Python Programming for Biology: Bioinformatics and Beyond

Table  11.2.   The  relative  entropy  formulation  to  measure  sequence  repetitiveness.

The  repetitiveness  of  a  biological  sequence  may  be  formulated  mathematically  by

calculating  a  relative  entropy  value  D

KL

 (the  Kullback-Leibler  divergence).  This  is

simply  the  summation,  considering  all  the  residue  (amino  acid  or  nucleotide,

depending  on  the  molecule)  types,  of  the  observed  proportion  of  each  type  (P

i

)

multiplied  by  the  log-ratio  of  the  observed  proportion  divided  by  the  proportion

expected in random sequences (Q

i,

which is always 0.25 in the above example). The

relative entropy is illustrated for various degrees of sequence repetition, showing that

the measure represents the variety of different residue types, in a sample of fixed size.