The Hill equation for the rate, V, of a cooperative enzyme reaction is V(S) =

VmaxS n

Kn + S n

, where n > 1 is usually an integer.

a. What is V(0)? What is V(Kn)?

b. Show that V 0

(S) is sometimes increasing, sometimes decreasing, but that, like the Michaelis–Menten equation, V 0

(S) → 0 as S → ∞.

c. Calculate V 0

(0) and V 0

(K) for n = 2, 3, 4. What do you think the curve will look like as n gets large?

d. Let K = 1 µM and Vmax = 1 µM s−1

, and plot V(S) for n = 2, 3, 4 and n = 50. Was your guess correct?