2.3. The molecular vector machine

 

2.3.1. Setting of the vectors direction

 

The problem of setting of the vectors directions is caused by the fact that they cannot be arbitrary, because they are recreated by amino acid side chains, having real physical parameters. One side chain differs from the other by a discrete number of atoms (one atom is replaced by another, but larger, one atom is added in the chain, etc.). All this suggests that for the 20 vectors may exist some geometrical figure (in the limiting case - ideally correct, but in reality, perhaps not ideal), in which the vectors fit, and thus set their direction. For 20 vectors spatial structure of the dodecahedron is suitable (Fig. 6).

 

 

As seen in Figure 6, the structure of the dodecahedron is well suited to the selected in section 2.2. series of vectors. This structure has 20 vertices. To set the vectors to the center of the dodecahedron was placed atom O_i-4,  at the very top of the vertices - atom N_i,  and all vectors were directed to the vertices of the dodecahedron. It was stored a division of bond area связи N_iH….O_i-4=C  by three planes, which ensured the preservation of the principles of symmetry in the position of vectors. Dimensions of the dodecahedron defined on the basis of the parameters of protein pentafragment.

 

In addition to the dodecahedron, Figure 6 shows two arrows associated with the i-th alpha-carbon atom. Blue arrow, designated R_i, represents the amino acid side chain directed toward the dodecahedron. Green arrow is also associated with the i-th alpha-carbon atom, directed at the i +1- th alpha-carbon atom. This arrow represents the peptide group HN–C=O, connecting the i-th and i +1- th alpha-carbon atoms.

 

Since both arrows are firmly fixed on the i-th alpha-carbon atom, they are interconnected. Changing the direction of blue arrows, due to the length of the side chain, which is located at a given time at the i-th alpha-carbon atom, leads to a change in the direction of green arrows to the i +1 alpha carbon atom, which determines the direction of growth of the polypeptide chain. This interconnected system of vectors, because of the resemblance to the popular device for carrying water, we call the "yoke."

 

2.3.2. Designations of vectors

 

  In order to define a vector, it is necessary to know the position of two points - the initial, from which the vector proceeds, and the final, where it is directed to. In our case, the initial point of all the vectors can be taken as the center of dodecahedron (atom O_i-4), and final points are vertices of the dodecahedron. For vertices, under which name will be called also vectors, in the dodecahedron following notation were introduced (Fig. 7).

 

 

In the plane I two series of vertices is allocated: in series I is a vertex, denoted by the letter A, which is associated with an atom of N_i (Fig. 6) and symmetrical to it, located under the plane III, designated as - A. The series 2 also includes two vertices, which are placed perpendicular to the previous two. They are designated as B and –B.

 

 Two other series connected by symmetry and containing on 8 vertices, have received following names. A series of the vertices symmetric concerning a plane I and III, more close located to a plane I, have been designated by letter A with indexes: at the left all vertices have an index on the right below, and on the right - an index at the left above. So, near to A the vertices which are behind a plane II are designated as A₁ and ¹A, and more remote, located before a plane II, - as A₂ and ²A. For the vertices located under a plane III, these designations will be, accordingly as–A₁, –¹A (before a plane II), and –A₂, –²A (behind a plane II).

 

Similarly 8 vertices of the second series more close located to a plane III, are designated by letter B with indexes. Vertices which are more close to vertice B, behind a plane II are designated as ¹B and B₁, and vertices before a plane II - as ²B and B₂. In relation to vertice –B, symmetric vertices are designated, accordingly, as –¹B and –B₁ before a plane II, both –²B and –B₂ behind a plane II. Thus, all 20 vertices to which the allocated 20 vectors are directed, have received the names.

 

 Now compare the proposed nomenclature of the dodecahedron vertices with introduced on the page http://amino-acids-20.narod.ru/dodecahedron.htm designations of elements system on the dodecahedron. It is easy to see that the proposed designations of vertices, we denote for vectors, and the system of symbols of the elements on the dodecahedron are identical. Obviously, this is due in both cases the general principles of symmetry planes conducting through the dodecahedron.

