A culture of E. coli bacteria, with its DNA completely labeled with the heavy isotope ¹⁵ N , is transferred to a medium containing the normal isotope ¹⁴ N . After 80 minutes of growth, the DNA is extracted and analyzed via CsCl density gradient centrifugation. What will be the ratio of light DNA to hybrid DNA molecules in the sample?

Step-by-step solution

The generation time of E. coli is 20 minutes. Number of generations in 80 minutes = 80 20 = 4 . Total number of DNA molecules after 4 generations = 2^4 = 16 . Initially, the DNA is completely heavy ( ¹⁵ N -¹⁵ N ), containing 2 heavy strands. During replication in a ¹⁴ N medium, these 2 heavy strands separate and act as templates, forming exactly 2 hybrid DNA molecules ( ¹⁵ N -¹⁴ N ) in all subsequent generations. The remaining DNA molecules will be completely light ( ¹⁴ N -¹⁴ N ). Number of light DNA molecules = 16