[SagarikaGhosh]

A restriction endonuclease is an enzyme which cuts the DNA sequence at the middle instead of at the terminal like an exonuclease. Restriction endonucleases are molecular scissors that cut the sequence at a specific region known as the recognition site. Depending on the type of Restriction Endonuclease, the cut ends can be blunt (clean cut) or sticky( hanging ends) . Most RE’s recognition sites are composed of 4 to 6 nucleotides.

EcoR1 is a restriction endonuclease derived from the bacteria Escherichia coli. EcoR1’s recognition site is GAATTC , it scans the DNA sequence for this site and makes a sticky cut.

NNNNNNNNNNNNGAATTCNNNNNNNNNNNNNNNN

EcoR1

NNNNNNNNNNNNG
AATTCNNNNNNNNNNNNNNNN
( where N can be any nucleotide A,G,T or C)
These sticky ends can easily join back together and hence the name.
As per your question, you have to calculate the number of times (frequency) that the recognition site for EcoR1 will be present in a given DNA sequence. Here’s the solution:

Desired Sequence – G A A T T C
Size of sequence – 1 2 3 4 5 6
Random DNA sequence of 6 ntds- N N N N N N
Now each N can be any 1 of 4 possibilities - A,G,C or T
Hence for each N there are 4 options, and there are 6 Ns.
Therefore, the frequency of GAATTC is 4x4x4x4x4x4 ( 4 multiplied 6 times) or 46. This is equal to 4096 bp. Therefore, the recognition site for EcoR1 can occur once every 4096 bp.