Biomedical Engineering Reference
In-Depth Information
When performing a sequence analysis, the solution is obviously not known in ad-
vance. However, we often know which aspects of the solution can be considered as
possible for the current analysis, and which ones cannot. For instance, we may know
that a peptide under analysis contains at least a certain number of molecules of some
amino acid or does not contain another amino acid, etc. At worst, if nothing else is
known, simply every generic aspect of the solution should be considered as possible.
This may be formalized by evaluating the number n of possible compo-
nents (the amino acids) that must be considered for the current analysis, the set
N
Df
1;2;:::;n
g
of the indices i corresponding to such components in increasing
weight order, the set
A
Df
a
1
;a
2
;:::;a
n
g
;
a
i
2 R
C
of the weight values of such components (the molecular weights of the amino acids)
that must be considered for the current analysis, together with the sets
Min
Df
m
1
;m
2
;:::;m
n
g
;m
i
2 Z
C
Max
Df
M
1
;M
2
;:::;M
n
g
;M
i
m
i
;M
i
2 Z
C
;
respectively, of the minimum and the maximum of the possible number of molecules
of each component that must be considered for the current analysis, the number d of
decimal digits that can be considered significant for the current analysis, and a value
ı
2 R
C
of the maximum numerical error that may occur in the current analysis.
Amino acids can link to each other into a peptidic chain by connecting the aminic
group NH
2
of one molecule with the carboxyl group COOH of another molecule.
The free NH
2
extremity of the peptide is called N terminus, while the free COOH
extremity is called C terminus. Some amino acids, especially the modified ones, can
be situated only in particular positions of the sequence, i.e., only N-terminal or only
C-terminal. Since each of the peptidic bonds releases an H
2
O molecule, the weight
of a peptide is not simply the sum of the weights of its component amino acids.
Moreover, the weights observed in the spectrum correspond to the actual weights
only for the ionized molecules (ions) which retain one single electrical charge.
When, on the other hand, an ion retains more than one charge, the weight observed
in the spectrum is only a fraction of the actual ion weight. By considering the set
Y
0
Df
y
1
;y
2
;:::;y
n
g
;
i
2 Z
C
of the numbers of molecules of each component (here the amino acids) contained in
the overall polymer (here the peptide), and the number e
0
1 of electrical charges
retained by the ionized peptide, the observed weight
w
0
of the overall peptide is
given by the following equation:
P
i 2N
.y
i
.a
i
c
a
//
C
c
a
C
c
0
e
0
e
0
w
0
D
˙
ı;
(1.1)
where c
a
and c
0
are constant values. When considering d
D
3 decimal digits, c
a
is
18.015 and c
0
is 1.008.
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