 

 

2.3.3. Comparison of the dodecahedron designations system to structure of the canonical set of amino acids

 

Let's compare the nomenclature of vertices of a dodecahedron with an arrangement of a canonical set of 20 amino acids on a dodecahedron, offered by us earlier      ( http://amino-acids-20.narod.ru/AA_dodecahedron.htm , section 3.4.). For convenience of discussion both structures nearby (Fig. 8, a, b) are resulted.

 

 

If we imagine, that the system of designations together with vectors is located in the area of bond  N_iH….O_i-4=C (unite mentally Fig. 6 and 8) in general directions of vectors of action should be provided as follows:

– Vectors, directed upwards, towards vertice A (vertices  A with indexes 1 and 2), should be recreated by shorter side chains;

– Vectors, directed to the right-to the left and downwards (accordingly, to B, –B and –A) – by longer side chains.   

 

 Comparison with the amino acid system (Fig. 8,b) reveals that the side chains are located on the dodecahedron in this way: in order of increasing molecular weight or (that coincides) in order of increasing the length of the side chain. For example, at the top are very short side chains (Ser, Thr, Cys, Met), below - the longer (Asp, Asn, Glu, Gln. As well as Arg, Lys). Finally, below are the most massive cyclic side chains (His, Phe, Trp, Tyr). Thus, instead of the notation system of vectors in the area of bond связи N_iH….O_i-4=C you can substitute the names of amino acids that occupy these locations in the amino acids system. Then the structure takes the form shown in Figure 9. This is the molecular vector machine (MVM) of proteins.

 

 

On the first page of the site  http://amino-acids-20.narod.ru   was promised that the nature of the proposed system of amino acids on the dodecahedron will be explained on the site  http://vector-machine.narod.ru . We make this promise. The nature of this model structure, as it can be concluded from the above, is associated with its participation as one of the parts of the molecular vector machine.

 

2.3.4. Components of the molecular vector machine of proteins and principle of its action 

 

As seen in Figure 9, MVM consists of four main parts:

 

• dodecahedron containing a group of 20 vectors of action - the radii of the dodecahedron (red arrows inside the dodecahedron); the vertices of the dodecahedron are marked with the three-letter names of amino acids that recreate these vectors;

• the canonical set of exchangeable physical operators (blue arrow with the R_i letter at the end);

• the i-th tetrahedral alpha-carbon atom (hereinafter - the alpha atom), to which the physical operators (blue arrow) are attached, and which sets the direction of the growing protein chain (green arrow), together forming the "yoke";

• fragment of five amino acids (penafragments) forming the frame of MVM, within which all the processes formation of the secondary structure of proteins are deployed.

 

The operating principle of MBM is as follows [1-5].

 

The side chains of amino acids, being guided to the vertices of the dodecahedron corresponding to this amino acid, implement their action as a physical operator of connectivity  or operators anti-connectivity and recreate the structure encoded by the triplets.

 

The operators of connectivity operate mainly in the direction of  N_iH….O_i-4=C, and both groups would tighten N_iH and O_i-4=C to each other.

 

At the same time, operators of anti-connectivity, as can be imagined, by the collision with the group O_i-4=C will push it in the opposite direction from a group of N_iH and thereby prevent the emergence of bond N_iH….O_i-4=C.

 

Simultaneously, the side chain, rigidly connected with the i-th alpha-carbon atom, defines through the "yoke" of this atom the direction of a free peptide bond

O_i=C_i–N_i+1H, which determines the nature of the growing polypeptide chain.

 

Further properties of each of first three parts МВМ will be considered (section 3).

At first properties of vectors will be analysed (section 3.1.).

 

As to pentafragments, their properties have been considered on the basis of experimental data and about them it is told in a final part of a page (section 5).

 

 

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