Biochemistry /a 5-dimensional model applied in different sciences -


To the background model

Files here

All files in one document,
pdf, 127 pages

Latest updated




The protein synthesis. Why does it look like this?

From DNA to Amino Acids - the Protein Synthesis:

At this very complicated level there are some remarkable, simple features, which seem to illustrate a dimension chain of the kind suggested in the pages about Physics:

There are about 5 steps in the process (as in figure above of a dimension chain on the model):
from DNA →mRNA →rRNA →tRNA →single amino acid to proteins
(peptide chains).

Forms in the process:
- mRNA as with a vector character, 4
- rRNA as "balls", volumes,            3
- tRNA a surface structure:              2

                 double DNA-chains ----- mRNA ----- rRNA --- tRNA ---- ams-----

1. We have the double DNA-spiral or chain in the central nucleus of the cell, a double-directed chain, with bonds between complementary code bases T--A, G--C as complementary poles "0 - 00". (About the complementary character see here.)

2. This double chain gets polarized, the chains separate - and one gets copied through contradictory direction from the manifold of single code bases in the surrounding (as anticentre") to mRNA, a single thread which moving outwards to the cytoplasm has a vector character, (d-degree 4). It is directed to the ribosomes located between the "centre and the anticentre" of the cell, between the nucleus and cell wall.

3. rRNA, the ribosomes, have the 3-dimensional form of small spherical balls where the mRNA gets attached.
   Here the meeting between tRNA and rRNA occurs (at right angles, of natural reasons, but compare the assumed angle 90° in d-degree 3 in the model).

4. tRNA, transferRNA, are shorter chains of code bases as nucleotides, chains separate for separate amino acids, as each lower dimension degree is a manifold in relation to the higher d-degree.
   tRNA has the form of cloverleafs, partly loops, partly linear, a 2-1-dimensional figuration.
In the middle of the central loop the codon for a certain amino acid is located.

5. In the opposite end of the tRNA, at the linear end which is similar in all tRNA molecules (bases A-C-C-), the individual amino acid gets attached.
   Then the similar parts of the amino acids, here called the "B-chains", get bound through condensation to protein chains, (in their turn then forming 1-2-3-4-dimensional structures).

The 5-dimensional chain can be understood as double-directed from, 5→4→3 → etc.
and "the other way around" from 5 to 0/00 and inwards.

(1-dimensional degrees branched off in steps outwards transformed to motions in d-degree 0/00 and bound to 1-2-dimensional forms meeting from anticentre (from "outside", according to description in Presentation of the model.)

Note: There are 5 histones, proteins of a certain, fundamental kind, on which DNA is rolled up: one of these 5 (called H1 or H5) seems to have a function related with this "all-embracing" character of "the other way around", linking DNA at both ends of a spool of 8 histones, the "nucleosome" (reference: Wikipedia). (Each spool binds 146 base pairs of DNA: note the number, 1/2 x 292: See page about Numbers or the pdf-file "Exponent series".)

Opposite directions in the process and the relation mRNA - tRNA:
The difference between T- and U-base represent the opposite directions:
- T inward direction towards the DNA strand, when not active, replaced by the
- U-base when a DNA-strand is copied to mRNA in the synthesis.
The only difference is a CH3-group in the T-base, obviously the chemical expression for inward direction.
   Many bases in tRNA have got this group added too, as if it were a fundamental chemical sign for "inwards" (+ 14 A).

In the 4 examples of tRNA given in the used reference here,
there is also a T-base in position 23 from the A-C-C-end, a single one. Rather odd. And at this position appears the same order of the 5 bases:
T - U - C - G - A.
   The ordinary U-bases of RNA is in tRNA also turned (to "pseudouridine"), as by an angle step, in their bond to the ribose part of the nucleotides. Compare the presumed angle steps in the dimension chain.

tRNA with its 2-dimensional, partly wavelike form (cf. suggested convex-concave as geometrical poles of d-degree 2) and only 3 bases, the codon, apparently essential for the protein synthesis, has similarities with the stage where mRNA on its way to rRNA, undergoes change: irrelevant parts of
its chain are cut off.

