Passive Spread Current (continued)

[somasimple]

https://www.physicsforums.com/showpost.php?p=1876004&postcount=49

This is in agreement with the measured experimental data (aka facts) as shown in fig 7. Note in the upper part of fig 7 how the amplitude decays between nodes of Ranvier; this fact agrees with the cable theory. Note in the lower part of fig 7 how there is no measurable propagation delay between the nodes of Ranvier; this fact also agrees with the cable theory.

You must consider the two other curves even if they contradict the cable theory.

You are clearly mistaken about fig 7 showing that the shape of the AP is not changing. For example, in the bottom part of the figure note that at t = 0.55 ms the peak voltage (line B) is uniquely located at position d = 1 mm. In contrast, at t = 0.6 ms the peak voltage (line B) is simultaneously at all points from d = 1 mm to d = 3 mm. That is a definite change in shape, and this idea is repeated throughout the bottom part of fig 7.

The shapes change under the myelin I didn't took this case in example and I do not contest the fact that the signal is dampened with distance. They recorded every 0.1 mm (100 µm). A node is 1µm wide. This is source of error (and they explained it in the paper).

It is always hard to understand your plots since you never label anything and never describe your derivation. But from what I can guess (assuming you are doing everything correctly) you are modeling the cable equation response to a square pulse current input. If so, you correctly note that the cable model predicts that there is no delay between the "near" and "far" measurements, and also the cable model predicts that there is a decreasing amplitude between the "near" and "far" measurements.

You can give your values for the components of the circuit. We will be in agreement.

ps: That is the second time the treads I started are closed without any advice and any rules violation from my own.

 

[somasimple]

You are clearly mistaken about fig 7 showing that the shape of the AP is not changing. For example, in the bottom part of the figure note that at t = 0.55 ms the peak voltage (line B) is uniquely located at position d = 1 mm. In contrast, at t = 0.6 ms the peak voltage (line B) is simultaneously at all points from d = 1 mm to d = 3 mm. That is a definite change in shape, and this idea is repeated throughout the bottom part of fig 7.

I don't know what irrational bias against these models causes you to misunderstand the facts so eggregiously.

The paper tells us clearly that they recorded a point at a time. A great patience for these pioneers. Then, they computed the data and obtained the graphs A, B and C.

The graph I provided is a simultaneous recording at several nodes and it is in agreement with the collected data and conduction velocity.

 

[atyy]

It's too bad they closed your other thread. I thought your questions were excellent.

For the sake of clarity, could you restate your question, so that we have a well-defined issue to discuss?

 

[somasimple]

About the car or an electric signal:
http://www.grc.nasa.gov/WWW/K-12/airplane/conmo.html

The mass of an AP may be, by example, its integration.
Even if the shape changes under the myelin, this change is minor in constrast of its velocity.
So you get this:
Q1 quite egal to Q2
Vnode*Q1<<< Vinternode*Q2.
The cable theory predicts a passive event under myelin.

 

[somasimple]

Here is a new graph:

I plotted the conduction velocity in red.
I centered the APs, at nodes, on this line.
Each quite horizontal segment is the internode event.

The blue region shows all active nodes (n2, n3, n4 and n5) when AP at node 2 (n2) exists.

Do you agree?

 

[atyy]

Here is a new graph:

I plotted the conduction velocity in red.
I centered the APs, at nodes, on this line.
Each quite horizontal segment is the internode event.

The blue region shows all active nodes (n2, n3, n4 and n5) when AP at node 2 (n2) exists.

Do you agree?

What do the brown lines in the internode region represent (which part of the internode event)?

Could you give the details of your reasoning (step by step) - which figure/data in their paper did you use, and how did you use it, to obtain the lines in your figure.

Also, which part in particular are we suppose to examine - give us more guidance about what your question specifically is other than "Do you agree?". What in their data or the theory about their data is puzzling you?

 

[atyy]

Take a look at Fig 10. Their text on that figure includes the comment "In order to see whether the transition between the two forms of action potential takes place as predicted ..." (p325).

Evidence for saltatory conduction in peripheral myelinated nerve fibres
A. F. Huxley and R. Stämpfli
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1392492

 

[somasimple]

What do the brown lines in the internode region represent (which part of the internode event)?

Could you give the details of your reasoning (step by step) - which figure/data in their paper did you use, and how did you use it, to obtain the lines in your figure.

Also, which part in particular are we suppose to examine - give us more guidance about what your question specifically is other than "Do you agree?". What in their data or the theory about their data is puzzling you?

The brown lines are the events that may happen under the myelin. (I made them brown to show a kind of discontinuity).
The blue ones are the APs recorded at nodes.
All values were rounded ( see fig 7 => APs are shortened by lines) to make a simpler figure.

Values on horizontal axe are distances and time are plotted as vertical values.

The figure 10 shows the problem I told you earlier: The sampling distance may change the AP shape around nodes.

The shapes change under the myelin I didn't took this case in example and I do not contest the fact that the signal is dampened with distance. They recorded every 0.1 mm (100 µm). A node is 1µm wide. This is source of error (and they explained it in the paper).

The red line shows the conduction velocity.
It seems reasonable to plot APs (at nodes) separated by 2 mm (from their graphs) ?
It shows that following Ap is well initiated when the previous reaches a good value.

The blue transparent zone shows active nodes that occur during a single AP (node 2).

 

[atyy]

I am referring to H&S's Fig 7 in my comments on your next 3 quotes.

