One of the main uses for surface plasmon resonance lies in the characterization of kinetic rates for interactions between small molecule inhibitors and their protein targets. for this problem, assume a protein with a molecular weight of 30,000 g/mol (e. g., 30 kda) and a small molecule inhibitor with a weight of 500 g/mol. the size of the sensor chip is 1 mm^2 , and assume 10^4 binding sites per chip. concentration of ligand in solution is 10 nm.

a. for this small molecule-protein interaction, assume k_on= 3x10^5 m^−1 s^−1 and k_off = 5x10^- 4 s^−1. how many resonance units will be detected at equilibrium, assuming the protein is attached to the surface and the small molecule is in solution? how much does the signal level improve with the small molecule attached to the surface and the protein in solution.

b. how long will it take this experiment to reach equilibrium? for this question, you can use a fraction of equilibrium to estimate the time to reach full equilibrium.

c. for a second small molecule, k_on is identical but k_off is twice as fast. how does changing the off rate of the interaction affect the time to equilibrium? provide a quantitative answer and a qualitative reason for this change.