Biology / An elementary 5-dimensional model applied in different sciences
II. Nerve cells and the nerve impulse

1. Cell types in the nervous system (Ns):

Besides nerve cells there are several other additional cells around them in nervous tissue, with a generic term called glial cells. They correspond to anticenter in relation to central nerve cells in a polarization of neural tissue, also representing higher dimension degree (shortened d-degree) versus next lower one.
   If on the cell level nerve cells illustrate d-degree 4 in our model, with their long axons and their dendrites (directions outwards/inwards), glial cells will represent 3 (mass) and 2 (surfaces).

The glial cells derive from the neural crest, anticenter to the invaginating neural tube.
   They are further about 10 times as many, i.e. make up most of mass in the brain, a multitude versus nerve cells. This information concerns humans (Mf). (One hypothesis in the dimension model has been that d-degree steps are connected with 10-power steps.)
   Moreover, glial cells develop later in the fetus and in the history of evolution. They are absent in certain simply organized organisms, and myelin sheaths for instance, formed by glial cells, are mostly missing in invertebrates (Fz).
   Additionally, the relation between nerve cells and glial cells is expressly said to be of the complementary type in their internal processes: changes proceed in opposite directions. Increase of a substance in the one type gives a decrease in the other and the reverse (Kz p. 264, BA p. 115).

Apart from the immense amount of new knowledge, there are 5 types of glial cells mentioned in older references here: 3 in central Ns (CNS), 2 in peripheral Ns (PNS) and among these it's possible to identify steps towards lower d-degrees.
   Central types: astrocytes, oligodendrocytes and microglial cells.

Central glial cells:

Astrocytes are star-shaped (fig, Nf p. 293) and have functions and geometries illustrating both d-degree 3 and 2 in our model with outer poles 4a - 4b of directions and radial and circular poles of d-degree 2. Their extensions form" radii" (~ pole 3b) between nerve cells and blood vessels and are thought to be responsible for transport of nourishment to the nerve cells. Circularly (~ pole 3a) they tightly surround nerve cells. They are a filling material with supporting functions and in addition make up surfaces, lining all membranes and surfaces of mesodermal origin in the brain. Astrocytes exist both in the gray and the white substance of the brain.

Oligodendrocytes are mostly found in the white substance of nerve fibers - as if representing a step-displacement from astrocytes. They seem to enclose the nerve cells in a more ring-shaped way at their extensions. They form myelin sheaths around axons in the central Ns through fusion; cf. fusion as out of inward direction. It's a polarity of the type nucleus - shell, a relation d-degree 3 to 2 in structure. Cf. about peripheral Schwann-cells below.

Microglial cells, the 3rd type in central Ns, have been considered not to belong to the real neuroglial but to originate from mesoderm.
  The cells are phagocytes and have an amoeboid mobility. Thus, they seem to be a kind of wandering mesenchyme cells, the final step in the chain of tissue kinds.

To summarize, these three kinds of glial in central Ns have features that can be associated with last three steps in a dimension chain: 3 →> 2 →> 1→> 0/00.

Peripheral types of glial cells: Schwann cells and Satellite cells:

Satellite cells are small cells whose short projections surround the cell bodies of the big nerve cells: a typical anticenter as periphery and also a multitude in relation to the unit of the nerve cell (Photo Kz p. 162).

Finally, the Schwann cells form myelin sheaths around the long extensions (projections) of nerve cells, the axons, in PNS.
   In opposition to the cells that surround the very nerve cell bodies in CNS and in opposition to the similar role of oligodendrocytes that surround axons in CNS, these sheaths are formed through a rolling up their membranes (d-degree 2) around the axons as a kind of spiraling rotation. This opposition could be taken as an example of how the 0-00-relation center - anticenter changes character towards PNS and lower d-degrees: the rotational motion as 2-dimensional an expression for debranched degrees in lower steps.


Fig Ns-21-85

They give also an illustration of how a magnetic field, surrounding an electric wire, may be substantiated towards higher, superposed levels. Or geometrically an analogy to this. The relation becomes perpendicular as proposed in step 3 - 2, the radial versus circular poles.
   In their function it's possible to see a parallel to the polarity inhibition - stimulation but rapidly repeated on the same signal, a quantifying of a line. They maintain membrane polarization, equivalent with inhibition, with nodes between them for depolarizations, ~ stimulation. Also a form of pacing out a distance as we have described the last d-degree step 1 →> 0/00 in the model.
   And the physical quantity velocity increases through this arrangement.

