4. Graphing the results from kinetics experiments with enzyme inhibitors The following kinetic data were obtained for an enzyme in the absence of inhibitor (1), and in the presence of two different inhibitors (2) and (3) at 5 mM concentration. Assume [Er] is the same in each experiment. [S] (mm) 1 (1) v (umol/mL sec 12 20 29 35 40 2 4 8 (2) v (umol/mL sec (3) v (umol/mL sec 5.5 9 13 16 12 18 Plot these data as double-reciprocal Lineweaver-Burk plots and use your graph to answers a. and b. a. Determine Vmax and Km for the enzyme. What type of inhibition does each inhibitor display? 4.3 8 14 21 26

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**Enzyme Kinetics with Inhibitors: A Study Using Lineweaver-Burk Plots**

In enzyme kinetics experiments, understanding the effects of inhibitors on enzyme activity is crucial. This study involves analyzing kinetic data for an enzyme in the absence and presence of two different inhibitors. The experimental conditions are controlled such that the enzyme concentration (\([E]_t\)) remains constant across all trials.

### Experimental Data

The kinetic data are presented below with substrate concentration \([S]\) in mM, and the reaction velocity \(v\) in \(\mu\text{mol/mL} \cdot \text{sec}\):

| \([S]\) (mM) | \(v\) (1) \(\mu\text{mol/mL} \cdot \text{sec}\) | \(v\) (2) \(\mu\text{mol/mL} \cdot \text{sec}\) | \(v\) (3) \(\mu\text{mol/mL} \cdot \text{sec}\) |
|--------------|-----------------------------------|-----------------------------------|-----------------------------------|
| 1            | 12                                | 4.3                              | 5.5                              |
| 2            | 20                                | 8                                | 9                                |
| 4            | 29                                | 14                               | 13                               |
| 8            | 35                                | 21                               | 16                               |
| 12           | 40                                | 26                               | 18                               |

### Analysis Instructions

1. **Plotting**: Transform these data into a double-reciprocal Lineweaver-Burk plot.
   
2. **Determination of Kinetic Parameters**:
   - **\(V_{\max}\)**: Maximum reaction velocity.
   - **\(K_m\)**: Michaelis constant, reflecting substrate affinity.

3. **Questions**:
   - **(a)** Determine \(V_{\max}\) and \(K_m\) for the enzyme using the plots.
   - **(b)** Identify the type of inhibition exhibited by each inhibitor.

### Objective

Understanding the type of inhibition helps in identifying how inhibitors impact the enzyme's efficiency and affinity. This knowledge aids in drug design and in elucidating enzyme mechanisms in biochemical pathways.
Transcribed Image Text:**Enzyme Kinetics with Inhibitors: A Study Using Lineweaver-Burk Plots** In enzyme kinetics experiments, understanding the effects of inhibitors on enzyme activity is crucial. This study involves analyzing kinetic data for an enzyme in the absence and presence of two different inhibitors. The experimental conditions are controlled such that the enzyme concentration (\([E]_t\)) remains constant across all trials. ### Experimental Data The kinetic data are presented below with substrate concentration \([S]\) in mM, and the reaction velocity \(v\) in \(\mu\text{mol/mL} \cdot \text{sec}\): | \([S]\) (mM) | \(v\) (1) \(\mu\text{mol/mL} \cdot \text{sec}\) | \(v\) (2) \(\mu\text{mol/mL} \cdot \text{sec}\) | \(v\) (3) \(\mu\text{mol/mL} \cdot \text{sec}\) | |--------------|-----------------------------------|-----------------------------------|-----------------------------------| | 1 | 12 | 4.3 | 5.5 | | 2 | 20 | 8 | 9 | | 4 | 29 | 14 | 13 | | 8 | 35 | 21 | 16 | | 12 | 40 | 26 | 18 | ### Analysis Instructions 1. **Plotting**: Transform these data into a double-reciprocal Lineweaver-Burk plot. 2. **Determination of Kinetic Parameters**: - **\(V_{\max}\)**: Maximum reaction velocity. - **\(K_m\)**: Michaelis constant, reflecting substrate affinity. 3. **Questions**: - **(a)** Determine \(V_{\max}\) and \(K_m\) for the enzyme using the plots. - **(b)** Identify the type of inhibition exhibited by each inhibitor. ### Objective Understanding the type of inhibition helps in identifying how inhibitors impact the enzyme's efficiency and affinity. This knowledge aids in drug design and in elucidating enzyme mechanisms in biochemical pathways.
The table presents data specific to enzyme kinetics, showing substrate concentration and reaction rates with and without inhibitors. Here's the transcription and description:

| [S] (mM) | no I (µmol/mL sec) | #1 (mM/min) | #2        | no I       | #1        | #2        |
|----------|-------------------|-------------|-----------|------------|-----------|-----------|
| 1        | 12                | 4.3         | 5.5       |            |           |           |
| 2        | 20                | 8           | 9         |            |           |           |
| 4        | 29                | 14          | 13        |            |           |           |
| 8        | 35                | 21          | 16        |            |           |           |
| 12       | 40                | 26          | 18        |            |           |           |

### Explanation:
1. **Columns:**
   - **[S] (mM):** Represents substrate concentration in millimolar.
   - **no I (µmol/mL sec):** Enzyme activity without any inhibitor, measured in micromoles per milliliter per second.
   - **#1 and #2 (mM/min):** Reaction rates with two different inhibitors, given in millimoles per minute.
   - **1/[S]:** Intended to be the inverse of substrate concentration, but the data is not filled in.
   - **1/Vo:** Represents the inverse of initial velocity for each condition (no inhibitor, inhibitor #1, inhibitor #2); this data is missing.

The table data could be used to analyze enzyme activity with and without inhibitors, potentially for constructing a Lineweaver-Burk plot, which aids in determining kinetic parameters like Km and Vmax.
Transcribed Image Text:The table presents data specific to enzyme kinetics, showing substrate concentration and reaction rates with and without inhibitors. Here's the transcription and description: | [S] (mM) | no I (µmol/mL sec) | #1 (mM/min) | #2 | no I | #1 | #2 | |----------|-------------------|-------------|-----------|------------|-----------|-----------| | 1 | 12 | 4.3 | 5.5 | | | | | 2 | 20 | 8 | 9 | | | | | 4 | 29 | 14 | 13 | | | | | 8 | 35 | 21 | 16 | | | | | 12 | 40 | 26 | 18 | | | | ### Explanation: 1. **Columns:** - **[S] (mM):** Represents substrate concentration in millimolar. - **no I (µmol/mL sec):** Enzyme activity without any inhibitor, measured in micromoles per milliliter per second. - **#1 and #2 (mM/min):** Reaction rates with two different inhibitors, given in millimoles per minute. - **1/[S]:** Intended to be the inverse of substrate concentration, but the data is not filled in. - **1/Vo:** Represents the inverse of initial velocity for each condition (no inhibitor, inhibitor #1, inhibitor #2); this data is missing. The table data could be used to analyze enzyme activity with and without inhibitors, potentially for constructing a Lineweaver-Burk plot, which aids in determining kinetic parameters like Km and Vmax.
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