Axon: Soliton? Analogies and Divergencies

[bernard]

Hello folks,

I come back with my old horse and I'll try, this time, that Diane's Grandmother and Groutcho's child understand clearly my deep model of axon.

A child of five would understand this. Send someone to fetch a child of five.
Groucho Marx
US comedian with Marx Brothers (1890 - 1977)

Do not weep; do not wax indignant. Understand.
Baruch Spinoza
Dutch Jewish philosopher (1632 - 1677)

[bernard]

1/ Action potential is a wave!

It looks like a sea wave and obeys to some of its physical rules:
It is a travelling wave that doesn't really make a trip.
Like a sea wave, it is a longitudinal wave.

In fact, the sea wave analogy is a bit too strong with such a tiny thing.
Perhaps a ripple over a calm water surface may be more accurate for our example.

[bernard]

The previous movie is, of course, a top view.
Here is a lateral view: you see the two travelling ripples.

[bernard]

1.1/ Analogies

The waves travel in the two cases.
The amplitudes of waves are "thin" phenomena.
They use water and some "salts".

The origin of the ripple is information and this information is seen at distance as the ripple. Information was transformed in a ripple.
The action potential is a way to send the information like the ripple.

1.2/ Divergencies

The ripple is a message sent in all directions.
The AP is normally unidirectional.

The ripple loses the information with distance.
The AP is sent without loss.

The ripple "functions" on flat surfaces.
The AP works with "tubes".

[bernard]

The ripple loses the information with distance.
The AP is sent without loss.

I made this movie to show this divergency.
The green spot is the nerve one.

[bernard]

Of course it make understandable that some active mechanism is responsible of this singular difference.

[bernard]

Of course, a real sea wave is more complex.

Water Waves
Water waves are an example of waves that involve a combination of both longitudinal and transverse motions. As a wave travels through the waver, the particles travel in clockwise circles. The radius of the circles decreases as the depth into the water increases. The movie below shows a water wave travelling from left to right in a region where the depth of the water is greater than the wavelength of the waves. I have identified two particles in blue to show that each particle indeed travels in a clockwise circle as the wave passes.

Animation courtesy of Dr. Dan Russell, Kettering University

[bernard]

It is a travelling wave that doesn't really make a trip.

You can see that information (the travelling wave) moves but the supporting medium suffers only a local and transitory trip.
Information (action potential) is like a surfer on the top of a wave and the wave itself.

[Diane]

Bernard, you might like this blog, REWIRING NEUROSCIENCE. The author admits there is a big hole in the knowledge base about how a neuron actually works.

[bernard]

Diane,
I found some explanation here => The Corduroy Neuron

But I do not follow, at all, this view.
In my view, and if I take the "same" analogy than the author then dendrites and synapses use effectively numbers but axons transmit information when the sum of these numbers reaches a certain level.
But the AP, itself, remains a "all or nothing" mechanism because a travelling wave doesn't support easily another analogic mechanism.

I will show why... later.

[Diane]

I just put it there to show that you are not alone in your questioning of the matter, nor in thinking that there are big questions that still need to be answered.

[bernard]

The particles do not move down the plane with the wave; they simply oscillate back and forth about their individual equilibrium positions. Pick a single particle and watch its motion. The wave is seen as the motion of the compressed region (ie, it is a pressure wave), which moves from left to right.

[bernard]

Originally Posted by Diane

I just put it there to show that you are not alone in your questioning of the matter

Of course but the present model seems inaccurate and doesn't fit the facts.
An axon is a "transmission line" and its function is to preserve the message in a very noisy body.

You need a good message/noise ratio because you want the message arrive and not really interested by the noise.

An analogic message,as proposed, is the best way to lose the message since the ratio is varying with amplitudes => little message may be seen only as noise and precision is low.

A better solution is coding information with intervals and spikes: you make an analogic to "digital" conversion that has a very good immunity to noise.

Facts are numerous to prove that Nature used this strategy (but a priority question remains...).

[bernard]

An important divergency comes with fluids that are in presence.

In sea waves, you have saline water and air.
In cells you have saline water on both sides.
It becomes understandable that waves can't be of the same kind since the expansion can't occur in the same manner.


This is a huge difference but the major of them is the presence of an "impermeable" barrier, the membrane that separates the two sides.
This beautiful material provides many communication features and it is helped by several kind of passive and active gates.

