Question

Three loci, mitochondrial malate dehydrogenase that forms \(a\) and \(b(M D H a, M D H b),\) glucouronidase that forms 1 and \(2(G U S 1\) \(G U S 2\) ), and a histone gene that forms \(+\) and \(-(H+, H-),\) are located on chromosome \(\\# 7\) in humans. Assume that the \(M D H\) locus is at position \(35, G U S\) at position \(45,\) and \(H\) at position 75 A female whose mother was homozygous for \(M D H a, G U S 2,\) and \(H+\) and whose father was homozygous for \(M D H b, G U S 1,\) and \(H-\) produces a sample of 1000 egg cells. Give the genotypes and expected numbers of the various types of cells she would produce. Assume no chromosomal interference.

Short answer

Answer: 630

Step-by-step solution

Determine the parental genotypes

The mother is homozygous for MDHa, GUS2, and H+, and the father is homozygous for MDHb, GUS1, and H-. Thus, the mother's genotype is (MDHa MDHa, GUS2 GUS2, H+ H+) and the father's genotype is (MDHb MDHb, GUS1 GUS1, H- H-).

Calculate recombination frequencies

The recombination frequency is calculated according to the map distance: recombination frequency = map distance / 100. Given the map distances of the loci, we have: - MDH - GUS: (45 - 35) / 100 = 0.1 - GUS - H: (75 - 45) / 100 = 0.3 - MDH - H: (75 - 35) / 100 = 0.4

Determine possible gametes

The female can produce four possible gametes based on the recombination frequencies: 1. MDHa GUS2 H+ (no crossover) 2. MDHa GUS2 H- (crossover between GUS and H) 3. MDHa GUS1 H+ (crossover between MDH and GUS) 4. MDHa GUS1 H- (double crossover)

Calculate the probabilities of each gamete

Using the recombination frequencies calculated in Step 2, we can now determine the probabilities of each gamete being produced: 1. Probability(MDHa GUS2 H+) = (1 - 0.1)(1 - 0.3) = 0.63 2. Probability(MDHa GUS2 H-) = (1 - 0.1)(0.3) = 0.27 3. Probability(MDHa GUS1 H+) = (0.1)(1 - 0.3) = 0.07 4. Probability(MDHa GUS1 H-) = (0.1)(0.3) = 0.03

Calculate the expected number of each type of egg cell

The female produces a total of 1000 egg cells, so we can now calculate the expected number of each type of egg cell based on the probabilities in Step 4: 1. Expected number of MDHa GUS2 H+ cells = 0.63 * 1000 = 630 2. Expected number of MDHa GUS2 H- cells = 0.27 * 1000 = 270 3. Expected number of MDHa GUS1 H+ cells = 0.07 * 1000 = 70 4. Expected number of MDHa GUS1 H- cells = 0.03 * 1000 = 30

Final answer:

The female is expected to produce the following types and numbers of egg cells: 1. 630 MDHa GUS2 H+ cells 2. 270 MDHa GUS2 H- cells 3. 70 MDHa GUS1 H+ cells 4. 30 MDHa GUS1 H- cells

Key concepts

Chromosome Mapping

Chromosome mapping is a powerful tool used in genetics to determine the position of genes on a chromosome. It helps to unravel the intricate puzzle of genetic inheritance. Imagine a chromosome as a long road map with different genes as distinct destinations along the route. In our exercise scenario, we are focusing on three specific loci: MDH, GUS, and H, located on chromosome #7 in humans. Each of these loci corresponds to a specific genetic trait or marker.
The positions of these loci were given in standard map units, which reflect their relative distances: MDH at position 35, GUS at position 45, and H at position 75.
These positions allow us to calculate the distances between them, which are crucial for determining the likelihood of recombination during gamete formation. Thus, chromosome mapping not only lays out a blueprint of gene locations but also acts as a predictive tool for genetic variation in offspring.

Gamete Formation

Gamete formation is a fundamental process in sexual reproduction that leads to the creation of egg and sperm cells. In the genetic context, it is the phase where genetic recombination occurs, introducing genetic diversity. During gamete formation, chromosomes undergo a special type of cell division called meiosis. This process ensures that each gamete inherits one copy of each chromosome from the parent.
In our example, a female produces egg cells, each with a different combination of genetic traits from her parents. The mother, being homozygous for MDH, GUS, and H, provides one set of alleles, while the father provides another. Recombination during meiosis results in four possible types of gametes with different gene combinations.

• MDHa GUS2 H+
• MDHa GUS2 H-
• MDHa GUS1 H+
• MDHa GUS1 H-

Though recombination introduces variety, the process is not entirely random, and certain combinations appear more frequently depending on the recombination frequency, making some gametes more common than others.

Recombination Frequency

Recombination frequency is the measure of genetic variation resulting from recombination during gamete formation. It is expressed as a percentage and directly related to the distance between genes on a chromosome. Greater distances between loci generally translate to higher recombination frequencies, as there is more "room" for crossovers to occur.
In the exercise, we calculated the recombination frequencies for each pair of loci, as follows:

• MDH - GUS: 10%
• GUS - H: 30%
• MDH - H: 40%

These calculations were based on their map distances. Such recombination frequencies predict the likelihood of specific combinations of alleles being present together in gametes. For instance, a low frequency suggests that genes are closely linked and are less likely to be separated during the crossover events of meiosis, while a high frequency implies a greater chance of genes being shuffled.
This makes recombination frequency an essential concept for understanding hereditary patterns and predicting genetic outcomes in offspring.