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4. GENETIC CODE NUCLEON NUMBER

4. GENETIC CODE NUCLEON NUMBER



Besides the strict, above-shown regularities of the genetic code, regularities characterize the genetic code in other ways as well. If codon systematization is observed not only in quartets but also in octets (Rumer,1966) we get exactly two classes of separate binary symmetrical codon doublets (the first and second base of the codon), the first class being within the first octet, and the second class within the second octet (Table 1 in Shcherbak,1989, p 272). The ratio of the number of doublets is 1:1 (or 8:8); which also corresponds to the number of codons in the two classes: 1:1 (32:32). As to the codon-coded entities (for amino acids and/or for termination entity), the ratio of four-codon and non-four-codon entities is 1:2 (that is, 8:16). Finally, the relation of the number of "strong" (C,G) to the number of "weak" bases (U,A) in codon doublets of the first octet is that of 3:1, whereas that relation in the second octet is 1:3.

4.1. Union of Chemistry, Physics and Boolean Arithmetic



However, what is in a way unexpected and most surprising is the fact that (binary) symmetricality and proportionality is achieved through the number of nucleons (Fig. 1 in Shcherbak, 1994, p 475). Namely, from the aspect of nucleon number, 16 of the non-four-codon entities are symmetrically separated into the "head" and the "body" (the side chain) in one way, and the 8 four-codon entities in another. The first way "uses the same symbols", and the second way has "the numbers arranged by cyclic permutation", but in both cases the numbers in question are those taken from the table of the multiples of the number 037, which form a system arranged in accordance with module 9 (Table 1 in Shcherbak, 1994, p 476). The relation of the number of nucleons in the "heads" and "bodies" of non-four-codon entities is that of 1:1 (that is, 1110:1110), whereas the relation of the whole (molecule) to that of one of its individual parts "heads" and "bodies" is 2:1. On the other hand, the relation of the number of nucleons in the "heads" to that of the "bodies" of the four-codon entities (amino acids only!) is 16:9; that is, when the wholeness of the molecule is taken into account, proportionality is then reduced to very small numbers, not to any number, but to those numbers which demonstrate the squares of the first three Pythagorean numbers 32.:42:52. (Hint. Not only the total amino acid nucleon number, but also the total pu-pyr nucleon number is related to the multiples of 037; cf footnote in Shcherbak,1994, p 476). Shcherbak's assumption that "the laws of additive-position notation of numbers... have analogies with quantum physics" (Shcherbak, 1994, p 476) make sense and is scientifically based only on condition that "the numbers" generate in the Boolean space: "When the highest state aj = q is attained, there is a quantum transition to a further level j + 1, its value being increased by unity and so forth" ("where a are natural series symbols... q is the base of the system"). If this is so, and if for the number 03710 , from all the two-digital numbers, the law of modulo ordering by way of "the same symbols" and/or "cyclic permutation" (Shcherbak, 1994, p 475) holds, then we can give an important hypothesis-prediction (Prediction 5) which follows. Position 37 and its inverse form 73 must have a specific role in the make-up and organization of all linear-generated bio-macromolecules, as nucleic acids are, for example, and proteins and their aggregations. This must also be the case for positions 03/30 & 07/70, 33 & 77, etc. On the other hand, by means of these positions, relations among all other positions in the bio-macromolecule are established (see Appendix 2). (cf Osawa et al., 1992, p 234: “Nucleotide 37, adjoining the third anticodon position in tRNA, is often extensively modified... .In contrast, the tRNA nucleotide at position 33 is an invariant unmodified U”; Saenger, 1984, p 347: “The hypermodified, semi-invariant base at position 37... serves to locate the codon in proper register and to prevent misreading due to frame shifting”). What is especially important is the fact that determination by way of nucleon number holds not only for the categorization of amino acids into four-codon and non-four-codon amino acids, but also for categorization within the four stereochemical types (see Surveys 2‑3 and Solutions 1‑7; see in Popov, 1989, p 79, about the categorization of amino acids into four types; see also Discussion).  

        
         
         
         
         
         
         


