A research group discovers a new version of happyase, which they call happyase*,

Question

A research group discovers a new version of happyase, which they call happyase*, that catalyzes theMp chemical reaction APPY SAD The researchers begin to characterize the enzyme (a) In the first experiment, with [E.J at 4 nM, they find that the Vmax is 3.40 M s-1. Based on this experiment, what is the keat for happyase? In another experiment, with Et] at 1 nM and [HAPPY] at 40 LM, the researchers find that Vo 689 nM s-1. What is the measured Km of happyase* for its substrate HAPPY? Number Number C 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 Vmax in (a) is increased to 6.80 MM s-1, and the measured Km in (b) is now 10.4 M. For the inhibitor ANGER, calculate the values of a' and ?. Number Number Please scroll d) Based on the information given above, what type of inhibitor is ANGER? down. O uncompetitive inhibitor

Explanation / Answer

Ans. #a. Kcat = Vmax / [E]t

= 3.40 uM s-1 / 4 nm                                                ; [1 uM = 103 nM]

= (3.40 x 103 nM s-1) / 4 nM

= 850.0 s-1

Hence, Kcat for Happyase = 485.714 s-1

#b. The Vmax of a reaction mixture is proportional to enzyme concentrations.

We have,        Vmax at [E] of 7 nM = 3.40 uM s-1

Have to calculate Vmax at [E] = 1 nM

Now,

            Vmax at [E] of 1 nM = Vmax at [E] of 4 nM x ([E] of 1 nM)

                                                = (3.40 uM s-1 / 4 nM E) x 1 nM E

                                                = 0.85 uM s-1

Hence, at [E] of 1 nM, the Vmax = 0.85 uM s-1 = 850.0 nM s-1

# Calculate Km using MM equation- Vo = Vmax [S] / (Km + [S])

Re-arranging the above equation-

            Km = (Vmax [S] / Vo) – [S]

Putting the values in above equation-

Km= (850. nM s-1 x 40 uM / 689 nM s-1) – 40 uM

Or, Km = 49.347 uM – 40 uM = 9.347 uM

Hence, Km of Happyase = 9.347 uM

#c. So far we have-

            Vmax (in presence of Anger, #a) = 3.40 uM s-1 = Vmax,app

Km (in presence of Anger, #b) = 9.347 uM = Km,app

Vmax (Inhibitor free) = 6.80 uM s-1

Km (Inhibitor free) = 10.4 uM

# Now, using the formula-

            a’ = Vmax / Vmax,app = Vmax (In presence of inhibitor)/ Vmax (Inhibitor free)

            Or, a’ = 6.80 uM s-1 / 3.40 uM s-1

            Hence, a’ = 2.00

# Now, using the formula-

            a = (a’ x Km,app) / Km = (2.00 x 9.347 uM) / 10.4 uM = 1.80

#d. Type of inhibitor:

Both Vmax and Km are decreased by different factors (because a and a’ are different). Decrease in Vmax and Km by different factors in the characteristic of mixed inhibition.

Therefore, ANGRY is a mixed inhibitor.

# Note: In competitive inhibition, Vmax remains the same but Km is increased.

In uncompetitive inhibition, both the Km and Vmax are decreased by same factor (i.e. a = a’).

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