[bernard]

In a "normal" cell, communication is quite omni-directional. There is no privileged direction of exchanges.

[bernard]

We saw in post #15 there is a vertical communication in cells.

Neurons enhance the system with longitudinal transports. One that occurs superficially and the other in the lumen of the axon.

[bernard]

You have to remember that this elegant communication process is only a result of observations. The two opposite communications may then occur at the same time since they do not exist at the same place.

Unfortunately since it implies a "skin effect" for the fast one, it violates the actual standards describing the membrane potential (they use a volume in the calculation and we are talking about a thin layer limiting the process).

But do not forget that the facts contradict this artificial computation.

[bernard]

When you look at the ions motion that create an Action Potential we see it is a vertical but sequential process that involve ions channels (and membranes).

[bernard]

From this site The Nerve Impulse.

There is a very good introduction. Each word was chosen carefully and reflects the facts.

Originally Posted by F. Bezanilla

INTRODUCTION

Axons are responsible for the transmission of information between different points of the nervous system and their function is analogous to the wires that connect different points in an electric circuit. However, this analogy cannot be pushed very far. In an electrical circuit the wire maintains both ends at the same electrical potential when it is a perfect conductor or it allows the passage of an electron current when it has electrical resistance. As we will see in these lectures, the axon, as it is part of a cell, separates its internal medium from the external medium with the plasma membrane and the signal conducted along the axon is a transient potential difference(1) that appears across this membrane. This potential difference, or membrane potential, is the result of ionic gradients due to ionic concentration differences across the membrane and it is modified by ionic flow that produces ionic currents perpendicular to the membrane. These ionic currents give rise in turn to longitudinal currents closing local ionic current circuits that allow the regeneration of the membrane potential changes in a different region of the axon. This process is a true propagation instead of the conduction phenomenon occurring in wires.

My bold (red and black).

But the next phrase contradicts all the previous that was said.

Originally Posted by F. Bezanilla

To understand this propagation we will study the electrical properties of axons, which include a description of the electrical properties of the membrane and how this membrane works in the cylindrical geometry of the axon.

[bernard]

Originally Posted by F. Bezanilla

The plasma membrane is made of a molecular lipid bilayer. Inserted in this bilayer, there are membrane proteins that have the important function of transporting materials across the membrane. The lipid bilayer acts like an insulator separating two conducting media: the external medium of the axon and the internal medium or axoplasm. This geometry constitutes an electric capacitor(2) where the two conducting plates are the ionic media and the membrane is the dielectric.

Here is the definition of an electric capacitor.

Is it possible to accept such an affirmation?

[bernard]

1/ Electric devices are used in electric circuits that carries electric current (a flow of electrons).
2/ Electric circuits have definite shapes and contacts points.
3/ The only thing that moves is electrons.

But,

1/ There is no definite circuit in our body, even on a µm of axon.
2/ Axons work with ions that are not electrons.
3/ Ions cross physically the membrane.

[bernard]

Back to our "electric" capacitor =>

Originally Posted by F. Bezanilla

The lipid bilayer acts like an insulator separating two conducting media: the external medium of the axon and the internal medium or axoplasm. This geometry constitutes an electric capacitor

If I agree we have two possible conducting media, is it sure they use these electric properties?

A first problem comes with electroneutrality.

http://en.wikipedia.org/wiki/Membrane_potential

Electroneutrality

In most quantitative treatments of membrane potential, such as the derivation of Goldman equation, electroneutrality is assumed; that is, that there is no measurable charge excess in any side of the membrane. So, although there is an electric potential across the membrane due to charge separation, there is no actual measurable difference in the global concentration of positive and negative ions across the membrane (as it is estimated below), that is, there is no actual measurable charge excess in either side. That occurs because the effect of charge on electrochemical potential is hugely greater than the effect of concentration so an undetectable change in concentration creates a great change on electric potential.

[bernard]

Originally Posted by Bernard

If I agree we have two possible conducting media, is it sure they use these electric properties?

We are made of 70% of saline water and saline water may conduct electricity when this water in wired in an electric circuit but only in that case.

1/ It is not because saline water may conduct electricity that saline water conducts by itself, electricity. It doesn't use this electric property.
2/ There isn't any electronic imbalance accross the membrane.
3/ only differs the # ions.

