PKU counselling: using family history instead of the population carrier rate
Ana and Ben are unrelated and both unaffected by phenylketonuria (PKU), an autosomal recessive condition caused by variants in the PAH gene. Ana's brother and Ben's sister both have PKU. Neither Ana nor Ben has been genetically tested. The carrier frequency of PKU in the general population is about 1 in 50. Ana's parents are both healthy and have no other affected children. Ben's parents are also healthy. Ana and Ben plan to have a child and ask a genetic counsellor for the probability that the child will have PKU. The counsellor explains that family history changes the calculation from the population figure. Assume full penetrance and no new mutations.
1. Calculate the probability that Ana and Ben's first child will have PKU. Show your reasoning at each step.
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Because Ana's brother has PKU, both of Ana's parents must be carriers: each has one disease allele and one normal allele. Ana is unaffected, so she could be a non-carrier (normal/normal) or a carrier (normal/disease). Among the unaffected children of two carriers, the expected proportions are 1/3 non-carrier and 2/3 carrier, so Ana's probability of being a carrier is 2/3. The same reasoning applies to Ben: his sister has PKU, so his parents are carriers and Ben, being unaffected, has a 2/3 chance of being a carrier. For the child to have PKU, both Ana and Ben must be carriers and both must pass on the disease allele. The probability that both are carriers is 2/3 × 2/3 = 4/9. If both are carriers, the chance that both pass the disease allele is 1/4. Therefore the overall probability is 4/9 × 1/4 = 1/9, about 11%. The 1 in 50 population carrier frequency is not used for either parent because each has a close affected relative, which gives much stronger information about their carrier status.
2. Explain why the population carrier frequency of 1 in 50 is not appropriate for Ben in this calculation, and state one assumption that could change your answer.
Read the worked answer
The 1 in 50 figure is the chance that a randomly chosen person from the general population is a carrier. Ben is not a random person: his sister has PKU, so his parents must both be carriers. Given that Ben is unaffected, his chance of being a carrier is 2/3, not 1/50. Using the population figure would ignore the family information and produce a much smaller, incorrect risk, about 2/3 × 1/50 × 1/4 = 1/300 for the child. The family history is more relevant because it directly tells us about the alleles segregating in Ben's family. One assumption that could change the answer is that Ana and Ben have not been genetically tested. If Ben were tested and found not to carry a PAH variant, his carrier probability would fall, and the child's risk would change. Other assumptions include full penetrance, no new mutations, correct diagnosis in the affected siblings, and that both sets of parents are true carriers. The calculation also assumes the condition is autosomal recessive and that there is no consanguinity.