A baby that was apparently normal at bih begins to show a delay in motor development by 3 months of age. At one year of age, the child begins to develop spasticity and writhing movements. At age three, compulsive biting of fingers and lips and head-banging appear. At pubey, the child develops ahritis, and death from renal failure occurs at age 25. This patient's condition is due to an enzyme deficiency in which of the following biochemical pathways?