Python Programming for Biology: Bioinformatics and Beyond

Restriction enzyme example

Taking the DNA example a little further, let’s consider a restriction enzyme called HindIII

that is commonly used in molecular biology and which cuts DNA at the specific sequence

AAGCTT.  Using  a  simple  probabilistic  model  about  the  likelihood  of  finding  a  given

letter at a given position in an otherwise random DNA sequence, we can estimate various

properties, like how often the enzyme cuts or what the size of the fragments will be after

cutting.  A  DNA  sequence  actually  isn’t  totally  random,  but  the  approximation  is

nonetheless good enough to get useful predictions.

Assuming that the nucleotide at one position does not depend in any way on what the

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nucleotides  are  at  the  other  positions  (i.e.  the  nucleotides  at  different  positions  are

independent),  we  can  calculate  the  probability  of  a  HindIII  site  at  any  six  residue  sub-

sequence to be Pr(A) × Pr(A) × Pr(G) × Pr(C) × Pr(T) × Pr(T). This is about one cut in

4096  (4

6

)  positions,  if  we  assumed  equal  probabilities  for  all  nucleotides.  Hence  for  a

DNA sequence of length N we would expect N ×

1

/

4096

restriction enzyme cut sites. Also,

on  average  we  could  expect  the  separation  to  be  about  4096  bases.  Calculating  the

probability of the cut site using the non-equal nucleotide probabilities calculated above we

get:

cutSite = 'AAGCTT'

probSite = 1.0 # Starting value

for letter in cutSite:

probSite *= letterProbs[letter]

print(probSite) # 0.00023637 – approx one in 4230

Because the occurrence of a site is effectively random we will expect a distribution of

different values for the number of cut sites in a given length and also for the lengths of the

fragments.  In  other  words  because  the  sites  are  random,  and  not  regular,  the  spacing

between sites will generally be more or less than 4230. We will consider models for the

shape of such probability distributions later in this chapter.