Ch 5b: Genetic Linkage and Mapping in Eukaryotes: Three-Point Crosses

Genetic Linkage and Mapping in Eukaryotes

Three-Point Crosses

Three-point crosses are a fundamental genetic technique used to determine the order and relative distances between three linked genes on a chromosome. This method is essential for constructing genetic linkage maps in eukaryotes.

Key Concepts

• Genetic linkage: The tendency of genes located close together on a chromosome to be inherited together.

• Recombination: The process by which linked genes can be separated during meiosis due to crossing over between homologous chromosomes.

• Three-point cross: A cross involving three genes to analyze recombination frequencies and gene order.

Three-Point Cross: Parental and Recombinant Types

In a three-point cross, two individuals heterozygous for three genes (e.g., a b c / a b c) are crossed. The resulting progeny can be classified as parental (non-recombinant) or recombinant based on their genotype.

• Parental (non-recombinant) genotypes: Progeny with the same combination of alleles as the parents.

• Single crossover: Recombination event between two of the three genes (either between a and b, or b and c).

• Double crossover: Two recombination events, one between a and b and another between b and c. Double crossovers are less common than single crossovers.

Example: Three-Point Cross in Maize

Consider a cross between two maize lines:

• Parent 1: V Gl Va / V Gl Va (Green, rough, normal)

• Parent 2: v gl va / v gl va (yellow, glossy, variable)

The F1 progeny are test-crossed to the triple recessive parent, and the phenotypes/genotypes of the offspring are scored.

Classification of Progeny

Phenotype	Genotype	Type
Green, rough, normal	V Gl Va / v gl va	Parental
Yellow, glossy, variable	v gl va / v gl va	Parental
Green, glossy, normal	V gl Va / v gl va	Single crossover (between Gl and Va)
Yellow, rough, variable	v Gl va / v gl va	Single crossover (between V and Gl)
Green, rough, variable	V Gl va / v gl va	Single crossover (between Va and Gl)
Yellow, glossy, normal	v gl Va / v gl va	Single crossover (between V and Gl)
Green, glossy, variable	V gl va / v gl va	Double crossover
Yellow, rough, normal	v Gl Va / v gl va	Double crossover

Observed and Expected Progeny Numbers

Phenotype	Number Observed	Number Expected	Genotype
Green, rough, normal	60	90.75	V Gl Va / v gl va
Yellow, glossy, variable	48	90.75	v gl va / v gl va
Green, glossy, normal	4	90.75	V gl Va / v gl va
Yellow, rough, variable	270	90.75	v Gl va / v gl va
Green, rough, variable	235	90.75	V Gl va / v gl va
Yellow, glossy, normal	7	90.75	v gl Va / v gl va
Green, glossy, variable	40	90.75	V gl va / v gl va
Yellow, rough, normal	62	90.75	v Gl Va / v gl va

Chi-square test: $\chi^2 = 811.6;\ p < 10^{-16}$

Gene Order and Recombination Frequency

• Gene order can be determined by comparing the frequency of double and single crossover classes. The rarest classes are double recombinants.

• Recombination frequency (RF) is calculated as the number of recombinant progeny divided by the total number of progeny.

Formula:

$\text{Recombination\ frequency} = \frac{\text{Number\ of\ recombinant\ progeny}}{\text{Total\ number\ of\ progeny}}$

Recombination frequencies can be used to estimate the genetic distance between genes (in centiMorgans, cM).

Crossover Interference

Crossover interference refers to the phenomenon where the occurrence of one crossover event reduces the probability of another crossover occurring nearby.

• Coefficient of coincidence (c): The ratio of observed double crossovers to expected double crossovers.

• Interference (I): The degree to which one crossover interferes with another, calculated as $I = 1 - c$.

Formulas:

$\text{Coefficient of coincidence} = \frac{\text{Observed double crossovers}}{\text{Expected double crossovers}}$

$\text{Interference} = 1 - \text{coefficient of coincidence}$

Summary Table: Types of Crossovers

Type	Description	Frequency
Parental (non-recombinant)	No crossover between the three genes	Most frequent
Single crossover	Crossover between one pair of genes	Intermediate frequency
Double crossover	Crossover between both pairs of genes	Least frequent

Applications and Importance

• Three-point crosses are used to determine gene order and map distances on chromosomes.

• They help in understanding genetic linkage and recombination mechanisms in eukaryotes.

• Linkage maps are essential tools in plant and animal breeding, as well as in genetic research.

Additional info:

• Double crossovers are rare because the probability of two independent crossover events occurring between three genes is low.

• Chi-square analysis is used to test the hypothesis of independent assortment versus linkage.