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


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Classes of substances

Some tested aspects from the viewpoint of the dimension model.

1. How many main classes of substances to count on? 3-6 ?

- Carbohydrates — Porphyrines
- Proteins —     Nucleic acids, bases of the genetic code
- Lipids — Steroids (isoprenes)

We can try regarding the left and right classes as complementry pairs:

The classes as "poles" in a 3-dimensional co-oodinate system?

Connection between the classes in pairs:

Carbohydrates - via keto acids →to Succinyl~(CoA) → to Porphyrines,
Porphyrines → chlorophyll→ photosynthesis → synthesis of carbohydrates...

Proteins, amino acids - via Asp and Gly → to synthesis of pyrimidines and purines, the nucleic acids, U-C-T and A-G. (Asp ~ ½ of U-C-bases. Gly starting centre in A-G-bases) → to protein synthesis...

Lipids, fatty acids one branch from Acetyl~ , the other branch to isoprenes, steroids, carotenoids, uinones.

The polarity between open ("radial") chains and closed ("circular") rings may be observed, as one feature of complementary poles in the dimension model:
   (Condition: carbohydrates divided and transformed to keto acids.)

Interpretation of the 3 "coordinate axes" in a dimension chain as 3 levels ?

Level III                    Lipids         Steroids            
Level II                Amino acids    Bases (nucleic acids)
Level I               Carbohydrates   Porphyrines                               

Here we see the closing to ring forms as following from steps in lower d-degrees. (The order here of levels I-II-II corresponds to characteristic atom kinds O - N - C and their "A-Z-numbers".) From other aspects, the order of level I and II should be the opposite.

2. Classifications from aspects on elementary molecules:

2.1. D-degree of main form character:

Inward direction: fatty acids - hydrophobic
Outward direction: carbohydrates - hydrophilic
Secondarily polarized: amino acids of both kinds: hydrophilic/hydrophobic

2.2 Characterizing elements - valences:

Forms of the molecular parts: 3-2-1-dimensional;
Roles when bound together in macromolecules: 4-3-2-dimensional.
   Thus, the synthesis of the small molecular parts implies an increase of the dimension degree with 1 step :

(This aspect is of course a simplification. Amino acids for instance make up also structural part of d-degree 3, the radial 3b-pole in the model here. And lipids may be seen as characterized by the C-atom and have a more high degree role than usually are attributed to them?...)

2.3 Genes - proteins - carbohydrates - lipids in the cell as a "fruit":
   Growing and increasingly circular potentials towards lower d-degrees as one hypothetical aspect on a dimension chain:

Core - pulp - peel:

Ring forms as through inward direction in d-degree steps,
chains as outward direction in the pair of classes respectively?

4-3- and 2-1-steps: chains in outward direction, ring-forms in inward direction?
3-2 step: as double directed: carbohydrates.
0/00: outer poles meeting as 5', porphyrines.

2.5 The treatment of water:


Inside/outside mitochondria:

2.6. Synthesis in number of C-atoms as an aspect:

O: Carbohydrates C5   +   C1 → C3 + C3 (Pentosephosphate cycle: 3 C5 →5 C3)
N: Amino acids    C4   +   C2 → - C1 → C5 Glu (from citrate cycle); also ams from C3 molecules in glycolysis...
C: Fatty acids       C3   -    C1 + C2 x n.

Fatty acids: inverted direction in middle-step 3← 2.
- Pentosephosphate cycle 3C5→ 5C3: compare sum 15 of the elementary number series.

Middle level C4 + C2 → Citrate cycle - keto acids
                                                                Succinyl~ + Gly = C4 + C2,    
                                                                                                   ↓ - C1
                                                                        Porphyrines → Chlorophyll

A note about porphyrines and their "side-chains" or "rope ends" at the rings:
- Rings: C5 x 4
Chain ends         4 x (C3 + C2) before turning
becomes             1 x (C3 + C3), 2 x (C3 + C2), concerns Uroporphyrinogen III),
becomes             1 x (C3 + C3), 2 x (C2 + Cl), 1 x (Cl+CI),
                                                               this a principal in Haeme and Chlorophyll.
Reduction/cut/diminution of chain ends as a kind of step displacements ?
Cytochrome a: addition of an isoprene chain (isopentenyl~).

