Final answer:
Individuals with xeroderma pigmentosum cannot repair thymine dimers caused by UV exposure, resulting in a high skin cancer risk. In the US, the mutant allele frequency (q) is calculated to be 2 x 10^-3 and the carrier frequency (2pq) is approximately 4 x 10^-3 based on the Hardy-Weinberg principle.
Step-by-step explanation:
People with xeroderma pigmentosum (XP) cannot utilize the nucleotide excision repair mechanism to fix damage caused by UV light exposure. Specifically, they are unable to repair thymine dimers, which are a type of pyrimidine dimer that occurs when two adjacent thymine bases bond together after absorbing UV radiation. Thymine dimers distort the DNA structure, making it difficult for the cell to accurately replicate DNA. This increased risk of replication errors can lead to skin cancer.
As the condition is recessive and given the frequency of affected individuals in the US is approximately 1/250,000, we can use the Hardy-Weinberg principle to calculate the frequency of the mutant allele (q) and the carrier frequency (2pq). Let the frequency of affected (homozygous recessive) individuals be q^2, where q^2 = 4 x 10^-6.
Therefore, q (the mutant allele frequency) is the square root of 4 x 10^-6, which is 2 x 10^-3. The frequency of carriers (heterozygous individuals) is 2pq, which we can find by calculating 2p(2 x 10^-3), assuming that p (the frequency of the normal allele) is approximately 1 since q is very small. Thus, the carrier frequency is approximately 2 x (1)(2 x 10^-3) = 4 x 10^-3.