2. The nerve cell:

Nerve cells and sex cells are in certain respects opposites as 00- and 0-poles: 

Fig Ns-22-31-2

Sex cells have potential for maximal differentiation while nerve cells are fully developed at start - and earlier thought not capable to divide. Sex cells are haploid before fertilization, nerve cells often tetraploid, so for instance in cerebellum.- a relation 1/4 in number of chromosomes.

The earliest nerve cell in history of evolution seems to have been a combined sensory and motor cell, a sensory receptor cell with motor axon. Indications of such cells have been found in the tentacles of sea anemones for instance (Ez p. 385 f).
   Then, the development has gone towards further polarizations, a division of functions on sensory cells and motor cells etc.

In the nerve cells from neural plate and neural tube the inward conducting projections, the dendrites, are many, the outward conducting projection one, the axon, as the 00-pole represent multitudes versus unity of the 0-pole.

A nerve cell: dendrites and axon:
   Fig Ns-23-87

In the macrostructure of Ns it's the motor neurons that first gather to centers in invertebrates - possible to see as an example of the primary function of the 0-pole.
   Arrangement of dendrites can have different structure but is generally more or less circular around the cell body (inward direction transformed to circular structure in 3rd d-degree according to the dimension model). While the axon outwards branches radially at target organs, an example of radial structure in d-degree 3 originating from 0-pole in the model.
   (Diameter of a nerve cell is about 5 - 100 μ, the one of an axon about 1 - 20 μ (LEL p. 27). Thus, the quotient should be circa 5/1.)

Other types of nerve cells are the bipolar and "pseudounipolar" ones which develop from the neural crest, i.e. from anticenter in relation to the neural tube.

Fig Ns-24-88-1

These cell types are possible to interpret as secondary in relation to the multi-dendritic ones. They belong to the inward-conducting sensory, peripheral system, the bipolar one for instance found in the retina.
   The pseudounipolar type develops from the bipolar, which can be regarded as expression for a center displacement, the conducting fiber displaced out from body of the cell. Center displacements towards lower degrees and higher levels are one principle in the dimension model.
   Thus, the series multi-dendritic →> bipolar →> pseudounipolar cells could be described in terms of angle steps of their extensions, from 360° to 180° in/out to 90° in relation to the cell body.

Fig Ns-25-88-2

Nerve cells contain much of protein filaments and tubuli in the cell body and out in plasma extremities, dendrites and axons as well as in cilia. Such organelles are common in other cells too as cell skeleton in the cytoplasm. A coordination of motions is also found in unicellular organism without a nervous system as protozoans (Ez p. 385) - organelles with conductive ability.
   Hence, nerve cells seem to be a specialization in this respect of primary radial transport structures and vector fields.

3. Nerve signals:

a) Two-way → one-way direction:
Some information indicates that nerve signals in an earlier stage of evolution were two-way directed - first later become one-way directed through chemical one-way direction over synapses. One has for instance found a "mirror symmetry" over synapses in jellyfishes with synaptic bladders on each side of the synapse (BA p. 114).
   In the early evolution of Ns dendrites and the very membrane of the cell body seem to have had an ability to react on electrical impulses, while they later only are chemically excitable. According to another source (Ez p. 385) nerve impulses in invertebrates sometimes seem to go in all directions in diffuse nerve nets.
   Such observations, if still valid, indicate an evolutionary polarization from double-direction to differentiation of functions and directions as in step 4 →> 3 →> 2 in our model. Cf. a similar polarization regarding stimulation - inhibition above.