2.7 More complex molecules, the combinations:

3. A dimension chain with elementary physical concepts as suggested in files about Physics, connected tentatively with classes of substances:

The figure refer to a mix of aspects: connections agree approximately with forms and functions in the cell. (Lipids as responsible for potentials +/- over cell membranes.)
   However, connections don't agree with the view of polarization steps outwards in the chain: Bases don't "polarize" into proteins even if they guide the differentiation of amino acids. And proteins assuredly don't polarize into carbohydrates but individual amino acids "break down" to different stations in glycolysis and citrate cycle and most steps in these are double-directed. Hence, proteins may this way be transformed to carbohydrates. With the aspect of synthesis, this appears double-directed inwards and outwards respectively.

Most obvious example of a polarization giving complementary "poles" as partial structures in accordance with the dimension model is naturally the division of carbohydrates (hexose Glucose → Fructose) leading to amino acids (proteins) and fatty acids (lipids) respectively: Two forms making up radial versus circular parts in the cell as poles 3b versus 3a.
   (We may regard the radial 3b-pole as derived from the 0-pole in a haploid chain, the "circular" 3a-pole as derived from the 00-pole:
                        3a <— <— <—- 00
0 —> —> —> 3b                             )

To get this polarization - regarding direction of synthesis - in some correspondence with the figure above, a version of the loop model seems needed, the three polarization steps 5→ 3/2, 5 →4/1, 5 → 0/00:

[Cf. in the figure vertically 5-5-5 and Pentosephosphate cycle 3 x C5 → 5 x C3.]

Proteins: step 4-3, poles 4a/4b:

- Amino acids which in synthesis ( ~ inward direction) give parts of the codon bases.
- Enzymes as forces, polarizing / binding as 4a/4b-poles,
(- L/D-forms of amino acids (example of secondary double-direction), where one direction has been selected as dominating in higher species.)

Carbohydrates; step 3-2, poles 3a/3b;
- Number of C in pentoses 3 + 2, in glucose 3+1+2: The 6th C-atom gets bound in the middle of the C-chain. Hexoses divided C3/C3 as poles 3a/3b.
- 3a as the part transformed to glycerine, building "circular" backbone form of lipids,
3b developing to Pyruvate and Acetyl~ C2, starting synthesis of fatty acids.
- Also another polarity on macro-scale: 3a as cellulose type, with role as "spherical" coating, 3b amylos or glycogen as stored substrate in the cells, a complementarity similar to the type space / mass in the model.

Lipids, 2:
- Synthesis from the parts of carbohydrates, the poles 3b/3a.
- Number of C-atoms in syntheses: 2 + (3 -1), x n, Plus C3 for the backbone to    triglycerides."Linear" chains coupled to glycerine into 2-dimensional forms.
- Roles in membranes as demarcation, "shell", surfaces, d-degree 2.
- Charge (assumed as property defined as such at d-degree 2) across the membrane: negative inside, positive outside, inversely to the distribution of charge of atoms.(! Life as antimatter on a higher level! Cf. life as processes, the dimension chain in opposite directions to structure degrees.)
- The 2/1-division of triglycerides in directions from binding backbone (glycerine) to P-lipids and more complex .molecules as glycolipides.

Ring structures:

→ (squalene) → steroids → carotenoids → quinones: 2 → 1 → (0/00):
This class with the derivatives of isoprenes illustrate in many ways the d-degree steps 2 1 (0/00, the porphyrines).

- Synthesis of an isoprene as of fatty acids from Acetyl~, C2 but from 2 x C2 plus a third branch C2:(as a step 2 →2a/2b)
                       C2 + C2
                        + C2
- Lipids versus isoprenoids: two different ways to form 2-dimensional macromolecules: in lipids: 2 crossing coordinate axes, in steroids: wavy forms of chains closing to rings in opposite directions. This opposite use of C2-molecules seems to reflect a polarity of the kind radial versus circular in the synthesis itself.

