ES-chain and main codon
domains of ams:

The elementary number series 5 to 0 with exponent 2**/**3 times
10^{2} 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 5^{2/3} - 4^{2/3} - 3^{2/3}
- 2^{2/3} - 1^{2/3} - 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** (5^{2/3} x 10^{2}) 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 = **2.92**9947

lg 16 **/** lg 3 = **2.52**3719...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.**

To **Mass
distribution on other bases than codons**