Concept explainers
To explain: How the features described in the text accurately represent the Michaelis-Menten equation.
Introduction: Enzymes are the protein molecules that catalyze the

Explanation of Solution
The Michaelis-Menten equation is used for enzyme kinetics reaction. It is given as follows,
Refer to Fig.4-35, “An enzyme’s performance depends on how rapidly it can process its substrate”, in the text book. This figure shows a hyperbolic relationship of enzymes at high substrate concentration. In this figure, the rate of enzyme reaction (V) increases with an increase in the substrate concentration to reach the maximum value (Vmax). At this point, the enzymes become saturated and the rate becomes limited. KM indicates the Michaelis rate constant and the substrate concentration on half of the maximum value (Vmax). Hence, the descriptions given in the text book represents the Michaelis-Menten equation.
The descriptions given in the text book represents the Michaelis-Menten equation.
(A)
To determine: How the Michaelis-Menten equation from the given substrate concentrations is simplified if [S] is much smaller than the KM.
Introduction: The Michaelis–Menten equation is generally used for enzyme kinetics reaction.
(A)

Explanation of Solution
Option (A) is given as, “[S] is much smaller than the KM". When [S] << KM, the term ([S] +KM) nearly equal to the term KM.
So the equation (1) can be simplified as follows,
Therefore, the rate of enzyme reaction is directly proportional to the substrate concentration.
When [S] is much smaller than the KM, then the rate is directly proportional to the substrate concentration.
(B)
To determine: How the Michaelis-Menten equation from the given substrate concentrations be simplified if [S] equals the KM.
Introduction: KM is the Michaelis-Menten constant. Vmax is the maximum velocity with which the enzyme catalyzes the reaction.
(B)

Explanation of Solution
Option (B) is given as, “[S] equals the KM”.
So, Equation (1) can be simplified as follows,
Therefore, the rate of the reaction is half of the maximal rate.
If [S] equals the KM, then the rate of enzyme reaction is half of the maximal rate.
(C)
To determine: How the Michaelis-Menten equation from the given substrate concentrations would be simplified if [S] is much smaller than the KM.
Introduction: KM is the Michaelis-Menten constant and [S] is the substrate concentration.
(C)

Explanation of Solution
Option (C) is given as, “[S] is much smaller than the KM”. When [S] >> KM, the term ([S] +KM) nearly equal to the term [S].
So, Equation (1) can be simplified as follows,
Therefore, the maximum rate of the reaction occurs at its maximal rate.
If [S] is much smaller than the KM, the maximum rate of the reaction occurs at its maximal rate.
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Chapter 4 Solutions
ESSENTIAL CELL BIOLOGY (LL)-TEXT
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