Research Article Open Access
The 24-Quadruplet Genetic Code: Merits Of The Projected Quadruplet Codons, From Combinatorial Perspective
W.B. Bozegha*
*Numeration science literature, Development research project, No. 9 Otiotio road, Yenagoa, Bayelsa state, Nigeria.
*Corresponding author: W.B. Bozegha, Numeration science literature, Development research project, No. 9 Otiotio road, Yenagoa, Bayelsa state,Nigeria. Tel: +2348068029860; e-mail : wbbozegha@yahoo.com
Received: March 05, 2018; Accepted: September 26, 2018; Published: September 29, 2018
Citation: W.B. Bozegha (2018) The 24-Quadruplet Genetic Code: Merits Of The Projected Quadruplet Codons, From Combinatorial Perspective. Int J Gen Sci 5(2): 1-10. DOI: 10.15226/2377-4274/5/2/00126
Abstract
Statement of the Problem: Triplet codons have held sway since 1954, when the 64-triplet genetic code emerged as the mathematical solution to the molecular biologists’ quest for producing at least 20 code words from 4 nucleotide bases to account for their observation in 1953 that the sequence of the four bases in the nucleus of a cell influenced the sequence of the twenty amino acids of a protein in the surrounding cellular cytoplasm. The 64 triplet codons then formed the genetic code, derived from a sequence of the four bases. The genetic code is ridden with several irregularities which are only widely discussed in genetics literature without remedies, apart from bogus[a1] theories[a2], like the wobble phenomenon, frozen accident etc for their explanation.

Methodology and theoretical orientation: Square kinematics scheme, a new technique for computing permutations of 4 from 4 by view mixing is presented in consideration of the fact that the problem of generating at least 20 code words from 4 bases is combinatorial, bordering on permutations of 4 from 4 i.e-4P4 = 4!=4x3x2x1=24 quadruplets.

Conclusion and significance: A 24-quadruplet genetic code free from irregularities produced from a sequence of the four nucleotide bases in response to the molecular biologists’ quest of 1953 to raise a code to typify the observed relationship between the four nucleotide bases and the twenty amino acids of protein. The 24 quadruplets of this new genetic code structure represent the ‘workforce’ in protein synthesis, where 20 codons take charge of the placement of 20 amino acids in a sequence corresponding to theirs at one codon per amino acid, with four spare codons for four place/time based start/stop control signals.

Recommendation: Experimental experts to take the challenge of spelling the new 24-quadruplet genetic code to render it fit for adoption [a4].

Keywords: Quadruplet Codons; Permutations; Four; Twenty; Twenty-Four.
Introduction
The scientific observation by molecular biologists in 1953[a5] that the sequence of the DNA four bases A, T, G, C, (Adenine, Thymine, Guanine, Cytosine) in the nucleus of the cell influenced the sequence of the twenty amino acids of protein in the surrounding cytoplasm of the cell is the crux of protein synthesis, bordering on protein type proliferation and diversification.

Following this discovery, molecular biologists sought for ways by which the ATGC four-base combination regarded as four-letter alphabet could be made to generate enough code words to attend to the 20 amino acids of protein individually in protein synthesis and studies. This is a functional relationship also called the genetic code. Thereupon, they set about a quantitative reasoning that gave them 64 triplets which they also produced by the indirect base-four neo-digibreed[a6] method using Punnett Square[a7]. Unfortunately, they went astray in their interpretation of the following combinatorial terms of selections for permutation synthesis involved therein.

(i) The selection 1 from 4 as $4{}^{1}$ = 4 singlets, instead of ${}_{4}P{}_{1}=\frac{4!}{\left(4-1\right)!}=\frac{4!}{3!}=\frac{4x3x2x1}{3x2x1}=4$ singlets.

(ii)The selection 2 from 4 as ${4}^{2}$ = 4x4=16 duplexes, instead of
${}_{4}P{}_{2}=\frac{4!}{\left(4-2\right)!}=\frac{4!}{2!}=\frac{4x3x2x1}{2x1}=12duplexes$

(iii) The selection 3 from 4 as $4{}^{3}$ = 4x4x4 = 64 triplets (adopted), instead of
${}_{4}P{}_{3}=\frac{4!}{\left(4-3\right)!}=\frac{4!}{1!}=\frac{4x3x2x1}{1}=24$ triplets.

