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 5.  The two 12-groups of amino acids - details I. 12-group 770: Table 2: 12-group 770: Division of 385 in 176 -/+1 and 209 -/+1 in table 2 appears in the ES-chain as interval 177 and number 208 = 3', the sums of columns U1 and A1. (-/+2 gives G1 + C1.)       Number 385 from another, simpler series, an additional note: 3/5 + 3/4 + 3/3 + 3/2 , x 102 =  385     3/5 + 3/2, x 102 = 210   (7 x 30, 6 x 35)     3/4 + 3/3, x 102 = 175   (7 x 25, 5 x 35)   a) Individual codon groups are closely related to intervals in the chain: Fig 5-1: Mass of ams on individual codons in the ES-chain: UG: Trp + Cys, GA Glu + Asp,  AG Arg + Ser, GU Val, AC Thr, CA His + Gln, UC Ser, CU Leu. Note: 544 divided in a third way, 177 and 367: C2 = 133 = 177 - 44, G2 = 411 = 367 + 44. b) Factor 77 times 5 divided 3-2 is a remarkable feature in the 770-group of ams, table 5. In the ES-chain 77 is the interval 544 - 467, i. e.,. the whole chain divided in step     4' — 3'.  Table 5: Factor 77: Factor 11: It's suggested here that this factor 77 and factor 11 characterizing this group is derived from a deeper, more elementary level, a double-directed chain:                                                                           Cf. a file here. Mirror-codons, 1st and 2nd bases, code for masses of ams that all are dividable by factor 11:    UG + GU = 11 x 20, CA + AC = 11 x 18, GA + AG = 11 x 24, UC + CU = 11 x 8. A support for the suggestion of a two-way direction of the chain on this level is also that 4 →3 gives 43 + 34 = 77: the division of sums 231 in the table: 3 x 43 = 129, 3 x 34 = 102, +/-1 gives Trp (130) and Arg (101). +/-2 gives Asp + Gln (131) and Val + Leu (100).    (Cf. perhaps in 734-group: 2 x 54 = 108 = Tyr +1, 2 x 45 = 90 = Phe -1.) Factor 11 appears in the individual sums (-/+1), sum 132 in several pairs, GA, AG, also AU as Meth + one Ileu, besides in 88 -/+1 and UG 176 +1, CA 154 -1. (Biochemically it's perhaps natural to search for it's root in the CO2-molecule, 44A?) (It may be mentioned that halved numbers in the ES-chain x 10, with the inverted exponent 3/2, as 14,63/2, 12,63/2 etc. if abbreviated downwards to integers, give the chain 55 - 44 - 33 - 22 - 11.     Such a chain with increasing factor 1 to 5 as the following one gives the sum 385: 1 x 55 + 2 x 44 + 3 x 33 + 4 x 22 + 5 x 11 = 55 - 88 - 99 - 88 - 55 = 385: Odd steps = 209 = 11 x 19,, even steps 176 = 11 x 2 x 8.. (55 + 99 = 154, 2 x 88 + 55 = 231.). Factors 5 and 7 in 385 as 11 x 35 appear as the elementary numbers 5 and 4 + 3 in the basic series, also the numbers of ams in Gl, C1 and U2, A2 groups. (More about number 35 in the file here.) Factors 27 and 8: We observe that the sum of ams with differentiating 3rd base is 385 + 209 = 594, 2 x 11 x 27. The last row = 2 x 1 x 8.    For more about these factors 3^3 and 2^3, see file 14. c) 3rd bases are with one exception A or G in the row 1 of tables above with heavier ams, U or C in the lighter row 2. Exception is the CA-pair His - Gln, possibly connected with the fact that His is the only ams not derived from stations in Glycolysis - Citrate cycle but from the A-base. His can brake down to the end station α-ketoglutarate, origin for Glu and Gln. It may express a turn of direction regarding 3rd base, since U/C-coded ams generally derives from an earlier station than the A/G-coded, sharing first two bases - as along an axis Orotate <—> Hypoxanthine. Cf. U-base from Orotate and all U1-U2-coded ams from glycolysis. d) The equivalence between groups G1 + A1 with Form-coded ams and U1 + C1 with the Cross-coded ams follows from the one between pairs in row 3, both 88: Val +Thr and Leu + Ser. If the CU-codon sometimes gets translated as Ser as it's said, it could perhaps depend on this UC-CU-group as decided by number 88 and reflect the suggested underlying two-way direction in an elementary chain. e) N-Z-division in 770-group shows up to be the same -/+1 as between Form- and Cross-coded ams: 2 x 176 - 1 = 351 and 2 x 209 +1 = 419.    In the the other 12-group 734 the same concerns the A-U-group: N = U1-coded +1, Z = A1-coded -1. This is one among several examples of similar number divisions within different basis of mass divisions as along different coordinate axes. It makes the table of mixed codons almost 3-dimensional.     