Diabetes is a global epidemic affecting more than 240 million people worldwide. The vast majority of the cases are Type 2. Recently a drug, Januvia (J), was discovered to treat Type 2 diabetes. When food enters the stomach, a peptide, GLP-1 (glucagon-like peptide 1) is released, which leads to glucose-dependent insulin secretion and glucagon suppression. The half-life of GLP-1 is very short because it is rapidly degraded by an enzyme dipeptidyl peptidase-IV (DPP-IV), which cleaves the two terminal amino acids of the peptide thus deactivating it. DP-IV rapidly cleaves the active form of GLP-1 (GLP-1[7-36] amide) to its inactive form (GLP-1[9-36] amide) with a half-life of 1 minute, that is, t_1/2 = 1 min., and it is thought to be the primary enzyme responsible for this hydrolysis. Also see (a) J. J. Holst and D. F. Deacon, Diabetes, 47, 1663 (1998); (b) B. Balkan, et al., Diabetiologia, 42, 1324 (1999); (c) K. Augustyns, et al., Curr. Med. Chem., 6, 311 (1999). GLP-1(9-36)←E.GLP-1(7-36) →BadE GLP-1(7-36)→GoodActs in pancreas tostimulate insulinrelease and suppressglucagon Inhibition of the DPP-IV Enzyme, (E), therefore, is expected to significantly reduce the extent of the inactivation of GLP-1[7-36] and should lead to an increase in circulating levels of the active form of the hormone. Supporting evidence for this comes from DPP-IV-enzyme-deficient mice, which have elevated levels of GLP-1[7- 36] amide. As a very rough approximation, let’s treat the reaction as follows: The new drug, an inhibitor of the DPP-IV enzyme (E), is Januvia (J), which prevents the
enzyme from deactivating GLP-1.

D. Marguet, et al., Proc. Natl. Acad. Sci., 97, 6864 (2000). E + GLP-1 ⇄ E • GLP-1 → Glucose Release
Inhibited E + J ⇄ E • J (Inactive) By delaying the degradation of GLP-1, the inhibitor is able to extend the action of insulin and also suppress the release of glucagon.
a. Plot the ratio of reaction of –rGLP (without inhibition) to the rate –rGLP (with inhibition) as a function of DDP-4 inhibitor constant for both competitive inhibition and uncompetitive inhibition.
b. Assuming the body is a well-mixed reactor, develop a model similar to Problems P8-5 and P8-6 for the dosage schedule for Januvia.