(iv) The selection 4 from 4 as ${4}^{4}$ = 4x4x4x4 = 256 quadruplets (ignored (a8)), instead of ${}_{4}P{}_{4}$ = 4! = 4x3x2x1 = 24 quadruplets.

This mistake led to their acceptance of the 64triplets as the code words. The 64-triplet code structure (a mixture of 24 permutations and 40 non-permutations) accepted and adopted after ‘spelling’ in 1968(a9) has been a thorn in the flesh of molecular biology (a10)studies of protein synthesis to date, and scientists are now researching to see, if the bases could be increased to more than 3 per codon[a11]. (Internet on Francis Crick).http/en.wikipedia.org/wiki/Francis-Crick.
Materials and Methods
Materials
The materials consist of the RNA four bases in the sequence of A,U,G,C (Adenine, Uracil, Guanine, Cytosine) and the DNA four bases in the order of A, T, G, C (Adenine, Thymine, Guanine, Cytosine) as carried in a particular rung of the double helix and are used as input set of 4 bases in the multiplicative replication input/output system in computational combinatorics developed by this author in the 1990’s[a12].
Method
Direct Method, Designated as Square Kinematics View Mixing Technique.
The input set of RNA four bases A,U,G,C .[a13]are loaded at the corners of the square in clockwise direction as depicted in Fig.1. The loaded square is deployed in three ways as depicted in Fig. 1 (a), (b), and (c) to generate 8 combinatorially [a14]valid quadruplets per deployment per section using kinematics and view mixing as shown in Chart 1 carrying a genetic code structure of 24 quadruplet codons from lines (1) to (24). [a15]. Square Kinematics Technique for generating permutations of 4 from 4: input[a16]set AUGC (Chart 1).
Figure 1 :(a) Sides deployment
(b) Diagonals deployment
(c) Parallels deployment
Chart 1 :
Results
(a) A genetic code structure of 24 permutation quadruplets is presented in Table I as a computational reality for the result, being a combinatorial derivation. The list of 20 amino acids of protein[1] is adapted from the book, The World of the Cell by Becker, Wayne M. (1986), Fig. 17.4, p. 529.

(b) In the parlance of computer science both hardware (square kinematics scheme) and software (view mixing using square kinematics scheme) for the computation of permutations of 4 from 4 associated with the production of the quadruplet codons are made available.[a17]
Table 1: New genetic code of 24-quadruplet codon structure
a List of 20 amino acids of protein.(a18) adapted from Fig. 17.4, The World of the Cell, p.529 by Becker, Wayne M. (1986).[a19]
b By Jill Wright et al (1988) in their book, Prentice Hall Life Science at page 63 with regard to protein synthesis, where it is stated that the RNA in the ribosomes, along with the RNA sent out from the nucleus directs the production of proteins.
Key
AYTBD = Allocation yet to be determined
Signal 1 = Place start signal
Signal 2 = Time start signal
Signal 3 = Place stop signal
Signal 4 = Time stop signal
Discussion
The discussion is geared to highlight the merits of the quadruplet codons of the new genetic code produced by combinatorics. In addition to the presentation of an irregularity-. [a20]free 24-quadruplet genetic code, a new technique for permutation of 4 from 4 using a square kinematics scheme based on view mixing is made available for an extra to the merits [a21] of the quadruplet codons. That is to say, in computer parlance both hardware (square kinematics scheme) and software (view mixing using square kinematics scheme) for the computation of permutations of 4 from 4 are associated with the production of the quadruplet codons whose merits are being discussed now.

This newly produced 24-quadruplet genetic code represents the natural (true) [a22] genetic code and serves its purpose in protein synthesis. It has 24-quadruplet codons as a workforce of 24 workers comprising 20 ‘labourers’ and 4 “supervisors’. The 20 labourers are meant to be responsible for the placement of the 20 amino acids in a sequence at one labourer per amino acid turn by turn and the 4 supervisors to serve as four signals for start/ stop control in respect of place and time during the building of the sequence of amino acids for a protein type at one supervisor per specific signal.

