To estimate the number of cleavage sites in a particular piece of DNA with a known size, you can apply the formula N/4ⁿ where N is the number of base pairs in the target DNA and n is the number of bases in the recognition sequence of the restriction enzyme. If the recognition sequence for BamHI is GGATCC and the $\lambda$ phage DNA contains approximately 48,500 bp, how many cleavage sites would you expect?

Verified step by step guidance

1. Identify the total number of base pairs (N) in the DNA. Here, N = 48,500 bp.
2. Determine the length of the recognition sequence (n) for the restriction enzyme BamHI. The sequence is GGATCC, which has 6 bases, so n = 6.
3. Apply the formula to estimate the number of cleavage sites: \( \frac{N}{4^n} \). This means you divide the total base pairs by 4 raised to the power of the recognition sequence length.
4. Calculate \( 4^n \) by raising 4 to the power of 6, since the recognition sequence is 6 bases long.
5. Divide the total number of base pairs (48,500) by the value obtained in the previous step to estimate the number of BamHI cleavage sites in the phage DNA.

Key Concepts

Restriction Enzyme Recognition Sites

Restriction enzymes recognize specific short DNA sequences, called recognition sites, where they cut the DNA. For example, BamHI recognizes the sequence GGATCC, which is 6 bases long. The frequency of these sites in a DNA molecule depends on the length and sequence specificity of the enzyme.

Probability of Recognition Site Occurrence

The expected number of recognition sites in a DNA sequence can be estimated using the formula N/4ⁿ, where N is the total number of base pairs and n is the length of the recognition sequence. This formula assumes equal base distribution and random sequence, calculating how often a specific sequence appears by chance.

Application of the Formula to DNA Size

By applying the formula to a DNA molecule of known size, such as a 48,500 bp phage DNA, and a recognition sequence length of 6 bases (BamHI), you can estimate the number of cleavage sites. This helps predict how many fragments will result from enzyme digestion.