5. Consider the amino acid sequence of a section of a protein that is 5 amino ac

Question

5. Consider the amino acid sequence of a section of a protein that is 5 amino acids long. Assume the sequence is a random selection of the 20 amino acids which are all equally likely to appear in any location of the sequence.

What is the probability the sequence is pro-leu-gly-leu-val ?

What is the probability the sequence is arg-arg-arg-arg-arg ?

What is the probability the sequence is composed only of a single type of amino acid?

What is the probability the sequence has no his?

What is the probability the sequence has none of lys, arg or his?

What is the probability the sequence has no amino acids other than lys, arg or his?

Explanation / Answer

1) total number of 5 amino acid long sequence = 20^5   {as there are 20 options to fill each place }

probbaility of any uniques sequence = 1/20^5

hence

probability the sequence is pro-leu-gly-leu-val = 1/20^5

2)

probability the sequence is arg-arg-arg-arg-arg = 1/20^5

3)

probability the sequence is composed only of a single type of amino acid = 20 /20^5 = 1/20^4

there are 20 ways to select one amino acid (say A) , then sequence is fixed A-A-A-A-A

hence 20/20^5 = 1/20^4

4)

probability the sequence has no his

number of sequence without "his" = 19^5

hence required probability = (19^5/20^5) = 0.773780

5)the probability the sequence has none of lys, arg or his

similar to previous part there are 17 ways to fill any position

hence required probability = 17^5 /20^5

6)the probability the sequence has no amino acids other than lys, arg or his

= 3^5/20^5      {there are 3 ways to fill any position}

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