Complete and Exact Peptide Sequence Analysis Based on Propositional Logic - Mathematical Approaches to Polymer Sequence Analysis and Related Problems - page 9

Example 1.1. A small peptide with sequence Leu-His-Cys-Thr-Val ionized by only
one charge, considering only d D 2 decimal digits, has an observed weight of
w 0 D .131:18 18:02/ C .155:16 18:02/ C .121:16 18:02/ C .119:12 18:02/
C .117:15 18:02/ C 19:02 ˙ ı D 572:69 ˙ ı.
Several different types of fragments can be obtained during the fragmentation pro-
cess. In particular, there are three possible standard N-terminal ionized fragments,
called a-ion, b-ion and c-ion, and three possible standard C-terminal ones, called
x-ion, y-ion and z-ion, as illustrated in Fig. 1.2 . Note that b-ions and y-ions are gen-
erally the most common.
Again, each fragment has a weight which is not simply the sum of those of its
component amino acids. By considering the number f of fragment peaks selected
in the spectrum; the set F Df 1;2;:::;f g of the indices j corresponding to such
peaks in decreasing weight order; the set

W Df w 1 ; w 2 ;:::; w f g ; w j 2 R C

of the weights corresponding to such peaks (so that w 0 remains the weight of the

overall peptide); the sets

Df y 1 ;y 2 ;:::;y n g ; i 2 Z C Y j j D 1;:::;f

of the numbers of molecules of each component contained in the fragment of weight
w j , j D 1;:::;f; the number t max of all the possible standard types of fragments
that should be considered for the current analysis; the set

T Df 1;2;:::;t max g

of the indices t corresponding to such types; the maximum number of electrical
charges e max that a ion may retain in the current analysis; the set

E Df 1;2;:::;e max g

of the numbers e of electrical charges that a ion may retain in the current analysis;
the type t j 2 T of the fragment of weight w j ;j D 1;:::;f; the number e j 2 E of
electrical charges retained by the fragment of weight w j , j D 1;:::;f, the relation
that can be observed in the spectrum between the weight of each fragment and the
weights of its components is the following.

P i 2N

Œy i .a i c a / C c t C c 0 e j
e j

w j D ˙ ı; j D 1;:::;f (1.2)

Va l u e s c a and c 0 are as above, and c t is a constant value depending on the type t j
of the fragment. When considering d D 3 decimal digits, c t is 28:002 for a-ions,
0.000 for b-ions, 17.031 for c-ions, 44.009 for x-ions, 18.015 for y-ions and 1.992
for z-ions.