Complete and Exact Peptide Sequence Analysis Based on Propositional Logic - Mathematical Approaches to Polymer Sequence Analysis and Related Problems - page 12

Those clauses are called interpretation clauses. In order to get rid of the fact that
the weight of peptides and of their fragments is not simply the sum of those of their
component amino acids, we define now a different (theoretical) model of polymeric
compound, as follows.

Definition 1.9. Given a (real) single charge peptide of observed weight w 0 ,the nor-
malized peptide associated with it is a (theoretical) polymeric compound having
weight w 0 .c a C c 0 /. The possible components of such normalized peptide are
(theoretical) components having the following weights (which are those that amino
acids assume in the internal part of the peptidic chain)

A Df .a 1 c a /; .a 2 c a /;:::;.a n c a / g

As a result, the weight of the normalized peptide, as well as the weights of its frag-
ments, is simply the sum of those of its components. By the above definition, the
normalization of a single charge real peptide of observed weight w 0 is composed
by a number of molecules of each of the components in A equal to the number of
molecules Y 0 Df y 1 ;y 2 ;:::;y n g of each amino acid contained in the real peptide
of observed weight w 0 .
Example 1.3. The normalized peptide corresponding to the real peptide of weight
572.69 of Example 1.1 has a weight of .572:69 19:02/ D 553:67, and its compo-
nent have the following weights: .131:18 18:02/ D 113:16, .155:16 18:02/ D
137:14, .121:16 18:02/ D 103:14, .119:12 18:02/ D 101:10, .117:15 18:02/ D
99:13. If such normalized peptide breaks for instance in Leu-His and Cys-Thr-
Val, such fragments, respectively, have weights: .113:16 C 137:14/ D 250:30 and

.103:14 C 101:10 C 99:13/ D 303:37.
We will consider for such normalized peptide the above described topological con-
cepts of N-terminus, C-terminus, peptidic bonds, etc., in their intuitive sense, as if it
was a real peptide.
When a peak receives an interpretation, an hypothesis has been done about
where the cleavage occurred in the peptide, and also about which was the chem-
ical structure of the peptide in that point. Asserting that, for a single charge peptide
of observed weight w 0 , peak w j is, for instance, a single charge b-ion means that
starting from the N-terminus of the normalization of that peptide, there has been a
cleavage between a CO and an NH, and that the part of such normalization going
from the N-terminus to that cleavage has weight

w j 1:008 ˙ ı

On the contrary, asserting that, for the same peptide, the same peak w j is now,
for instance, a single charge y-ion means that starting from the C-terminus of the
normalization of that peptide, there have been a cleavage between an NH and a CO
and that the part of such normalization going from the C-terminus to that cleavage
has weight w j 19:023 ˙ ı. Therefore, the part of the same normalization going
from the N-terminus to that cleavage weights