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) 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

Loose-leaf Version For Calculus: Early Transcendentals

4th Edition

ISBN: 9781319055912

Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Question

Chapter 2.7, Problem 49E

To determine

(a)

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

To determine

(b)

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 48E

Chapter 2.7, Problem 50E

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Chapter 2 Solutions

Loose-leaf Version For Calculus: Early Transcendentals

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

(b) 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)

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

(b)

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