Question

Cleavage frequency. The restriction enzyme AluI cleaves at the sequence \(5^{\prime}-\mathrm{AGCT}-3^{\prime},\) and \(N\) ot \(\mathrm{I}\) cleaves at \(5^{\prime}-\mathrm{GCGGCCGC}\) \(3^{\prime}\). What would be the average distance between cleavage sites for each enzyme on digestion of double-stranded DNA? Assume that the DNA contains equal proportions of \(A, G, C\) and \(T\)

Short answer

The average distance between cleavage sites for AluI is 256 bp and for NotI is 65536 bp.

Step-by-step solution

Determine Base Probability

Since the DNA consists of equal proportions of A, G, C, and T, each base has a probability of 1/4 or 0.25 of occurring at any given position in the DNA sequence.

Calculate Cleavage Probability for AluI

AluI recognizes the sequence AGCT. The probability of randomly finding the specific sequence AGCT in a DNA strand is the product of the probabilities of each base occurring, \[P(\text{AGCT}) = (0.25)^4\]Calculating this,\[P(\text{AGCT}) = 0.25 \times 0.25 \times 0.25 \times 0.25 = 0.00390625.\]

Calculate Average Distance for AluI

Since the probability of the AGCT sequence is 0.00390625, on average, one such sequence will occur every 1 divided by this probability. \[\text{Average distance for AluI} = \frac{1}{0.00390625} = 256.\]

Calculate Cleavage Probability for NotI

NotI recognizes the sequence GCGGCCGC. The probability of this sequence occurring in a DNA strand is the product of the probabilities of each base, \[P(\text{GCGGCCGC}) = (0.25)^8\]Calculating this,\[P(\text{GCGGCCGC}) = 0.25^8 = 0.0000152588.\]

Calculate Average Distance for NotI

Since the probability of finding GCGGCCGC is 0.0000152588, on average, one such sequence will occur every 1 divided by this probability. \[\text{Average distance for NotI} = \frac{1}{0.0000152588} \approx 65536.\]

Key concepts

DNA Cleavage

DNA cleavage is an essential process in molecular biology where specific enzymes, known as restriction enzymes, cut DNA molecules at specific sequences. These enzymes act like molecular scissors. They are crucial for DNA analysis and manipulation in research and biotechnology.
Restriction enzymes identify short DNA sequences, called recognition sites, and cleave the DNA at or near these sequences. This activity is vital for genetic engineering, cloning, and mapping DNA.

• AluI is an enzyme that cleaves at the sequence 5'-AGCT-3'
• NotI is another enzyme that cleaves at the sequence 5'-GCGGCCGC-3'

Each enzyme's specificity allows for precise cutting, which is fundamental for experimental accuracy.

Base Probability

When considering the randomness of DNA sequence arrangements, the concept of base probability becomes important. If the DNA has equal amounts of adenine (A), guanine (G), cytosine (C), and thymine (T), then the probability of any specific base being in a particular position is 0.25 (or 1/4). This assumption simplifies the calculation of more complex sequence probabilities such as those recognized by restriction enzymes.
The probability for a sequence like AGCT, recognized by AluI, is calculated by multiplying the likelihood of each base appearing in sequence:

• \[P(\text{AGCT}) = (0.25)^4 = 0.00390625\]

This probability indicates that in a random DNA sequence, AGCT appears with a probability of about 0.39%.

Average Distance Between Cleavage Sites

To determine how frequently a sequence is recognized and cleaved in the DNA, we calculate the average distance between cleavage sites. This involves taking the inverse of the sequence probability. By understanding this distance, scientists can predict enzyme activity along a strand of DNA.
For AluI, recognizing AGCT with a probability of 0.00390625, the average distance is calculated as:

• \[\frac{1}{0.00390625} = 256\]

This implies AGCT will generally appear every 256 bases.
For NotI with the sequence GCGGCCGC, the process is similar, and the lower sequence probability means a longer average distance:

• \[\frac{1}{0.0000152588} \approx 65536\]

Thus, GCGGCCGC appears approximately every 65,536 bases.

Sequence Recognition

Sequence recognition by restriction enzymes is crucial for their function. These enzymes are protein molecules that scan the DNA strand to find their specific sequence fit. This scanning means they bind to a recognition site, allowing the enzyme to perform its cutting function, which is pivotal for applications such as DNA cloning and genome mapping.
The sequence needs to match exactly with the recognition site for the enzyme to bind and cleave.

• AluI identifies the sequence AGCT, precisely recognizing and cutting at specific sites
• NotI identifies and binds to GCGGCCGC, offering precise DNA manipulation

Understanding sequence recognition enhances the efficiency and accuracy of many genetic research techniques and ensures effective DNA analysis.