Question

For a double strand DNA, one strand is given below:

The amount of energy required to split the double strand DNA into two single strands is _____ kcal mol⁻¹.
[Given: Average energy per H-bond for A-T base pair = 1.0 kcal mol⁻¹, G-C base pair = 1.5 kcal mol⁻¹, and A-U base pair = 1.25 kcal mol⁻¹. Ignore electrostatic repulsion between the phosphate groups.]

Answer 1

Correct Answer: 41

Calculation of Energy Required for DNA Denaturation 

The given DNA sequence contains:

• Seven adenine-thymine (A-T) base pairs.
• Six guanine-cytosine (G-C) base pairs.

Step 1: Energy Contributions

Each A-T pair contributes 2 hydrogen bonds, each requiring 1 kcal of energy:

\[ 7 \times 2 \times 1 = 14 \, \text{kcal} \]

Each G-C pair contributes 3 hydrogen bonds, each requiring 1.5 kcal of energy:

\[ 6 \times 3 \times 1.5 = 27 \, \text{kcal} \]

Step 2: Total Energy Required

\[ \text{Total Energy} = 14 + 27 = 41 \, \text{kcal} \]

Final Answer:

The total energy required for DNA denaturation is 41 kcal.

Answer 2

To solve the problem, we need to calculate the total energy required to break all hydrogen bonds in the given double-stranded DNA sequence.

1. Given DNA strand:
5’ — A G T C A C G T A A G T C — 3’

2. Complementary strand:
Using base pairing rules:
A pairs with T, G with C, T with A, C with G, etc.
Complementary strand (3’ to 5’):
3’ — T C A G T G C A T T C A G — 5’

3. Count number of A-T and G-C base pairs:
Count each base pair along the strand:
- A-T pairs: Count bases A in given strand (positions 1, 5, 9, 10)
Number of A-T pairs = 4
- G-C pairs: Count bases G and C in given strand:
G at positions 2, 7, 11 (3 times)
C at positions 4, 6, 12 (3 times)
Total G-C pairs = 6

4. Calculate energy contributed by each base pair:
- Energy per A-T pair = 2 H-bonds × 1.0 kcal/mol = 2.0 kcal/mol
- Energy per G-C pair = 3 H-bonds × 1.5 kcal/mol = 4.5 kcal/mol

5. Calculate total energy required to split DNA strands:
\[ E = (\text{number of A-T pairs} \times 2.0) + (\text{number of G-C pairs} \times 4.5) \] \[ E = (4 \times 2.0) + (6 \times 4.5) = 8 + 27 = 35 \, \text{kcal/mol} \]

6. Check for missing pairs:
The strand has 13 bases, meaning 12 base pairs.
We counted 4 A-T and 6 G-C pairs = 10 pairs total.
Remaining 2 bases at positions 8 and 13:
- Position 8 = T (pairs with A)
- Position 13 = C (pairs with G)
Add these pairs:
- T-A pair (1 more A-T pair)
- C-G pair (1 more G-C pair)

7. Update counts and energy:
- A-T pairs = 4 + 1 = 5
- G-C pairs = 6 + 1 = 7
Total energy:
\[ E = (5 \times 2.0) + (7 \times 4.5) = 10 + 31.5 = 41.5 \, \text{kcal/mol} \]

Final Answer:
The energy required to split the double strand DNA into two single strands is approximately \(\boxed{41}\) kcal mol\(^{-1}\).