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 3.  The exponent 2/3 number series (ES) Mass of codon grouped amino acids ES-chain and main codon domains of ams: The elementary number series 5 to 0 with exponent 2/3 times 102 shows up to highly correlate with mass distribution on codon domains of ams, both the division on codons G+C — U+A (544 and 960), the 12-grouos of ams from tables 2 and 3 (770 and 734), codon type pairs as G+A — C+U and individual codon groups, especially the G- and C-groups. 1. Total mass and codon groups G+C and U+A: The series 52/3 - 42/3 - 32/3 - 22/3 - 12/3 - 0, times 100, gives the abbreviated numbers 292 - 252 - 208 - 159 - 100 - 0. Marking these numbers 5' - 4' etc. we have that 2 times 5' + 4' + 3' give mass sum of the 24 ams R = 2 x 752.    Note the correlation with number of ams, 2 x (5 + 4 + 3). Fig 3-1: The ES-chain: To repeat the way of writing: G1, C2, etc. refer to mass sums of side-chains (R) of ams coded by G as 1st base and those coded by C as 2nd base respectively etc.    G+C or U+A refers to the sums of coded ams (R), equal in 1st and 2nd base order. G + C = 292 + 252 = 544 U + A = 292 + 252 + 2 x 208.= 960 2. Number of ams, correlating with the elementary numbers 5 - 4 - 3: Fig 3-2: Number of ams: The individual and pairs of codon groups are given through minus/plus lower numbers or intervals in the series, reminding of the principle view of debranched degrees meeting "the other way around" in the background model:     Fig 3-3: A dimension chain, the loop version of the model: (For a very short description of the model, see here.) 3. Mixed and not-mixed codons, 12-groups 770 and 734: The two 12-groups of ams presented in tables 2 and 3 are given directly in a simple way, groups 544 and 208, -/+ 159 times 2: Fig 3-4: The two 12-groups 770 and 734: U- and A-groups in 734-group = 2 x 208 + 159 = 575,   G- and C-groups in 734-group = 159 (575 also = 3' + 2' + 1' = 467, + interval 3' - 1' = 108. UU + AU + AA = 467 +1, Tyr UA = 108 -1.) GG + GC + CC (Gly + Ala + Pro) = interval 59, -1, CG (Arg) = end interval 100, +1. Arg can transform to Pro leaving its end-group CN3H5 = 59. [In the background model the last step 1→ 0 is interpreted as a step from d-degree 1 into motions. It has been told that Arginine is especially rich in the tails of sperms. However, number 101 appears also in other contexts.] See further details in file The two 12-groups of ams. It may be added already here (see further file Mass division on atom kinds...) Mass of C-atoms in 770-group = 444 = 544 - 100 Mass of C-atoms in 734-group = 516 = 416 + 100, Cross- + RNA-codons: ams = 418 + 412 = 830 = 2 x 416, -2 Form- + Pair-codons:   ams = 352 + 322 = 674 = 2(544 - 208), +2 Adding bound B-chains to these codon type groups, we get sums approximately equivalent (~) with the division in R- and B-chains:   Cross   RNA    Form    Pair     418     412      352      322 R +  336     336      336      336 B     754     748      688      658 =      1502                1346      ~ R -2              ~ B +2 [In the sum of cross- plus pair-coded ams with R = 740, the close to equal division between U+G-codons and C+A-codons (the keto-/amino polarity) should be noted:: UU + GG + UG + GU = 370 -1 CC + AA + CA + AC = 370 + 1     See Short files,  17.9, 3. 370 equivalent with 5 B-chins unbound à 74 A. 370 = 367 +3, the other 2 codon-groups 2 x 382 = 2 x 385 - 3 ] 4. Purine - pyrimidine base pair groups, G+A and C+U: Base pair group divided in purine and pyrimidine kinds are shown below. It should be noted that we can regard the whole chain included through number 934 as 2 x 467: Fig 3-5: Base pair groups C+U, G + A: A division of 5', number 544, gives the purine and pyrimidine codon pairs from G+C, U+A: Or: G1 + A1 = 960 -  272 = 688       C1 + U1 = 544 + 272 = 816 Halving of 3', number 208, distributed inwards - "backwards" to 292 and 252  gives both a division on codon groups and on atom kinds, see file 04. 