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?

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Answer:

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.