In class we have discussed how enzyme assays can be used to determine the enzyme kinetic constants V_max and K_m but in this assignment you will do the reverse. You will use known V_max and K_m values to calculate expected rates for a pair of enzyme catalyzed reactions.

Suppose that you are provided data about phenylalanine hydroxylase and phenylalanine aminotransferase (the enzyme that converts phenylalanine to phenylpyruvate in patients with PKU). You are told that the V_max and K_m values for phenylalanine hydroxylase in a standard enzyme assay are 100 µmol min^-1 and 10 µM respectively, and those for phenylalanine aminotransferase are 10 µmol min^-1 and 1000 µM respectively.

Prepare a table that reports expected values of enzyme velocity (v) at the following substrate concentrations ([s]): 1, 2, 6, 10, 20, 40, 60, 100, 500, 1000, 2400, 5000 (all values are in µM).

Prepare Michaelis Menten plots that illustrate these kinetic data. Don't forget to carefully label the axes.

Now consider this pseudo-clinical case of two patients with PKU. Assume that the production of phenylpyruvate by phenylalanine aminotransferase at a rate of less than 1 µmol min^-1 as measured by this assay can be handled by the body (the phenylpyruvate is converted to something non-toxic or is excreted) and does NOT cause PKU.

A patient with mild PKU comes to the clinic with a blood phenylalanine concentration of 500 µM. When his phenylalanine hydroxylase is assayed as described above, V_max and K_m values are found to be 100 µmol min^-1 and 5000 µM respectively. Prepare a Michaelis Menten plot for his enzyme as described above using the same substrate concentration range. To what extent has the change in Km affected his enzyme's ability to convert phenylalanine to tyrosine, assuming that the substrate concentration it "sees" is the same as the patient's blood phenylalanine concentration? At this blood concentration of phenylalanine, at what rate is his phenylalanine aminotransferase producing phenylpyruvate? Is this rate consistent with a diagnosis of PKU (that is, is it above 1 µmol min^-1)?

A patient with strong PKU comes to the clinic with a blood phenylalanine concentration of 2400 µM. When her phenylalanine hydroxylase is assayed as described above, V_max and K_m values are found to be 2 µmol min^-1 and 10 µM respectively. Prepare a Michaelis Menten plot for her enzyme as described above using the same substrate concentration range. To what extent has the change in Vmax affected her enzyme's ability to convert phenylalanine to tyrosine, assuming that the substrate concentration it "sees" is the same as the patient's blood phenylalanine concentration? At this blood concentration of phenylalanine, at what rate is her phenylalanine aminotransferase producing phenylpyruvate? Is this rate consistent with a diagnosis of PKU that is more severe than the first patient?