Dihydrofolate reductase (DHFR) is an enzyme that reduces 7,8-dihydrofolate (DHF) to 5,6,7,8- tetrahydrofolate, a step in the biosynthesis of thymidine. Methotrexate (MTX) a structural analogue of dihydrofolate, inhibits this enzyme. MTX has been used in cancer therapies because the inhibition of DHFR restricts thymidine production required for cell division. In the absence of thymidine the cancerous cells cannot multiply. Using the following data of DHFR activity in the presence of MTX, i) Determine the inhibition mechanism of MTX and the maximum reaction rate. If Km for DHFR is 0.100 uM, what is Ki? ii) [DHF](MM) Rate w/100 nM Rate w/200 nM Rate w/50 nM MTX (mMs-¹) MTX MTX (mMs ¹) (mMs ¹) 7.38 5.56 3.72 8.84 7.38 5.55 9.46 8.29 6.65 9.79 8.84 7.38 369 12

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### Dihydrofolate Reductase (DHFR) and Methotrexate (MTX)

**Introduction**

Dihydrofolate reductase (DHFR) is an enzyme that reduces 7,8-dihydrofolate (DHF) to 5,6,7,8-tetrahydrofolate, a step crucial in the biosynthesis of thymidine. Methotrexate (MTX), a structural analogue of dihydrofolate, inhibits this enzyme. MTX has been employed in cancer therapies due to its inhibition of DHFR, which restricts thymidine production needed for cell division. This inhibition impedes the multiplication of cancerous cells.

**Objective**

Using the provided data of DHFR activity in the presence of MTX, the goals are to:
1. Determine the inhibition mechanism of MTX and the maximum reaction rate.
2. Calculate the inhibition constant \(K_i\) if the \(K_m\) for DHFR is 0.100 µM.

**Data Table**

The table below displays the reaction rate (in mMs\(^-1\)) of DHFR with varying concentrations of DHF and MTX:

| [DHF](mM) | Rate w/ 50 nM MTX (mMs\(^-1\)) | Rate w/ 100 nM MTX (mMs\(^-1\)) | Rate w/ 200 nM MTX (mMs\(^-1\)) |
|-----------|-------------------------------|---------------------------------|---------------------------------|
| 3         | 7.38                          | 5.56                            | 3.72                            |
| 6         | 8.84                          | 7.38                            | 5.55                            |
| 9         | 9.46                          | 8.29                            | 6.65                            |
| 12        | 9.79                          | 8.84                            | 7.38                            |

**Analysis**

- **Step 1:** Determine the inhibition mechanism
  - Compare the rates of reaction at different concentrations of MTX.
  - Analyze how the inhibition changes based on varying concentrations of DHF.
  - Identify patterns that suggest whether MTX acts as a competitive, non-competitive, or uncompetitive inhibitor.
  
- **Step 2:** Calculate the inhibition constant \(K_i\)
  - Use the given \(K
Transcribed Image Text:### Dihydrofolate Reductase (DHFR) and Methotrexate (MTX) **Introduction** Dihydrofolate reductase (DHFR) is an enzyme that reduces 7,8-dihydrofolate (DHF) to 5,6,7,8-tetrahydrofolate, a step crucial in the biosynthesis of thymidine. Methotrexate (MTX), a structural analogue of dihydrofolate, inhibits this enzyme. MTX has been employed in cancer therapies due to its inhibition of DHFR, which restricts thymidine production needed for cell division. This inhibition impedes the multiplication of cancerous cells. **Objective** Using the provided data of DHFR activity in the presence of MTX, the goals are to: 1. Determine the inhibition mechanism of MTX and the maximum reaction rate. 2. Calculate the inhibition constant \(K_i\) if the \(K_m\) for DHFR is 0.100 µM. **Data Table** The table below displays the reaction rate (in mMs\(^-1\)) of DHFR with varying concentrations of DHF and MTX: | [DHF](mM) | Rate w/ 50 nM MTX (mMs\(^-1\)) | Rate w/ 100 nM MTX (mMs\(^-1\)) | Rate w/ 200 nM MTX (mMs\(^-1\)) | |-----------|-------------------------------|---------------------------------|---------------------------------| | 3 | 7.38 | 5.56 | 3.72 | | 6 | 8.84 | 7.38 | 5.55 | | 9 | 9.46 | 8.29 | 6.65 | | 12 | 9.79 | 8.84 | 7.38 | **Analysis** - **Step 1:** Determine the inhibition mechanism - Compare the rates of reaction at different concentrations of MTX. - Analyze how the inhibition changes based on varying concentrations of DHF. - Identify patterns that suggest whether MTX acts as a competitive, non-competitive, or uncompetitive inhibitor. - **Step 2:** Calculate the inhibition constant \(K_i\) - Use the given \(K
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