The enzyme glycogen synthase kinase (GSK-3β) plays a central role in Alzheimer€™s disease. The onset of Alzheimer€™s disease is accompanied by the production of highly phosphorylated forms of a protein referred to as €œÏ„ .€ GSK-3β contributes to the hyperphosphorylation of Ï„ such that inhibiting the activity of this enzyme represents a pathway for the development of an Alzheimer€™s drug. A compound known as Ro 31-8220 is a competitive inhibitor of GSK-3β. The following data were obtained for the rate of GSK-3β activity in the presence and absence of Ro 31-8220 [A. Martinez et al., J. Medicinal Chemistry 45 (2002): 1292]:

Determine K_m and rate _max for GSK-3β and, using the data with the inhibitor, determine K^*_m and K_I.

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Rate, (µM s-1), [1) = 0 4.17 x 10-8 3.97 x 10-8 3.62 x 10-8 3.27x 10-8 2.98 x 10-8 2.31 x 10-8 Rate, (µM s-1)= 200 µM 3.33 x 10-8 2.98 x 10-8 2.38 x 10-8 181 x 10-8 139 x 10-8 [S](µM) 66.7 40.0 20.0 13.3 10.0 6.67 104 x 108