Enzyme E, which follows Michaelis- Menten kinetics, catalyzes the same reaction

Question

Enzyme E, which follows Michaelis- Menten kinetics, catalyzes the same reaction upon three different substates that are strucurally related (S1,S2, and S3) When the kinetic data for the three reactions are determined under the same reaction conditions, the data indicated below is otabined. The Km (Km1) for E and S1 is 1uM, that for E and S2 (Km2) is 80nM, and that for E and S3 (Km3) is 20nM. The Vmax for E and S1 is 115uMol/min (vmax1), Vmax2 is 385umol/min and Vmax3 is 380umol/min. Upon which substate does E1 exhibit a more efficint catalytic activity: S!, S2 or S3?

Explain answer please.

Explanation / Answer

Kinetic data is determined for three reaction under same condition, i.e initial enzyme concentration is same for three reaction and let say it is equal to E.

Now catalytic constant for an enzyme, Kcat= Vmax / [E]

If Michaelis- Menten constant is KM for an enzyme, then catalytic activity for the enzyme is Kcat / KM

In our case, E is same for all three case. Therefore, S1 : S2 : S3 = (Vmax1 / KM1) : (Vmax2 / KM2) :  (Vmax3 / KM3)

Therefore,  S1 : S2 : S3 = (115x103) / 103 : (385x103) / 80 : (380x103) / 20 [All the Vmax have been changed in nM/mint. and KM in nM.]

Therefore,  S1 : S2 : S3 = 0.115 : 4812 : 19000

Therefore, the enzyme E exhibit more efficient catalytic activity upon S3.

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