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


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Introduction + Phases

See also file "The Cell"  under menue Biology, first pages

Some first general aspects

1. A dimension chain in the model here has 5 steps, 6 "borders" or states.

5 → 4 → 3 → 2 → 1 → 0/00

There are 5-4 bases in the genetic code.
There are 5-6 atoms forming the rings (C, C-N) in carbohydrates and bases.
There are 4-5-6 elements as the essential building stones for the structures of life chemistry (P-C-N-O/S-H) with valences 5-4-3-2-1.

- 4-5 or 5-6 cyclic processes have been regarded as condition for life (Marquand: Life, 1970).
- 4-5 cells in the development of the fertilized ovum becomes the embryo, according to some source.

Hence, there is a lot (and more than these things) to be said in favour of counting on 5 primary dimensions.
   Why "dimensions"? Here is assumed that numbers ultimately, at bottom, are rooted in dimensions, and a transformation through dimension steps to dimension degree (d-degree) 1 for instance give 5 x 1 units. (With d-degree 0/00 substantiated 6.

2. There are the millions of chemical substances - all the butyric acids, malic acids, formic acids of the chemists and thousands of other unpronounceable molecules which change names and identity only because they exchange an atom or move a group, all becoming a brushwood for non-chemists. Perhaps it could be regarded as an attempt to describe a forest through its spatial forms instead of in terms of trees, earth, stones?
   Perhaps all substances are as matrices to what in reality is simple; perhaps it is the processes as matrices to the individual substances that draw the simple patterns, or the gist of these processes?
   Dimension chains on a field level may be imagined working as fretsaws in the molecular substance as at production of jigsaw puzzles, a dimensional process of inward / outward developments where the small pieces get increasingly complex to interpret in comparison with the whole, the entirety.

3. The aspect from the entirety towards the parts has in the dimension model the same validity as a view in the opposite direction, the synthesizing aspect from parts toward the more complex units.
   If so, one should at a "pre-material" field level have mass numbers, virtual weights, which get distributed on atoms, translated to differentiated molecules and compounds. We have also that most elements in practice are found in the form of molecules.

(Is it possible to imagine that nuclear fission and molecular structures could occur simultaneously under certain density and temperature conditions? A differentiation of a whole mass to a multi-centre molecule? Atoms interpreted as "poles" out of a bigger unit in a process of varying fragmentation and simultaneously creating of bonds?
   It's probably only imaginable on an underlying level where the Time axis still is double directed? In macrocosm however, double and multiple stars seem to differentiate more or less simultaneously out of cosmic clouds: a fragmentation into bound systems as through "development inwards".)

Atoms can also be analysed as wave functions, as matter waves (in d-degrees (3)--2--1-- according to our model here). This makes it perhaps easier to understand their mutual connections as through underlying fields - and processes of disintegration and association as results of such things as diffraction and interference..

4. A conclusion of the dimension model is that the mass numbers ought to have a much bigger importance for which chemical compounds and molecules that are created than the common biochemistry is willing to count on.


5. A dimension chain where each step develops to whole new secondary dimension chains and steps in these to tertiary dimension chains, is equal to what here is called a level chain. It surely implies the same as"fractals".
   A first level chain:

We should imagine that a level chain is double directed at bottom, between outer poles in d-degree 4 or between macrocosm and microcosm, between a part, a unit and its surrounding, centre and anticentre.
   An alternative aspect is to regard a counterdirected unit O → ← O with equal energy level) from outside, from the environment, as a condition for new level steps.

Another aspect is to look at the dimension chain in right angle to the main axis, polarization steps as 5→4/1, 5→3/2: the development evolving through step 3--2 when the analysis concerns the dimension degrees of material units.
   Possibly too one could imagine underlying levels "inverted" to superposed ones as expression for the pole exchange 0--00, centre --- anticentre and change of direction.

6. According to first hypotheses in the dimension model the level development also implies
- centre displacement where anticentre becomes a new centre, as a kind of growing "strangeness", and
- a process towards increasing unidirection, differentiation to more and more specified addresses.