Whence two basic functions per quadruplet codon emerge to the effect that a quadruplet codon (i) can serve as incumbent prototype codon in the place of a seed for the reproduction of the whole genetic code plant of 24 quadruplet permutation codons [a23]; (ii) be responsible for the placement of a specific amino acid or be a specific signal in protein synthesis and studies. This portrayal is suited to the design and purpose of the natural genetic code that is efficiently engaged in protein synthesis throughout nature since creation.
Merits of the genetic code quadruplet codon intrinsic qualities thereof
(a) When a particular sequence of the RNA four bases e.g. AUGC is used as input set in the input/output format of the combinatorial multiplicative replication system for permutation of 4 from 4, an output of factorial complement of 24 quadruplets is obtained, given by ${}_{4}P{}_{4}$ =4! =4x3x2x1=24 quadruplets. These are permutations which are traditionally called codons individually and genetic code collectively. Each quadruplet codon is a true copy of the RNA input set because of bearing the complete set of base types in a unique sequence of its own, except the incarnation codon which has the same base sequence and therefore identical to the input set. This presence of all four base types per quadruplet codon confers a quality known as codon integrity upon all the quadruplets belonging to the genetic code. There is no single case of absent base type to cause under utilization of base types or repeated base type to bring about redundancy of base type in the quadruplet structure and texture of the new codon, unlike the old triplet codon where these flaws[a24] abound.
Illustrating(1)Chargaff’s Rules
2(A=U=12) lines per genetic code sequence of 24 quadruplet codons
2(G=C=12) lines per genetic code sequence of 24 quadruplet codons
(2) Watson-Crick’s base pairing rules
2(A/U x 12) lines and 2(G/C x 12) lines per genetic code sequence of 24 quadruplet codons
(b) The workings of both Chargaff’s rules and Watson-Crick’s base pairing[a25] rules can be illustrated in every genetic code sequence of 24-quadruplet codons as per Diagram 1, New Genetic Code Structure in Dendritic Dichotomization.
Functional perspective
(a) Each quadruplet codon can be deployed as incumbent input prototype for the production of the genetic code of 24 quadruplets, reflecting potency.

(b) In addition, each quadruplet codon in the setting of the genetic code is functionally responsible for either the placement of a specific amino acid in the building of a protein type or the actuation of one of four specific signals in protein synthesis, showing uniqueness.

(c) The much desired collinearity between the 24 quadruplet code words of the genetic code and 20 amino acids of protein and 4 codon-size empty compartments left by 4 signals is evident in one to one correspondence.

(d) The four quadruplet codons in the genetic code which serve as four signals for start/ stop controls for place and time and convey no amino acids in the formation of protein type occasion four corresponding empty compartments amidst the sequence of 20 amino acids of a protein type. Each unit compartment is equivalent to the length of a quadruplet codon.

These four empty compartments in their rightful places or positions in any protein type sequence are beneficial in two ways as follows:-

(i) They bring to perfection the collinearity between genetic code and the protein type it codes by ensuring that the quadruplet codons on the one hand and the amino acids/unit empty compartments on the other hand maintain serial positional parity, as illustrated in the twin rows per chamber of Chart 2, depicting protein type proliferation and diversification as being diametrically opposite across the two parallels.

(ii)These empty compartments exist as flexible portions of protein types for protein folding, necessary for protein packaging for eventual disposal from factory. This brings us to the threshold of understanding protein folding and packaging. The appearance of the folded or packaged protein is seen to be in block form, of which the content per block can be surmised as being made up of 24 sequences of diverse protein types bearing 480 amino acids and 96 empty unit compartments corresponding to a batch of 24 consecutive input quadruplet codons in permutation synthesis in terms of proliferation and diversification.