4b. Parents of he codon bases with mass 292 distributed to following numbers:  Number 292 (52/3 x 102) is the sum of Orotate (156) and Hypoxanthine (136), the parents to the pyrimidine and purine bases U, C and G, A. Just a coincidence?     Transferred to following two numbers in the ES-chain, times 2, happen to give the codon domain sums of ams in 1st base order, curiously enough: Fig 3-6: Remains to explain how this rather remarkable, simple derivations of mass numbers could be interpreted in terms of biological processes.    4c. Keto-/amino-acid polarity, a note: G1 + U2 = 628 = 920 (2 x 460) - 292 C1 + A2 = 876 = 584 (2 x 292) + 292 5. Single code base groups: G- and C-groups illustrate remarkably a similar -/+ operation of lower numbers in the chain: Fig 3-7: G-C-groups and numbers 100 - 159: G1 = 292 -  101 = 191,        C21 = 292 - 159 = 133 C1 = 252 + 101 = 353.        G21 = 252 + 159 = 411 U22 = 544 -  107 = 437       U1 = 252 + 208, +3 A22 = 416 + 107 = 523       A1 = 208 + 292,  -3 1 Note the changed order from 1st to 2nd base. U1 and A1 groups are less clear in derivations from the ES-chain than the G-C-groups; an alternative view with "polarization" of 544 in +/- 272: U1 = G1 (191)          + 272 = 463 A1 = C1 (353) + 416  - 272 = 497 Or: U2 = 544 – 208 = 336, + 101 A2 = 416 + 208 = 624, - 101 Or: A1: 500 (= 292 + 208) + ½ x 208 = 604, - 107 (~Tyr) = 497 U1: 460 (= 252 + 208), - ½ x 208 = 356, +107 (~Tyr) = 463 U1 and A1 mass sums of ams may naturally be indirectly derived exactly though operations from G1+A-group 688, - G1, U1+C1-group 816, - C1.     See also file 04, point 2. Another way to write the derivations: G1 = 5' - 1', -1        A1 = (5' + 4') - (3' - 2'), +2 = 497 C1 = 4' + 1', +1      U1 = ( 2 x 3') + (3' - 2'), - 2 = 463 C2 = 5' - 2'             U2 = (5' + 4') - (3' - 1'), +1 = 437 G2 = 4' + 2'            A2 = ( 2 x 3') + (3' - 1'), -1 = 523   About Tyr 107 and Arg 101: Since Tyr derives from Phe, UU-coded, we could eventually regard Tyr as an expression for the step U2 →.A2. Arg, which gets its end-group from the G-base, eventually from an G1-code?)    In the same way A1 = 544 - 47, U1 = 416 + 47: 47 = mass of Cys R with UG-codon, as if from Meth AUG-codon - but Cys generally is regarded as derived from Ser.    With interval 3' - 1' -1 = 107 and 2' - 1' = 59 +1 (see below), the difference become 47. (In the background model last step 1 to 0 represent the step to the d-degree of motions. Cf. that Arginine is said to be especially rich in the tails of sperms! However, number 101 appears also in other contexts.) (C1 = 4' + 3' = 460, - inerval 3' to 1', +1 ~ Tyr 107.) Interval 59 in step 2 →1, -/+ 1 = 58 and 60, gives the difference between code-base groups in 1st and 2nd base order: C2 = G1 -  58 G2 = C1 + 58 U1 = A2 -  60 A1 = U2 + 60 (Interval 59 in step 2' —1' may be associated with main contributions from outside into the citrate cycle: acetyl(-Coa) + OH, 59 (60) in the step from oxaloacetate 132 to citrate 192. Corresponding step 4'→> 3' in the ES-chain = 44 ~ CO2, the preceding contribution in the cycle, with pyruvate giving malate. 