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duplication mechanism of this molecule, and DNA helix is implied by simple ge-
ometrical principles aimed at satisfying economy in space occupancy and an effi-
cient associative mechanism based on hybridization. An important consequence of
the helix arrangement of the two strands is the possibility of a second level of DNA
packing where the DNA “rope”, packed in the helix cylinder, can be again wound by
wrapping it around some support (histone proteins, where DNA is wrapped around
forming spherical packing units, glued by chromatin proteins, called nucleosomes).
As is well, known in the craft of rope-making, even since ancient times, a “screw
thread” is a helical ridge on the outside of a screw, or bolt, or on the inside of a
cylindrical hole, to allow two parts to be screwed together. The same logic underlies
a DNA formation, where strands are twisted together along a helix. This structure,
not only provides the bilinearity postulated by the template driven duplication, but
increases the robustness of the linear structure, making it able to keep its integrity in
spite of its length, and in spite of other wrapping levels. Another illuminating com-
parison regarding DNA anti-parallelism can be found in folk dances where many
dancers are arranged in two paired rows. Each dancer D corresponds to the dancer
D' in front of him/her in the paired row, but due to the chirality of the human body,
the dancer who is on the right of D corresponds to the dancer who is on the left
of D'. It is surprising that rope technology and the art of dancing share important
aspects with DNA structure.
Figure 2.14 shows 10 different forms of double DNA strings, where parallelism
between lines refers to hybridization between strings, while Y forms correspond to
the cases where extremal parts of single strings do not hybridize (in YY forms this
happens on both sides). Of course, these forms do not cover all possible DNA forms,
but they identify all the possibilities of pairing two different strands. Circular forms,
hetero-duplex and hairpins are considered in Fig. 2.15.
A DNA simple branch is formed by three linear strands such that each of them
hybridize with the other two. Such kinds of branches can produce any kind of graph,
if we identify a cycle of branches as a single node. Figure 2.17 shows the way
branches are combined for producing a node with degree five.
Ta b l e 2 . 2
Basic Requirements in DNA Pool Operations
mix
(
P
1
,
P
2
)=
P
1
+
P
2
split
(
P
)=(
P
1
,
P
2
)
⇔
P
=
P
1
+
P
2
,
Type
(
P
1
)=
Type
(
P
2
)=
Type
(
P
)
length
(
P
)=
{|
η
||<
η
> ∈
Type
(
P
)
}
separate
}
Type
(
denature
(
P
))
⊇{
α
|
β
∈
Type
(
P
)
}
Type
(
hybridize
(
P
))
⊇{
α
rev
(
P
,
n
)=
{
s
∈
P
||
type
(
s
)
|
=
n
(
β
)
|
α
,
β
∈
Type
(
P
)
,
α
][
β
}
Type
(
ext end
(
P
))
⊇{
αγβ
(
δγβ
)
αγ
(
δγβ
)
∈
P
}
Type
(
in f ix
(
P
,
γ
,
δ
))
⊇{<
γαδ
> | <
α
> ∈
Type
(
P
)
}
|
c
c
