Enzyme Kinetics: Example Problems

Try to solve these problems before watching the solutions in the screencasts.

Example Problem 1

Consider the following proposed mechanism for the reaction of two separate reactant molecules (substrates S1 and S2) to produce a product P catalyzed by an enzyme E.

E + S1 → ES1         (1)

ES1 → E + S1         (2)

ES1 + S2 → P + E  (3)

Derive the rate expression for product formation (assuming that the steady-state approximation applies) in terms of the rate constant for each step, the concentrations of substrate species, and the total concentration of enzyme. According to this mechanism, will the reaction rate ever be less than first order in S2? Briefly explain.

Example Problem 2

The enzymatic conversion of a certain substrate (S) is conducted in an isothermal CSTR. The substrate enters at a concentration of 1.0 mol/L. The reaction is known to follow Michaelis-Menten kinetics with Vmax = 0.65 mol/L-min and KM = 0.54 mol/L.

a) What reactor space time is required to achieve 80% conversion?

b) Due to an upstream process upset, the feed becomes less pure, and contains 0.10 mol/L of a component that inhibits the enzyme according to an uncompetitive mechanism. The required space time to achieve 80% conversion is found to increase by a factor of 2. What is the equilibrium constant for binding of the inhibitor onto the enzyme?