Biochemistry
Biochemistry
9th Edition
ISBN: 9781305961135
Author: Mary K. Campbell, Shawn O. Farrell, Owen M. McDougal
Publisher: Cengage Learning
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Chapter 6, Problem 25RE

MATHEMATICAL For an enzyme that displays Michaelis–Menten kinetics, what is the reaction velocity, V (as a percentage of V max ), observed at the following values?

(a) [ S ] = K M

(b) [ S ] = 0.5 K M

(c) [ S ] = 0.1 K M

(d) [ S ] = 2 K M

(e) [ S ] = 10 K M

Expert Solution & Answer
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Interpretation Introduction

Interpretation:

The reaction velocity V (as the percentage of Vmax) of an enzyme that displays Michaelis–Menten equation is to be calculated.

Concept introduction:

In 1913, Leonor Michaelis and Maud Menten discovered an equation that proved to be an eminent model for the enzyme kinetics. To measure the velocity or rate of a reaction, the Michaelis–Menten equation is used. The equation is as follows:

= Vmax[S]Km + [S]

Answer to Problem 25RE

V = 0.5 Vmax

V = 0.33 Vmax

V = 0.09 Vmax

V = 0.67 Vmax

V = 0.91 Vmax

Explanation of Solution

[S] = KM is given and calculating the reaction velocity (V) on the basis of the Michaelis and Menten equation,

= Vmax[S]Km + [S]

Since [S] = KM, substituting the value in the above equation,

= Vmax KMKM + KM= Vmax KM2KM= Vmax2= 0.5 Vmax

[S] = 0.5 KM is given and calculating of reaction velocity (V) on the basis of Michaelis and Menten equation,

= Vmax[S]Km + [S]

Since [S] = 0.5 KM, substituting the value in the above equation,

= Vmax 0.5 KMKM + 0.5 KM= Vmax 0.5KM1.5KM= Vmax3= 0.33 Vmax

[S] = 0.1 KM is given and calculating of reaction velocity (V) on the basis of Michaelis and Menten equation,

= Vmax[S]Km + [S]

Since [S] = 0.1 KM, substituting the value in the above equation,

= Vmax 0.1 KMKM + 0.1 KM= Vmax 0.1KM1.1KM= Vmax11= 0.09 Vmax

[S] = 2 KM is given and calculating of reaction velocity (V) on the basis of Michaelis and Menten equation,

Since [S] = 2 KM, substituting the value in the above equation,

= Vmax 2 KMKM + 2 KM= Vmax 2KM3KM= 2 Vmax3= 0.67 Vmax

[S] = 10 KM is given and calculating of reaction velocity (V) on the basis of Michaelis and Menten equation,

Since [S] = 10 KM, substituting the value in the above equation,

= Vmax 10 KMKM + 10 KM= Vmax 10KM11KM= 10 Vmax11= 0.91 Vmax

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Chapter 6 Solutions

Biochemistry

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