b) Two phases in signal transportation, chemical and electric:
The synapses could be described as a discontinuity, an "energy gap" with a term from plasma physics. Such energy gaps should correspond to a transition from one physical quantity to another according to suggestions here, ultimately a change between d-degrees in a fundamental underlying dimension chain.
   The "carriers" of the nerve signal as a force changes from electric to chemical to electric again.
   From the viewpoint of biochemical phases, defined by types of chemical elements and bonds, the chemical phase with organic transmitters with bonds in 3 dimensions may be defined as phase 3 in relation to the electrolytic phase with metal ions, carriers of the electric signal.
   Underlying these two phases we have the elementary physical quantities Mass - Charge, assumed as a relation d-degree 3 - 2 in the dimension model.
   D-degree 3 may be regarded too as a deeper, underlying level, a binding force between charges on the superposed level, appearing in the synapses. To compare with how hormones were carrier of the information system before a nervous system developed. (In the dimension model higher d-degree is defined as binding force in relation to next lower one.)
   In addition, transport of the transmitters occurs in the center of axons, transport of charge along its surface, its membrane, also showing on the polarity 3 - 2 with its roots in the 0-00-polarity.

c) Charge - electromagnetic waves (EM-waves):
Charge as a physical quality in d-degree 2 according to presumption in the dimension model becomes connected with surfaces. An axon of a nerve cell is excitable even without cytoplasm. The electric potential should then be located to the border layer at membrane (d-degree 2) of the axon (Zf p. 182).
   The electric current follows from changes in the voltage-potential over axon membrane, carried through by inflow of Na+(sodium) and outflow of K+(potassium).
   The outflow of K+starts first about 0,5 ms after the inflow of Na+, when this reaches its maximum. This "phase displacement" resembles the one between electric and magnetic components in an electromagnetic wave and could probably be interpreted as a related formulation of the same structural principle - with K- and Na-ions corresponding to E- and M-factors in an EM-wave.

d) "Motions to / from each other" as poles 1a - 1b:
When Na+flows in through the membrane at an impulse, it means a depolarization over the membrane to 0 as in the dimension model "motions towards each other", pole 1a with origin in inward direction defines a 0'-pole. When K+ then flows out, it implies a re-polarization as "motions from each other" (pole 1b) with origin in outward direction defines an anticenter, a 00'-pole.

Fig Ns-26-91-1

The signal propagates at straight angle to in- and outflows as in EM-waves. Axons as lines are quantified.

Fig Ns-27

e) How does the nervous signal propagate within the axons?
The answer seems not very clear. The transport of electric currents is not depending on ion wandering in its cytoplasm. One theory is that the "wave" propagates through displacements of charge in a "bridge" of water molecules (Zf p. 202).
   It's was said above that an axon is excitable even without cytoplasm. In later sources (Wikipedia) the "electrically conductive" cytoplasm is seen as explanation for the internal spread of a wave from the local action potentials.
   Myelin sheaths that inhibit in- and outflows, increase the velocity of propagation (distance per second). They increase length of the steps between nodes, the distance. Hence, it cannot be transport of the ions in cytoplasm that drives the propagation but some more immediate change of charge as through electron displacements.

The action potential is transversal, the propagating "wave" longitudinal. It's processes in different dimensions. We could think about "waves" that in relation to "mass" may be interpreted as a development - or aspect - in the less substantial lower d-degrees 2 → 1 → → 0/00.
   In the series of chemical forces as expressed in bonds we have identified ion bonds in d-degree step 3 - 2, dipole bonds in step 2 - 1 and van der Waals bonds in step 1 - 0/00. The nervous signal appears as an expression for steps between these ion and dipole forces (probably also van der waals moments involved).
   The exchange of ions (Na+ / K+) with same charge seems driven by a concentration gradient, in terms of density mass/volume, and becomes in some sense a "binding force" as of higher d-degree in relation to quantified "dipole" waves of charge as electric currents. Mass versus charge in the model defined as a relation d-degree 3 to 2 and higher d-degrees postulated as binding force in next lower d-degree.
   There is the step from ions as whole atoms to electrons as carrier of the forces, and these simultaneously coupled to a step in phases, corresponding to d-degrees 3→>2 →> 1: crossing of membrane as mass in relation to the more fluid medium inside membrane.
   Another feature is the step from two-way to one-way direction, also an expression for a polarization step: An action potential (the ion exchange) may actually give electric currents in two directions, for instance when ignited at the middle of an axon. The phase displacement between in- and outflows of the ions becomes responsible for - or transformed to - the one-way direction of the current.

Direction (d-degree 4 in the model) of the concentration gradient and the electric current is closely connected, seems to guide all steps.
   Experiments show that if the polarity over the cell membrane artificially is reversed to positive inside, negative outside, the nerve impulse takes the opposite direction, backwards in axons.
   Expressed in terms of the dimension model it reveals the interdependence between polarizations in different d-degrees and poles that have the same character inherited from 0- or 00-pole.

