Given the following reaction and equation for the initial velocity of the reaction:k₁ k3E+S ES E + PV=Keat [ES] = k3 [ES]k₂where keat is the rate constant for the reaction which forms the product from theES complex. Explain in words why the velocity is directly proportional to theamount ofenzyme added in the presence of saturating substrate levels.

Answered: Given the following reaction and…

Biochemistry

9th Edition

ISBN:9781319114671

Author:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.

Publisher:Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.

Chapter1: Biochemistry: An Evolving Science

Section: Chapter Questions

Problem 1P

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Question

Given the following reaction and equation for the initial velocity of the reaction:
k₁ k3
E+S ES E + P
V=Keat [ES] = k3 [ES]
k₂
where keat is the rate constant for the reaction which forms the product from the
ES complex. Explain in words why the velocity is directly proportional to theamount of
enzyme added in the presence of saturating substrate levels.

Expert Solution

Rate defining step in a reaction

We are given two equations for initial velocity (V).

$V = k_{c a t} [E S] - - - - - - - (e q 1) a n d V = k_{3} [E S] - - - - - - - - (e q 2) S o, k_{c a t} = k_{3}$

k_catis the the rate constant that describes the limiting rate of any enzyme catalyzed reaction at saturating substrate concentration. If one of the steps in the reaction mechanism is clearly the rate limiting step, then k_cat becomes equal to the rate constant of that rate limiting step. This is the case that we see here. The rate limiting step in the reaction given is the conversion of ES to E and P. Hence, k_cat = k₃ .

We know that, the concentration of total enzyme added to the reaction mixture is equal to the sum of concentrations of free enzymes and the ES complex.

$[E_{t}] = [E_{f}] + [E S] [E S] = [E_{t}] - [E_{f}] h e r e,' [E_{t}]' i s t h e c o n c e n t r a t i o n o f t o t a l a m o u n t o f e n z y m e a d d e d .' [E_{f}]' i s t h e c o n c e n t r a t i o n o f f r e e (u n b o u n d) e n z y m e .' [E S]' i s t h e c o n c e n t r a t i o n o f E n z y m e - S u b s t r a t e c o m p l e x .$