This question is based on a protein tyrosine kinase (PTK) enzyme that transfers a phosphoryl group from ATP to a Tyr residue on a peptide.

You develop an assay for the PTK and a model synthetic peptide substrate. You measure the k_cat (5 min^-1), and K_m for the peptide (300 M) and ATP (40 M).

a. Graph the V vs. S plots for PTK (50 nM) and peptide, and PTK and ATP. Indicate the V_max and K_m on the plots and also plot the same data in Lineweaver-Burk plots.

b. You design an inhibitor Pep-ATP in which the targeted peptide Tyr is modified and connected to the gamma-phosphate of ATP via a short chemical linker. Pep-ATP shows an IC₅₀ of 100 nM in the presence of 300 M peptide substrate and 40 M ATP.

(i) What kind of inhibitor do you think Pep-ATP is? What does its potency suggest about the enzyme mechanism?

(ii) Based on your inhibition model, draw Lineweaver-Burk plots with varying substrate and varying ATP to illustrate the expected inhibition patterns assuming a lack of preference of ATP or peptide binding first to the PTK.

(iii) Describe how making the chemical linker in Pep-ATP shorter or longer could affect potency and why?