Hypothetical disease X is an autosomal recessive disorder that causes the patien

Question

Hypothetical disease X is an autosomal recessive disorder that causes the patient to be unable to repair damaged DNA. The symptoms develop between around age 40 and can be quite debilitating. The incidence of this disorder is 1 in 50,000. Please predict the frequency of obligate carriers (heterozygotes), and homozygotes for the wild-type allele in the population.

a. Please calculate the frequencies of the wild-type (p) and disease-causing allele (q)

b. Please calculate the frequency of obligate carriers in the population.

Explanation / Answer

Answer:

Since the disease is an autosomal recessive disorder, that means only those individuals that are homozygous recessive will have this disorder.

This can be solved based on Hardy-Weinberg law

p2 + 2pq + q2 = 1 and p + q = 1

Where,

Incidence of X disorder = 1/50000 = 0.00002 (q2)

Since q2 = 0.00002, therefore q = sqrt(0.00002) = 0.0044

Since p + q = 1

therefore p = 1 - q = 1-0.004472 = 0.9956

Therefore frequency of wild type (p) allele in population is 99.56% and disease causing allele q is 0.44%

b) frequency of obligate carriers = 2pq = 2*0.9956*0.0044 = 0.0089 or 0.89%

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