Eco RI and Rsa I restriction endonucleases require 6 bp and 4 bp sequences respectively for cleavage. In a 10 kb DNA fragment how many probable cleavage sites are present for these enzymes

Options

A. 0 Eco RI and 10 Rsa I
B. 1 Eco RI and 29 Rsa I
C. 4 Eco RI and 69 Rsa I
D. 2 Eco RI and 39 Rsa I

Explanation

To solve the problem of determining the probable cleavage sites for the restriction endonucleases Eco RI and Rsa I in a 10 kb DNA fragment, we can follow these steps:

### Step 1: Understand the DNA Length
- The length of the DNA fragment is given as 10 kb (kilobases).
- Since 1 kb equals 1000 base pairs, 10 kb equals 10,000 base pairs.

### Step 2: Determine Recognition Sites for Each Enzyme
- **Eco RI** requires a recognition sequence of 6 base pairs.
- **Rsa I** requires a recognition sequence of 4 base pairs.

### Step 3: Calculate the Number of Cleavage Sites
- The number of possible recognition sites for a restriction enzyme can be calculated using the formula \(4^n\), where \(n\) is the number of base pairs in the recognition site.

#### For Eco RI:
- The recognition sequence is 6 base pairs.
- Therefore, the number of possible cleavage sites is:
\[ 4^6 = 4096 \]

#### For Rsa I:
- The recognition sequence is 4 base pairs.
- Therefore, the number of possible cleavage sites is:
\[ 4^4 = 256 \]

### Step 4: Calculate the Number of Cleavage Sites in the 10 kb DNA Fragment
- To find the probable number of cleavage sites in the 10,000 base pairs of DNA, we divide the total length of the DNA by the number of base pairs in each recognition site.

#### For Eco RI:
- The number of cleavage sites is:
\[ \text{Number of cleavage sites} = \frac{10,000 \text{ base pairs}}{4096 \text{ base pairs/site}} \approx 2.44 \]
- Since we can only have whole cleavage sites, we round down to 2.

#### For Rsa I:
- The number of cleavage sites is:
\[ \text{Number of cleavage sites} = \frac{10,000 \text{ base pairs}}{256 \text{ base pairs/site}} \approx 39.06 \]
- Rounding down gives us 39 cleavage sites.

### Final Answer
- For Eco RI, there are approximately **2 cleavage sites**.
- For Rsa I, there are approximately **39 cleavage sites**.

### Summary
- Eco RI: 2 cleavage sites
- Rsa I: 39 cleavage sites