How many H-bonds are formed between the two strands of dsDNA of `170A^(@)` length if the cytosine is `20%`

Options

A. 130
B. 110
C. 120
D. 180

Answer

To determine the number of hydrogen bonds formed between the two strands of double-stranded DNA (dsDNA) of 170 Å length, given that cytosine constitutes 20% of the bases, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the Length of One Base Pair**:
- The length of one base pair in DNA is approximately 3.4 Å.

2. **Calculate the Total Number of Base Pairs**:
- To find the number of base pairs in a 170 Å length of DNA, divide the total length by the length of one base pair:
\[ \text{Number of base pairs} = \frac{170 \text{ Å}}{3.4 \text{ Å/base pair}} = 50 \text{ base pairs} \]

3. **Calculate the Percentage of Cytosine and Guanine**:
- Given that cytosine (C) is 20%, and since guanine (G) pairs with cytosine, guanine will also be 20%. Therefore:
- Percentage of G = 20%
- Percentage of C = 20%
- Total percentage of G-C pairs = 20% + 20% = 40%

4. **Calculate the Number of G-C Base Pairs**:
- Since 40% of the base pairs are G-C pairs:
\[ \text{Number of G-C base pairs} = 50 \text{ base pairs} \times 0.40 = 20 \text{ G-C base pairs} \]

5. **Calculate the Percentage of Adenine and Thymine**:
- The remaining percentage of base pairs will be adenine (A) and thymine (T):
\[ \text{Percentage of A + T} = 100\% - 40\% = 60\% \]
- Since A pairs with T, both A and T will constitute 30% each.

6. **Calculate the Number of A-T Base Pairs**:
- Therefore, the number of A-T base pairs is:
\[ \text{Number of A-T base pairs} = 50 \text{ base pairs} \times 0.60 = 30 \text{ A-T base pairs} \]

7. **Calculate the Total Number of Hydrogen Bonds**:
- Each G-C pair forms 3 hydrogen bonds, and each A-T pair forms 2 hydrogen bonds.
- Total hydrogen bonds from G-C pairs:
\[ \text{Hydrogen bonds from G-C} = 20 \text{ G-C pairs} \times 3 \text{ H-bonds/pair} = 60 \text{ H-bonds} \]
- Total hydrogen bonds from A-T pairs:
\[ \text{Hydrogen bonds from A-T} = 30 \text{ A-T pairs} \times 2 \text{ H-bonds/pair} = 60 \text{ H-bonds} \]

8. **Sum the Total Hydrogen Bonds**:
- Finally, add the hydrogen bonds from both types of pairs:
\[ \text{Total hydrogen bonds} = 60 \text{ H-bonds (G-C)} + 60 \text{ H-bonds (A-T)} = 120 \text{ H-bonds} \]

### Final Answer:
The total number of hydrogen bonds formed between the two strands of dsDNA of 170 Å length is **120**.

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