Biochemistry
9th Edition
ISBN: 9781319114671
Author: Lubert Stryer, Jeremy M. Berg, John L. Tymoczko, Gregory J. Gatto Jr.
Publisher: W. H. Freeman
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K = 5 μm
V = 10 μm/s
Transcribed Image Text:5. Now let's interpret the constants \( V \) and \( K \), starting with \( V \). Evaluate \(\lim_{{s \to \infty}} R(s)\) and use the result to explain why \( V \) is the maximum production rate. Is there any value of \( s \) for which the production rate equals \( V \)?
![**Enzymes and Michaelis–Menten Kinetics**
Enzymes are catalysts that facilitate the biochemical reactions that occur within all living organisms. One of the fundamental laws of enzyme kinetics was proposed by Leonor Michaelis and Maud Menten in 1913. The law has been supported by laboratory experiments and explained through mathematical modeling. Today, Michaelis–Menten kinetics are used in many biological models.
An enzyme molecule is designed to “fit” another molecule called a substrate. The substrate (S) and enzyme (E) form an intermediate complex (ES), which then dissociates to form the final end-product of the reaction (P) and the original enzyme (which can be re-used; see figure). An important question concerns the rate at which product molecules are formed. Under certain assumptions, Michaelis–Menten kinetics relates the rate of production of P to the amount of S present.
**Diagram Explanation**
The diagram shows the following sequence:
1. **E + S**: Enzyme (E) combines with substrate (S) to form an intermediate complex.
2. **ES**: This intermediate complex is denoted as the enzyme-substrate complex (ES).
3. **E + P**: The complex dissociates into the enzyme (E) and the product (P), allowing the enzyme to be reused.
**Mathematical Representation**
1. We let \( R \) be the rate of production of the final product \( P \) and we let \( s \) be the concentration of the substrate \( S \) initially present. Concentrations are measured in units such as micro-moles \( (\mu M) \), while \( R \) is measured in \( \mu M/s \). (Time is usually measured in seconds.) The Michaelis-Menten law states that
\[
R(s) = \frac{V s}{K + s}
\]
This relationship provides a crucial understanding of how enzymes work and the rate at which they can produce products in biological systems.](https://content.bartleby.com/qna-images/question/4e3da8d7-5e45-4b35-92f7-ecdb5bd91ee7/e934e974-b4c3-4bd6-b0e8-42d52f02ea15/0hh3z6n_processed.jpeg)
Transcribed Image Text:**Enzymes and Michaelis–Menten Kinetics**
Enzymes are catalysts that facilitate the biochemical reactions that occur within all living organisms. One of the fundamental laws of enzyme kinetics was proposed by Leonor Michaelis and Maud Menten in 1913. The law has been supported by laboratory experiments and explained through mathematical modeling. Today, Michaelis–Menten kinetics are used in many biological models.
An enzyme molecule is designed to “fit” another molecule called a substrate. The substrate (S) and enzyme (E) form an intermediate complex (ES), which then dissociates to form the final end-product of the reaction (P) and the original enzyme (which can be re-used; see figure). An important question concerns the rate at which product molecules are formed. Under certain assumptions, Michaelis–Menten kinetics relates the rate of production of P to the amount of S present.
**Diagram Explanation**
The diagram shows the following sequence:
1. **E + S**: Enzyme (E) combines with substrate (S) to form an intermediate complex.
2. **ES**: This intermediate complex is denoted as the enzyme-substrate complex (ES).
3. **E + P**: The complex dissociates into the enzyme (E) and the product (P), allowing the enzyme to be reused.
**Mathematical Representation**
1. We let \( R \) be the rate of production of the final product \( P \) and we let \( s \) be the concentration of the substrate \( S \) initially present. Concentrations are measured in units such as micro-moles \( (\mu M) \), while \( R \) is measured in \( \mu M/s \). (Time is usually measured in seconds.) The Michaelis-Menten law states that
\[
R(s) = \frac{V s}{K + s}
\]
This relationship provides a crucial understanding of how enzymes work and the rate at which they can produce products in biological systems.
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