[bernard]

A second problem that comes with this "electric" capacitor is the charge transfer:

A "regular" capacitor maintains an exact but opposite charge (of electrons) on each plate.
This charge transfers is never made through the dielectric. It is achieved by the electric circuit.
When a charge occurs through the insulator it just means that we get a bad capacitor with a leakage current.

[bernard]

But it said that we are in presence of a very good capacitor =>

As the thickness d is only 25 angstroms, the specific capacitance of the membrane is very high, close to 1 µF/cm².

1 µF/cm² : An impressive capacitor. I say that because I do not understand why this property wasn't exploited by technology. We aren't able to manufacture a capacitor that has only 1/10 of this marvelous property. And a cherry on the cake: it functions in saline water without any short circuit.

BTW, the cm² area makes me trouble since we have said there is around 330 holes (ions channels) per µm².

[bernard]

This 330 number doesn't make an effect...

But you have to remember (that's for Jon) some Mathematical conversion:

1 cm is 10^-2 m
1 µm is 10^-6 m

then
1 cm is 10⁴ µm

and at last

1 cm² contains 330 10⁸ ions channels: quite nothing!

just 33 000 000 000 holes per cm²

I'm understanding, now, why electric designers discarded the thing: It is an absurd idea.

[bernard]

Here is a magnified little piece of an axon.
Its real area is 0.25 µm² (You need 4 of these pieces to make 1 µm²). The ions channels proportions are respected but I suspect that it is not so well ordered.

[bernard]

Even if the existence of a functional membrane capacitor becomes dubious, a problem stays!
The charge (ions) transfer isn't solved at all.
Many facts and observations agree that ions channels make the job.
I do not contest the facts.
But it is said that membrane depolarization is the key motor of ions channels and propagation.
If I accept such an hypothesis, I must argue that an ion channel is coupled to the membrane capacitor and it is this last one that feeds the capacitor since it is the only one that moves ions.

Unfortunately, it doesn't work either since you try to feed the feeder with the fed.
One may say that a previous membrane patch makes the job.
Yes, it works for sure but what happens at IC.

The IC (Initial Conditions) is a valuable situation in electronics. We accept that a situation is like we decide, often far from real conditions. It is a raw simplification for computations.

But even if I decided that the first membrane patch works, Mother Nature will immediately replies: You can't cheat boy, find a better solution.

[BB]

Bernard,

Are you suggesting that depolarization is an effect of the mechanical propagation of an action potential and not its cause? That seems consistent with propagation of an action potential but not the creation of one.

The ion transfer is an active as well as a passive process which creates the ionic current. How is that transformed into the wave like propagation you demonstrate?

[bernard]

Cory,

There is no electric depolarization at all.
1/ Many studies are focused on the propagation of AP. My present words try to explain propagation not initiation (it will come later).

2/ There is no passive sequence. It is a dynamic process in all cases. It works like a chain reaction (it is one). If the trigger is too weak it returns in a waiting state.

I can't explain all the thing so quickly. I'm only opening some ions channels in your brain which help you to look at facts with a new eye and objective criticism.

Come on guys, shoot at me. If the theory is weak, you will point it out but if I find arguments that you can't deny...

[bernard]

Another problem that comes with membrane observation as capacitor is the initial latency duration. The HH model is currently unable to consider this fact.
Normally when you charge a capacitor, the voltage grows like this.
The charge begins at time 0. when we consider a membrane patch, there is a incompressible delay.

In the original theory voltage gated ions channels (K⁺ and Na⁺) are designed as voltage gated resistances. (conductance).
Sorry but I can't get it like that.

[bernard]

Voltage gated channels act much more like electric controlled taps.
They allows the flow of tiny balls (ions, water...) to cross the membrane in defined sequences.

There are only four possible sequences:
1 & 2/ if the outgoing candidate is a water molecule then the following may be water or an ion.
3/ if the outgoing candidate is an ion then the following is water.
4/ An outgoing ion can't be followed by another ion.

1/ water => water
2/ ion => water
3/ water => ion
4/ ion => ion

The HH models that is considering only charged particles (ions) miss another gamer: water.

A resistance that carries such properties can't be called a resistance and it depends heavily of possible ingoing candidates.

