Derive hill equation - explain what in vitro selection is

Question

1. Derive θ = [L]/ ([L] + K_d) where θ is the fraction bound, L is ligand, P is protein, and Kd is dissociation constant.
(hint: the protein has only one binding site)

2. Derive Hill equation. (hint: the protein has n binding sites)

3. Derive the Michalis - Menton equation using the steady-state approximation. Show all your steps.

4. Use a program like Excel to draw a plot (hint: x axis: 1/S, y axis: 1/v ) and calculate the K_m and v_max for the
following data.

5. Draw a plot and calculate the K_m and v_max using the data in column v_A. Then calculate K_m and v_max using the
data in column v_B. (hint: A is for substrates only, B is for substrate with inhibitor).

6. For question #5 B, what type of inhibitor was used? Explain by drawing the potential structure of enzyme and
where the inhibitor is binding.

7. Explain what "in vitro selection" is and what it is useful for.