Based on theoretical estimates, the probability of occurrence of nitrogen bases in adjacent positions in a DNA strand is radom . Identify the expected number of recognitions sites in the `lambda` phage genome of 49 kb long having recognition sequences of 6pb(5'GAATTC3'3'CTTAAG5').

Options

A. 4096
B. 14
C. 12
D. 256

Answer

To determine the expected number of recognition sites in the lambda phage genome (49 kb long) for the recognition sequence of 6 base pairs (5' GAATTC 3' and 3' CTTAAG 5'), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Length of the Genome**:
- The lambda phage genome is 49 kb, which is equivalent to 49,000 base pairs.

2. **Identify the Recognition Sequence**:
- The recognition sequence we are interested in is 6 base pairs long (GAATTC).

3. **Calculate the Probability of the Recognition Sequence**:
- Each base in DNA can be one of four nucleotides (A, T, G, C).
- The probability of any specific base occurring is \( \frac{1}{4} \).
- For a sequence of 6 bases, the probability of the specific sequence (GAATTC) occurring is:
\[ P = \left(\frac{1}{4}\right)^6 = \frac{1}{4096} \]

4. **Determine the Expected Number of Recognition Sites**:
- To find the expected number of occurrences of this sequence in the 49,000 base pairs, we can use the formula:
\[ \text{Expected Number} = \text{Total Number of Base Pairs} \times P \]
- However, we need to consider that the recognition sequence can start at any position from 1 to 49,000 - 6 + 1 (i.e., 49,000 - 5 = 48,995 positions).
- Therefore, the expected number of recognition sites can be calculated as:
\[ \text{Expected Number} = 48,995 \times \frac{1}{4096} \]

5. **Calculate the Expected Number**:
- Performing the calculation:
\[ \text{Expected Number} \approx 48,995 \div 4096 \approx 11.97 \]
- Rounding this to the nearest whole number gives approximately 12.

### Final Answer:
The expected number of recognition sites in the lambda phage genome is **12**.

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