The chemical substances become connected over increasing distances as a result of this secondary development of new chains in each step of earlier dimension chains, connected via underlying levels in the same way as people's journeys over geographical distances and distant contacts may have roots in their earlier relationships and underlying psychological levels.
   (An illustration could be the cutting of mRNA before the translation process as redundant information. Back to the relevant level of connection? )
   Energy levels (as numbers) could function as addresses. Each step in a dimension chain or level chain may be assumed as representing a certain energy level, and molecular structures as complex results of dimension processes then get different energies. Interpreted as numbers (equivalent with personal code numbers) could then represent addresses to equal (complementary) poles or structures on a related level.

7. Assumptions in the dimension model is also that number of motion moments increases towards lower degrees and higher levels. "Lost" d-degrees in structure become translated into motions (and/or meeting "the other way around").
   This becomes also related to the optional level of analysis: the more dimensions attributed to the structure, the less to motions. In one formulation the number of "freedom degrees" should increase with increasing complexity of the molecules.
   If a simple atom or ion only has an unsophisticated pathway motion in its local area before it gets bound, a more complex molecule can be assumed to move in 1-2-3 dimensions, move on and between others keeping its unbound freedom with a more or less differentiated address (~ receptor) - as human beings on floors, between walls, through streets towards their destinations.

8. Level development could also imply displacements in roles of the involved atoms and molecules, a rising or lowering of the dimension degree or d-degree step that the unit, atom or molecule represents in relation to others at a certain stage or in a bigger context? A displacement in its role, expressed through displacements and angle changes on its underlying levels, as changed binding directions, variations in their relative electronegativity, changes in oxidation numbers etc.

Coordinate axes - directions - angle steps:

9. It should follow from the analysis of electron shells that all electrons involved in molecular bonds, orbitals and directions in space around an atom differ mutually, represent different dimension degrees and steps and levels or different poles of a d-degree. No coordinate axes can be equivalent in the sense that they are all the same, the magnetic polarity N-S included.
   One example is the central C-atom in amino acid tetrahedrons.

In addition to the division of the 4 directions into 3 + 1 (1 for the side chains) one has the R-H-axis in opposition to the axis NH2 -----COOH with character of inward / outward direction respectively, poles of d-degree 4, e. g. hydrophobic versus hydrophilic directions in Glu, and the axis of the peptide bindings, secondarily polarized in + and -, NH3+ and COO-, a polarization in the property charge.

Atoms direct the space.

It should be possible to regard them as micro-codes for dimension chains, therewith also for biochemical processes on superposed levels: codes similar to the genes in DNA for the proteins of cells, although of a more directly involved character.
   And different levels within the atoms should act on different superposed levels in the chemical processes via the orbitals as "field lines" in the environment?

10. The coding language on the chemical level is also an angle language. Compare for instance sp-hybridizations, boat- and chair forms of carbon rings etc. One may wonder if perhaps within the atom as "autonomous" a dimensional process is going on as a kind of "standing wave", then through the angle steps in repetition.

The magnetic poles of the Earth reverse now and then, a "pole exchange". Then perhaps the magnetic coordinate axes in atoms do the same? Of the same obscure reason. With the result that bonds get broken. (Perhaps an answer to why substances age, break down, have to be renewed?)
   If there is a connection between mass and angles, perhaps mass numbers - and valences - not unambiguously are integers (in number of u or e-). Binding capacity or potential could lie between integers and this become a factor in the force driving chemical processes. (Also to regard as a consequence of the assumed secondary development of new dimension chains in steps of the first one. Cf. fractals.)

11. In the parts about physics here it's suggested that we have a kind of polarity matter - antimatter on all levels. Then L/D-forms of amino acids would be one example on the molecular level. (Fungi and eventually some bacteria contain both forms, so it's said, but all higher organisms only the L-forms.) This would be one example of increasing unidirection in the development towards lower d-degrees and superposed levels.
   Perhaps, mentioned only as a speculation, the D-form of amino acid tetrahedrons in its elementary form exists as part or interval structure within DNA, as the complementary picture, its "negative" - regarded from a certain angle in the DNA-helix? Analogous then to the hypotheses (some decades ago) about a p --- anti-p-relation in the centre of atomic nuclei. (Cf. a pyrimidine ring as ring structure, in relation to two B-chains of an amino acid as a zigzag-way in the ring: C-C-N.)

