A heavy DNA `(N^(15)N^(15))` of E. coli is allowed to replicated in `N^(14)` medium for 80 minutes. What would be the proportions of light `(N^(14)-N^(14))` and hybrid densities of DNA `(N^(14)-N^(15))` molecules?

Options

A. `50:50`
B. `75:25%`
C. `87.5:12.5%`
D. all hybrid

Answer

To solve the problem of determining the proportions of light (N14-N14) and hybrid (N14-N15) densities of DNA molecules after allowing heavy DNA (N15-N15) of E. coli to replicate in N14 medium for 80 minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- We start with E. coli containing heavy DNA (N15-N15). This means both strands of the DNA are heavy.

2. **First Replication Cycle (0-20 minutes)**:
- During the first 20 minutes, the heavy DNA (N15-N15) replicates in the N14 medium.
- Each of the two strands of the original heavy DNA will serve as a template for new strands synthesized from the N14 medium.
- After this cycle, we have:
- 2 hybrid DNA molecules (N14-N15) (one strand from N15 and one from N14).

3. **Second Replication Cycle (20-40 minutes)**:
- In the next 20 minutes, the two hybrid DNA molecules (N14-N15) will replicate.
- Each hybrid DNA will again use the N14 medium to synthesize new strands.
- After this cycle, we have:
- 2 hybrid DNA (N14-N15) from the original hybrids.
- 2 light DNA (N14-N14) from the new strands synthesized.
- Total after this cycle: 2 hybrids + 2 lights = 4 DNA molecules.

4. **Third Replication Cycle (40-60 minutes)**:
- In this cycle, the 4 DNA molecules (2 hybrids and 2 lights) will replicate.
- Each of the 4 strands will again use the N14 medium.
- After this cycle, we have:
- 2 hybrids (N14-N15) from the original hybrids.
- 4 light DNA (N14-N14) from the new strands synthesized.
- Total after this cycle: 2 hybrids + 4 lights = 6 DNA molecules.

5. **Fourth Replication Cycle (60-80 minutes)**:
- In the final cycle, the 6 DNA molecules (2 hybrids and 4 lights) will replicate.
- Each of the 6 strands will again use the N14 medium.
- After this cycle, we have:
- 2 hybrids (N14-N15) from the original hybrids.
- 8 light DNA (N14-N14) from the new strands synthesized.
- Total after this cycle: 2 hybrids + 8 lights = 10 DNA molecules.

6. **Final Count**:
- After 80 minutes, we have:
- 2 hybrid DNA (N14-N15)
- 8 light DNA (N14-N14)
- Therefore, the proportions are:
- Light (N14-N14): 8
- Hybrid (N14-N15): 2

7. **Calculating the Ratio**:
- The ratio of light to hybrid DNA is 8:2, which simplifies to 4:1.

### Conclusion:
The final proportions of light and hybrid densities of DNA molecules after 80 minutes are:
- Light (N14-N14): 8
- Hybrid (N14-N15): 2
- Ratio of light to hybrid = 4:1