2. The kinetics of an enzyme are measured as a function of substrate concentration in the presence and absence of 100 uM inhibitor. Show calculations, include the table of values needed to make your graphs and provide full explanations for each of the following. Velocity (UM/minute) [S] (UM) No inhibitor Inhibitor 3 10.4 2.1 5 14.5 2.9 10 22.5 4.5 30 33.8 6.8 90 40.5 8.1 i) Calculate the values of Km and Vmax in the absence of the inhibitor? Show all calculations. Circle your final answers. Make sure units are included II) What are the values of Km and Vmax in the presence of the inhibitor? Show all calculations. Circle your final answers. Make sure units are included. iii) What type of inhibition is this? Explain your reasoning
2. The kinetics of an enzyme are measured as a function of substrate concentration in the presence and absence of 100 uM inhibitor. Show calculations, include the table of values needed to make your graphs and provide full explanations for each of the following. Velocity (UM/minute) [S] (UM) No inhibitor Inhibitor 3 10.4 2.1 5 14.5 2.9 10 22.5 4.5 30 33.8 6.8 90 40.5 8.1 i) Calculate the values of Km and Vmax in the absence of the inhibitor? Show all calculations. Circle your final answers. Make sure units are included II) What are the values of Km and Vmax in the presence of the inhibitor? Show all calculations. Circle your final answers. Make sure units are included. iii) What type of inhibition is this? Explain your reasoning
Chemistry & Chemical Reactivity
9th Edition
ISBN:9781133949640
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Chapter14: Chemical Kinetics: The Rates Of Chemical Reactions
Section: Chapter Questions
Problem 92SCQ
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Concept explainers
Catalysis and Enzymatic Reactions
Catalysis is the kind of chemical reaction in which the rate (speed) of a reaction is enhanced by the catalyst which is not consumed during the process of reaction and afterward it is removed when the catalyst is not used to make up the impurity in the product. The enzymatic reaction is the reaction that is catalyzed via enzymes.
Lock And Key Model
The lock-and-key model is used to describe the catalytic enzyme activity, based on the interaction between enzyme and substrate. This model considers the lock as an enzyme and the key as a substrate to explain this model. The concept of how a unique distinct key only can have the access to open a particular lock resembles how the specific substrate can only fit into the particular active site of the enzyme. This is significant in understanding the intermolecular interaction between proteins and plays a vital role in drug interaction.
Question
![**Enzyme Kinetics Analysis**
The kinetics of an enzyme are measured as a function of substrate concentration in the presence and absence of 100 µM inhibitor. The data below will enable the making of graphs and provide full explanations for the following requirements.
### Data Table
| Substrate Concentration [S] (µM) | Velocity (µM/minute) No inhibitor | Velocity (µM/minute) Inhibitor |
|------------------------------------|------------------------------------|---------------------------------|
| 3 | 10.4 | 2.1 |
| 5 | 14.5 | 2.9 |
| 10 | 22.5 | 4.5 |
| 30 | 33.8 | 6.8 |
| 90 | 40.5 | 8.1 |
### Questions and Calculations
**i) Calculate the values of Km and Vmax in the absence of the inhibitor. Show all calculations. Circle your final answers. Make sure units are included.**
To determine Km and Vmax, you can use methods like the Michaelis-Menten equation or a Lineweaver-Burk plot. Here are the steps laid out for a general approach using the Lineweaver-Burk plot:
1. **Reciprocal Plotting**:
- \( \frac{1}{V} \) vs. \( \frac{1}{[S]} \)
- Plot the data points and find the y-intercept (which corresponds to \( \frac{1}{V_{\text{max}}} \)) and the slope (which corresponds to \( \frac{K_m}{V_{\text{max}}} \)).
2. Alternatively, use software to find the best fit for Michaelis-Menten parameters:
- Use software tools to perform nonlinear regression fitting to the Michaelis-Menten equation and extract Km and Vmax.
**ii) What are the values of Km and Vmax in the presence of the inhibitor? Show all calculations. Circle your final answers. Make sure units are included.**
Follow the same approach as above with the data in the presence of the inhibitor.
**iii) What type of inhibition is this? Explain your reasoning.**
To determine the type of inhibition, you can analyze changes in Km and Vmax:
- **Competitive Inhibition**: Km increases and Vmax stays the same](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50ee8c08-bdb6-49cd-9014-91cd3b523354%2Fb1e100c7-9588-4e42-a603-a612b5d79e1f%2F93k7ztc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Enzyme Kinetics Analysis**
The kinetics of an enzyme are measured as a function of substrate concentration in the presence and absence of 100 µM inhibitor. The data below will enable the making of graphs and provide full explanations for the following requirements.
