4. Two-layer model of the molecular vector machine
4.1. Prerequisites to the construction of two-layer
model of MVM
In Section 3.3.2 we have already mentioned that the need for further
development of MVM is associated
with the contradiction between the
number of possible conformations, encoded by the genetic code (61-62) and the number of side-chain amino acids (20), which provide their recreation. This contradiction is removed if we include into consideration not only the side chains, but also those groups that
they carry.
As a concrete example, consider two states of the amino acid asparagine
(Asn), shown
in Figures 17,a
and 17,b.
As seen in Figure 17, a, when the group O=C-NH2 oriented by its NH2-group to the right, during the formation of its H-bond in pentafragment two edges of the
connectivity - between the i-i-2
and i - i-4
can occur (in the matrix it corresponds to a value
of 101 in the first row),
and the edge connectivity i-4 - i-2 is absent (x6 = 0). At the same time, if
the group O=C-NH2 is oriented
by NH2-group to the left (Fig. 17, b), then there is one more edge of connectivity - between
the i-4 - i-2 (x6
= 1).
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а |
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б |
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Fig. 17. Comparison of the two states of the side chain of asparagine. a
– NH2-group is located on the right, edge
of connectivity of the alpha- atoms
i-4 – i-2 is absent (x6=0); b – NH2-group is on the left, there is an edge of connectivity of the atoms of alpha-i-4 – i-2 (x6=1). |
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Thus, although
the basic description of the
edges of connectivity of the
pentafragment in
the matrix does not change, the
variable X6 takes the values 0 and 1. This variable is coded by the third base
of triplet, for asparagine – C and U (triplets AAC and AAU). In our variant of pairs of variables correspondence to code letters
– C = 00 and U
= 01 (see http://genetic-code.narod.ru/transform.htm).
In practice, this means
that the vectors of action should be directed not strictly in the vertice of the dodecahedron, but form a "bunch
of vectors", which occupies a region near the corresponding vertice. Obviously, depending on the type of this
terminal group the number of vectors in the
beam, i.e. the degree of degeneracy of the states of this amino acid (physical
operator) will vary - from one to five or more. The majority of side chains
capable of forming two hydrogen bonds will have a degeneracy
equal to two.
4.2. Romboikosododekahedron as a possible polyhedron for a two-layer model of MVM
We have shown above
that to describe the position of all vectors that can occur due to the
degeneracy of the terminal groups (splitting the original vectors), a simple
model of a dodecahedron is not enough. The attention was drawn that the general direction of the side chain
in the degenerate states (Fig. 17 a, b) remains unchanged. For this reason a polyhedron,
which is suitable for the purpose of describing all of the
62 vectors, must fit into the structure of the dodecahedron and to make its
underlying layer.
As a second polyhedron, in addition to the dodecahedron, in the two-layer model of MVM can be
romboikosododekahedron (Figure 18, shown by red lines) [ 5 ]. Recall that
this polyhedron has 62 faces, 60 vertices and
120 edges. 20
faces of the total number are triangular, 12 - pentagonal and 30 - rectangular.
Romboikosododekahedron, as
seen in Figure 18, fit in a dodecahedron in such a way that its pentagonal faces are on the faces
of the dodecahedron. The centers
of the triangular faces are located
directly below the vertices of dodecahedron, which is clearly seen in Figure 18 for the vertices of the dodecahedron 2A, A2, 2B, and B2-B. Thus, the centers of the faces of romboikosododekahedron (there are a total of 62) located near the
vertices of the dodecahedron, can be used to describe groups of vectors
realized by degenerate states of side chains.
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Fig.
18. Dodecahedron with inscribed romboikosododekahedron as possible
polyhedrons of two-layer model of
the molecular vector machine. |
Although this model
seems to us promising, it has not been brought to the end [5], i.e. to the degree
of completion, at which one could see the localization of various bunches of
vectors. Significant technical difficulties prevented us to do it. We provide
the opportunity to undertake this work to visitors of this page.
We looked at virtually most of the aspects
related to the problem of MVM.
Only pentafragments
themselves, which are an important part
of MVM, were not analyzed. This
analysis can be performed on the
basis of available experimental
data in the literature. In Section
5, which is placed at the end of the main page, a material associated with
this analysis is given.
Address for connection: vector-machine@narod.ru
