1.
Introduction
Let's remind that as an elementary object in the theory of
topological coding of proteins acts protein pentafragment
(or its mathematical equivalent - 4-arc chain graph). Figure 1 shows a top view
of it. Alpha-carbon atoms of pentafragment (except
for the i-th)
are shown as gray spheres, and designated on as i, i-1, i-2, i-3, i-4.
In a cyclic pentafragment the single
hydrogen bond between the NiH….Oi-4=C is formed (shown by conventional cross-dashed
lines).
The side chains of amino acids (the physical operators, in this case - operators of connectivity) are attached to the
i-th alpha-carbon
atom and are able to form hydrogen bonds
with the carbonyl Oi-4=C (shown by
dashed lines too), thereby forming
a cyclic pentafragment with hydrogen bond NiH….Oi-4=C.
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Fig. 1. The action of the antisymmetric in structure side chains of amino acids
(the physical operators of connectivity) in the area of bond NiH….Oi-4=C of protein pentafragment (top view). a - glutamic amino acid, b - aspartic amino acid. The side chains of
amino acids are shown in red, the growth direction of the chain – in green. |
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Let's consider the work of two amino acids with similar properties as the physical operators in the area of hydrogen bond NiH….Oi-4=C – glutamic acid (Fig. 1, a) and aspartic
acid (Fig. 1, b).
As
can be seen in Figures 1,a and 1,b, these amino acids are similar in properties, but different in length (non-mirror antisymmetry - see
page
http://amino-acids-20.narod.ru). In the course of their work as
a physical operators, they will have different
directions of pulling effort. Thus, the nitrogen atom
of glutamic acid (Fig. 1 a), because of sufficient length of the side chain, due to the hydrogen
bonding can pull an atom Oi-4 to
the left (shown by arrow), which leads to
the appearance of connectivity lines of alpha-carbon atoms i-2 and i-4 (shown
in dotted lines). At the same time, the nitrogen atom of the shorter aspartic
acid (Fig. 1,b), due to the similar hydrogen bond
can pull the atom Oi-4 to
the right, which makes atoms i and i-2 connected.
Thus, two similar side
chains implement different directions of impact (it can be said, the vectors of
action or simply the vectors) to the atom, Oi-4. This question will be the main subject of the
analysis on the given page (Section
2).
The result of this analysis is the introduction
of the
concept of the molecular vector machine of proteins (MVM).
In Section 3
we will analyze the properties
of the components of MVM
– the system of vectors as a mathematical group, of the canonical set of amino
acids as a group of irreducible representations of vectors, and the i-th
tetrahedral alpha-carbon atom to which the interchangeable
side chains of amino
acids are attached.
Section 4 discusses the two-layer model of MVM, the appearance of which is associated with a deeper comprehension of the problems of MVM.
At last, in the final part (Section 5), which is located at the end of the
main page will describe aspects of MVM, which have important practical
implications. Our results in this
area are supposed to be elaborated
on a special page. However, it will be probably much later,
so for those who want to see them in this section we shall provide links to our
publications and patents, which readers can learn directly on the page
or download.
Address for connection: vector-machine@narod.ru