- The wavy form of squalene as oscillation forms of max/min, convex/concave: equivalent with (~) poles 2a/2b, closed to steroids: flat planes (2).
- Steroids among other things parts of membranes, hence closely related lipids.
- Functions: among other things as hormones, the chemical signal system. Connected with light, electromagnetic waves, as in D-vitamin. In these functions also representing less of structure building, more of motions as in the polarity particles/waves in physics.

- Further carotenoids, xanthophylls connected with organelles for photolysis and a derivative as visual purple (rhodopsin) for light absorption in eyes. Long "linear" chains with ring-closed ends as in d-degree 1 with poles: 2a----1-----2b. Note the complementary directions of ring bows at the ends.

- Quinones: 1b ----- (0/00): Only "1-dimensional" isoprene chains, here connected to a ring from the amino acid Tyr (side chain 107 A), as from a 4-1-loop from proteins to last step.
- Function: Ubiquinone for instance: directly part of the "pathways" (cf. Distance), "elevator ropes", for photon energy and H2-transportation in the respiration cycle.

Porphyrines, 0/00:
- The synthesis giving a picture of inward directed vectors, pole 4a (Gly and Succinyl~) under rotation pointing to location for the metal ion. In some sense similar to "black holes" in macrocosm, "catching" light energy. (Outer poles of d-degree 4 = 0 and 00, from polarized d-degree 5.)
- As chlorophylls key substances in the big loop photolysis - respiration cycle (vegetative/animal worlds).
- In type of form c/ac-figures, centre - anticentre, 0 and 00-poles.

The polarity on the more fundamental, underlying level of chemical elements, appears here inverted: Non metals as representing outward directions from 0-pole form here anticenter (from 00-pole), while metals representing inward direction from 00-pole become centres. (Such a pole exchange has been assumed in he background model. Also in agreement with the general principle of stepwise building-in of the environment as anticenter. )

Codon bases in nucleic acids, the building stones for the genes:
- Responsible for integration of the "whole" (d-degree 5) , the unity of a cell.
- In the figure above proposed as representing a step 5 ← 4.
- Constructed by amino acids and some other molecules, as in synthesizing, inward    direction, associated here with ring forms.
- Are 5-4 in number.
- Represent the most typical complementarity in a pair relation as poles of a dimension degree in our model.
- Synthesis characterized by centre — anticentre respectively, the partial structures out of polarized d-degree 5.
- In one sense it's the polarization of base pairs to one-way direction which leads to the proteins, the class associated with d-degree 4-3: the separation of the double helix of DNA for copying of mRNA.
- The "haploid" role becomes a condition for the function of bases as "forces"in their role as coenzymes. Cf. that one-way direction is a condition for a force to be acting. Balanced, opposite forces cancel each other.)

- The "outer poles" (or partial structures) of d-degree 4 meet in the last step, in "d-degree 0/00" (of motions) to which the class of porphyrines has been attached here. DNA is also present in chloroplastes with chlorophyll for photolysis as in mitochondria with cytochromes for the respiration cycle. And in both Gly contributes at the synthesis, the simplest amino acid. (Gly as outward vector from 0-pole, centre, in G- and A-bases, as anticentre (?) vector inwards in porphyrines when combined with Succinyl~ chains).

8. Application of other aspects on a dimension chain:

a. Increasing one-way direction toward lower d-degrees.
One possible aspect is the number of bond directions of the macro-molecules:
- Proteins, folding or not, with bonds in at least 3 directions, surely often 4 as coenzymes. - Carbohydrates with bonds in 2-3 directions (3 for instance in glycogen with branched chains).
- Lipids with bonds in 1-2-directions (2 with glycerine).

b. Motional moments as Vibration - Rotation - Translation in 3 dimensions:
The aspect in the dimension model that d-degree of motions increases when d-degree of structure decreases in steps towards lower degrees have been dealt with in files about physics, applied to the atomic level. Surely it seems silly trying to apply this elementary hypothesis about motions, built on 1-2-atomic molecules, on the very complex biochemical level. Yet, here some views on the molecules from a similar aspect.

