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
To Backbone chains.