### Data Table
| Substrate Concentration [S] (µM) | Velocity (µM/minute) No inhibitor | Velocity (µM/minute) Inhibitor |
|------------------------------------|------------------------------------|---------------------------------|
| 3 | 10.4 | 2.1 |
| 5 | 14.5 | 2.9 |
| 10 | 22.5 | 4.5 |
| 30 | 33.8 | 6.8 |
| 90 | 40.5 | 8.1 |
### Questions and Calculations
**i) Calculate the values of Km and Vmax in the absence of the inhibitor. Show all calculations. Circle your final answers. Make sure units are included.**
To determine Km and Vmax, you can use methods like the Michaelis-Menten equation or a Lineweaver-Burk plot. Here are the steps laid out for a general approach using the Lineweaver-Burk plot:
1. **Reciprocal Plotting**:
- \( \frac{1}{V} \) vs. \( \frac{1}{[S]} \)
- Plot the data points and find the y-intercept (which corresponds to \( \frac{1}{V_{\text{max}}} \)) and the slope (which corresponds to \( \frac{K_m}{V_{\text{max}}} \)).
2. Alternatively, use software to find the best fit for Michaelis-Menten parameters:
- Use software tools to perform nonlinear regression fitting to the Michaelis-Menten equation and extract Km and Vmax.
**ii) What are the values of Km and Vmax in the presence of the inhibitor? Show all calculations. Circle your final answers. Make sure units are included.**
Follow the same approach as above with the data in the presence of the inhibitor.
**iii) What type of inhibition is this? Explain your reasoning.**
To determine the type of inhibition, you can analyze changes in Km and Vmax:
- **Competitive Inhibition**: Km increases and Vmax stays the same
![**Understanding the Kinetics of Penicillinase: A Step-by-Step Guide**
**Introduction:**
Penicillin is hydrolyzed and thereby rendered inactive by penicillinase, an enzyme present in some penicillin-resistant bacteria. The molecular weight of this enzyme in *Staphylococcus aureus* is 29.6 kilo Daltons (kDa). The amount of penicillin hydrolyzed in 2 minutes in a 10-mL solution containing 10^-9 g (1 ng) of purified penicillinase was measured as a function of the concentration of penicillin. Assume that the concentration of penicillin does not change appreciably during the assay.
*[Hint: Convert everything to the same concentration terms]*
**Task Overview:**
You are required to show all calculations and include spreadsheets and graphs to determine Km (Michaelis constant), Vmax (maximum velocity), and kcat (turnover number) for this enzyme. Ensure your final answers have correct units.
*[Additional hint: Note that [S] and amount hydrolyzed are already in concentration terms. So you don’t need to worry about the volume for calculating [S] and V.]*
**Data Provided:**
| Penicillin Concentration (µM) | Amount Hydrolyzed (nM) |
|-------------------------------|------------------------|
| 1 | 110 |
| 3 | 250 |
| 5 | 340 |
| 10 | 450 |
| 30 | 580 |
| 50 | 600 |
**Tasks:**
*i. Plot \( V_0 \) versus [S] and \( 1/V_0 \) vs \( 1/[S] \) for these data. Does penicillinase appear to obey Michaelis-Menten kinetics? Explain. If so, calculate the value of Km. Show all calculations. Circle your final answer.*
*ii. Calculate the value of Vmax. Show all calculations. Circle your final answer.*
*iii. What is the turnover number of penicillinase under these experimental conditions? Assume three active sites per enzyme molecule. Show all calculations. Circle your final answer.*
*iv. What is the catalytic efficiency of penicillinase under these experimental conditions? Show all calculations. Circle your final answer.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50ee8c08-bdb6-49cd-9014-91cd3b523354%2Fb1e100c7-9588-4e42-a603-a612b5d79e1f%2F5ganxls_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding the Kinetics of Penicillinase: A Step-by-Step Guide**
**Introduction:**
Penicillin is hydrolyzed and thereby rendered inactive by penicillinase, an enzyme present in some penicillin-resistant bacteria. The molecular weight of this enzyme in *Staphylococcus aureus* is 29.6 kilo Daltons (kDa). The amount of penicillin hydrolyzed in 2 minutes in a 10-mL solution containing 10^-9 g (1 ng) of purified penicillinase was measured as a function of the concentration of penicillin. Assume that the concentration of penicillin does not change appreciably during the assay.
*[Hint: Convert everything to the same concentration terms]*
**Task Overview:**
You are required to show all calculations and include spreadsheets and graphs to determine Km (Michaelis constant), Vmax (maximum velocity), and kcat (turnover number) for this enzyme. Ensure your final answers have correct units.
*[Additional hint: Note that [S] and amount hydrolyzed are already in concentration terms. So you don’t need to worry about the volume for calculating [S] and V.]*
**Data Provided:**
| Penicillin Concentration (µM) | Amount Hydrolyzed (nM) |
|-------------------------------|------------------------|
| 1 | 110 |
| 3 | 250 |
| 5 | 340 |
| 10 | 450 |
| 30 | 580 |
| 50 | 600 |
**Tasks:**
*i. Plot \( V_0 \) versus [S] and \( 1/V_0 \) vs \( 1/[S] \) for these data. Does penicillinase appear to obey Michaelis-Menten kinetics? Explain. If so, calculate the value of Km. Show all calculations. Circle your final answer.*
*ii. Calculate the value of Vmax. Show all calculations. Circle your final answer.*
*iii. What is the turnover number of penicillinase under these experimental conditions? Assume three active sites per enzyme molecule. Show all calculations. Circle your final answer.*
*iv. What is the catalytic efficiency of penicillinase under these experimental conditions? Show all calculations. Circle your final answer.*
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