(e) The four base types per quadruplet codon are usually motile to the effect of causing variation of sequence of a codon, which is responsible for the uniqueness of codons in the new genetic code.
 CORRIDOR (A) TRUNK (B) MARGIN (C) ATGC INITIAL INPUT SET USING SQUARE KINEMATICS TECHNIQUE (SEE APPENDIX) PRO- DUCTS ATGC 1 AUGC CGUA UGCA ACGU GCAU UACG CAUG GUAC AGCU UCGA UCAG GACU GAUC CUAG CUGA AGUC ACUG GCUA UAGC CGAC CAUG UGAC ACUG GUCA GS 1 S 1 S 2 AC 1 AC 2 AC 3 AC 4 AC 5 AC 6 AC 7 AC 8 AC 9 AC 10 AC 11 AC 12 AC 13 AC 14 AC 15 AC 16 AC 17 AC 18 AC 19 AC 20 S 3 S 4 PT 1 CGTA 2 CGUA AUGC GUAC CAUG UACG GCGA ACGU UGCA CUAG GAUC GACU UCAG UCGA AGCU AGUC CUGA CGAU UAGC GCUA AUCG ACUG GUCA CAGU UGAC GS 2 S 2 S 1 AC 6 AC 5 AC 4 AC 3 AC 2 AC 1 AC 12 AC 11 AC 10 AC 9 AC 8 AC 7 AC 14 AC 13 AC 18 AC 17 AC 16 AC 15 S 3 S 4 AC 19 AC 20 PT 2 TGCA 3 CGCA ACGU GCAU UACG CAUG GUAC AUGC CGUA UCAG GACU GAUC CUAG CUGA AGUC AGCU UCGA UGAC CAGU GUCA ACUG AUCG GCUA UAGC CGAU GS 3 AC 1 AC 2 AC 3 AC 4 AC 5 AC 6 S 1 S 2 AC 9 AC 10 AC 11 AC 12 AC 13 AC 14 AC 7 AC 8 AC 20 AC 19 S 4 S 3 AC 15 AC 16 AC 17 AC 18 PT 3 ACGT4 ACGU UGCA CGUA AUGC GUAC CAUG UACG GCAU AGUC CUAG CUAG GAUC GACU UCAG UCGA AGCU ACUG GUCA CAGU UGAC UAGC CGAU AUCG GCUA GS 4 AC 2 AC 1 S 2 S 1 AC 6 AC 5 AC 4 AC 3 AC 14 AC 13 AC 12 AC 11 AC 10 AC 9 AC 8 AC 7 S 3 S 4 AC 19 AC 20 AC 17 AC 18 AC 15 AC 16 PT 4 GCAT 5 GCAU UACG CAUG GUAC AUGC CGUA UGCA ACGU GAUC CUAG CUGA AGUC AGCU UCGA UCAG GACU GCUA AUCG CGAU UAGC UGAC CAGU GUCA ACUG GS 5 AC 3 AC 4 AC 5 AC 6 S 1 S 2 AC 1 AC 2 AC 11 AC 12 AC 13 AC 14 AC 7 AC 8 AC 9 AC 10 AC 16 AC 15 AC 18 AC 17 AC 20 AC 19 S 4 S 3 PT 5 TACG 6 UACG GCAU AUGC UGCA CGUA AUGC GUAC CAUG UCGA AGCU AGUC CUGA CUAG GAUC GACU UCAG UAGC CGAU AUCG GCUA GUCA ACUG UGAC CAGU GS 6 AC 4 AC 3 AC 2 AC 1 S 2 S 1 AC 6 AC 5 AC 8 AC 7 AC 14 AC 13 AC 12 AC 11 AC 10 AC 9 AC 17 AC 18 AC 15 AC 16 S 4 S 3 AC 20 AC 19 PT 6 1                 2                3               4               5                 6                 7               8                 9               10               11              12              13               14             15              16              17              18               19             20             21             22             23             24 CATG 7 CAUG GUAC AUGC CGUA UGCA ACGU GCAU UACG CUGA AGUC AGCU UCGA UCAG GACU GAUC CUAG CAGU UGAC ACUG GUCA GCUA AUCG CGAU UAGC GS 7 AC 5 AC 6 S 1 S 2 AC 1 AC 2 AC 3 AC 4 AC 13 AC 14 AC 7 AC 8 AC 9 AC 10 AC 11 AC 12 AC 19 AC 20 S 3 S 4 AC 16 AC 15 AC 18 AC 17 PT 7 GTAC 8 CAUG CAUG UACG GCAU ACGU UGCA CGUA AUGC GACU UCAG UCGA AGCU AGUC CUGA CUAG GACU GUCA ACUG UGAC CAGU CGAU UAGC GCUA AUCG GS 8 AC 6 AC 5 AC 4 AC 3 AC 2 AC 1 S 2 S 1 AC 10 AC 9 AC 8 AC 7 AC 14 AC 13 AC 12 AC 11 S 4 S 3 AC 20 AC 19 AC 18 AC 17 AC 16 AC 15 PT 8 AGCT 9 AGCU UCGA GCUA AUCG CUAG GAUC UAGC CGAU ACUG GUCA GUAC CAUG CAGU UGCA UGCA