Question

Two theoretical genetic strains of a virus \(\left(a^{-} b^{-} c^{-} \text {and } a^{+} b^{+} c^{+}\right)\) were used to simultaneously infect a culture of host bacteria. Of 10,000 plaques scored, the following genotypes were observed. Determine the genetic map of these three genes on the viral chromosome. Decide whether interference was positive or negative.

Short answer

Answer: The genetic map for the three genes is ordered as a - 13.1 cM - c - 0.6 cM - b. The interference is negative, as the observed number of double recombinants is greater than the expected number, indicating that one recombination event increases the probability of a second recombination event happening nearby.

Step-by-step solution

Organize the given data

First, we need to tabulate the given data and express it in terms of recombination frequencies. Let's represent the wild type as (+) and the mutant type as (-). Here are the observed genotypes and their occurrences out of 10,000 plaques scored: - a+b+c+: 3,140 - a-b-c-: 3,080 - a+b-c-: 1,740 - a-b+c+: 1,660 - a-b-c+: 675 - a+b-c+: 635 - a+b+c-: 25 - a-b+c-: 35

Determine the recombination frequencies

Now, we will calculate the recombination frequency for each possible pair of genes. The recombination frequency is the proportion of recombinant offspring as a result of recombination events between the two genes. - Recombination frequency between a and b: Since a+b-c- and a-b+c- genotypes are recombinants for a and b, we calculate the ratio in the following way: \(\frac{1,740 + 1,660}{10,000} = 0.340\) - Recombination frequency between a and c: Similarly, using the genotypes a-b-c+ and a+b-c+, we calculate: \(\frac{675 + 635}{10,000} = 0.131\) - Recombination frequency between b and c: Using the genotypes a+b+c- and a-b+c-, we calculate: \(\frac{25 + 35}{10,000} = 0.006\)

Create the genetic map

To create the genetic map, we multiply each recombination frequency by 100 to convert it to a map distance in centiMorgans (cM). - Map distance between a and b: \(0.340 \times 100 = 34 \text{ cM}\) - Map distance between a and c: \(0.131 \times 100 = 13.1 \text{ cM}\) - Map distance between b and c: \(0.006 \times 100 = 0.6 \text{ cM}\) Since the distance between a and c is smaller than the distance between a and b, we can order the genes as follows: a - c - b. So, the genetic map is: a - 13.1 cM - c - 0.6 cM - b

Determine interference

To determine if interference is positive or negative, we need to look at the actual number of double recombinants observed versus the expected number of double recombinants, assuming no interference. The expected number of double recombinants is calculated by multiplying the total number of progeny (10,000) by the product of the recombination frequencies between genes a and c, and genes b and c. Expected double recombinants \( = 10,000 \times 0.131 \times 0.006 = 7.86 \approx 8\) The actual observed number of double recombinants is 25+35=60. Since the observed number of double recombinants (60) is greater than the expected number (8), the interference is negative. This means that the occurrence of one recombination event increases the probability of a second recombination event happening nearby.

Key concepts

Recombination Frequency

Recombination frequency is a crucial concept in genetic mapping. It helps scientists understand how often recombination occurs between two genes during the formation of gametes. Recombination results in the exchange of genetic material between chromosomes, leading to genetic diversity. When measuring recombination frequency, you are essentially identifying how often two genes are separated due to crossovers during meiosis or viral infection cycles in the case of viruses. Understanding Recombination Frequency
Recombination frequency is expressed as a percentage or a decimal and is calculated using the formula:

• Recombination Frequency = (Number of Recombinant Offspring)/(Total Number of Offspring) × 100%

For example, in the viral experiment provided, one might calculate the recombination frequency between two genes by dividing the number of recombinant viruses by the total number of plaques observed. A higher frequency of recombination suggests that the genes are located farther apart on the chromosome, which means there's more opportunity for a crossover to occur, whereas a lower frequency suggests they are closer together.

Chromosome Mapping

Chromosome mapping, or genetic mapping, is a method used to determine the position of genes on a chromosome. This is done by using recombination frequencies as indicators of the distance between genes. In the exercise, recombination frequencies are translated directly into map distances. This visual representation of gene order is crucial for understanding genetic linkage and for exploring the genetic architecture of organisms. Creating a Genetic Map
To create a genetic map, follow these steps:

• Calculate recombination frequencies between each pair of genes.
• Convert these frequencies into map distances by multiplying them by 100 to express them as centiMorgans (cM).
• Use these distances to arrange the genes, typically in a linear fashion, reflecting their order on the chromosome.

In the provided problem, the genes a, b, and c were mapped in the order of a - 13.1 cM - c - 0.6 cM - b. This arrangement is based on the calculated recombination frequencies between each pair of genes, showing the relative positions on the viral chromosome.

Interference in Genetics

Interference in genetics refers to the phenomenon where the occurrence of one crossover event affects the occurrence of another crossover in its vicinity. Interference can either be positive or negative:

• Positive interference implies a decrease in the likelihood of another crossover happening nearby, reducing double recombinants.
• Negative interference suggests an increase in the chance of additional crossovers, leading to more double recombinants than expected.

In our viral genetic mapping exercise, the interference was determined by examining the difference between observed and expected double recombinant frequencies. Analyzing Interference
Calculate expected double recombinants by multiplying individual recombination frequencies:

• Expected Double Recombinants = Total Progeny × (Recombination Frequency of First Pair) × (Recombination Frequency of Second Pair)

Then, compare this with the observed number of double recombinants. The problem revealed negative interference since the observed double recombinant number was greater than the expected, indicating increased likelihood of nearby crossover events.