[bernard]

Here is a picture of all the possible sequences.

[bernard]

Then it becomes more understandable why the ion channel current fluctuates even when it stays opened.

[bernard]

Some explanations about my previous post:
1/ the channel is observed out off its dynamic context. An action potential has a duration of 2 ms and the the graph is more than 150 ms.
2/ when an water molecule crosses the channel, the current isn't modified but the internal milieu is and may push/close the voltage sensor/paddle.
3/ If the mental process that occurs in my mind is close to the reality then only few ions may cross the membrane and perhaps, after, the system is blocked.

[bernard]

Some numbers about the original experiments on the giant squid axon;

1/ its diameter is 0.5 mm => 500 µ
2/ its speed is 20 ms^-1
3/ Action potential length is 40,000 µ => 40 mm.
4/ Surface of this patch is 62,800,000 µm²
5/ it contains 20,700,000,000 ions channels
6/ its circumference is 1,571 µm
7/ this circumference has an average of 28,535 ion channels.
8/ each slice of 1 µm contains 518,000 ions channels.

I bring these numbers because it is necessary to see their importance in the process and that it may be difficult to simplify the computations.

[bernard]

Some numbers about a little C fibre of 0.5µ;

1/ its diameter is 0.5 µ
2/ its speed is 0.5 ms-1
3/ Action potential length is 2,000 µ => 2 mm.
4/ Surface of this patch is 3,140 µm²
5/ it contains 1,040,000 ions channels
6/ its circumference is 1.57 µm
7/ this circumference has an average of 28 ion channels.
8/ each slice of 1 µm contains 518 ions channels.

[bernard]

It is possible to suppose that the slow axon is also an economic one.
That is not really true since each ion channel transports only 77 ions in the squid axon and the C fibre is more solicited since it brings 1,540 ions during a single action potential.

[bernard]

To make the things more clear, I'll summarize, with little drawings, the major differences that exist between an electric capacitor and a membrane capacitor.

[bernard]

Another difference

[bernard]

And another one;

[bernard]

Of course the previous post doesn't explain the initiation of the action potential since we need that some positive ions enter in a bottom tank, starting the chain reaction.

Really? But there is a simple way to walk around this problem!!!

[bernard]

Some of you may have found the model explains, also, refractory periods, in an elegant manner that is explained here.

But I need to explain the threshold level.

[bernard]

You need a membrane patch where it is figured some blue areas: These zones are the limits (at 1/10) of influence of the center of the ion channel (the center of attraction for our electrostatic forces).
You have to remember that Nature needs a system that works in quite all circumstances. Thus, it needs a good "noise immunization" then its sensitivity is limited by design.

[bernard]

I forgot to say that you could consider some initial conditions;
The stimulation is weak or may be large.
An electric stimulation implies a ion motion: ions are attracted or repulsed by the electric field.

It is this ion motion that opens the ions channels.

[bernard]

Yes, for some pieces and no for the most of this blog.

[bernard]

Back to the stimulation simulation.
It seems obvious to suppose there is a direct link between the stimulation current and the stimulated area.

Then, it becomes also obvious that you need a minimal amount of stimulation to provoke an action potential initiation. It works only if you can move a definite number of ions channels at the same time.

[bernard]

Cory,

You begin to understand the thing but some notions remains fuzzy in your mind. That comes from my language problem.
Gap junctions are another affair and myelin wasn't "reached" at this time of discussion.

[bernard]

Originally Posted by BB

OK, I think I'm catching up. You are showing the difference between electric conductance (the term most commonly used when describing neural function) and propagation (more accurate).

I'm speaking about propagation telling differences that exist between a real electric circuit an the one described arbitrary in axons.
The second uses components that have properties that are far from those described and known.

Originally Posted by BB

I understand the tank model you made.

The upper tank is the external side of the axon like here
The lower tank is the opposite side of the membrane under the ion channel.
The tube is an ion channel (with a ionic/electric tap).

Originally Posted by BB

Also, I remember Kandel writing of gap junctions as actually having some electric properties different than the propagation properties of a synapse.

chemical synapes are the best way to enable communication between neurons of different kinds and it is a way to change their bahaviour.
Gap junctions create networks of synchronous neurons => Super neurons.

[bernard]

Here is a little drawing showing some basic electric rules.