Calculate the number of week hydrogen bonds in a DNA strand `204Å` long with 15% thymine bases.

Options

A. 154
B. 162
C. 138
D. 120

Answer

To calculate the number of weak hydrogen bonds in a DNA strand that is 204 Å long with 15% thymine bases, follow these steps:

### Step 1: Calculate the number of base pairs in the DNA strand
The distance between two base pairs in DNA is approximately 3.4 Å. To find the total number of base pairs in the DNA strand, divide the total length of the DNA by the distance between the base pairs.

\[ \text{Number of base pairs} = \frac{\text{Length of DNA}}{\text{Distance between base pairs}} = \frac{204 \, \text{Å}}{3.4 \, \text{Å}} = 60 \]

### Step 2: Determine the percentage of adenine (A) and thymine (T) bases
Since thymine (T) makes up 15% of the bases, adenine (A) will also make up 15% because A pairs with T. Therefore, the total percentage of A and T is:

\[ \text{Percentage of A and T} = 15\% + 15\% = 30\% \]

### Step 3: Calculate the number of base pairs that are A-T
To find the number of base pairs that are A-T, multiply the total number of base pairs by the percentage of A and T:

\[ \text{Number of A-T base pairs} = \frac{30}{100} \times 60 = 18 \]

### Step 4: Calculate the number of hydrogen bonds between A and T
Adenine and thymine form 2 hydrogen bonds. Therefore, the total number of hydrogen bonds between A and T is:

\[ \text{Hydrogen bonds from A-T} = 18 \times 2 = 36 \]

### Step 5: Determine the percentage of guanine (G) and cytosine (C) bases
The remaining percentage of bases will be guanine and cytosine. Since A and T make up 30%, the remaining percentage is:

\[ \text{Percentage of G and C} = 100\% - 30\% = 70\% \]

This means guanine and cytosine each make up half of this remaining percentage:

\[ \text{Percentage of G} = \text{Percentage of C} = \frac{70}{2} = 35\% \]

### Step 6: Calculate the number of base pairs that are G-C
Now, calculate the number of G-C base pairs:

\[ \text{Number of G-C base pairs} = \frac{35}{100} \times 60 = 42 \]

### Step 7: Calculate the number of hydrogen bonds between G and C
Guanine and cytosine form 3 hydrogen bonds. Therefore, the total number of hydrogen bonds between G and C is:

\[ \text{Hydrogen bonds from G-C} = 42 \times 3 = 126 \]

### Step 8: Calculate the total number of hydrogen bonds
Finally, add the hydrogen bonds from A-T and G-C to get the total number of weak hydrogen bonds in the DNA strand:

\[ \text{Total hydrogen bonds} = \text{Hydrogen bonds from A-T} + \text{Hydrogen bonds from G-C} = 36 + 126 = 162 \]

Thus, the total number of weak hydrogen bonds in the DNA strand is **162**.

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