In Survey 2, we can see that the five pairs of the alanine type (S-T, C-M, N-Q, D-E, and K-R) plus one pair of the valine type (V-I) form the specific Boolean logical square: (0) N,D,K - (1) S,V,C - (2) Q,E,R - (3) T,I,M, for which "the law of diagonals" holds: the number of binary values along its diagonals is equal. In the original Boolean square: 0 + 3 = 1 + 2; here, in this model (reality-model!): 189 + 177 = 121 + 245 = 366, or read according to module nine: 0 + 6 = 4 + 2 = 6 (zeroth position for D,N,K is expected from the reasons of chemistry: D is the simplest acid amino acid; N is its the simplest derivative; K is the simplest base amino acid. This position is expected also from the position D-N-K in Table 1, in contrast to position for E-Q-R). Within this "large" square there are the "small" squares (Surveys 2 - I, II, III) which show a unified categorization from the chemical aspect (the chemical nature of the molecules) and the physical aspect (the number of nucleons in the atom's nucleus which form its molecular composition). That union is achieved, as we can see, by way of strict Boolean arithmetic (including Boolean logic and algebra). What is especially important here is the fact that as the final result we have the pairing off of two base amino acids with the pair C-M and of the two acid amino acids with the pair M-C* (Crossing over! See the next chapter-section 4.2.), where, in the first case, the "player" is sulpho-cysteine, and in the second case, seleno-cysteine (in the first case with the first i.e. lightest isotope of sulphur S-32, and in the second case with the first isotope of selenium Se-74). As far as the three pairs of the stereochemical alanine type (A-L, H-W, and F-Y in Survey 3) are concerned, the Boolean square does not exist, or if it does exist, then it is not so easily noticeable; this has to be established by future research. However, the connectedness of these three pairs with the six pairs in Survey 2 is clearly obvious. Thus in solution (1) we can see that "the diagonal" A-Y corresponds to the both diagonals of the "large" square in Survey 2, and that in the following manner: ; the diagonal F-W in Solution (2) is an inversion of its previous one ; finally, the diagonal F-L in Solution (3) is reduced to the same numerical value which we have found for the diagonal M-E, or D-C* in Survey 2(III)B. In Solutions (4-7) further proportional relations between the system with six and the system with three pairs of amino acids are presented (see Survey 1, chapter 3.3, for the way in which quantities 3 and 6 are conditions for the best possible harmony; in chapter 6.3. see why W must be excluded). ... In the final result we can see the connection between the two systems determined by the sequence of numbers 1-27 (Solution 7), by whose sequence the categorization of amino acids into four-codon and non-four-codon amino acids has been determined (cf. Table 1 in Shcherbak, 1994, p 476; as to why the amino acids G, P, and W have been excluded, see Chapter 6.3; the connection between the 18 amino acids from the two yes-pairing types and the two amino acids from the 2 non-pairing types - G & P - remains to be discussed in another article; see Appendix 7).

4.2. Amino Acid Systematization



The important fact is that the four-codon entities (through the nucleon number) are separated into a specific system. But the number of nucleons (their order according to quantity) has also been used for the further classification (and systemitization) of codon entities into: one-codon, two-codon, and three-codon entities. In the drawing (Fig. 1 in Shcherbak, 1994, p 475) it can be seen that in the non-four-codon entity system in the end positions are located, on one side C-I, and on the other side M-W. Using these same amino acids, the symmetrical division of the Gray genetic code model has been determined (Fig. 1 in Swanson, 1984, p 188). The amino acids from the pair M-W divide in such a way that one occupies the "north" position and the other the "south" position in the codon ring. There are exactly 32 codons to the left of the north-south line, and 32 to the right of this line as well (including M-W). Behind the M-W pair and moving to the right the C-I pair follows, but in such a way that in relation to the nucleon system they realize an interesting "crossing-over". This happens in the following way: In the nucleon system, observing the order, we have the C-I and the M-W pair; in other words, the C-M and the I-W pair (the first amino acid pairs off with the first, the second amino acid with the second); in the codon ring then a "crossing-over" occurs, thus we have the pairs W-C and M-I.

Remark 4.1. The classification of Cys into that of three-codon amino acids, as has been done in Figure 1 in Shcherbak, 1994, p 475, can be understood only when it is known that there is a non-standard genetic code in which, besides UGU and UGC which code for Cys , still UGA codes for the same amino acid (cf. Osawa et al., 1992, p 250: "In Euplotes octacarinatus, UGA is a codon for Cys, in addition to the universal Cys codons UGU and UGC"). In order for us to follow all these relations (but not only that) it is necessary to "transform" the Gray code model into a binary tree (Fig. 1 in this Supplement). This transformation will also entail another "crossing-over", so that the W-C pair becomes the C-W pair, and the M-I pair becomes the I-M pair. The binary tree itself reflects the natural binary division of the Codon ring into 32 codons of the pyr type (the left side of the tree) and 32 codons of the pu type (the right side of the tree).

Remark 4.2. In civilizations in which the writing process moves from left to right the zeroth codon UUU has to be on the far left side; in civilizations in which writing is directed from right to left, it is the opposite; in civilizations where writing moves from the bottom up, the zeroth codon UUU has to be on the bottom; in civilizations where it is the other way around (from top to bottom), the zeroth codon has to be at the top. Now we can see how the symmetry of the codon ring has been determined by the M-W and I-C pairs (which correspond to the determination of the nucleon system by the pairs M-W and C-I). The division of the codon ring into 32 pyr and 32 pu codons, in comparison to the division of the ring by the M-W line, has been achieved through another binary and symmetrical crossing-over, which, with the use of the binary tree of the genetic code, is easily noticeable: at position M the pyr half of the codons has been "reduced" by exactly one codon class, or by "rosette" 3 (T,A), whereas at position W the pyr half of the codons has been "increased" again by exactly one codon class, that is, by "rosette" 5 (C,W,R).

 

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