Explanation Given: The Michaelis-Menten equation R ( s ) = A s K + s In enzyme kinetics, by definition the limiting reaction rate means the maximum attainable reaction rate for a given enzyme substrate system. The reaction rate can be altered by addition of new substrate, however there is a value beyond which the reaction rate does not increase. The limiting reaction rate is reached when the substrate concentration is in excess compared to the available enzyme concentration. This in mathematical terms means that the substrate concentration is approaching infinity. Thus, the limiting concentration is reached when the substrate concentration is approaching infinity. By finding the limit lim s → ∞ R ( s ) in the Michaelis-Menten equation R ( s ) = A s K + s , we can determine the limiting reaction rate. To determine limit at infinity for a given fraction of polynomials, divide the numerator and denominator by the highest power in the denominator and then apply the appropriate infinity properties. Formula used: Infinity properties ∞ + ∞ = ∞ lim x → ± ∞ c x = 0 lim x → ∞ x n = ∞ lim x → ∞ a n x n + a n − 1 x n − 1 + ... + c = ∞ when, a > 0 lim x → ∞ a n x n + a n − 1 x n − 1 + ... + c = − ∞ when, a < 0 lim x → − ∞ a n x n + a n − 1 x n − 1 + ... + c = − ∞ when, a > 0 and n is odd lim x → − ∞ a n x n + a n − 1 x n − 1 + ... + c = ∞ when, a > 0 and n is even lim x → − ∞ a n x n + a n − 1 x n − 1 + To determine (b) To show: The reaction rate attains one-half of the limiting value A when s = K. To determine (c) The substrate concentration at which the reaction rate is 75% of its limiting value

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 2.7, Problem 45E

To determine

(a)

To show:

A is the limiting reaction rate in the given Michaelis-Menten equation.

To determine

(b)

To show:

The reaction rate attains one-half of the limiting value A when s = K.

To determine

(c)

The substrate concentration at which the reaction rate is 75% of its limiting value

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Chapter 2.7, Problem 44E

Chapter 2.7, Problem 46E

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Chapter 2 Solutions

CALCULUS (CLOTH)

Ch. 2.1 - Prob. 1PQ Ch. 2.1 - Prob. 2PQ Ch. 2.1 - Prob. 3PQ Ch. 2.1 - Prob. 4PQ Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E

Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.2 - Prob. 1PQ Ch. 2.2 - Prob. 2PQ Ch. 2.2 - Prob. 3PQ Ch. 2.2 - Prob. 4PQ Ch. 2.2 - Prob. 5PQ Ch. 2.2 - Prob. 6PQ Ch. 2.2 - Prob. 7PQ Ch. 2.2 - Prob. 1E Ch. 2.2 - Prob. 2E Ch. 2.2 - Prob. 3E Ch. 2.2 - Prob. 4E Ch. 2.2 - Prob. 5E Ch. 2.2 - Prob. 6E Ch. 2.2 - Prob. 7E Ch. 2.2 - Prob. 8E Ch. 2.2 - Prob. 9E Ch. 2.2 - Prob. 10E Ch. 2.2 - Prob. 11E Ch. 2.2 - Prob. 12E Ch. 2.2 - Prob. 13E Ch. 2.2 - Prob. 14E Ch. 2.2 - Prob. 15E Ch. 2.2 - Prob. 16E Ch. 2.2 - Prob. 17E Ch. 2.2 - Prob. 18E Ch. 2.2 - Prob. 19E Ch. 2.2 - 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(a) To show: A is the limiting reaction rate in the given Michaelis-Menten equation.

Solution Summary: The author explains that A is the limiting reaction rate in the given Michaelis-Menten equation.

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(a) To show: A is the limiting reaction rate in the given Michaelis-Menten equation.

(b) To show: The reaction rate attains one-half of the limiting value A when s = K.

(c) The substrate concentration at which the reaction rate is 75% of its limiting value

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Chapter 2 Solutions

(a)

To show:

A is the limiting reaction rate in the given Michaelis-Menten equation.

(b)

To show:

The reaction rate attains one-half of the limiting value A when s = K.

(c)

The substrate concentration at which the reaction rate is 75% of its limiting value