The total concentration of enzyme in a reaction, [E], is made up of the concentration of enzyme bound to substrate, [ES], and the concentration of enzyme still free in solution, [Ef]. Similarly, the total amount of substrate is made up of [Sf] and [ES]. We can assume that the concentration of enzyme is much less than that of the substrate, [E] << [S]. Assuming the steady state condition and the relationships between [E], [Ef] and [ES], and similar ones for S, given in lectures, derive an expression for the saturation factor,  , in terms of [S] and . (Note that [E] and [S] denote the total amounts of enzyme and substrate added to the reaction, respectively. You may assume that [S]>>[E].)

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
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The total concentration of enzyme in a reaction, [E], is made up of the concentration of enzyme bound to substrate, [ES], and the concentration of enzyme still free in solution, [Ef]. Similarly, the total amount of substrate is made up of [Sf] and [ES]. We can assume that the concentration of enzyme is much less than that of the substrate, [E] << [S].

  1. Assuming the steady state condition

and the relationships between [E], [Ef] and [ES], and similar ones for S, given in lectures, derive an expression for the saturation factor,  , in terms of [S] and .

(Note that [E] and [S] denote the total amounts of enzyme and substrate added to the reaction, respectively. You may assume that [S]>>[E].)

Expert Solution
Introduction

An enzyme catalyses the reaction S P. The rate of the reaction depends on the concentration of substrate. Since substrate concentration changes through the reaction, we estimate the rate of the reaction at the very beginning of the reaction where changes in [S] is less. Then the initial rate of the reaction vo can be represented as a function of [S]. 

Michaelis Menten postulated that free enzyme reacts with the substrate reversibly to form an enzyme-substrate complex and this reaction occurs quickly. The ES complex then breakdown into free enzymes and products and this reaction is comparatively slower. 

When the enzyme is first mixed with an excess of substrate, [ES] is very less. This period is called the pre-steady state and lasts for microseconds. Soon, the reaction achieves a steady state where [ES] remains constant over time. The measured vo reflects the steady state. 

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