Considering the electrical component of the action potential (see Figure 1): it has a duration that depends on the type of neuron being considered.

d A P = t 2 − t 0 (2)

The duration of the effective signal of the action potential, the spike, is almost constant regardless of the type of neuron considered.

d s p i k e = t 1 − t 0 (3)

There is only one spike at any given time t and at a location x on the axon.

This uniqueness suggests that its purely electrical nature may be already questionable. This is particularly true since it is constantly stated that a tiny fraction of the locally available ions are used. What is the phenomenon that prevents most of the unused ions from reacting and neutralizing the action potential at this place?

On the other hand, it is possible to have several action potentials on the same axon and at the same time but of course located at different locations. This primordial and undeniable concept, which has been observed time and again, is not in favor of an electrical propagation.

Each AP is electrically independent of the others that may be present on the axon. Even when there is a pulse train, electrical interference only occurs during the refractory period.

The AP moves (usually) along the axon in only one direction. Its speed of displacement or conduction velocity v depends on the nature of the surrounding myelin.

The conduction velocity is always higher for myelinated neurons. The exception concerning giant axons is very controversial: Most would be a fusion of several hundred of axons, which suggests a very different functioning that may involve neurons selection.

v u n m y e l < v m y e l (4)

The electrical component of the action potential is incompletely recorded. It does not reflect in any way its spatial dimension related to its geometry. He is also unable to give us back a major notion, his conduction velocity.

Because it has a duration d s p i k e and also because it has a velocity ( v m y e l or v u n m y e l ), it is possible to say that the spike has a length.

The spike occupies a finite surface on the axon. It can therefore be said that it has a rather cylindrical shape that has a length l m y e l or l u n m y e l .

It should be noted, however, that while the length appears to be proportional to the conduction velocity for unmyelinated fibres, the spike length appears to be fixed for myelinated axons.

This raises more questions about the electrical nature of the AP, a second time.

l m y e l = C o n s t (5)

l u n m y e l = v u n m y e l ⋅ d s p i k e (6)

All axons are myelinated [7] . They are all surrounded by specialized cells that produce a myelin barrier that may or may not be compact [8] . It is interesting to ask the question of the existence of so-called unmyelinated fibers since neuro-cytology dispels this myth through anatomical evidence [6] [9] (Figure 2).

The worst example is the giant squid axon [10] used as a model in the HH model: It is surrounded by the thickest (0.7 to 1.3 μm) myelin layer in the animal kingdom and yet we are taught that it is not myelinated and it is a fusion of multiple axons [11] .

Most of the electrical component of the AP is negative. It is only at the moment of the peak that the voltage becomes very transiently positive before returning to negative again.

The propagation of the action potential on the unmyelinated axon is continuously observable.

It is therefore possible to know the position at a time t. of the AP by simple computation, with x 0 the position of the AP at a time t 0 :

d t = v u n m y e l ⋅ t + x 0 (7)

We have seen that for unmyelinated fibers, the action potential has a physical length on the axon. The usual cylindrical shape of the neuron extension allows us to conclude that the AP occupies a surface proportional to the speed.

s = 2 π ⋅ r u n m y e l ⋅ ( v u n m y e l ⋅ d s p i k e ) (8)

s ∝ v u n m y e l (9)

It is therefore also possible to assume that energy consumption is proportional to speed. It is also likely that the ionic quantities and their counterparts, the ion channels involved, will become too large to ensure any propagation.

It is also perfectly understandable that this operating mode for signal transmission, robust for low speeds, becomes a candidate for failure because it is exposed to possible mechanical obstacles.

The speeds normally observed for this type of neurons are between 0.2 and 3 m∙s⁻¹.

The spike has a more or less constant duration, this length varies between 2 × 10⁻⁴ and 3 × 10⁻³ m.

In myelinated neurons, conduction is called saltatory although this statement is not yet clear-cut [12] [13] [14] [15] . It is stated, without irrefutable evidence, that the action potential seems to jump from noR to the next one [16] [17] . The process would of course be linked to the presence of myelin, which would improve electrical conduction while reducing energy costs [18] .

