A research group discovers a new version of happyase, which they call happyase*, that catalyzes the chemical reaction HAPPY SAD. The researchers begin to characterize the enzyme In the first experiment, with [E_t] at 4 nM, they find that the V_max is 1.6 mu M s^-1. Based on this experiment, what is the k_cat for happyase *? (Include appropriate units.) In another experiment, with [E] at l nM and [HAPPY] at 30 mu M, the researchers find that V_o = 300 nM s^-1. What is the measured K_m of happyase* for its substrate HAPPY? Include appropriate units.) Further research shows that the purified happyase* used in the first two experiments was actually contaminated with a reversible inhibitor called ANGER. When ANGER is carefully removed from the happyase* preparation and the two experiments repeated, the measured V_max in is increased to 4.8 mu M s^-1, and the measured K_m in is now 15 mu M, For the inhibitor ANGER, calculate the values of alpha and alpha' Based on the information given above, what type of inhibitor is ANGER?

Explanation:

a. kcat = Vmax/[Et] = (1.6 Mμ/s) / 0.004 ∪M = 400 s-1

b. Vmax = [Et] kcat = [1 nM] (400 s-1) = 400 nM/s which is 0.4μM/s.

Now we can use the Michaelis-Menten equation if all the units are similar (all molar conc in nM or in this case μM):

V0 = Vmax*[S] / Km+[S] = 0.3μM/s = (0.4μM/s) (30μM) / (Km+30μM)

Then solving for KM, we get:

(0.3 M/s) (Km + 30μM) = 0.4μM/s (30 μM)

0.3μM/s(Km) + 9μM2/sec = 12μM2/s

0.3μM/s(Km) = 3μM2/s

Km = 10μM

Another way to do this would be to first rearrange the Michaelis-Menten equation to:

V0/Vmax = [S] / Km+[S]

(300 nM/s) / (400 nM/s) = 3/4 = [S] / (Km + [S])

4 [S] = 3 Km + 3[S]

Km = [S]/3 = 30μM / 3 = 10μM

c. After removal of ANGER, the Vmax increased to 4.8μM/s and the Km became 15μM. It is a mixed because it is affecting both Vmax and Km.

Because Vmax increased by a factor of 3, ∝'=3.

Similarly, Km varies as a function of ∝Km/\alpha'. Given that Km increased by a factor of 1.5 when ANGER was removed (that is, the inhibitor decreased the observed Km by 2/3 and ∝'=3, then ∝=2.

d. Because both ∝ and ∝' are affected, ANGER is a mixed inhibitor.