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 4.  Mass division on atom kinds and on other bases than codons 1. Mass division on kinds of atoms: First to observe is the fact the mass division on C-atoms versus other atoms is the same as between U+A-coded ams and G+C-coded ones: C-atoms, 80     = 960 N + O + S + H = 544 The division on codon grouped ams of the "substituents", N, O, S, H = 544: G1 + A1: 292 C1 + U1: 252 Mass of C-atoms in 12-group 770 = 444 = 544 -  100 Mass of C-atoms in 12-group 734 = 516 = 416 + 100, H-atoms: 252 - 100 = 152 = 4' - 1' N+O+S-atoms: 292 + 100 = 392 = 5' + 1' The division between N-atoms and S+O+H-atoms could perhaps be noted too: Mass of atoms in R: C + N = 3 x 376, ½ (5' + 4' + 3'). O + S + H = 376 10 O + 2 S + 152 H = 376 = 1/2 x 752                                                     |- 2 x 208 12 N = 168                       = 1/2 x 336 (544 - 208). 80 C + 12 N = 1128 = 3 x 376 2. The division of C-atoms on codon groups Purine - Pyrimidine pairs: and simultaneously on codon groups: s G1 + A1: 33 C = 292 + ½ x 208 = 396 C1 + U1: 47 C = 460 + ½ x 208 = 564   When one of the two 208-groups is divided on first numbers 292 - 252, we get the relations between mass division on atom kinds and on codon groups of ams shown below: Fig 4-1: Division of atom kinds and ams groups, halving 208 In table 4       below we find number 104 as the difference between groups G1 +C1 and U1 + A1. With number 416 uncounted, the sums get equally divided vertically and horizontally.    The arrangement could perhaps reveal a symmetric phase in step 5'- 4' along two axes (544) in opposite directions: C-atoms to/from "substitutes", before a stage 3' (416). 3. The keto-/amino acid polarity: Table 4: Mass of C-atoms in G+C = mass of other atoms in U+A The domain groups of ams along the third polarity between bases, the keto-/amino types, shows in 2nd base order a mass division on atom kinds with strong regularity: C-atoms: G2 + U2 = 576 = 3 x 192 (292 - 100). Other atoms = 272               C2 + A2 = 384 = 2 x 192 (292 - 100). Other atoms = 272 Cf. in B-chains unbound: C = 576, O = 2 x 384; N = 336 (544 - 208), H 96 - 4. 4. Number 192: This number 192 appears in many sums in the genetic code. Why? In the ES-chain = 5' - 1', the interval 292 -- 100. (I's the mass of citrate, isocitrate, however not an explanation. It's 3 times 64, 6 times 2^5.). 1536 - 1344 - 1152 - 960 - 768 - 576 - 384 - 192    8        7        6        5       4       3       2       1  x 192 1536 = sum of all C-atoms in 24 ams, R + B. 1344 = sum of 24 bound B-chains (24 x 56) 960 = U+A-coded ams 768 +2 = ams with mixed codons, 2 x 384 576 -1 = U+A-group in non-mixed codons 192 -1 = G1-coded ams 5. C-atoms in R-chains of ams as basis for mass division: This division doesn't concern codon distribution but seems related to the ES-series and number 584, 2 x 292, with certain assumptions. (Here C for carbon.)    Phe and Tyr are synthesized as 3C- plus 4C-molecules, Trp as 3C + 4C + 5C - 1C. Trp gets its B-chain from Ser, shares codon with Cys and can brake down to Ala, hence here regarded as "meeting the other way around", added to the l C group. Fig 4-2: Cn: 4C, 7C, 3C +0C, 2C, 1C + 9C (4 C: Arg1, Arg2, Lys, His = 356, + Leu1, Leu2, Ile1, Ile2 = 228. 7 C: Phe + Tyr = 198; 3 C: Glu, Gln, Val, Meth, Pro = 305;    0 C = Gly = 1; 2 C = Asp, Asn, Thr = 162; 1 C: Ala, Ser1, Ser 2, Cys = 124; 9 C: Trp = 130.) 6. Number of C-atoms in codon groups of ams as halvings: We may also note that number of C-atoms are approximately distributed on codon groups as 2/3 - 1/3 in two steps    53 C in U1+A1-coded ams (+1 in A2 + U2), ~ 2/3 x 81    27 C in G1+C1-coded ams (- 1 in G2 + C2), ~ 1/3 x 81     ↓→18 in C1, 19 in G2, ~ 2/3 x 27              9 in G1,   7 in C2, ~ 1/3 x 27 7. End atoms of R-chains as basis for mass division: - Ams with end atoms CHx plus Gly (H) = 420. - Ams with end atoms O, OH, S and no N = sum 468 - N in end-groups or in rings (Trp and His), including Gln and Asn = 616. 420 + 468 = 2 (544 - 100)  = 888 616           = 2 (208 + 100).