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 6.  Backbone chains √π,  x  10^3 = 1772.45 ~ 24 B-chains unbound              .        √π x10^3     = 56.05 ~ one B-chain bound               . √56 56 56    = 752.101 ~ half the R-chains If these operations have sense, it remains for more advanced mathematicians to explain. What kind of geometry could correspond to the square root of π ? ————————————————————————————— The similar parts of ams, the backbone (B) part, make up a separate coordinate axis, not governed by codons. It gives a good reason not to include them when studying differentiation of R-chains. The B-chains appear in the ES-chain in groups of 6 (cf. the 4 codon type groups?).                                    R                                     | B-chains:    (H)NH2—CH—COO(H)   = 74 A. Times 6 = 444. Minus 1 H in the 4 ams Arg1,2 and Lys (charged), plus Pro gives 443. Total sum 1776 - 4H = 1772. Groups and condensations to bound B-chains are shown in figure 6-1: Fig 6-1: Condensation of B-chains in groups of six The division of the 6 unbound B-chains (444) in two intervals around the middle of the ES-chain supports the recognition of B-chains in this chain and connects R-chains with the middle step    Interval 544 to 367 = 177 = 6 x 29,5, the NH2(+H)-CH-part of a B-chain, and 367 to 100 = 267 = 6 x 44,5, the COO(H)-part of this chain as illustrated below. The decimal 0,5 may illustrate the displacement of H in COOH to N-group, charging both ends of B-chains. After condensation there is balance 28-28 between the groups, times 6 = 168 - 168. Fig 6-2: Division of interval 444 as 6 B-chains (Interval 292 to 208, 5' - 3', = 84 = 1,5 x 56, the bound B-chain. 111, 1/4 of 444 = 1,5 x 74, the unbound B-chain. Perhaps an aspect on why peptide bonds go on as if always a half was lacking?) The number of B-chains from the exponent series was grouped in 6: Two of the number series giving the R-chains with the operation below are not enough for the B-chains:     544 + 208, x 2 = 1504 = 24 R-chains     544 - 208, x 2  =   672 = 12 B-chains bound Should the first three steps in the exponent series eventually be read both forward and backwards, (as in the “triplet series 5-4-3 + 3-4-5 = 888, x 2 = 24 unbound B-chains à 74 A)? Eventually connected in some way with the opposite directions of R-chains in proteins? More about this triplet series in file II: 15.      It's often said that Asp - or Ala - constitute the elementary form of an ams.     Whole mass of Asp R+B = 133 = interval 292 <—>159 in the ES-chain, its R-chain 59 is following interval, 159 - 100, figure 6-3.     Number 74 for B-chains becomes a secondary interval as Ala, R 15, the secondary interval 44 - 59. (Cf. that origin of Ala can be both Pyruvate in glycolysis (2 x 44) and Oxaloacetate (132) in citrate cycle. Fig 6-3: Asp-Ala, R-chains 59, 15 A-base 135, /\ = 740740740...x10x: (Sign /\ here for inversion.) At the protein synthesis it is the A-base as AMP that binds to B-chains of ams and transports them to tRNAs. Square of this number 1/135 gives the "factor chain"                                                                . 1 x 54 = 54               ---> √ 54-86-96-84-50 = 74074,074074074... 2 x 43 = 86 3 x 32 = 96               370 / 5 = 74. Corresponding "factor chain" inwards = 235 4 x 21 = 84               = 5 x 47: 47 = R-chain of Cys which binds protein strings to more 5 x 10 = 50              complex structures. Sum     370        ~ 5 x 74 Two times the inverted number of the C-base 111 A gives 18 (~ H2O) as periodic number, 180180180...and with one 10-power of displacement it gives the difference* to inverted A-base 560560560..., the bound B-chains à 56.    It looks like a connection with the common A-C-C-ends of tRNAs at which the ams get attached, an intricate relation between mass of codon bases and ams where inversions appear as resonances in a complementary field? Only random associations? *(Inversion of the G-base as bound (150A) to the period 66666..x10x gives a difference to the inverted A-base that only is a displacement of one 10-power in the period 740740... as if guiding the move of tRNAs between positions on ribosomes?) Another association about ACC-ends of tRNAs:Sums of ams (R) with A- and C-contenting codons in 1st and/or 2nd position: A = 888+1.= AA + AU + AG + AC + GA + CA + UA C = 444 = CC + CG + CA + CU + GC + AC + UC, These sums happen to approximate numbers for groups of B-chains. A- plus two C-groups gives about the sum of 24 B-chains à 74 A. If the ACC-ends of tRNAs eventually should be part of a reference system, it seems surely very intricate. Keto-/amino polarity between bases: Peptide bonds when O- and N-groups meet from two ams remind of the keto-/amino polarity between the bases U + G versus A + C. Two groups of codons divided by this polarity give sums of ams R = 370, 5 x 74, -/+1 (Pair- + Cross-coded): UU + GG + UG + GU = 370 - 1 AA + CC + AC + CA  = 370 + 1. 370, corresponding to 5 B-chains à 74 A Number of different atoms in the B-chains unbound:     C 48 = 576 = 3 x 192     O 48 = 768 = 4 x 192 ...(Note C+ O ~1344, sum of bound B-chains.)     N 24 = 336     H = 96 -4 H (in Arg1, Arg2, Lys (charged) and in Pro)   *

Individual research
E-mail: a.wohlin@u5d.net

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,
pdf

Latest updating
2018-11-20

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