ACGU AGUC CUGA GACU UCAG UACG GCAU AUGC CGUA GS 9 AC 7 AC 8 AC 16 AC 15 AC 12 AC 11 AC 17 AC 18 S 3 S 4 AC 6 AC 5 AC 19 AC 20 AC 1 AC 2 AC 14 AC 13 AC 10 AC 9 AC 4 AC 3 S 1 S 2 PT 9 TCGA 10 UCGA AGCU CGAU UAGC GAUC CUAG AUCG GCUA UGAC CAGU CAUG GUAC GUCA ACUG ACGU UGCA UCAG GACU CUGA AGUC AUGC CGUA UACG GCAU GS 10 AC 8 AC 7 AC 18 AC 17 AC 11 AC 12 AC 15 AC 16 AC 20 AC 19 AC 5 AC 6 S 4 S 3 AC 2 AC 1 AC 9 AC 10 AC 13 AC 14 S 1 S 2 AC 4 AC 3 PT 10 TCAG 11 UCAG GACU CAGU UGAC AGUC CUGA GUCA ACUG UAGC CGAU CGUA AUGC AUCG GCUA GCAU UACG UCGA AGCU CUAG GBUC GUAC CAUG UGCA ACGU GS 11 AC 9 AC 10 AC 19 AC 20 AC 14 AC 13 S 4 S 3 AC 17 AC 18 S 2 S 1 AC 15 AC 16 AC 3 AC 4 AC 8 AC 7 AC 12 AC 11 AC 6 AC 5 AC 1 AC 2 PT 11 GACT 12 GACU UCAG ACUG GUCA AGUC UGAC CAGU GCUA AUCG AUGC CGUA CGAU UAGC UACG UACG GCAU GAUC CUAG AGCU ACGA UGCA ACGU GUAC CAUG GS 12 AC 10 AC 9 S 3 S 4 AC 13 AC 14 AC 20 AC 19 AC 16 AC 15 S 1 S 2 AC 18 AC 17 AC 4 AC 3 AC 11 AC 12 AC 7 AC 8 AC 1 AC 2 AC 6 AC 5 PT 12 1                  2               3                4               5             6               7               8               9              10             11             12             13              14            15           16             17             18              19             20              21            22             23              24 GATC 13 GAUC CUAG AUCG GCUA UCGA AGCU CGAU UAGC GUCA ACUG ACGU UGCA UGAC CAGU CAUG GUAC GACU UCAG AGUC CUGA CGUA AUGC GCAU UACG GS 13 AC 11 AC 12 AC 15 AC 16 AC 8 AC 7 AC 18 AC 17 S 4 S 3 AC 2 AC 1 AC 20 AC 19 AC 5 AC 6 AC 10 AC 9 AC 14 AC 13 S 2 S 1 AC 3 AC 4 PT 13 CTAG 14 CUAG GAUC UAGC CGAU AGCU UCGA GCUA AUCG CAGU UGAC UGCA ACGU ACUG GUCA AUAC CAUG CUAG AGUC UCAG GACU GCAU UACG CGUA AUGC GS 14 AC 12 AC 11 AC 17 AC 18 AC 7 AC 8 AC 16 AC 15 AC 19 AC 20 AC 1 AC 2 S 3 S 4 AC 6 AC 5 AC 13 AC 14 AC 9 AC 10 AC 3 AC 4 S 2 S 1 PT 14 CTGA 15 CUGA AGUC UGAC CAGU GACU UCAG ACUG GUCA CGAU UAGC UACG GCAU GCUA AUGC AUGC CGUA CUAG GAUC UCGA AGCU ACGU UGCA CAUG GUAC GS 15 AC 13 AC 14 AC 20 AC 19 AC 10 AC 9 S 3 S 4 AC 18 AC 17 AC 4 AC 3 AC 16 AC 15 S 1 S 2 AC 12 AC 11 AC 8 AC 7 AC 2 AC 1 AC 5 AC 6 PT 15 AGTC 16 AGUC CUGA GUCA ACUG UCAG GACU CAGU UGAC AUCG GCUA GCAU UACG UAGC CGAU CGUA AUGC AGCU UCGA GAUC CUAG CAUG GUAC ACGU UGCA GS 16 AC 14 AC 13 S 4 S 3 AC 9 AC 10 AC 19 AC 20 AC 15 AC 16 AC 3 AC 4 AC 17 AC 18 S 2 S 1 AC 7 AC 8 AC 11 AC 12 AC 5 AC 6 AC 2 AC 1 PT 16 ATCG 17 AUCG GCUA UCGA AGCU CGAU UAGC GAUC CUAG ACGU UGCA UGAC CAGU CAUG GUAC GUCA ACUG AUGC CGUA UACG GCAU GACU UCAG AGUC CUGA GS 17 AC 15 AC 16 AC 8 AC 7 AC 18 AC 17 AC 11 AC 12 AC 2 AC 1 AC 20 AC 19 AC 5 AC 6 S 4 S 3 S 1 S 2 AC 4 AC 3 AC 10 AC 9 AC 14 AC 13 PT 17 GCTA 18 GCUA AUCG CUAG GAUC UAGC CGAU AGCU UCGA GUAC CAUG CAGU UGAC UGCA ACGU ACUG GUCA GCAU UACG CGUA AUGC AGUC CUGA GACU UCAG GS 18 AC 16 AC 15 AC 12 AC 11 AC 17 AC 18 AC 7 AC 8 AC 6 AC 5 AC 19 AC 20 AC 1 AC 2 