It can be said that it is not possible to increase the transmission speed of a signal without increasing the energy expenditure. This goes beyond the thermodynamic principles and all the theories we apply and therefore successfully test every day on electrical signals.

We will demonstrate this without any uncertainty or ambiguity.

As mentioned above, the action potential, for myelinated fibers, is observed over a constant length related to the anatomy of the myelin surrounding the axon. This is the size of the noR which is about 1.0 μm. The small surface area suggests a better robustness.

However, the AP is continuously observable, in time, at this same noR.

On the other hand, the surface area occupied on the axon is greatly reduced and it could therefore be assumed that there is a reduction in the energy and physical resources (ion channels) involved.

This configuration contradicts any possible electrical propagation.

If we know the internode length, it is perfectly possible to know both the distance covered since the instant t 0 but also the number of jumped nodes n o R t .

In the same way, we calculate the distance covered, which will then be divided by the length of the internode and the length of the node itself.

Let us not neglect any length because all of them seem to be more crucial than they appear [19] [20] [21] .

d t = v m y e l ⋅ t (10)

n o R t = d t l i n o R + l n o R (11)

This gives us with a l i n o R value of 10⁻³ and l n o R of 10⁻⁶ m and a speed between 4 and 150 m∙s⁻¹:

This gives already extraordinary numbers for our neurons of 4000 and 149,850 noR jumped in only 1 second.

It is also perfectly possible to state without any doubt with Equation (10) and Equation (11) that the number of noRs crossed is both proportional to the duration t and the conduction speed v m y e l .

Our trains have a length determined by their speed and type. They are more or less long as described above for unmyelinated neurons. A train, on the opposite, appears relatively compressed (it should be even more so) and reflects the length of the AP at a noR (see Figure 3).

The axons will look like rails, of course.

We add tunnels to represent, as it should be, the compact myelin because in fact much of the riddle lies in the darkness of their understanding.

Our observer is asked to position himself at location X and start his stopwatch as soon as he sees the headlights of a train and stop it when he sees the taillights.

He is certain: the transit time was almost identical for all 3 trains.

He noted that the farthest train seemed to go the fastest. Anyway, faster than the one on the central line.

He has a doubt about the last one: it seems that he appeared directly between the two tunnels and disappeared in the same way. He even had the impression that the train was running well in front of him but more like a movie than a real train, weird.

Let’s twist the neck once and for all to this saltatory conduction.

We have been led to believe for too long that the action potential jumps from noR to noR and that is what explains its increased speed [12] [22] .

Let’s place a second observer at the exit of the first tunnel and ask him to perform the same measurements at the same time as the first one.

The second observer must see the train’s headlights while the first observer must see the rear lights: there would then be an unequivocal saltatory conduction (see Figure 4).

That is not what is being witnessed [23] !

Otherwise, the observation time should necessarily decrease as the speed increases.

There is only one solution that can satisfy our observation: There are two trains.

It can be said that the number of APs existing on the axon is proportional to the conduction speed (see Figure 5).

We already knew this truth from the beginning of this article with the Equations (1), (10) and (11).

Some of us cannot of course be convinced by this evidence. It doesn’t matter because mathematics is always uncompromising.

Let us take an easy and uncontroversial example to satisfy potential critics.

A myelinated fiber with an internode length of 2 × 10⁻³ m, an AP (spike) of 5 × 10⁻⁴ s and an average velocity of 40 m∙s⁻¹.

If it is true that it is only at the end of the action potential that the signal jumps to the next noR then we should be able to confirm by computation the speed of 40 m∙s⁻¹.

