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Personal page number 3

Karasev Vladimir Aleksandrovich





Book V. Karasev and V. Luchinin "Introduction to the design of bionic nanosystems"




Sites V.A. Karasev:


Principles of topological
coding of proteins



Spatial structure of the canonical

set of amino acids


Aid to the atheist: A new theory explaining essence and origin of life


Dear visitors!


I thank, that you have glanced on my page


People used to say: all roads lead to Rome. Research conducted by scientists at the first sight, entirely independent direction, also sometimes lead to the same point of intersection.


The page, proposed to Your attention, is the third of a series of WEB pages devoted to the problem of topological coding of proteins, planned by the author.


The first page opens this series and has the common name "Principles of topological coding of proteins." It focuses primarily on the structure of the genetic code and the problem of assignment a triplet - an amino acid. The results obtained in Section 4.4. ( ) directly deduce to the idea of molecular vector machine.


On the second page, which is called "The spatial structure of the canonical set of amino acids", the spatial structure of the canonical set of amino acids is examined, being presented in the form of a dodecahedron. Trying to make sense of why there is such a structure, not the other, has also led us to the idea of molecular vector machine.


Thus, two independent paths of investigation have led us to the same idea of the molecular vector machine, which this page is devoted to.


The results of this work a few ahead of several colleagues, owing to what we practically have nobody to refer, except as to own results [1-5], and attempts to continue these studies in the original direction of the two independent masters [6-8]. However, this does not exclude that in the near future the proposed path of research interest to colleagues of different specialties, primarily physicists, mathematicians and molecular biologists, and these studies will be continued.




1.  Introduction

The object of analysis is the area of bond NiH….Oi-4=C in the protein pentafragment


In “Introduction” the subject of the forthcoming analysis is defined - area of bond  NiH….Oi-4=C in protein pentafragment and defined the stages of its consideration


2. Stages of construction of the molecular vector machine of proteins


2.1.   Allocation of the planes of symmetry

2.2.   The analysis of action vectors of physical operators

2.3.   The molecular vector machine







1.            In the area of bond NiH….Oi-4=C from a position of quantum chemistry three planes of symmetry dividing sp2--hybridized clouds on symmetric parts are introduced.


2.            Taking into account the allocated planes of symmetry four groups of vectors of action are received.


3.            The model of the molecular vector machine (МVМ) is offered, consisting:


- From system of the vectors localized in structure of a dodecahedron;

- The canonical set of side chains of amino acids (exchangeable physical operators);

- i-th tetrahedral alpha-carbon atom to which exchangeable side chains of amino acids are attached;

- Amino acid pentafragment of protein main chain.


3.Properties of parts of the molecular vector machine of proteins


3.1.   Mathematical properties of vectors

3.2.   The canonical set of amino acids

3.3.   The i-th tetrahedral alpha-carbon atom





1.                 The analysis of the vectors from the position of group-theoretic approach is carried out. It is concluded that 20 of the vectors inside the dodecahedron form a mathematical group containing neutral and inverse elements.


2.                 On the basis of group-theoretical approach the canonical set of side chains of amino acids are considered as a group of irreducible representations of the vectors.


3.                 From the standpoint of of representations of MVM and the group-theoretic approach, an explanation of the principles used for construction of spatial structure of the canonical set of amino acids on the dodecahedron ( is offered:


- The principle of an arrangement of side chains from top to bottom in order of increasing size;

- The principles of the side chains of amino acids antisymmetry.


It is concluded that these principles are related with a reconstruction them of symmetric vectors of action in МVМ.


4.                 The analysis of the properties of the i-th tetrahedral alpha-carbon atom, a kind of "yoke", which specifies the direction of growth of the polypeptide chain, depending on the type of side chain with respect to this atom is carried out.


5.                 It is assumed that the analysis of this region may be promising for the development of methods for predicting the secondary structure of proteins.


4. Two-layer model of the molecular vector machine


4.1. Prerequisites to the construction of


4.2. Romboikosododekahedron and dodecahedron as a elements of MVM





1.                 In order to resolve the contradiction between the number of side chains (20) and the number of coding triplets (61) a two-layer model of the molecular vector machine is proposed.


2.                 It is supposed that in addition to the dodecahedron, as a polyhedron, occupying the lower level of MBM can serve romboikosododekahedron.


5. The conclusion. Practical application of concepts of molecular vector machine


In concepts of the molecular vector machine it is possible to allocate two aspects. On the one hand, they are, as it often happens in a science, a formal abstraction ((similar to a Carnot heat engine), convenient for the description and an explanation of some the biological facts (for example, the nature of of the canonical set of amino acids).


On the other hand, these concepts are related to co-translational mechanism for the formation of the secondary structure of proteins [5], implying that the formation of the secondary structure of proteins occurs in the ribosome at the moment of its synthesis. For this reason they are quite useful as a specific machine, carrying out this process in the ribosome. Of course, this mechanism is still hypothetical, but it can be a guide for experts, both theorists and experimentalists, and serve as a starting point for further research in different directions.


In addition to the elements analyzed in Section 3, the structure of MVM also includes fragments of the five amino acids (pentafragments). In real protein amino acid sequence and structure of pentafragments bonds is the fixed reflexion of results of work МVМ. For this reason, besides the theoretical analysis of properties of the elements of MVM, it is possible to analyze pentafragments of proteins studied by X-ray diffraction analysis, preserving their hydrogen bonds in the protein, particularly in the secondary structure. We carried out such an analysis.


Its details, as we believe, can represent a wide interest.  In the future, at the end of the cycle of works, we expect to create a special page for the study and exposition of this approach.




- 16 classes of pentafragments, 8 of which are major and 8 – minor are found.

- The spatial structure for each class, isomorphic to the Boolean hypercube B6 is proposed.

- A complete structure of all pentafragments described by Boolean hypercube B4 is constructed, in which vertices hypercubes B6 are located.



For those who wish to familiarise with the received results, we inform, that they are published in works in [9-11], are available for reading and downloading.


On the basis of these results DATABASE of PENTAFRAGMENTS [12] has been created, and a method of predicting the secondary structure of proteins [13], which is also available for review and download,  is developed. This method can be performed both manually and by computer program PREDICTOR [14]. All these materials are integrated and can serve as a subject of licence sale. With questions on acquisition of the licence interested persons can address to the author via this page.


In proteins, which petafragments have been used for database creation, accuracy of a prediction of secondary structure makes 99%.


Now the demand on a methods of designing of primary structure of the protein with a given secondary structure is submitted. While it is at an examination stage.




We wish you the further scientific impressions!


Address for connection:

ã The Work was carried out at the Centre of Microtechnologies and Diagnostics (CMID) of the St.-Petersburg State Electrotechnical University "LETI", at financial support of University

I express my sincere gratitude to A.I. Belyaev for help in editing the English version of this page.


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