= 616* *(2 Arg charged = 200 +2, rest 416 - 2) Note that all N-contenting ams but Trp derive from the citrate cycle. (Another division: ams more or less polar: 468 + 616 = 2 x 544 - 4. Non polar ams, the CHx-group = 2 x 208 + 4.) 7x: Three notes: a) A division of the G+C group of aa 544, 1st base order, after kind of end atoms, approximates the one between mixed and non-mixed codons, 385 and 159: b) [ U1 +A1 group 960, if S-contenting aa are added to the CHx-group: CHx: UU, UU, AU1, AU2, =262 S UG, AUG = 122....................................................Sum 384, 2 x 192 O: UA, UC, AC, AG = 214 N: UGG, AA, AG = 304.......Sum 518 (2 x 259) O-N AA = 58.............................+ 58............. .........Sum 576, 3 x 192 ] c) RNA- and Pair-coded aa divided after end atoms: H + CHx: 7 aa 2 x 208 - 2 S, OH, O-N, NHx: 5 aa: 2 x 159 + 2 8.  81 - 47, a division of number 128 and number of atoms: There are 128 C-atoms in the R- + B-chains of the 24 ams 128 = 544 - 416. His 81 and Cys 47 (mass of R-chains) cooperate in an enzyme to break fructose at the start of the glycolysis. The number of atoms in R-chains are exactly twice the total number of C-atoms in R+B-chains in groups G + C and U + A:    G1+C1: R+B = 47 C → all atoms in R =   94; (G2 + C2 46 and 91)    U1+A1: R+B = 81 C → all atoms in R = 162; (U2 + A2 82 and 165) Fig. 17 files, 03-03: Which skeleton doubles its projection in its radical part? The human body in the brain!?    U1 + A1-coded ams: 81 C = entire number of C-atoms in R-chains +1    G1 + C1-coded ams: 47 = entire number of C-atoms in B-chains - 1 Minus / plus 81 and 47 gives also from the codon groups of ams from 544 and 416: ½ x 544 -  81 = G1, 191 ½ x 544 + 81 = C1, 353 544 - 81 = U1, 463.     544 - 47 = A1, 497 416 + 81 = A1, 497     416 + 47 = U1, 463....difference 34 = 81 - 47. Why this division of 128 in 81 - 47? Cf. figure 13-2 in file 13 about the 2x2-chain:. Total 94 x 16 or 47 x 32 = 1504         94 + 34 = 128, ½ x 94 = 47, + 34 = 81 Cf. R-chains of His 81 nd Cys 47 making up the active center of he enzyme halving fructose at the start of glycolysis. 9. A similar "perpendicular" relation between number of C and H in the same codon groups:    C + H: total in U+A-coded ams R = 152, ~ number of H in all R-chains    C + H: total in G+C-coded ams R =   80, ~ number of C in all R-chains. (See figure here.) 10. Some gatthered points from above and other files with a link to tables in an Appendix: 1. In ams groups G1 + C1 and U1 + A1 the number of atoms in side chains R is exactly 2 times the total number of C-atoms in R+B chains; (File 04 §8): G + C: 47 C (R+B) → 94 atoms (R) U + A: 81 C (R+B) → 162 atoms (R). 2. R + B chains unbound: G1 + C1 differs from G2 + C2 with 1 unit: 1282 → 1281. U1 + A1 1994 → U2 + A2 = 1995. 3. The keto-/amino acid polarity, ams R+B unbound, sum 3276: A1 + C1 = G2 + U2 = 1808 Number of atoms also the same1 267 G1 + U1 = A2 + C2 = 1468 - " - : 201 1 However, not equally divided on atom kinds. Cf. Transformations, file. 17, § 1.4.1. 4. The keto-/amino acid polarity, R-chains, (file 04-§3). A2 + C2 — G2 + U2: 384 — 576, a 2/3 division of C-atoms 544 divided equally on the groups: 272 — 272: 'substituents'. 5. Mass division between purines and pyrimidines: file 04 § 1, 2. 544 into 292 - 252 between purines and pyrimidines: A1+G1: C-atoms 292 + 104 = 396. Substituents 292 U1 + C1: C-atoms 252 + 104, + 208 (= 564). Substituents 252 6. R+B bound, sum 2848: C-atoms 1536, substituents 1312 = 4 x 192 (B) + 544 (R) See file 13 §6, 1760 - 224-steps. 7. R+B bound: Number of atoms without C = 272. (+ 128 C = 400.) Condensation from 468 atoms, R+B unbound, implying + 4H - 3 x 24. 8. 20 ams: 384 atoms, the two sets of ams with two codons = + 84 atoms (5' - 3'). 384 divided on R- and B-chains 207 — 177, about the same division as in the ES-chain and Table 1 on ams with mixed codons. Link to Appendix: Tables on mass division on atom kinds and number of atoms, 1st and 2nd base order, in R, R+B unbound and in R+B bound.

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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

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2018-11-20

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