Phenylketonuria (PKU) is an inborn error of metabolism, a condition in which the body cannot degrade the amino acid, phenylalanine, therefore causing an excess accumulation of phenylalanine.
The main reason why the body cannot degrade the amino acid is because it lacks the enzyme, phenylalanine hydroxylase (PAH), to do so. The enzyme deaminates phenylalanine to form phenylpyruvate which can then be excreted from the body. Although, phenylalanine is an essential amino acid needed in the body, accumulating such excess of it causes severe and irreversible brain damage. 
PKU is a recessive trait so it is fairly rare, occurring ratio is 1:15,000. Both parents would need to have a copy of the mutated allele to contribute to the child, who would need both copies of the mutated gene in order to have the phenotype of the disease. 
Prevention, Prognosis, & TreatmentEdit
There is really no prevention method that can prevent the disease entirely because it's based off mutations in the PAH gene. However, genetic screenings for the parents could predict the likelihood of the offsprings having the disease and taking extra precautions. Although, individuals who suffer from this metabolism error if detected detected early can have a good prognosis. Newborn screening, by pricking the heel for a blood sample, is very effective in identifying the disease. A low phenylalanine diet would be the treatment for this condition, espcially artificial sweeteners that contain aspartame should be cut out from the diet. Women who plan on having babies should plan for their pregnancy ahead of time to take precaution for pregnancy risks and diet changes. If it is left untreated, the individual would suffer from mental retardation. 
John Burke's GeneticsEdit
Fortunately, professor Burke does not have a mutation in the PAH gene. In order to display the phenotype of the disease, there must be two mutations in the PAH gene, if there is only one, the individual would be considered a carrier for the disease and their offspring would have a higher chance of getting the disease. Professor Burke does not have a mutation in the PAH gene that was found by 23andme but, it doesn't mean that he does not have any mutations within the gene.