Ten E.coli cells with ¹⁵N-dsDNA are incubated in medium containing ¹⁴N nucleotide. After 60 minutes, how many E.coli cells will have DNA totally free from ¹⁵N?

To answer this question, we need to understand the process of DNA replication in E. coli and how nitrogen isotopes (15N and 14N) are incorporated into the DNA strands during replication.

Step 1: Initial Condition

Initially, we have 10 E. coli cells, all of which contain DNA labeled with 15N, which is a heavier isotope of nitrogen. The DNA in these cells is double-stranded, meaning each strand contains the 15N isotope.

Step 2: Incubation in 14N Medium

These cells are now placed in a medium containing 14N nucleotides. The 14N isotope is lighter, and when the cells replicate their DNA, the new strands will be synthesized using the 14N nucleotides. This results in hybrid DNA where one strand contains 15N (old strand) and the other strand contains 14N (new strand).

Step 3: DNA Replication and Cell Division Cycle

In E. coli, the typical cell cycle, including DNA replication and cell division, takes approximately 20 minutes. In the 60-minute period given in the problem, we can determine the number of divisions that will take place:

Number of divisions = Total time / Time per division
                     = 60 minutes / 20 minutes/division
                     = 3 divisions

Step 4: Total Number of Cells

Starting with 10 cells, after 3 divisions, the total number of E. coli cells will be:

Total cells = Initial number of cells × 2^3
            = 10 × 8
            = 80 cells

Step 5: DNA Composition After Each Division

After each division, the DNA composition of the cells will change:

• First Division: Each of the 10 original cells divides into two, producing 20 cells. Each of these 20 cells will have hybrid DNA, with one strand containing 15N and the other strand containing 14N.
• Second Division: The 20 cells from the first division will divide again to form 40 cells. In this generation:
  • 20 cells will have hybrid DNA (15N/14N),
  • 20 cells will have completely 14N/14N DNA (free from 15N).
• Third Division: The 40 cells from the second division will divide into 80 cells. In this generation:
  • 20 cells will still have hybrid DNA (15N/14N),
  • 60 cells will have completely 14N/14N DNA (free from 15N).

Step 6: Final Count of Cells with DNA Free from 15N

After the third division, there will be 60 E. coli cells that have completely 14N/14N DNA, meaning they are free from 15N.

Conclusion:

Therefore, the final answer is that after 60 minutes, 60 E. coli cells will have DNA completely free from 15N.