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GATE 2020 BT Q.44: solution and answer

GATE 2020 · BTQ.44 · 2 marks · NAT

E. coli was grown in ¹⁵N medium for several generations. Cells were then transferred to ¹⁴N medium, allowed to grow for 4 generations and DNA was isolated immediately. The proportion of total DNA with intermediate density is ____ (round off to 2 decimal places).

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Answer and solution

ANSWER

The proportion of total DNA with intermediate (hybrid) density after 4 generations in ¹⁴N medium is 2/16 = 0.125 ≈ 0.13.

Official answer: 0.11 to 0.14Source: Official answer key, GATE 2020 BT (IIT Delhi)

  1. Start: 1 DNA duplex, fully heavy — both strands ¹⁵N.

  2. Semiconservative replication: in every generation, each existing duplex's two strands separate and each strand templates one new ¹⁴N strand, so every duplex present produces exactly 2 daughter duplexes per generation → total duplexes double each generation.

  3. Generation 1: the single ¹⁵N/¹⁵N duplex's two heavy strands each pair with a new ¹⁴N strand → 2 duplexes, both hybrid (¹⁵N/¹⁴N, intermediate density).

  4. Generation 2: each hybrid duplex separates into its heavy strand (pairs with a new light strand → stays hybrid) and its light strand (pairs with a new light strand → becomes fully light). From the 2 duplexes we get 4: the same 2 original heavy strands still yield 2 hybrid duplexes, and the 2 light strands now yield 2 fully-light duplexes.

  5. Key rule: because the two original ¹⁵N strands are never degraded and never re-paired with each other, they are the only strands that can ever produce a hybrid duplex — so the number of hybrid duplexes stays fixed at 2 in every generation from generation 1 onward, while the total number of duplexes keeps doubling.

  6. After n generations (n ≥ 1): total duplexes = 2^n; hybrid (intermediate-density) duplexes = 2.

  7. For n = 4: total duplexes = 2^4 = 16; hybrid duplexes = 2.

  8. Since every duplex carries the same amount of DNA, the proportion of total DNA mass at intermediate density = hybrid duplexes / total duplexes = 2/16 = 0.125 ≈ 0.13 (rounded to 2 decimal places).

KEY IDEA

In semiconservative replication starting from one fully-¹⁵N duplex, only the original two heavy parental strands ever end up paired with a new ¹⁴N strand — so the number of hybrid (intermediate-density) duplexes stays fixed at 2 in every generation after the first, while the total number of duplexes doubles each generation (2^n after n generations). Hence the hybrid fraction after n generations (n ≥ 1) is 2/2^n, not 1/2 (which is only true at n = 1) and not something that keeps halving indefinitely toward the "half the DNA is hybrid forever" myth.

WATCH OUT FOR

Assuming the fraction of hybrid DNA stays at 1/2 for all generations (true only after generation 1), or conversely assuming hybrid duplexes double along with total duplexes (they don't — the two original heavy strands are a fixed, non-renewable pool, since a strand is never destroyed or re-paired with another old strand). Both errors are avoided by explicitly tracking that hybrid count = 2 (constant) and total = 2^n (growing) separately.

From the GATE 2020 BT paper. Every question of this paper · Download the full paper · All 21 Gene expression questions, with notes

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