PKU Carrier Frequency Notes (Hardy-Weinberg)

Autosomal recessive inheritance of PKU

  • PKU (phenylketonuria) is an autosomal recessive genetic disorder.
  • Affected individuals have genotype aa (two recessive alleles).
  • Carriers are heterozygous Aa (one PKU allele, one normal allele). The dominant normal allele does not cause PKU when paired with a recessive allele.

Hardy-Weinberg basics for allele frequencies

  • Let q be the frequency of the recessive PKU allele in the population.
  • Let p be the frequency of the normal allele, where p + q = 1.
  • Under Hardy-Weinberg equilibrium, genotype frequencies are:
    • p^2 for homozygous normal (AA)
    • 2pq for heterozygous carriers (Aa)
    • q^2 for homozygous recessive affected (aa)
  • The sum p^2 + 2pq + q^2 = 1.

Given allele frequencies and calculation used in the example

  • In the example, the PKU allele frequency is given as q = 0.01 (1%).
  • Therefore, p = 1 - q = 0.99.)
  • The carrier frequency is 2pq = 2\cdot 0.99 \cdot 0.01 = 0.0198\,.
  • This equals approximately 1.98\%, which is about 2\% of the population.
  • The affected frequency is q^2 = (0.01)^2 = 0.0001 = 0.01\%.

Step-by-step calculation

  • Start with the allele frequencies: p = 1 - q = 1 - 0.01 = 0.99, \, q = 0.01.
  • Compute carrier frequency: 2pq = 2(0.99)(0.01) = 0.0198 \approx 1.98\% \approx 2\%.
  • Compute affected frequency: q^2 = (0.01)^2 = 0.0001 = 0.01\%.
  • Summarize: about 2% carriers, about 0.01% affected, under Hardy-Weinberg assumptions.

Numerical examples and interpretation

  • If you apply this to a population of N individuals:
    • Expected number of carriers ≈ 0.0198 \times N.
    • Example: In 100,000 people, carriers ≈ 1,980; affected ≈ 10.
  • If two random individuals who are both carriers have a child, the probabilities are:
    • AA (unaffected, non-carrier): \tfrac{1}{4}
    • Aa (carrier): \tfrac{1}{2}
    • aa (affected): \tfrac{1}{4}
    • Therefore, if two carriers mate, there is a 25% chance the child is affected.

Genotype frequencies under Hardy-Weinberg for this scenario

  • With p = 0.99 and q = 0.01:
    • Homozygous normal: p^2 = (0.99)^2 = 0.9801 \,(98.01\%)
    • Heterozygous carriers: 2pq = 0.0198 \,(1.98\%)
    • Homozygous recessive affected: q^2 = 0.0001 \,(0.01\%)

Assumptions and caveats

  • Assumes Hardy-Weinberg equilibrium: large population, random mating, no selection, no migration, no mutation, no genetic drift.
  • Real populations may deviate due to:
    • Population substructure and ethnic variation in allele frequencies.
    • Non-random mating patterns.
    • Selection pressures (though carriers often have no PKU phenotype).
    • Migration and demographic changes.
  • The 1% allele frequency and the resulting 2% carrier frequency are approximate for illustrative calculation.

Connections to foundational principles and real-world relevance

  • Demonstrates the use of Hardy-Weinberg to estimate carrier and affected frequencies from allele frequencies.
  • Connects to population genetics, genetic screening, and public health planning.
  • Practical implications include:
    • Screening programs to identify carriers in populations with higher frequencies.
    • Genetic counseling for prospective parents who are carriers.
    • Prenatal and newborn screening for PKU to enable early dietary management.

Ethical, philosophical, and practical implications

  • Screening access and equity: ensuring diverse populations have access to testing.
  • Privacy and potential discrimination based on genetic information.
  • Reproductive decision-making influenced by carrier status and available options.
  • The balance between public health benefits and individual autonomy.

Quick recap and takeaways

  • PKU is autosomal recessive; carriers are Aa, affected are aa.
  • Under Hardy-Weinberg: p^2 + 2pq + q^2 = 1 with p = 1 - q.
  • For q = 0.01: carrier frequency ≈ 2pq = 2(0.99)(0.01) = 0.0198 \approx 1.98\% \approx 2\%.
  • Affected frequency ≈ q^2 = (0.01)^2 = 0.0001 \approx 0.01\%.
  • Real-world values vary by population; use as approximate guidance for population-level expectations.