S 3 S 4 AC 3 AC 4 S 2 S 1 AC 14 AC 13 AC 10 AC 9 PT 18 1                 2              3                4              5               6                7              8               9              10              11             12             13             14             15              16            17            18             19             20             21             22             23           24 TAGC 19 UAGC CGAU AGCU UCGA GCUA AUCG CUAG GAUC UGCA ACGU ACUG GUCA GUAC CAUG CAGU UGAC UACG GCAU AUGC CGUA CUGA AGUC UCAG GACU GS 19 AC 17 AC 18 AC 7 AC 8 AC 16 AC 15 AC 12 AC 11 AC 1 AC 2 S 3 S 4 AC 6 AC 5 AC 19 AC 18 AC 4 AC 3 S 1 S 2 AC 13 AC 14 AC 9 AC 10 PT 19 CGAT 20 CGAU UAGC GAUC CUAG AUCG GCUA UCGA AGCU CAUG GUAC GUCA ACUG ACGU UGCA UGAC CAGU CGUA AUGC GCAU UACG UCAG GACU CUGA AGUC GS 20 AC 18 AC 17 AC 11 AC 12 AC 15 AC 16 AC 8 AC 7 AC 5 AC 6 S 4 S 3 AC 2 AC 1 AC 20 AC 19 S 2 S 1 AC 3 AC 4 AC 9 AC 10 AC 13 AC 14 PT 20 CAGT 21 CAGU UGAC AGUC CUGA GUCA ACUG UCAG GACU CGUA AUGC AUCG GCUA GCAU UACG UAGC CGAU CAUG GUAC ACGU UGCA UCGA AGCU CUAG GAUC GS 21 AC 19 AC 18 AC 14 AC 13 S 4 S 3 AC 9 AC 10 S 2 S 1 AC 15 AC 16 AC 3 AC 4 AC 17 AC 18 AC 5 AC 6 AC 2 AC 1 AC 8 AC 7 AC 12 AC 11 PT 21 TGAC 22 UGAC CAGU GACU UCAG ACUG GUCA CUGA AGUC UACG GCAU GCUA AUCG AUGC CGUA CGAU UAGC UGCA ACGU GUAC CAUG CUAG GAUC UCGA AGCU GS 22 AC 20 AC 19 AC 10 AC 9 S 3 S 4 AC 13 AC 14 AC 4 AC 3 AC 16 AC 15 S 1 S 2 AC 18 AC 17 AC 1 AC 2 AC 6 AC 5 AC 12 AC 11 AC 8 AC 7 PT 22 ACTG 23 ACUG GUCA CUGA AGUC UGAC CAGU GACU UCAG AUGC CGUA CGAU UAGC UACG GCAU GCUA AUCG ACGU UGCA CAUG GUAC GAUC CUAG AGCU UCGA GS 23 S 3 S 4 AC 13 AC 14 AC 18 AC 19 AC 10 AC 9 S 1 S 2 AC 18 AC 17 AC 4 AC 3 AC 16 AC 15 AC 2 AC 1 AC 5 AC 6 AC 11 AC 12 AC 7 AC 8 PT 23 GTCA 24 GUCA ACUG UCAG GACU CAGU UGAC AGUC CUGA GCAU UACG UAGC CGAU CGUA AUGC AUCG GCUA GUAC CAUG CAUG UGCA AGCU UCGA GAUC CUAG GS 24 S 4 S 3 AC 9 AC 10 AC 19 AC 20 AC 14 AC 13 AC 3 AC 4 AC 17 AC 18 S 2 S 1 AC 15 AC 16 AC 6 AC 5 AC 1 AC 10 AC 7 AC 8 AC 11 AC 12 PT 24 1              2              3               4               5             6               7               8              9              10             11           12             13             14             15             16            17            18             19            20             21            22            23             24 PT GS
The climax of the merits of the quadruplet codon is the protein type proliferation and diversification engineered by the genetic code which is the offspring of the quadruplet codon. The attributes of the genetic code in nature are well represented by this newly derived genetic code of 24 quadruplet codons as illustrated in Chart 2 captioned “Protein type proliferation and diversification…”
Chart 2 configuration and content.
Chart 2 titled “Protein Type Proliferation and Diversification: Climax of Merits of Quadruplet