12. Many amino acids and some nucleic acids too can spontaneously be formed in a soup of smaller molecules with the supply of energy in some form (Miller 1953 and many subsequent experiments). One may then imagine that the lightning or the other energy supplied defines a centre, that is a 0-pole as the condition for a dimensional development according to primary laws: a centre equivalent with a pole of d-degree 5. Or that it defines the main axis in a dimensional chain which also represents the energy steps?


13. A general aspect on biochemical processes is to regard them as efforts by a fragmented matter to recreate entireties - and at the same time solve number demands of dimension chains (probably with different types of mathematics in different d-degrees).
   The metabolism of the cell, its energy transports, copying processes, feedback mechanisms etc. should according to the hypotheses here be possible to describe as dimension chains through all levels from the elementary particle level to the cell level, to and fro, out- and inwards, in a certain similarity with standing waves.

14. With a Time aspect, we could adopt the description that what is "quantum jump" happenings on an underlying level, more and more develops in time toward superposed levels to increasingly more of processes in several steps.
   That which in the centre of an atom eventually may be called a "pole exchange" or an inversion, can on a biochemical level have developed to a long process (while other "jumps" still may be more as jumps, not yet have had the time to a secondary development in many steps)?
   Perhaps one example is the move of one oxygen atom from one end to the other in the aldehyde part of fructose: a process in about 10 steps in the glycolysis (from Glycerin-aldehyde to Pyruvate).

(Even if the cell chemistry seems fully developed from "the beginning", it may have taken some important seconds, equivalent with the creation of a material Universe after Big Bang. )

Interpreting processes as a fragmentation into several steps, it could also motivate a summation of the stages as in opposite direction, with exclusion of the Time axis.

Different stages - in simultaneous existence - becomes also free actors in different other processes.

15. Further, it has been assumed in this model that there is a gradual substantiation of the last steps in a dimension chain through counterdirection from other units. This could be one way to regard the covalent bonds, where atoms (as 0-poles) with their free valences as virtual lines or field lines are saturated with corresponding "field lines" from other atoms and chains as linear and get bound to surfaces and further to volumes through folding.
   The chemical principle addition (through condensation of similar units to "linear" chains) may generally be regarded as such a substantiation of the 1st d-degree on a superposed macromolecule level. Carbohydrate chains as n x glucose is one example, protein synthesis another.
    These additions could probably be interpreted as expressions on the biochemical level for longitudinal waves on the level of physics.
   Other additional processes are in reality summation of different stages of "the same" substance, as Acetyl~ and Malonyl~ in the fatty acid synthesis. (See Fatty acids.)

16. In the biochemical processes the wanderings or migrations of 2H are central.
The last step in a dimension chain, 1 →0/00, as a polarization into poles 1a/1b gives the sum of poles 2, 2 "E" as a potential value in the d-degree of Motions, the processes. This according to our assumptions in the model.

In each step outwards 2 E are debranched, corresponding with the 2H-migration.
(Cf. the way to write NADPH+H: indicating a difference between the 2 H, as between poles 1a and 1b, or roles of poles 0 and 00 in d-degree 0/00.
   On the elementary geometrical level the poles 1a and 1b represent virtual (haploid) lines - presumably for catching and aggregating from the environment. Representing possible connections with other dimension chains.

17. "Activating" of a substance, a molecule, could hypothetically be interpreted as a displacement half a step, corresponding to 1/2 dimension degree (perhaps from a pole to the main axis) or between interval and border in the dimension chain, (towards a binding or polarizing centre). The activation implies reasonably also a displacement of charge within the molecule - perhaps analogous with the depolarization in a nerve cell which releases a nervous signal when charge over the cell membrane becomes zero.

18. A consequence of the dimension model could be that also processes as motional patterns, as structures, could appear as 1-2-3-4-dimensional.
   It would be possible then to have "linear" processes and cyclic ones, rotating processes (as that in the porphyrine synthesis), wavy ones (as the synthesis of fatty acids could be described), double-directed versus unidirected processes, pole exchanges (as perhaps in the move of the COO-group in Pyruvate to Malonyl~ via Acetyl~ ). We could also find the geometrical opposition between radial versus circular/spherical structures when processes on a macro level are studied more closely, as between glycolysis and citrate cycle.