            4   mRNA       3                2     tRNA  1

This similarity could be read as a relation between step 4 → 3 outwards and
2 1 inwards, the dimension chain seen "orthogonal" as double directed with a meeting in step 3-2.
   According to the model we could have a 2-dimensional motion resulting from step 4→3, appearing inwards as a 2-dimensional structure.

(Chemists have asked how it is possible for the right ADP-transported amino acid to find the right tRNA when it is attached to the opposite end of the tRNA in relation to the place of its codon? If we presume more of motions in d-degree 2 according to the model, we could perhaps imagine fast moments of neighbourhood between these ends or "poles": other stages of structure impossible to detect in a laboratory ?)

Why this A-C-C-end of tRNA?
Similar in all tRNA:
    Triplets of a dimension chain inwards and mass numbers (A) of the bases:

       123....sum: 135 = A-base
       234....sum: 357 = A+C+C. Sum of the bases with +1 for the bond to ribose.

Intervals between the triplet numbers = 111 = C-base, mass-number.

the last triplet inwards, happens to be the mass-number of the G-nucleotide in chain bond, also = cGMP. GTP (523 A) was, at least earlier, suspected to take part in the peptide binding of the amino acids.


rRNA - the ribosomes:

We can note the locality of the small spheres on the "endoplasmatic reticulum", a structure of membranes in cytoplasm - 3-dimensional forms on 2-dimensional surfaces and, as said above, in "the middle" between the poles centre - anticentre of the cell.

It is said (page 336 in the English reference) that "groups of 5 or 6 individual ribosomes are held together" by a molecule of mRNA. Why just 5-6?
It's said too that bacteria has 5 ribosomes!

We can also note that ribosomes are made up of two parts with a mass relation 2/1:
"50 S" and "30 S": 1,1 x 10-6 u and 0,55 x 10-6 u.
The parts unite through the participation of Mg2+.

Still another thing about numbers:
Ribosomes consist of 40 - 60 % RNA, 60 - 40 % proteins, a 3-2- or 2-3 relation, as in the meeting in the middle of the dimension chain between the opposites:
code bases <--> proteins.
   Another reference says the relation is 64 % RNA, 36 % protein:
that would be a relation 8<2 - 6<2: compare the E-numbers in d-degrees 3-2, squared.


Number of bindings in the synthesis:
- DNA - DNA, in the double chain: a H-bond between atoms N ... H--O
- DNA - mRNA
- mRNA - rRNA
- tRNA - mRNA
- amino acid - tRNA
- Amino acid - amino acid: NH2---=O meeting,, condensation (-H2O)


Number of bases in the codons:

There are 5 bases, T-U-C-G-A, getting 4 in DNA and mRNA, getting 3 in the codons in the protein synthesis, or 3 - 2,5 - 2:
   the 3rd base indifferent in 1/3 if 24 codons and only separates A/G from U/C-bases in 1/3 of the codons, ~"2,5" bases,
- getting 1 base in the role as coenzymes: TTP-UTP-CTP-GTP-ATP
(or in -DP-form as in the figure.)


Bases - elementary kinds of substances:

Carbohydrates - Lipids - Proteins - Transportations
       T - U               C            G                    A

T- and U-bases in their role as coenzymes, TTP and UTP, are used for bonds in Carbohydrates (different kinds).
   Note too that all amino acids with U in first or second position in their codons are derived from the first stages of the glycolysis where carbohydrates are broken down.

C as coenzyme CTP is active in synthesis of Lipids.

G as coenzyme GTP takes part in the Protein synthesis above.

A as coenzyme represent the central energy store, as such corresponding to a lot of transportation.