- Protein chains in the muscle fibres (actine/myosine) and their motion in/out may be regarded as a vibration (through pacing by hooks on the chains), an 1-dimensional motion as assumed in d-degree 4. (Muscles the organ for motions.)
   Perhaps the function of protein microtubules in cilia, elementary "linear" organs for motions, could be regarded as a substantiated form of linear vibration? (The motions of kinesin and dynein as "motor proteins", "walking" on tubules, see Wikipedia.)
  The first folding of protein chains on the underlying, elementary level could possibly be interpreted as a stepwise 1-dimensional motion through the 3-dimensional space.
   Surely however, a lot of other aspects on protein motions could multiply the degrees of motional patterns.

- Motional pattern of carbohydrates?
Do the macromolcules of amylos, glycogen or starch rotate, a 2-dimensional motion?!
  ( The spirals of amylos implies rotation in the structure, the branching of glycogen may be regarded as "translation in 3 dimensions", but these are examples of patterns in the synthesis. They don't correspond to motional patterns for the macromolecules, the aspect here.)

- With lipids associated in structure with d-degree step 2 (then 2-1 in elementary form) )the motional patterns should be 3-4-dimensional. The amoeba-like motions of membranes, in- and out invaginations, could be identified as an expression for such a 3-4-dimensional motion. Cf. in structure poles 4a/4b defined as outward/inward direction.

- About steroids as 2 ← 1-dimensional in structure and often attached and integrated in lipids, they assuredly move around 3-dimensionally in inner space - as sex hormones for instance, but also take part in the regulating of gene activity. Cf. the connection 4 - 1 in the loop model which should give a connection between genes/bases or repressors of proteins and steroids in the figure above. If this latter function could be interpreted as an expression for a 4-dimensional motional pattern is debatable. Originally "pumping" has been proposed as the form of 4-dimensional motion. Maybe also a typical vector character (with address) of a motion could be regarded as 4-dimensional?
   Long chains of isoprenes (polyprenoles) transport carbohydratepeptides through the cell wall in bacteria.

- A "5-dimensional" motion, when structure d-degree is zero (in d-degree 0/00) is in the model presumed as only the "pole exchange", the "germ" to Motions in itself. It could perhaps be identified as just the mentioned positioning of metal ions in the centre of porphyrines? And/or only with an internal change in charge, in electronic energy. In other aspects the porphyrines interpreted as principally 5-dimensional structures seem to be characterized of great immobility.

c. Higher d-degrees defined as binding forces in relation to lower d-degrees as structures:

Is this postulated definition in the model in any sense applicable to the classes of substances? "Binding" (sign <) - in which sense? And which molecule binds which in an addition?
    Generally it may be said that bases in the form of coenzymes with their P-groups (valence 5) binds many other substances and that proteins as enzymes act as both binding and polarizing forces.
   Regarding the classes in the suggested order, application of the aspect seems very debatable, even if some examples may be found illustrating it.

Bases <Proteins < Carbohydrates < Lipids < Isoprenes< kinones < porphyrines

- Bases< Proteins? (The inverse in histones !) How in rRNA, in repressors?
- Proteins < Carbohydrates ? Examples could be Glycoproteins (nearly all proteins in plasma are said to be of this kind, and often proteins extending through cell membranes).
- Carbohydrates < Lipids ? Glycerine < fatty aids, okay. The inverse in membranes? In glycolipids and gangliosides* (much of these in grey areas of brains), the complex combination of carbohydrates and fatty acids (including a transformation of amino acid Serin), it may really be discussed which part binds which.
- Lipids < Isoprenes as polyprenoles, okay, but
- Isoprenes < karotenes (fat-soluble) or quinones ?
- Quinones < porphyrines ?

