how many fragments?

Question

If i have a string of 34 letters, how many unique fragments of five letters can I obtain? The letters are contiguous.

More specifically, I need to know how many peptides (of five amino acid residues each) I can obtain from a larger peptide that 34 amino acid residues in length. For example the larger peptide is:

VPTELSAISMLYLDENEKVVLKNYQDMVVEGCGC

So, I can obtain a fragment of VPTEL, PTELS, etc...how many of these five residue fragments are possible?

Please also let me know what formula you used to get the answer.

Answer 1

This is really more of a math than a biology question. It's a bit unclear whether the order of the amino acids in the peptides of length 5 matters, but I would assume it does because your polymer will be different depending on the order of the amino acid monomers. This is to say that ABCDE is not the same as AEDBC. So the formula you need here is for permutations - how many ways you can take a set of 5 items out of a set of 34 in which order does count. If order didn't matter and it was just the unique sets of 5 that mattered you could use combinations instead.

The formula for permutations is

P(n,r) = n! / (n-r)!

The ! is the factorial sign which means multiplying together all the integers below and including the number. For example 4! = 4 x 3 x 2 x 1 = 24.

P(n,r) is the number of permutations of r items you can take from a full list of length n. So we're looking for P(34,5) which equals:

34! / (34-5)! = 34! / 29!

I'll let you figure out the answer from here, but it's a lot! You can find the value of the factorials online so you don't need to multiply everything out.

Note that on old calculators permutations were done with the nPr button while combinations were done with the nCr button. Make sure you understand the difference between them.