1. While working at a biotech startup, you isolate an inhibitor against an important drug target, the dimeric protein known as Enzyme X. Answer the following:

a. The binding of your inhibitor to Enzyme X appears to involve an allosteric mechanism and two different KDs are measured: KD1 = 10 nM and KD2 = 1 nM. What is the fraction of protein with ligand bound when [inhibitor] = 100 nM?

b. Sketch the binding isotherm for each single binding site as well as the cooperative binding isotherm for the inhibitor below. Label the axes and note on the plot where one can determine the Hill Coefficient and whether this specific binding mechanism displays positive or negative cooperativity.

c. The inhibitor is extremely effective in initial drug trials, but in some patients mutations mutation in Enzyme X arise that reduces its potency. These mutations are found on the dimer interface and reduce the Hill Coefficient to nH = 0.25. What is the new KD2 and what is the fraction of protein with bound drug at 100 nM now?