* A ganglioside looks like an outline of an insect larva
(fatty acid part) eating leaves (the carbohydrate hexoses).

In short, the more complicated molecules seem integrating several steps along the suggested chain for classes.

d. The different classes of substances may be seen as undergoing different number of steps from chains towards higher d-degrees on superposed levels:

(5)-4-3-2-1:        4-5 levels of storage for DNA.
(4)-3-2-1:           3-4 for proteins as fibres, folded surfaces, globular forms to
                                    enzymes with coenzymes as 4-dimensional.
3-2-1                   2-3 for carbohydrates (C6), chains to rings to macro-chains,
                                    branched or folded or spiralled to volumes.
2-1:                     1-2 for steroids from isoprene chains.

9. Can the codon bases be connected with different classes of substances?
Only to a certain extent as it seems. Here bases as nucleotides - coenzymes.
According to limited data:

- TTP - cellulose synthesis
- UTP - carbohydrates, glucose synthesis, (also cellulose)

- CTP - lipids: connection between the amino acid Ser and fatty acids
- GTP - participation at protein synthesis on rRNA (and in the citrate cycle)
- ATP - general energy storing and transportations.

Most obvious is the connection UTP/TTP with carbohydrates. T/U-bases represent directions inwards (T) towards DNA and outward direction (U) towards active RNA, an essential opposition. (We could see the similar opposition expressed in cellulose as inward" enclosing cover in plant cells and the other carbohydrates inside the cells or parts of them outward directed from lipid membranes of the cells.)   
   There is also the fact that most of the essential amino acids which human beings cannot synthesize are U-base-coded.
   All amino acids with U in 1st and/or 2nd position in their codons derive from stations in the glycolysis of carbohydrates (glucose →fructose), a fact that presumably is connected with the role of UTP.

GTP-GDP keeps citrate cycle going around, by transforming Succinyl~ to Succinate. (Keto-acids in the cycle closely related amination.)
   GTP-GDP is also a factor in the protein synthesis at rRNA.
   "G proteins" act as "molecular switches", in transport of signals.
These data may give reason for connecting G-base more specifically to proteins?

CTP is said to be more specific: taking part as a coenzyme in the synthesis of glycerophospholipids and glycosylation of proteins (Wikipedia.) It is involved in adding the amino acid Serin to phospholipids.

ATP (with the A-base part in NADP, NAD and FAD) is obviously the least specified, a main energy storing molecule and engaged in a lot of processes.
    AAA+ proteins: - many polarizing functions - (as "protein degradation") and "intracellular transportations" and motions in cilia...
    As NAD the A-base is also involved in the respiration cycle with ubiquinone (located to d-degree 1-- 0/00).

A summary could look like this:


With the view on carbohydrates as fructose polarized a) towards keto- and amino acids in synthesizing direction inwards and b) toward fatty acids and lipids outwards, we get following picture, with d-degree steps marked:

Three number operations - without sense?
Mass sums of bases with +1 for bond to ribose:
G 151, A 135, T 126, U 112, C 111.

Wiith U/T-bases regarded as representing the division of directions of d-degree 4 (inwards: T/outwards: U), as in the views on protein synthesis:

a) T/4 + A/1 + G/3 + C/2 = 1/2 x 544,666. 544 an essential number in the mass analysis of the genetic code.

b) 4 x U +3 x G + 2 x C + 1 x A = 1258, = sum of side-chains of the 20 amino acids in the genetic code, + 1 C + 1 A = + 246 = 1504 = 20 + 4 double-coded ams R.

c. Dimension loops 4-1, 3-2 with similar numbers 141, 232, sum 373 =
mass numbers of T+U+A (126 + 112 + 135) and C+G+C ( 111 + 151 + 111).
373 in number-base system (nb-x) 8 = 251 in nb-10 =1/3 of 753, sum of triplets in the elementary number series 5 - 0, 543 + 210 or 432 + 321.


- Fatty acids - some general aspects
- 1/7 - fatty acids and collagen
- Carbohydrates

© 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.