1.3. Topological structure of the triplet genetic code

It is possible to connect each base of triplet , as well as in doublets, by individual transitions with three other bases.
 The structure, isomorphic to the Boolean hypercube В6., resulted from this work In this structure, nine triplets, originated from ССС (3 from each base), are distinguished with red colour.

This is L-structure of Boolean hypercube. There is also D-structure, symmetric to it.

 

Let's try to understand this "abracadabra".

From the hypercube the topological structure of the genetic code has inherited circles and hierarchical organization

CIRCLES

 

т ттттттттттттттттттттттттттттттттттттттттттттттттттттттCIRCLES TRIPLETS

The structure contains

7 circles with a variable

number of triplets


тттт

тт 1

6

15

20

15

6

1

HIERARCHY of STRUCTURES

Two sets, each containing 32 triplets:

М1 and М2.

Four subsets, each containing 16 triplets:

SM1, SM2, SM3, SM4.

Eight octets: О1 - О8.

Specific properties derived from the genetic code: individual transitions, arrangement of amino acids and Rumer transformation

тттттттт

INDIVIDUAL TRANSITIONS

Transitions of C<-->G, U<-->A type(continuous lines)

Substitutions of C<-->U, G<-->A type(dotted lines)

between the first bases of triplets connect sets M1 and M2

  

in the first bases connect triplets inside octets from top to bottom and from right to the left

between the second bases connect triplets inside octets from the top to the bottom

in the second bases connect triplets inside octets from the top to the bottom and from left to the right

between the third bases connect triplets inside subsets

in the third bases connect triplets of subsets

SM1 - SM2 and SM4 - SM3
 

It is known that in the Boolean hypercube В6 each top is connected to the six neighbouring ones.

Actually, the shown six variants of individual transitions make up the structure, isomorphic to the Boolean hypercube В6.

The third type of transitions

C<-->A,

G<-->U

is superposed on this structure.

Hence, the topological structure of the genetic code, obtained by us, is a nine-dimensional simplex.

 

ARRANGEMENT of AMINO ACIDS

Each set of hypercube triplets (M1 and M2) it can be divided into two groups:
Top - (M11 and M21) and bottom
( M12 and M22).

In groups M11 and M21 quartets of triplets are located, each coding one amino acid, and two in groups M12 and M22.

 

RUMER'S TRANSFORMATION

Triplets from groups M11 and M21
will be transformed into
triplets of groups M12 and M22
by Rumer's rule:
C <---> A, G <---> U,
thus occupying rotational symmetric
position in hypercube, e.g. ACC <---> CAA, GCC <---> UAA,

CCC <---> AAA, CCU <---> AAG , etc..

To you and all "abracadabra".

 

Those, who wish, can print out a complete structure of the code on the wite background.

 

The following questions may arise:

- why is the structure of the genetic code isomorphic to the Boolean hypercube B6?

- how can the existence in the genetic code of two groups of amino acids, whose triplets are connected by Rumer's transformation, be explained?

- why do amino acids correspond to the given triplets, but not to the others?

 

All these questions can be answered on the basis of the developed model of topological bases of a genetic code.

 

You can read in the our book about how the topological structure of the genetic code was constructed.

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