Problem 8 (Inhibition by multivalent substrate binding, 20 pts). In class we considered competitive binding of an inhibitor to an enzyme. As another example of how enzyme catalysis may be inhibited, consider the case where a second substrate molecule could bind an enzyme and render it ineffective at converting the substrate to product. E+Sk1k1ESk2E+PES+Sk3k3ES2. a) Derive an expression for dcP/dt as a function of substrate concentration cS and total enzyme concentration cE0. An exact analytical expression is not possible, so you will need to make some approximations. Be sure to clearly state what approximations you make. b) Make a sketch of the rate of product formation versus substrate concentration with three curves on it. - The classic Michaelis-Menten equation. - Michaelis-Menten equation with competitive inhibition as we studied in class. (As a reminder, the reaction scheme for that was E+SESE +P, and E+IEI.) - The result you just derived in part (a)