252 ---|---208 -- 159 --|-- 100 44 <— 15 —> 59 COO - CH3              See more about glycolysis-citrate cycle.) Note 1: Number 544 may be regarded as divided in three ways: 292 -- 252, 336 -- 208 and in interval 544 - 367 = 177 and 367. C2 = 133 = 177 -  44 (the 2nd interval 4' - 3', G2 = 411 = 367 + 44 All four 2nd base groups (-/+1) from the interval 44: 544 -  367, - 44  = 133 = C2-coded ams 208 + 159, + 44 = 411 = G2-coded ams 272 + 208, - 44  = 436 = U2-coded ams - 1 272 + 208, + 44 = 524 = A2-coded ams +1 For groups G2 and C2 we have also: 4' + 3' = 460, - middle interval 49 = 411 5''-  3' =   84, + middle interval 49 = 133 Note 2: -/+ Tyr from C1 to U1 ? C1 = 252 + 208  (= 460), - 107 (~Tyr) = 353. U1 = 252 + ½ x 208 + !07 (~Tyr) = 463 Note 3: G1-group 191 divided after 2nd base: GG + GA = 133 = 5' - 2'; GU + GC = 58 = 2' - 1', -1. Divisions within single base groups in 2nd base order: In G2 + C2: 1st base G or A: sum of ams = 193, ~ G1 +2 (GG + AG = 133; GC + AC = 60.). 1st base U or C: sum of ams = 351, ~ C1 - 2 (CG + UG = 278; CC + UC = 73) In U2 + A2: 1st base G2 or A2: sum of ams = 495, ~ A1 + 2. (GU + AU = 232; GA + AA = 263.) 1st base C2 or U2: sum of ams = 465, ~ U1 + 2 (CU + CA = 210; UU + UA = 255.) Number of ams in single base groups with odd number of ams:: Odd numbers of ams Even numbers of ams     G1, 5 ams 2nd base G, A: 3 ams, 2nd base C, U: 2 ams.     C1: 5 ams. 2nd base G, A: 3 ams, 2nd base C, U: 2 ams... division 3 -/2     U2: 7 ams: 1st base G, A: 4 ams, 1st base C, U: 3 ams     A2: 7 ams: 1st base G, A: 4 ams, 1st base C, U: 3 ams... division 4 - 3.     (Thanks to Tyr without partner) Two sets of the single base groups in 1st and 2nd base order: 5'  2 x 292 = 584,                - 100 =   484 = C1 + C2 - 2 4'  2 x 252 = 504                 +100 =   604 = G1 + G2 + 2 3'  2 x 208 = 416 + 584        - 100 =   900 = U1 + U2 (U1+U2 from the C-groups) 3'  2 x 208 = 416 + 504        +100 = 1020 = A1 + A2 (A1+A2 from the G-groups) 7. Individual codons and amino acid mass numbers: See file 05. 6. 3rd base groups: Number 292 as the sum of Hypoxanthine and Orotate, the parents to the code-bases from which these bases get synthesized, are connected with differentiation of codons in 3rd base: A/G (+A or G) or U/C, implying a connection too with 1st base in the anti-codons in tRNAs.    Mass sum of ams with differentiated codons in 3rd base = 1169 = 4 x 292 +1. It shows up to be divided nearly equal. (Also a coincidence!?)    G1 + A1: 584          = 2 x 292    C1 + U1: 584 +1.    = 2 x 292 +1 All ams with indifferent 3rd base = 335 = 544 - 208 = 336, -1 (336 if Pro CC before ring closed.) ES-chain with intervals in steps 5' - 4' - 3': 292 --- (40) --- 252 --(44) -- 208 4 x 292 +1 = sum of ams with differentiating 3rds base in codons.        4 x 40 = 160, - 1 = 159 = "2-base-coded" ams among non-mixed codon group        4 x 44 = 176 = "2-base-coded" ams in the group with mixed-codons. 4 x 208 = 832 = G2 + A2 with differencing 3rd base:                                        G2: 1 x 208 + 101, A2: 3 x 208 - 101. 4 x   84 = 336, +1 = C2 + U2                                        C2: 0 + U2: 337 We get 8 ams in each group 8 ams with 3rd base A/G or A or G = 638 (3 ams only one choice: AUG, AUA, UGG), 8 ams with 3rd base U/C                = 531 8 ams with indifferent 3rd base       = 335 Numbers 638 and 531 may eventually be derived in this way:    A/G-coded ams: 272 + 367 = 639,- 1 = (½ x 5' + 3' + 2') -1    U/C-coded ams: 272 + 259 = 531      = (½ x 5' + 2' + 1') 8. Some extra annotations to base pair groups: a) 84 - interval 292 - 208 = “5 - 3”: U+A: 960, - 84  = 876 = C1 + A2 G+C: 544, + 84 = 628 = G1 + U2. (C1 + 84 = U2) C2 + U2 = 570, + 84 = 654 = G1 + U1 = C2 + A2 - 2 G2 + A2 = 934, - 84  = 850 = C1 + A1 = G2 + U2 +2 In general terms these number operations as +/- 84 (5' ↔ 3') could express a process outwards - inwards: “5 → 4 → 3 → ← 3← 4 ← 5”. b) Examples of similarities in N and Z between base pair groups: N-number:       G1 + U1 = 299         = 299 = A2 + C2                        G2 + U2 = 377         = 377 = A1 + C1 Z-number:        G1 + U1 = 355   +2  = 357 = A2 + C2                        G2 + U2 = 471   +2   = 473 = A1 + C1 Crosswise addition N-Z between G2-C2-groups, U2-A2-groups gives the same numbers as Cross- plus Form-coded ams = 770, RNA- plus Pair-coded ams = 734: G2: N + C2: Z = 262, → 734 ← 472 = U2: N + A2: Z.    