1 d s p i k e ⋅ l i n o R = 1 5 × 10 − 4 × 2 × 10 − 3 = 4.0   m ⋅ s − 1 ≪ 40   m ⋅ s − 1 (12)

Or by the opposite method of calculation;

v m y e l ⋅ d s p i k e = 40 × 5 × 10 − 4 = 2.0 × 10 − 2   m ≫ 2 × 10 − 3   m (13)

It is also possible to check that the system reaches its low operating limit of 4.0 m∙s⁻¹ which is well over the length of the internode.

v m y e l ⋅ d s p i k e = 4.0 × 5 × 10 − 4 = 2.0 × 10 − 3   m (14)

The system therefore only works when;

v m y e l ⋅ d s p i k e ≥ l i n o R (15)

It is only logical that it is the front of the train that triggers the departure of the next train. It is unlikely that the rear would be able to trigger an event that would be in front of the head of the train.

Saltatory conduction is not verified but we then have a major new problem: If there are several APs on the axon how, on arrival, there is only one left? Time is the obvious answer! If an AP starts at an noR #1 then it always ends before the one at noR #2. There is no possibility of it being transmitted a second time.

It is undeniable that the cells contain ions. It is also not disputed that the movement of these ions creates an electric field and also a potential difference.

It is perfectly possible to elicit an AP with an electrical stimulus, but where is the generator of this impulse in the neuron? A few ions that have changed places, nothing more but nothing less.

Nevertheless, in the absence of an electrical circuit, these movements remain governed by the laws of electrostatics.

Of course, we must try to prove it, whereas an abundance of articles use, for example, an “electric” neuron model, the Hodgkin and Huxley model. It’s a kind of reference, but is it accurate?

While it is true, and why contest it, that the action potential is closely linked to the presence of ion channels, it is also perfectly proven that myelin damage, compact or not (as in multiple sclerosis) leads to a slower conduction rate for all types of fibres. The action potential is even eliminated when the compact myelin disappears consecutively over a tiny length of the axon [24] .

It is therefore also perfectly possible to state that conduction can only be carried out correctly when ion channels are present (which is why unmyelinated fibres are less affected in MS). And, it is undeniably known that the internodal zone has an area where ion channels are completely absent. If the conduction stops then it cannot be electric in the sense that we mean it.

We will explain why the para-nodal zone, on the other hand, has totally essential ion channels.

It is accepted that the axon membrane undergoes a slight vertical deformation in unmyelinated fibers. We also know that there is no doubt that the membrane undergoes a phase transition during the AP. Nor can we dispute the essential presence of ion channels.

There are also many references [25] - [30] showing that the compression of axons, myelinated or not, leads to a slowing down and then the disappearance of APs.

As it is also known that the optimal conduction rate depends on the quality of the myelin.

We have enough evidence to understand that the basic propagation system is based on a vertical force associated with horizontal translation (see Figure 6). This process is repeated throughout the axon, which obviously wastes time and energy.

If we accept that increased speed is linked to an improvement in the basic system, then we must admit that by reducing the presence of action potential at noR, it leads to a summation of the forces we have described. We have a larger but slower vertical and horizontal component. The solution being of course to transform this large quantity gathered at the noR into a faster horizontal component than usual.

The best way to change the speed of a system that is too slow is to replace it with a faster one.

If the neuron membrane is prevented from deforming by surrounding it with a sufficiently rigid envelope made of layers, reinforced by tight junctions, the mechanical wave is then sent to the next node in a liquid medium without much loss.

And it works: We use this kind of device every day in the industry.

It is quite easy to verify because the available speed can go up to more than 1500 m∙s⁻¹.

We need to solve our last problem.

The AP that activates the next noR is not transmitted because the ion channels under the myelin activate as soon as the “liquid” wave passes. These firm locks provide better strength and pressure transmission and limit ionic movements at the noR (see Figure 6).

It becomes clear that the minimal functional unit of the nervous system is not, and has never been, the neuron alone.

It is always associated with myelin and cannot function without it.

It is therefore possible to state that there are several APs on the myelinated axon located, in sequence, at the nodes of Ranvier. It is therefore mandatory that they are electrically isolated. It is impossible for two consecutive APs, whose speed is very slow, to be electrically linked with an electrical phenomenon of higher speed.

This paradox is only solved if the APs are electrically insulated (the electromagnetic and electric fields persist even in the absence of an electric circuit).