Using the two equations, p + q = 1 and p2 + 2pq + q2 = 1, answer the following questions. Maple Syrup Urine Disease (MSUD) is an autosomal recessive condition that causes intellectual and physical disabilities, difficulty feeding, and a sweet maple syrup odor to the urine. In Costa Rica, the incidence of MSUD is calculated as approximately 1 in 8,000 newborns. Calculate the allele frequencies for the normal and disease alleles.
Using the two equations, p + q = 1 and p2 + 2pq + q2 = 1, answer the following questions.
Maple Syrup Urine Disease (MSUD) is an autosomal recessive condition that causes intellectual and physical disabilities, difficulty feeding, and a sweet maple syrup odor to the urine. In Costa Rica, the incidence of MSUD is calculated as approximately 1 in 8,000 newborns. Calculate the allele frequencies for the normal and disease alleles.
The Correct Answer and Explanation is :
To calculate the allele frequencies for the normal and disease alleles, we will use Hardy-Weinberg equilibrium equations. These equations help us determine the frequency of alleles and genotypes in a population under ideal conditions, assuming that the population is not affected by factors like selection, migration, or mutation.
Equations:
- ( p + q = 1 ) (where ( p ) is the frequency of the normal allele, and ( q ) is the frequency of the disease allele)
- ( p^2 + 2pq + q^2 = 1 ) (where ( p^2 ) represents the homozygous normal genotype, ( 2pq ) represents the heterozygous genotype, and ( q^2 ) represents the homozygous disease genotype)
Step 1: Determine the frequency of the disease allele (( q ))
The incidence of Maple Syrup Urine Disease (MSUD) in Costa Rica is given as 1 in 8,000 newborns, meaning that 1 in 8,000 people are born with the disease. Since MSUD is an autosomal recessive condition, individuals with the disease must have two copies of the recessive allele, represented by the genotype ( qq ). The frequency of individuals with the disease is therefore ( q^2 ).
Given the incidence is 1 in 8,000, we can write:
[
q^2 = \frac{1}{8000}
]
Taking the square root of both sides to find ( q ):
[
q = \sqrt{\frac{1}{8000}} \approx 0.0112
]
Step 2: Calculate the frequency of the normal allele (( p ))
From the first equation, we know that ( p + q = 1 ). Since we have calculated ( q ), we can now solve for ( p ):
[
p = 1 – q = 1 – 0.0112 = 0.9888
]
Conclusion:
- The frequency of the normal allele (( p )) is approximately 0.9888.
- The frequency of the disease allele (( q )) is approximately 0.0112.
These allele frequencies suggest that the normal allele is much more prevalent than the disease allele in Costa Rica. Since MSUD is a recessive condition, most individuals in the population are carriers (heterozygous, ( pq )) or unaffected (homozygous dominant, ( p^2 )).
The results of these calculations are consistent with the given incidence of MSUD in the population, and they help us understand the genetic structure of the population with respect to this condition.