Interval 208 +2. G2: Z + C2: N = 282. → 770 ← 488 = U2: Z + A2: N.    Interval 208 - 2. c) Displacements 220 and 26 between groups in 1st and 2nd position: G1 to G2 and C1 to C2: +/- 220 = 2 x 110 and A1 to A2: -/+ 26 (See further file 7 and file 13 about N-Z-division.) U1 to U2 It may be noted here that G+C = 544, + 26 = 570 = C2 + U2,                                       (G2 411 + 26 = U2 437. C2 133 + 26 ~ 159, - 26 = 107.) U+A = 960, -  26 = 934 = A2 + G2. U+A = 960, -  110 = 850 = C1 + A1 (~ U --> C); 960 - 220 = 740 = Cross + Pair coded ams G+C = 544, + 110 = 654 = G1 + U1 (~ C --> U); 544 + 220 = 764 = Form + RNA-coded ams. 9. Some general annotations: a) Half the number 292 = 146 is the mass of α-ketoglutarate, from which Glu (147 A) derives directly with a central role for amination of the amino acids b) 146* happens also to be the number of base-pairs in DNA winded around the histones in chromosomes. Why this curiously exact number? *(Later in Wikipedia changed to 147.) c) 292 is also the mass of P-P-ribose part of bases in the form of coenzymes.    (Ribose 150 + two H3PO4 (98, x 2), - 3 x H2O). d) Another feature is that G- and C-coded ams "come first" in the ES-chain as connected with the numbers 5'- 4'. This agrees with what scientist have found in experiments where ams appear in liquids. There are also indications of a pressure towards more A-T-rich DNA during evolution according to the scientists, as in agreement with steps 5' → 4' →3' in the ES-chain, ams with A-U-codons including number 2 x 3'. e) P-ribose groups in nucleotides: e1) The P-ribose-groups in chain binding = 195 uncharged, 194 charged (64 or 63 + 131): 584, 2 x 292 in the ES-chain → 3 x 195 (-1). Could this number from the ES-chain perhaps be one aspect on the cause for triplets of the bases in codons? e2) A suggestion by Copley et al (2005) is that ams could have been synthesized at the inner OH-group of ribose in a string of nucleotides. In the illustration to this hypothesis a P-P-¨ribose group binds to two nucleotides.(P-ribose + bases). The whole ES-chain could somehow illustrate the mass numbers where the synthesis of ams should appear in the middle step : Fig. 3-8: Copley-figure numbers in ES: (P-P-ribose: 2 x 98 + 150, - 3 x 18 =292, P-ribose: 98 + 150, - 18)     Yet, here is counted with ribose in RNA, not deoxyribose, but with base pairs in DNA with the T-base instead of the U-base. Bonds (-18) to the bases also neglected or somehow occurring in the middle step. (Cf. 385 - 367 = 18. 544 - 159, 208 + 159). A little extra note about log-numbers 52, 42, 32: lg 25 / lg 3 = 2.929947 lg 16 / lg 3 = 2.523719...Sum 5.453666 lg   9 / lg 3 = 2   Testing of the ES-chain? 1) Only e.g. heavy water or other deviating isotope of C, N or O in the type of Miller    experiment. Does it change the reactions in any way? 2) Construct a peptide with atomic masses in accordance with the ES-chain, e. g .:     Glu,Glu,Lys,Glu - His,Gln,Leu,Pro - Trp,Cys,Ser - Ala,Gly,Pro - Arg ? (In a liquid of Miller type, with small variations in pH. Does it have any effect?   A Survey of derivations of codon-grouped ams sums from number in the ES-chain is available here.

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

Links and Notes

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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