Step 1: Understanding the Concept:
This problem requires calculating the sizes of DNA fragments produced by restriction digestion of a circular recombinant plasmid.
To find the fragment sizes, we must map the positions of the restriction sites relative to each other on the circular plasmid map.
Key Formula or Approach:
The total size of the recombinant plasmid is the sum of the vector size and the insert size:
\[ \text{Total Size} = \text{Vector Size} + \text{Insert Size} \]
Using the given values:
\[ \text{Total Size} = 2800\text{ bp} + 1200\text{ bp} = 4000\text{ bp} \]
Let us set the EcoRI site as the reference point ($0\text{ bp}$) on this circular $4000\text{ bp}$ map.
Step 2: Detailed Explanation:
The cloning sites are adjacent, meaning the $1200\text{ bp}$ insert is located between the BamHI and EcoRI sites.
If the EcoRI site is at coordinate $0\text{ bp}$ (or $4000\text{ bp}$), the BamHI site is located adjacent to it.
Since the insert is $1200\text{ bp}$ long, it spans from coordinate $0\text{ bp}$ to $1200\text{ bp}$.
The remaining $2800\text{ bp}$ of the plasmid consists of the vector backbone, spanning from $1200\text{ bp}$ back to $4000\text{ bp}$.
The vector contains an XhoI site located $300\text{ bp}$ upstream of the BamHI site.
This position corresponds to coordinate:
\[ 4000\text{ bp} - 300\text{ bp} = 3700\text{ bp} \]
The recombinant plasmid is digested to completion with EcoRI and XhoI.
The digestion sites are:
One EcoRI site at coordinate $1200\text{ bp}$ (the insert-vector junction).
One vector XhoI site at coordinate $3700\text{ bp}$.
One internal XhoI site within the insert, located at an unknown position $x$ between $0\text{ bp}$ and $1200\text{ bp}$.
This digestion yields three fragments:
- Fragment 1 is between the EcoRI site ($1200\text{ bp}$) and the vector XhoI site ($3700\text{ bp}$):
\[ 3700\text{ bp} - 1200\text{ bp} = 2500\text{ bp} \]
This calculation confirms that one of the fragments must be $2500\text{ bp}$, which rules out options A and B.
- The remaining $1500\text{ bp}$ region of the plasmid is cleaved by the internal XhoI site at position $x$, producing two smaller fragments:
Fragment 2 (from $3700\text{ bp}$ through the $4000/0\text{ bp}$ junction to $x$): size = $300 + x$.
Fragment 3 (from $x$ to $1200\text{ bp}$): size = $1200 - x$.
The sum of these two fragments must be $1500\text{ bp}$ ($4000\text{ bp} - 2500\text{ bp} = 1500\text{ bp}$).
Let us test the remaining options:
- In Option C, the sizes are $700\text{ bp}$ and $800\text{ bp}$ (sum = $1500\text{ bp}$). If we set $300 + x = 700$, we find $x = 400\text{ bp}$, which is a valid position within the $1200\text{ bp}$ insert.
- In Option D, the sizes are $1200\text{ bp}$ and $300\text{ bp}$ (sum = $1500\text{ bp}$). Setting $300 + x = 300$ yields $x = 0$, meaning the internal XhoI site would overlap with the cloning site, which contradicts the problem.
Therefore, the correct fragment sizes are $2500\text{ bp}$, $700\text{ bp}$, and $800\text{ bp}$.
Step 3: Final Answer:
The DNA fragments visible on the gel correspond to 2500, 700, and 800 bp.