If E.coli containing `N^(15)-N^(15)` DNA was allowed to grow for 80 minutes in medium containing `N^(14)` then, what would be the percentage of light density and hybrid density DNA molecule ?

Options

A. 87.5% light density , 12.5% hybrid density
B. 75% light density , 25% hybrid density
C. 25% light density , 75% hybrid density
D. 12.5% light density , 87.5% hybrid density

Answer

To solve the problem regarding the percentage of light density and hybrid density DNA molecules in E. coli after growing in a medium containing \(N^{14}\) for 80 minutes, we can follow these steps:

### Step 1: Understand the Initial Conditions
Initially, the E. coli contains only \(N^{15}\) DNA, which is heavy due to the presence of the heavy nitrogen isotope.

**Hint:** Remember that \(N^{15}\) is heavier than \(N^{14}\).

### Step 2: Growth in Medium with \(N^{14}\)
After the initial growth, the E. coli is transferred to a medium containing \(N^{14}\). During replication, the DNA will incorporate \(N^{14}\) into the newly synthesized strands.

**Hint:** DNA replication involves pairing of bases and incorporation of nucleotides from the medium.

### Step 3: Determine the DNA Density Types
1. **Light Density DNA (L)**: This will consist entirely of \(N^{14}\) DNA.
2. **Hybrid Density DNA (H)**: This will consist of one strand of \(N^{15}\) and one strand of \(N^{14}\) (i.e., one old strand and one new strand).

### Step 4: Calculate the Proportions After One Round of Replication
After one round of replication in the \(N^{14}\) medium:
- Each original \(N^{15}\) DNA molecule will produce two daughter molecules:
- One will be \(N^{14}/N^{15}\) (hybrid).
- The other will be \(N^{14}/N^{14}\) (light).

Thus, after one generation:
- 50% of the DNA will be hybrid density (H).
- 50% of the DNA will be light density (L).

**Hint:** Consider how many generations have occurred and how DNA replication works.

### Step 5: Determine the Percentage After 80 Minutes
Assuming that the E. coli divides approximately every 20 minutes, in 80 minutes, there will be about 4 generations.

1. **After 1st generation**:
- 50% Hybrid (H)
- 50% Light (L)

2. **After 2nd generation**:
- Hybrid (H) from the first generation will produce:
- 50% Hybrid (H)
- 50% Light (L)
- Light (L) remains 50%.
- Total:
- 25% H (from H) + 50% L = 25% H + 75% L

3. **After 3rd generation**:
- Repeat the process:
- 50% of 25% H = 12.5% H
- 50% of 75% L = 37.5% L
- Total:
- 12.5% H + 37.5% L = 12.5% H + 87.5% L

4. **After 4th generation**:
- Repeat again:
- 50% of 12.5% H = 6.25% H
- 50% of 87.5% L = 43.75% L
- Total:
- 6.25% H + 43.75% L = 6.25% H + 93.75% L

### Final Calculation
After 4 generations:
- **Hybrid Density DNA (H)**: 6.25%
- **Light Density DNA (L)**: 93.75%

### Conclusion
Thus, after 80 minutes, the percentage of light density DNA molecules is 93.75%, and the percentage of hybrid density DNA molecules is 6.25%.