For another example of an "orthogonal" table, see for instance file 10 about number of atoms in codon bases. (Figure from "17 short files", 02-12.) f) There are three main divisions of number 752, 5' + 4' + 3':    752 = 292 - 460 in step 5'-4',    752 = 544 - 208 in step 4'-3', and    752 = 336 - 416, (544 - 208) - (2 x 208). The third division (+/-1) combines codon type groups in pairs across the two groups 770 and 734:    336 +1, x 2 = 674 = Form- + Pair-coded ams, 352 + 322    416 - 1, x 2 = 830 = Cross + RNA-coded ams, 418 + 412 II: 12-group 734: Table 3: 12-group 734 In this more irregular group it's the G+C-group versus U+A-group that appears as the main division, shown below. (The division in RNA- and Pair-coded deviates with -/+ 4 from 2 x 208 and 2 x 159.) Fig 5-2: Twelve-group 734: N-Z-division in the U+A-group: N = 256 ~U1-coded ams +1 Z = 319 = A1-coded ams -1. (The similar scheme as among mixed codon groups U1 = 255 = 208 + 49 -2, A1 = 320 = 2 x 159 + 2. Cf. an eventual displacement of Cys 47 from an A1-codon (Meth AUG?) to an U1-codon:          A1 = 497 = 544 - 47,          U1 = 463 = 416 + 47. It could support the thought of a displacement of Cys that we simultaneously, in the 12-group 734 A+U-coded ams = 575 have:          U1 = 255 = 208 + 47          A1 = 320 = 367 -  47 [Regarding the two 12-groups of ams 770 and 734 as 752 +/- 18, we can the division of the 734-group in G1 + A1 = 752 - 416 = 336, C1 + U1 = 416 - 18.(One reason perhaps why Pro, CC, has a tendency to get hydroxylated, yet only + O, 16 A?. Adding 2 H2O gives the sum 770 as in the other 12-group. Lys, AA-coded, in this 734-group has the same tendency.] Some individual mass numbers of ams approximately connected with the 12-group of non-mixed codons 734: 133 - 59 = 74, +/-1 Meth 75, Lys 73 59 -1, -2 = Asn 58, Ile1, Ile2, Leu2 = 57 252 - 159 = 93, -2 = Phe 208 - 100, -1 = Tyr 44, - 2 = Pro. 44 - 59 = 15 = Ala. 100 +1 = Arg. + Gly 1.] Asp and Ala are often regarded as typical for ams (a figure shown in file 06)..     Asp, R+B unbound = 133 = 5' - 2' in the ES-chain. R = 2' - 1'.    The difference as secondary interval defines the normal value 74 of B-chains.       Ala 15 becomes the secondary interval between intervals 4' - 3' and 2' - 1' = 44 --59,    bridging over the middle step 3' - 2'. Cf. that Ala may derive from Pyruvate or from    oxaloacetate. [Of the 24 individual mass numbers  of ams R, at lest 16 gather around number or intervals in the ES-chain: 4 around 73 with sum 292 +1, 4 around interval 44 with sum 177 (544 - 367), 6 at interval 59 -1,-2 with the two sets of Ile and Leu, 2 at 100 (+1) with two Arg.   ] III. A special operation, amino acid masses with exponent 2/3: If the mass numbers of R-chains of ams separately are "compressed" through exponent 2/3 (e.g. Trp 1302/3 = 25,66,), their codon grouped sums give approximate numbers at the middle of the ES-chain as shown in figure 5-3 below.     If not haphazard, it could hypothetically imply that the individualization of ams, if not occur, at least is connected with the middle of the chain. (Cf. an added dimensional aspect in end discussion.) Fig 5-3: Individually 'compressed' ams with exponent 2/3 Note the keto-amino polarity: C1 plus A1- groups 208,7., U1- plus G1-groups 158,2. Sum 366,8. ~ 367 = 3' + 2'.     Background tables for the sums in figure 5-3, see here (R) and here (R+B).   IV. Transformations between number-base systems (nb-x): To forestall later files:              nb-10   nb-8  G-base  151 = 227  C-base  111 = 157...Sum 384. Transformed together = 386. U-base  112 = 160 A-base  135 = 207...Sum 367 Here we have the central numbers of the two 12-groups. And two times the 4 bases transformed together (1018) gives 1772, exactly the sum of the unbound backbone chains (B-chains). These curious facts led to the investigations in files Transformations, such transformations eventually part of the reference system. See also about these numbers file Geometries and special arithmetic operations. and file Halved orbitals numbers in section II. V. The weight series of ams: Mass in order of heaviness: A division ~ 3/2 around the middle = 600 - 904: Gly → Asp = 14 aa, 1-15-31-31-42-43-45-47-57-57-57-57-58-59, sum 600 A Gln → Trp 10 aa, 72-73-73-75-81-91-101-101-107-130, sum 904

Individual research
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Table 24 amino acids (ams)
R-chsins, A, Z, N

Background model

Files here:
 I. The ES-chain Introduction 3. The exponent 2/3 number series Mass of codon grouped ams 4. Mass division on atom kinds, and on other bases 5. The two 12-groups - details 6. Backbone chains 7. N-Z-division and H-atoms 8. Geometries - Golden section Special arithmetical operations 9. Glycolysis and Citrate cycle: codon grouped amino acids on the basis of origin 10. The bases: - Some annotations 11. Transmitters and the ES-chain

 II. Simpler numeral series 12. Quotients. - Exponents 5-1 13. The 2x2-chain 16. An x3 series?

 III. Transformations between number-base systems 17. First observations 18. Totals and other notable things 20. Additions to files 17-18 21. Triplet series - An alternative series 22. Other substances

 Discussion References

All these files in 3 documents, pdf:
Section I, files 0-11

Section II, files 12-16
Section III, files 17-22
Discusssion, References in section III

The 17 files as one document,
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2018-11-20

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