Energy Required to Split Double Strand DNA into Single Strands

To determine the amount of energy required to split the double-stranded DNA into two single strands, we need to calculate the total number of hydrogen bonds (H-bonds) formed between the given single strand and its complementary strand, and then multiply by their respective H-bond energies.

1. Analysis of the Given DNA Sequence

The single strand of DNA is given from the $5'$ to $3'$ end as: $\text{5' -- A -- G -- T -- C -- A -- C -- G -- T -- A -- A -- G -- T -- C -- 3'}$

Counting the occurrence of each nitrogenous base in this strand:

• Adenine ($\text{A}$): $4$ (at positions $1, 5, 9, 10$)
• Thymine ($\text{T}$): $3$ (at positions $3, 8, 12$)
• Guanine ($\text{G}$): $3$ (at positions $2, 7, 11$)
• Cytosine ($\text{C}$): $3$ (at positions $4, 6, 13$)

Total number of bases $= 4 + 3 + 3 + 3 = 13$

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2. Base Pairing and Number of Hydrogen Bonds

In double-stranded DNA:

• $\text{A--T}$ Base Pairs:

  • Total number of $\text{A--T}$ pairs $= \text{Count of A} + \text{Count of T} = 4 + 3 = 7$ pairs.
  • Each $\text{A--T}$ base pair contains $2$ hydrogen bonds.
  • Total number of H-bonds in $\text{A--T}$ pairs $= 7 \times 2 = 14\text{ H-bonds}$.

• $\text{G--C}$ Base Pairs:

  • Total number of $\text{G--C}$ pairs $= \text{Count of G} + \text{Count of C} = 3 + 3 = 6$ pairs.
  • Each $\text{G--C}$ base pair contains $3$ hydrogen bonds.
  • Total number of H-bonds in $\text{G--C}$ pairs $= 6 \times 3 = 18\text{ H-bonds}$.

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3. Calculation of Required Energy

Given:

• Average energy per H-bond for an $\text{A--T}$ pair $= 1.0\text{ kcal mol}^{-1}$
• Average energy per H-bond for a $\text{G--C}$ pair $= 1.5\text{ kcal mol}^{-1}$

Calculating the total energy: $\text{Energy for A--T H-bonds} = 14 \times 1.0\text{ kcal mol}^{-1} = 14\text{ kcal mol}^{-1}$

$\text{Energy for G--C H-bonds} = 18 \times 1.5\text{ kcal mol}^{-1} = 27\text{ kcal mol}^{-1}$

$\text{Total Energy required} = 14 + 27 = 41\text{ kcal mol}^{-1}$

Final Answer: 41