected relative frequencies in the F2 generation if the genes segregated independently are Elongated Disc-Shaped Purple 9 3 Red 3 1 The observed frequencies in 381 plants in the F2 generation where Elongated Disc-Shaped Purple 284 21 Red 21 55 The observed data clearly do not fit what is expected under the model. The explanation: the petal color gene and the gene for pollen grain shape are linked. Let θ be the recombination fraction between the two genes. What is the probability of each possible plant type?

Sweet Peas Linkage Example

1 2 (1^ −^ θ)^ 1 2 θ^ 1 2 θ^ 1 2 (1^ −^ θ) PL Pl pL pl 1 2 (1 1 −^ θ)^ PL^ Purple/Long^ Purple/Long^ Purple/Long^ Purple/Long 21 θ^ Pl^ Purple/Long^ Purple/Disc^ Purple/Long^ Purple/Disc 1 2 θ^ pL^ Purple/Long^ Purple/Long^ Red/Long^ Red/Long 2 (1^ −^ θ)^ pl^ Purple/Long^ Purple/Disc^ Red/Long^ Red/Disc

P(red, disc-shaped)= pR/D = 14 (1 − θ)^2 P(red,elongated)= ( pR/L = 1 2 θ

2 θ

2 θ

2 (1^ −^ θ)

2 (1^ −^ θ)

2 (θ)

= 14 θ(2 − θ) P(purple, disc-shaped)= pP/D = 14 θ(2 − θ) P(purple, elongated)= pP/L = 12 + 14 (1 − θ)^2 We can form a likelihood for the data that is a function of the recombination fraction θ. We can find the value of θ that maximizes this likelihood.

Sweet Peas Linkage Example Likelihood:

Multinomial Distribution

Obtain the log-likelihood function to

l

nP/L, nP/D , nR/L, nR/D

∣∣pP/L, pP/D , pR/L, pR/D

= C +nP/Lln(pP/L)+nP/D ln(pP/D )+nR/Lln(pR/L)+nR/D ln(pR/D ) where C = ln

[(

N

nP/L, nP/D , nR/L, nR/D

)]

Remember that pP/L, pP/D , pR/L, pR/D are all functions of θ. Can obtain the maximum likelihood estimate of θ by taking the derivatives of the log-likelihood function with respect to θ and solving for 0.