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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![**Title: Enzyme Kinetics Analysis of Wild-Type and Mutant Enzymes**
---
**Graph Explanation:**
The provided graph is a Michaelis-Menten plot illustrating the enzymatic activity of a wild-type (WT) enzyme and a mutant (V105A) enzyme, both isolated from the bacterium *Staphylococcus aureus*. The plot shows enzyme velocity (\(v\), in \(\mu\)mol/s/mg) versus substrate concentration (\([s]\), in mM).
- **Curve for WT (black circles):** The wild-type enzyme shows a gradual increase in reaction velocity as substrate concentration increases. The curve appears to begin leveling off around a velocity of 0.5 \(\mu\)mol/s/mg.
- **Curve for V105A (red circles):** The mutant enzyme demonstrates a rapid increase in reaction velocity, leveling off at a higher maximum velocity compared to the WT, around 1.25 \(\mu\)mol/s/mg.
Both curves highlight the differences in kinetic behaviors between the wild-type and mutant enzymes.
---
**Questions and Discussion:**
**(a) Estimate the \(K_m\) and \(V_{max}\) for the wild-type and mutant enzyme from the graph.**
- **Wild-Type (WT):**
- \(V_{max}\) is approximately 0.5 \(\mu\)mol/s/mg.
- \(K_m\) is roughly where the velocity is half of \(V_{max}\), estimated around 250 mM.
- **Mutant (V105A):**
- \(V_{max}\) is approximately 1.25 \(\mu\)mol/s/mg.
- \(K_m\) is estimated around 100 mM, where the velocity reaches half of \(V_{max}\).
**(b) Calculate the \(K_{cat}\) and \(K_{cat}/K_m\) for the wild-type and mutant enzyme based on your estimated values in (a) if the total enzyme concentration is 0.5 \(\mu\mol\)/mg.**
- **Wild-Type (WT):**
- \(K_{cat} = \frac{V_{max}}{[\text{Enzyme}]} = \frac{0.5}{0.5} = 1 \, \text{s}^{-1}\)
- \(K_{cat](https://content.bartleby.com/qna-images/question/f800a840-0309-4834-92a3-4244363b7afa/e4124010-0a1b-4617-965c-d407d6565b9c/afpypzs_processed.jpeg)
Transcribed Image Text:**Title: Enzyme Kinetics Analysis of Wild-Type and Mutant Enzymes**
---
**Graph Explanation:**
The provided graph is a Michaelis-Menten plot illustrating the enzymatic activity of a wild-type (WT) enzyme and a mutant (V105A) enzyme, both isolated from the bacterium *Staphylococcus aureus*. The plot shows enzyme velocity (\(v\), in \(\mu\)mol/s/mg) versus substrate concentration (\([s]\), in mM).
- **Curve for WT (black circles):** The wild-type enzyme shows a gradual increase in reaction velocity as substrate concentration increases. The curve appears to begin leveling off around a velocity of 0.5 \(\mu\)mol/s/mg.
- **Curve for V105A (red circles):** The mutant enzyme demonstrates a rapid increase in reaction velocity, leveling off at a higher maximum velocity compared to the WT, around 1.25 \(\mu\)mol/s/mg.
Both curves highlight the differences in kinetic behaviors between the wild-type and mutant enzymes.
---
**Questions and Discussion:**
**(a) Estimate the \(K_m\) and \(V_{max}\) for the wild-type and mutant enzyme from the graph.**
- **Wild-Type (WT):**
- \(V_{max}\) is approximately 0.5 \(\mu\)mol/s/mg.
- \(K_m\) is roughly where the velocity is half of \(V_{max}\), estimated around 250 mM.
- **Mutant (V105A):**
- \(V_{max}\) is approximately 1.25 \(\mu\)mol/s/mg.
- \(K_m\) is estimated around 100 mM, where the velocity reaches half of \(V_{max}\).
**(b) Calculate the \(K_{cat}\) and \(K_{cat}/K_m\) for the wild-type and mutant enzyme based on your estimated values in (a) if the total enzyme concentration is 0.5 \(\mu\mol\)/mg.**
- **Wild-Type (WT):**
- \(K_{cat} = \frac{V_{max}}{[\text{Enzyme}]} = \frac{0.5}{0.5} = 1 \, \text{s}^{-1}\)
- \(K_{cat
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