When it concerns the chemical transport in the same direction within the axons, one has also found a type of peristaltic waves, which seem driven by the myelin sheaths. Cf. ring-shaped muscles around intestines. Such a peristaltic wave with transversal, circular and longitudinal contractions gets the same geometry on the chemical level as the nervous signal on the electric level.

Fig Ns-28-91-3

(Statically they get the form of standing EM-waves, cf. about worms in Evolution.)

f) "Ignition" of the nerve signal - curious details:

According to general descriptions the frequency modulated impulse gets ignited at outlet (hillock) of the axon from the cell body.
   One could possibly imagine the process as in this figure:


Fig Ns-29-92-1

However, it seems to be a curious fact that the action potential gets ignited from a trigger point further out in the axon (Nf p. 103).
   It sounds as if there was some sort of an "imaginary" quantum jump in the impulse through another dimension.
   In the dimension model 2 poles of a certain d-degree virtually exist as synchronous in next higher (underlying) d-degree, before the step of polarization to the lower d-degree has released 1 d-degree as a new factor of distance or time (motions).
   With the cell body as center, ~ a 0-pole, and the axon directed towards anticenter, the 00-pole, some location on this could be defined as a primary anticenter (decided by a distance or quantified by some other factor).
   It's then possible to think that the "quantum jump" passes through underlying, next higher d-degree (as d-degree 5 in the figure or d-degree 1 in relation to d-degree 0/00 of motions): the higher d-degree that includes both poles?


Fig Ns-30-92-2

Compare perhaps cilia where the motion can start furthest out and not seems driven by the cell body.

Another such curious observation: Out at sensory receptor cells the inward conducting nerve cells seem sometimes to have synapse vesicles towards the receptor cell, as if it sooner were the nerve fiber that affected the receptor cell than the reverse.
   This could perhaps be a related phenomenon, which could be described as a "picking up of stimulation" - from the opposite pole via another dimension, an underlying not polarized phase or d-degree?

g) The action potential, levels and ion numbers:

A nerve impulse:

Fig Ns-31-95-1

We can count on 5-6 levels of the potential over the membrane during one action potential:

Charge inside
­ impulse maximum - point for change of directions
­ 0 - zero charge - passage through the zero line
­ threshold level - "angle change" to "vertical" rise
­ | facilitated (graded)
­ normal rest potential - "horizontal" level
­ hyperpolarization - "horizontal" level

A sketch on the steps as a whole dimension chain:
- depolarizations interpreted as steps inwards towards higher d-degrees,
- polarizations as steps outwards towards lower d-degrees in the chain:

Steo 1 --> 0/00 debranched from step 5 --> 4:

Cell memrane in step 3 - 2. Inhibition -- Stimulation 2> 1 < 2
Amplitude modulation in d-degree 3. Impulse trigger in step 3 - 4
- Impulse between outer poles 0 -- 00.

Fig Ns-32-93-1

Ion numbers:
Na 11 Z, 3rd shell, as ionized 10 e-. 2nd shell
K   19 Z, 4th shell, as ionized 18 e-, 3rd shell
Numbers in the 2x2-chain behind the periodic system:


Fig Ns-33

Both atoms in the s-orbital of the shells, representing step 1-0/00.

Sum Z of Na + K = 30 = 2 times the sum of an elementary chain 5 →> 0:
15 -/+ 4 = Na Z - K Z.


Fig Ns-34-94-2

Concentrations of K+ and Na+ ions inside - outside the membrane in a certain part of the axon (1 μm x 1 μm x 0,1 μm according to reference Mf p. 35:


Fig Ns-35- 94-3a

Since the sums happen to give the sum 110 x 103 of the 2x2-chain above, the figures could be illustrated in this chain:


Fig Ns-36-94-3b

Cf. steps 1 - 2 - 3 and number relations between Na- and K-ions that get pumped in and out by the Na-K-pump to restore the rest potential concentrations. In different studies and different cells it has been found that the relation Na / K can be 2:1 or 3:1 or 3:2 (Nf. p. 43)


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© Åsa Wohlin
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Texts are mostly extractions from a booklet series, made publicly available in year 2000

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