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Fig. 2.2
The structure of a peptide link. The peptide structure above, the peptide bond below.
The bridge links two peptides, by fusing the head
NH
2
of one peptide with the tail
COOH
of
the other in
CONH
(a water molecule
H
2
O
is released).
2.2.1
DNA Notation and Double String Operations
Let us recall and extend some standard notation from Formal Language Theory
(see [213], and Chap. 6) in order to formalize fundamental operations related to the
structure of DNA molecules.
Let us consider the usual alphabet of bases
Γ
∗
of
strings
over this alphabet is comprised of the sequences (words) that can be arranged with
these four symbols (letters). Strings of
Γ
=
{
A
,
T
,
C
,
G
}
.Theset
Γ
∗
will be indicated by Greek letters. On
these strings, a binary associative operation of
concatenation
is defined, that given
two strings of
Γ
∗
yields a new string where all the symbols of the second sequence
are put, in the given order, after the last symbol of the first one. Concatenation be-
tween two strings
α
and
β
is denoted by the juxtaposition
αβ
. The length of a string
α
is the number of its symbol occurrences (each symbol is counted as many times as
it occurs) and is indicated by
|
α
|
,
that is, the
empty
string, where no symbol occurs (an abstract notion similar to zero
for numbers). Symbols are special strings of length 1. Mathematically speaking, the
structure
. A special string is that of length 0, denoted by
λ
Γ
∗
is referred to as the
free monoid
over the alphabet
Γ
∗
Γ
. Any subset of
is a (formal)
language
over the alphabet
. Since languages are sets, all the usual set
theoretical notions extend to languages (such as membership
Γ
∈
, inclusion
⊆
,empty
set 0).
The symbol of
α
that occurs in position
i
(1
≤
i
≤|
α
|
) is denoted by
α
(
i
)
,the
sequence of symbols of
α
occurring (in the given order) from position
i
to position
j