A dimension chain, according to the model here, implies steps towards growing amount of kinetic energy (motions).

Compare the similar order of the bases in tRNA at position 23...: T-U-C-G-A!
(If the 4 examples should be typical.)
   (Surely or presumably the coenzymes of the bases take part in many other special syntheses and beak downs.)

Circa 5 levels of storage of DNA:
Diameter (Ø) = 20 - 100 - 300 - 2000 - 6000 Å:

5 → 4: The double strand as helix, Ø 20 Å
4 → 3: This thread rolled up on balls or cylinders of proteins
(histones?), Ø 100 Å
3 → 2: These strand of balls drawn up in a big spiral, Ø 300 Å
2 → 1: This in its turned drawn up in a thicker spiral, Ø 2000 Å
1 → 0/00: In last step this thicker spiral drawn up in a still
thicker spiral, Ø 6000 Å,
   making the arms of the X-formed chromosomes,
   and as a centre of this the centromer, with a structure of the type
0/00. Centre - anticentre, ~5'

D-degrees should be viewed as a suggestion. Alternatively we could see the d-degree of motions, from linear (1), 20 Å, to rotation (2), on "balls", 100 Å, to spiral motions (3 dimensions), 300 Å, to spiralling of higher orders in d-degrees 4 to 5, 2000 Å - 6000 Å.

Protein structures 1 - 2- -3 -4 -:

1 - Linear chains,
2 - 2-dimensional surfaces of laterally bound chains
3 - 3-dimensionally folded proteins, globular proteins
4 - gathered globular chains with centres of coenzymes,
      4 in haemoglobin for example.

The cilia or centromer structure perhaps interpretable as a 5th level ?

DNA-bases - 5 bonds between the two pairs:

There are 5 H-bonds (H for hydrogen) between NH and O= , or NH and N divided 3-2:
3 between G- and C-base,
2 between A and U-base .

Note that G- and C-bases have both free NH2- and =O groups,
while A- and U-bases are "polarized", A-base having only a free NH2-group,
U-base only =O-groups (keto-oxygen).

Some additional remarks:

Chromosomes - "lumosomes":
- See figure about quotients between spectral lines of the H-atom, centre in the DNA double helix:

Lyman-, Balmer-, Paschen-series for spectral lines of the H-atom:

m = 2, N = 5, 4, 3,→     &λ = 4341 - 4863 - 6565 Å:

(1/4 - 1/25) / (1/4 - 1/16) = 112 x 10-2 112 = U-base l
(1/4 - 1/16) / (1/4 - 1/9 ) = 135 x 10-2 135 = A-base
(1/4 - 1/25) / (1/4 - 1/9 ) = 151,2 x10-2 151 = G-base

And what about C-base?
The lowest spectral line of Oxygen 4368 Å. Quotient to the the middle spectra line here for H: 4863 Å = 111,3. x 10-2. (?)

[Quotients between spectral lines could in some way have relations to phase waves.?]

Could chromosomes have some more fundamental property common with light beams,
be seen as "lumosomes" ? Structured through the help of electromagnetic waves?
What then should correspond to the E and M factors in the EM-waves?
   On the most fundamental level perhaps the basic NHx-groups, inwards, ~ M, versus the acidic OHx- or =O-groups, outwards, ~E ?
   On a secondary level perhaps the chains of amino acids as "radial" versus codon bases
as "circular" ?
   On a third level the polarity between U-C-bases and A-G-bases ?

In any case, the close relation between DNA/RNA and proteins could get us presume some kind of entity "DAP", (DNA-Amino acids-Proteins), preceding the development of the process, according to views in this model. An entity belonging totally to an underground of mathematics?

To DNA-RNA-bases - synthesis and complementarity
To Numbers of Codon bases and some relations to numbers of amino acids




© Åsa Wohlin
Free to distribute if the source is mentioned.
Texts are mostly extractions from a booklet series in Swedish, made publicly available in 2000.