In a cotransformation experiment (see question 4 of More GeneticTIPS), DNA was isolated from a donor strain that was proA+ andstrC+ and sensitive to tetracycline. (The proA and strC genes conferthe ability to synthesize proline and confer streptomycin resistance,respectively.) A recipient strain is proA− and strC− and isresistant to tetracycline. After transformation, the bacteria werefirst streaked on a medium containing proline, streptomycin, andtetracycline. Colonies were then restreaked on a medium containingstreptomycin and tetracycline. (Note: Each type of medium hadcarbon and nitrogen sources for growth.) The following resultswere obtained:70 colonies grew on the medium containing proline, streptomycin,and tetracycline, but only 2 of these 70 colonies grew whenrestreaked on the medium containing streptomycin and tetracyclinebut lacking proline. If we assume the average size of the DNA fragments is 2 minutes,how far apart are these two genes?
In a cotransformation experiment (see question 4 of More Genetic
TIPS), DNA was isolated from a donor strain that was proA+ and
strC+ and sensitive to tetracycline. (The proA and strC genes confer
the ability to synthesize proline and confer streptomycin resistance,
respectively.) A recipient strain is proA− and strC− and is
resistant to tetracycline. After transformation, the bacteria were
first streaked on a medium containing proline, streptomycin, and
tetracycline. Colonies were then restreaked on a medium containing
streptomycin and tetracycline. (Note: Each type of medium had
carbon and nitrogen sources for growth.) The following results
were obtained:
70 colonies grew on the medium containing proline, streptomycin,
and tetracycline, but only 2 of these 70 colonies grew when
restreaked on the medium containing streptomycin and tetracycline
but lacking proline.
If we assume the average size of the DNA fragments is 2 minutes,
how far apart are these two genes?

Co-transformation occurs when the two or more genes are located in very close proximity that they are transferred into the recipient bacterial strain together. It suggests that these genes are closely linked and there are fewer chances for recombination taking place between these genes. High co-transformation frequency suggests that the genes are highly linked.
in the given experiment, 70 colonies were grown on a medium containing proline, streptomycin, and tetracycline out of which only 2 colonies grew when restreaked on the medium containing streptomycin and tetracyclin but lacking proline. to find the cotransformation frequency:
To determine the distance between the two genes, we will use the formula to calculate cotransduction frequency. It is because cotransformation frequency can also be defined as cotransduction frequency.
Where,
d represents the distance between the two genes
L represents the size of the bacterial chromosomes which can be accumulated by the phage DNA during transduction.
Thus,
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