Final Answer: The molar ratio of hybrid DNA (15N–14N) to light DNA (14N–14N) after four generations is 0.14 (that is, 1:7 as a simple ratio).

Introduction

Understanding how the proportions of heavy, hybrid, and light DNA change across generations in E. coli is a classic application of the Meselson–Stahl experiment and semi-conservative DNA replication.

This type of numerical question frequently appears in CSIR NET, GATE, and NEET exams, testing conceptual clarity on DNA labeling with 15N and 14N.

Step-by-step Solution

Initial growth in 15NH4Cl

The question states that E. coli is first grown for many generations in a medium containing 15NH4Cl, so all chromosomal DNA strands are heavy (15N–15N) at the start.

Shift to 14NH4Cl (start of generation 1)

After the culture is shifted to a medium containing 14NH4Cl, DNA replication proceeds in a semi-conservative manner: each daughter duplex receives one old (parental) strand and one new (light) strand.

Therefore, the first replication in 14N medium produces 100% hybrid DNA (15N–14N) and 0% light DNA.

Tracking proportions generation by generation

A key rule is that hybrid molecules always replicate to yield one hybrid and one light molecule, while light molecules produce two light molecules.

Let the total DNA after each generation be normalized to 1 (or 100%). After each generation in the 14N medium, the fraction of hybrid DNA halves, because each hybrid duplex yields exactly one hybrid among two daughters.

Generational calculations in 14N medium

  • After 1st generation: Hybrid = 1; Light = 0.
  • After 2nd generation: Hybrid = 1/2 = 0.5; Light = 1/2 = 0.5.
  • After 3rd generation: Hybrid = 1/4 = 0.25; Light = 3/4 = 0.75.
  • After 4th generation: Hybrid = 1/8 = 0.125; Light = 7/8 = 0.875.

Thus, after four generations the culture contains 12.5% hybrid DNA and 87.5% light DNA.

Convert to molar ratio of hybrid to light DNA

Hybrid fraction = 1/8; Light fraction = 7/8.

So,

Hybrid : Light = (1/8) : (7/8) = 1 : 7 ≈ 0.14.

Rounded to two decimal places, the molar ratio of hybrid DNA to light DNA after four generations is 0.14.

Concept Reinforcement

In semi-conservative replication, the fraction of hybrid molecules after n generations in light medium (starting from fully heavy DNA and counting generations in light medium from 1) is (1 / 2n−1).

The complementary fraction, 1 − (1 / 2n−1), corresponds to light DNA, enabling quick calculation of ratios such as hybrid : light = 1 : (2n−1 − 1).

For n = 4, this gives hybrid : light = 1 : (23 − 1) = 1 : 7, confirming the ratio 0.14 used in the numerical answer.