19. Cyclic processes can be interpreted in several ways, departing from our dimension model: as an expression for rotation, appearing in d-degree step 4→3, but also as the development of the 0-pole through steps -4-3-2-1 with angle steps in the same direction, re-coupling to the start. In this respect also an expression for the 00-pole, the pole of repetition and for manyfoldness. (Cf. perhaps the respiration cycle "within" the citrate cycle. ?)
   In general terms cyclic processes becomes expressions for the increasing unidirection towards lower d-degrees as towards higher levels.


20. The aggregation forms of matter, its different phases, may be regarded as steps in a dimension chain:

There are the 3-dimensional crystals of minerals and the 2-dimensional, plane H2O-molecules of water for instance. Identifying gases as 1-dimensional in structure seems perhaps a bit more problematic. However, in 2-atomic gases there is just one linear relation and most gases exist in the forms of molecules. Inert gases should more correctly perhaps be described as 0-dimensional ("points"). The gas phase appears in steps 2→1→, and it's reasonable to see plasma as a phase of type 0/00, where even the elementary link between charges, protons and electrons, are broken.

According to first aspects on our dimension model, there are in direction outwards a stepwise decreasing d-degree of structure, increasing d-degree of motions as translation of the lost d-degrees in structure. In the opposite ("synthesizing") direction, an increasing number of structure building bonds.
   - Temperature = motions (as vibration, rotation, translation) as polarizing "force" from
d-degree 0/00, breaking structures towards lower aggregation forms.
   - Density gradients = assumed here as the "physical quantity" in d-degree step 5→4, decreasing towards lower d-degrees. (Pressure one factor.)

21. Phases corresponding to d-degrees 4 and 5?
The state of matter in neutron stars is of course another phase, but hardly of the same structural kind as the other "phases", sooner as a compressed form of plasma, the antithesis to plasma, individual neutrons without external relations, total lack of an expressed outer structure, through pressure.
   A 4- (or 5)-dimensional aggregation form of matter of the structuring kind would simply oppose the definitions adopted in this model that mass (or matter) isn't defined as property before d-degree 3. The property disappears in black holes and at Big Bang there is only a mathematical point or singularity.

However, in life chemistry it seems as if we could talk about a new phase, of underlying elementary phases appearing in a new combination. Inverted to a superposed level, through d-degree step 3-2. All "phases" represented, even 4-dimensional "vector phases" as gradients of different kinds.. The plasma phase for instance appearing in photolysis, the separation of e- and H+, united again in the respiration cycle. The higher d-degrees are of course inherent in mass.

Using the term "phase" here is of course only one way to look at the creation of structures.
   The co-ordination of processes to serve the unit as a whole implies or looks like building 4-3-2-1-0-dimensional structures of pure motions as "building stones".
(Perhaps, regarding the dimension chain of motions, counterdirected to that of structure and with our simple assumption that number of motion moments agree with lost d-degrees in structure, it would be possible to identify 15 elementary kinds of motions in a cell?) In any case the number of motional moments would increase on superposed levels.*

[*About motion moments in different aggregation forms on the elementary non-life level: The hypothesis that lost d-degrees in structure should be looked for and found in external motions may often seem too primitive even if well-founded, when looking to type and number of motions. Yet it may perhaps throw light upon some behaviour of matter in the different aggregation forms:
- Solids: There is of course no 2-dimensional motion of "rotation" in parts of solid matter on earth - as the rotation of celestial bodies and atomic nucleons in macro- and microcosm. But growth of crystals with new layers of surfaces - and oscillations in lattices.
- Liquids: Through surface tension creeping by capillarity; liquid Helium creeping 3-dimensionally over all surfaces… Other 3-dimensional streams in liquids have been detected and studied.
- Gases: The different, well studied motional moments of 1-2-atomic gases: vibration, rotation and translation in 3 dimensions…Expansion and contraction (as it seems in celestial hydrogen clouds)…
- Plasmas: In the behaviour of plasmas it sounds quite possible to identify motions in 5 dimensions according to fusion research: spiralling, pumping, elevation anti-gravitationally, pole turning etc.]







© 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.