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Published on November 22nd, 2013 | by Daphane Ng

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# Restriction enzymes and DNA palindromes

Certain molecules known as restriction enzymes are able to cut DNA strands in two. A restriction enzyme finds a specific sequence of nucleotides (represented by A’s, C’s, G’s and T’s) in a strand of DNA, called a recognition sequence, and then cuts the DNA at (or near) the location of this sequence.

In this problem we ask how many possible recognition sequences there are of various types.

(a) Recognition sequences vary in length, but are usually 4 to 8 nucleotides long.

How many possible nucleotide recognition sequences are there of length 4? Of length 5? Of length 8?

(b) Restriction sequences are often *palindromes*, meaning that they read the same backwards and forwards. There are two types of palindromes in this context.

The first type of palindrome is called a *mirror palindrome*. A sequence of DNA is mirror-palindromic if the sequence of A’s, C’s,
G’s, and T’s on the strand reads the same backwards and forwards, e.g. AAGCCGAA.

How many mirror-palindromic recognition sequences are there of length 4? Of length 5? Of length 8?

(c) The second type of palindrome is called an *inverted repeat palindrome*. In a DNA molecule there are two strands of nucleotides forming a double helix, and the sequence on one strand is *complementary* to the strand on the other. Complementary here means that if an A appears on one strand, then a T appears on the other strand in that position; and if a C appears on one strand, then a G must appear on the other strand in that position. Some examples of complementary sequences are

CAGCTG and AATCCGTC
GTCGAC TTAGGCAG

An inverted repeat palindrome is one that reads the same forward on one strand, as it reads backwards *on the complementary strand*. For example, of the two sequences above, CAGCTG is an inverted repeat palindrome but TTAGGCAG is not.

How many inverted repeat palindromic recognition sequences are there of length 4? Of length 5? Of length 8?

Question created by Chaitanya Rao, Daniel Mathews, Norman Do and Michael Evans

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