Codons” is basically divided into three sections: Corridor, Trunk and Margin from left to right

The much needed collinearity between a genetic code sequence (in upper subrow) and a protein type (in lower subrow) is evident in the paired upper and lower subrows of all 24 segments (chambers) of Trunk B in support of protein synthesis geared to protein type proliferation and diversification.

The quadruplet codon in a collective sense is represented by the genetic code which is concise, composite and precise. The newly derived genetic code is concise in having a factorial complement formulary of ${}_{4}P{}_{4}$ = 4!=4x3x2x1=24 quadruplets. The genetic code is composite in its workforce of 24 consisting of “20 labourers” and “4 supervisors” under one management. It is precise in application affording collinearity of one to one correspondence with the 20 amino acids of protein and 4 codonsize empty compartments left by four signals in protein synthesis.
Finally, this rendition conveys a fourfold breakthrough as follows:-
a. Square kinematics (one of twelve systematic techniques for generating permutations and combinations in fulfillment of predicted factorial complements in combinatorics for the first time) for producing the permutations of 4 from 4 dissimilar objects.

b. Application of permutation synthesis to the successful derivation of the true genetic code structure of 24 quadruplets from an input set of the four RNA bases A.U.G.C (Adenine, Uracil, Guanine, Cytosine) that confronted molecular biologists from the 1950s without solution until now.

c. Offering a genetic code that exhibits collinearity with all protein types of one to one correspondence between its 24 quadruplet codons and the 20 amino acids/4 codon-size empty compartments left by 4 signals in protein types during protein synthesis. This genetic code can best be described as a replica of the natural genetic code operating smoothly in protein synthesis in plants and animals [a26] since creation till date.

d. Presenting the novel theoretical finding that the sequence of 20 amino acids that makes a protein type is interspersed with 4 empty compartments corresponding to the 4 operational signals in the genetic code responsible for its formation. By unit compartment, it is meant, the equivalence of the length of the quadruplet codon. In effect the sequence of any protein type is discontinuous, thinking of the contiguity of the 20 constituent amino acids; unlike the genetic code sequence which codes it, that has 24 contiguous codons and therefore continuous.
Conclusion
The new 24-quadruplet genetic code as produced, being combinatorially fit is a worthy proposal for consideration for adoption. That the quadruplet codon is the seed source of the genetic code of 24 quadruplets servicing protein synthesis in plants and animals since creation is a remarkable credit to the honour of the new quadruplet codon. More highlights are offered on the theoretical aspects of protein synthesis up to the threshold of protein folding and packaging, from where we see that the folded or packaged protein consists of a number of blocks: each made up of 24 sequences of diverse protein types bearing a total of 480 amino acids and 96 empty unit compartments corresponding to the output of a batch of 24 consecutive input quadruplet codons in permutation synthesis. In other words Chart 2 reflects the content of a block.
Recommendation
This precise genetic code structure of 24 quadruplets is therefore recommended for spelling by experimental experts to render it fit for adoption in coding application in protein synthesis and studies.
References (PART ONE)
References (PART TWO)
1. a1 - Mine, original term
2. a2 - Mine, original term
3. a3 - Mine, original term
4. a4 - Truth in Science recommended for use by all stake holders.
5. a5 - George Gamow: https://en.wikipedia.org/wiki/George Gamow
6. a6 - Mine from Numeration Science Literature development
7. a7 - The World of the Cell by Wayne M. Becker, (1986). The Benjamin Publishing Company, Inc.
8. a8 - Biology A Functional Approach (1971) Page 492, by M. B. V. Roberts. The English Language Book Society and Nelson.
9. a9 - Genetics A Molecular Approach 2nd Edition (1992) Page 124 By T. A. Brown, Chapman and Hall London U.K.
10. a10 - Opinion, mine because of degeneracy and other irregularities associated with it.
11. a11 - Internet on Francis Crick, http/en.wikipedia.org/wiki/Francis.Crick
12. a12 - Maiden idea illustrated in Chart 2 captioned “Protein Type Proliferation and Diversification…” in view of input quadruplet in Corridor A and 24 output quadruplets in Trunk B.
13. a13 - Maiden idea on the application of the four RNA bases in the new technique of computing 4 from 4 permutations by Square Kinematics View Mixing Scheme.
14. a14 - Maiden idea validated by the output of eight unique permutation quadruplets (non-isodigitals) from each of three pathways in the working of the technique.
15. a15 - Maiden demonstration of performance of the new technique of generating 4 from 4 permutations numbering 24 quadruplets as displayed in lines 1-24 of Chart 1 in fulfilment of 4P4 = 4! = 4x3x2x1 = 24 quadruplets.
16. a16 - Maiden idea on the framing of components of the input/output multiplicative replication system using the Square Kinematics View Mixing technique invented by this author.
17. a17 - Maiden presentation of the result of 4 from 4 permutation i.e. 4P4 = 4! = 4x3x2x1 = 24 quadruplets as displayed in Chart 1, lines 1-24 as produced by the Square Kinematics technique.
18. a18 - List of 20 amino acids in Table 1 col. 1 adapted from Fig. 17.4 page 529 of The World of the Cell (1986) by Becker, Wayne M.
19. a19 - Ibid.
20. a20 - Irregularity-free 24-quadruplet genetic code produced in Chart 1 lines 1-24, and presented in Table 1 under Results.
21. a21 - Maiden opinion identifying the production of the 24-quadruplet genetic code from a quadruplet input codon as a merit of the quadruplet codons.
22. a22 - Maiden opinion based on collinearity between genetic code and protein type evident in Chart 2 in support of the Primordial choice of RNA four bases A, U, G, C as substitute for 20 amino acids of protein for input set in the input/output multiplicative replication system aimed at protein type proliferation and diversification being required of the working of the genetic code in protein building in Nature.
23. a23 - Maiden observation of the performance of the Square Kinematics View Mixing technique illustrated in Fig. 1 and Chart 1, involving one quadruplet input set yielding output sequence of 24 quadruplets representing the new 24-quadruplet genetic code.
24. a24 - Maiden categorization of certain base types missing in some triplet codons amounting to underutilization of them as flaws of the 64 triplet genetic code by this author based on combinatorial examination of the reigning 64 triplet genetic code.
25. a25 - “The World of the Cell” page 409, by Wayne M. Becker (1986), The Benjamin Publishing Company, Inc.
26. a26 - Maiden opinion in favor of the 24-quadruplet genetic code in efficacy and efficiency.

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