The red line shows the conduction velocity.

That looks ok.

It seems reasonable to plot APs (at nodes) separated by 2 mm (from their graphs) ?

That looks ok too, taking the nodes to be the "jumpy bits" of their plots.

It shows that following Ap is well initiated when the previous reaches a good value.

The blue transparent zone shows active nodes that occur during a single AP (node 2).

Plots A,B,C respectively represent the start, peak and end of the AP.

At t=0.5, the A curve is at node d=3 and the B curve is at node d=1, so the AP at node d=3 begins in the middle of the AP at node d=1. So yes, the AP at the next node is initiated in the middle of the AP at the previous node.

Now looking at node d=1, the AP starts at t=0.4 and ends at t=0.7. Draw horizontal lines at t=0.4 and t=0.7 across the whole figure, and count the number of jumpy bits between them to be 4, which is about the same as what you plotted.

Good.

The figure 10 shows the problem I told you earlier: The sampling distance may change the AP shape around nodes.

I really don't understand what your question is - do they say it changes shape but you don't think it does - or do they say it doesn't change shape but you think it does? Or do you think they interpreted their data incorrectly?

 

[Dale]

ps: That is the second time the treads I started are closed without any advice and any rules violation from my own.

I have to partially agree with somasimple here. Since somasimple's posts are in direct disagreement with mainstream science it is not surprising that his threads get closed, but it would help if the moderator who locks a thread give the justification.

 

[somasimple]

I really don't understand what your question is - do they say it changes shape but you don't think it does - or do they say it doesn't change shape but you think it does? Or do you think they interpreted their data incorrectly?

The position of the electrodes implies automatically the modification of the shape near the nodes.
They do not interpret incorrectly their data with their theory. I just want to show some aspects that were not discussed.

 

[Dale]

You must consider the two other curves even if they contradict the cable theory.

Certainly, but similarly you must consider the experimental data even if they support the cable theory, which they do.

The shapes change under the myelin I didn't took this case in example and I do not contest the fact that the signal is dampened with distance.

So if you agree with that part of cable theory then what part of cable theory do you disagree with? So far you agree with a key prediction of the cable theory (passive signal dampened with distance) and your objection (AP spatial length is greater than the space constant) is not a prediction of the theory.

About the car or an electric signal:
http://www.grc.nasa.gov/WWW/K-12/airplane/conmo.html

Electrical signals are not massive, they are not rigid, they do not have momentum, and they do not have inertia. Their velocity can change without force and their shape can change without stress. Your continued analogies in this direction are not helpful to your argument.

 

[atyy]

They do not interpret incorrectly their data with their theory. I just want to show some aspects that were not discussed.

-Good!
-Their discussion is already very complex, and one certainly shouldn't agree with all aspects of their discussion without intensive study, and examination of more recent data. Hodgkin and Stämpfli themselves note that some of their inferences are indirect, and that not all experimental evidence available at that time was unanimous.
-The major point is saltatory conduction, and that appears to be easily substantiated by their data, at least on quick perusal.
-They discuss whether the nodes and internodes are active or passive, and conclude that it is a good approximation to describe the nodes as active and the internodes as passive, but they do not rule out improvements or corrections to this idea.

The position of the electrodes implies automatically the modification of the shape.
They do not interpret incorrectly their data with their theory. I just want to show some aspects that were not discussed.

That means you are discussing very fine points! Excellent! But I will probably not be able to comment without reading their paper and more current literature carefully, so please take no offense if I don't comment. Hopefully someone else will be able to discuss such issues.

 

[somasimple]

So if you agree with that part of cable theory then what part of cable theory do you disagree with? So far you agree with a key prediction of the cable theory (passive signal dampened with distance) and your objection (AP spatial length is greater than the space constant) is not a prediction of the theory.

Agreeing with recorded facts is just a question of reason but it doesn't imply that I'm agreeing with the whole theory.
BTW, quite all domains of Physics exhibit phenomenons that fade with distance or time. You can't discard this eventuality before you examined the other possible solutions.

May I rephrase the content of the graph like this?

With
n=2, k=0.3, v=23,
A myelinated axon has a known conduction velocity of v
When the amplitude of an AP, that occurs at a node n and with a duration of k milliseconds, reaches the value of propagation, it triggers a transient event that has a very short duration (few µs). This very short event initiates a AP at node n+1 ans so on...

 

[somasimple]

A typo was made in the last sentence; ans so on => and so on...

 

[Dale]

Agreeing with recorded facts is just a question of reason but it doesn't imply that I'm agreeing with the whole theory.

Yes, I know that you do not agree with the whole theory. What I don't know is which parts of the theory you disagree with.

May I rephrase the content of the graph like this?

With
n=2, k=0.3, v=23,
A myelinated axon has a known conduction velocity of v
When the amplitude of an AP, that occurs at a node n and with a duration of k milliseconds, reaches the value of propagation, it triggers a transient event that has a very short duration (few µs). This very short event initiates a AP at node n+1 ans so on...

Are you just trying to restate the data or are you trying to place it in the context of a theory? If you are just restating the data then you shouldn't make any claims about what is happening at a node since only inter-node data is presented. If you are placing the data in a theoretical context then I don't know what you mean by "transient event". In the standard theory the passive "cable" conduction is always happening, and the active AP takes several tenths of a ms at each point.

 

[somasimple]

In the standard theory the passive "cable" conduction is always happening, and the active AP takes several tenths of a ms at each point.

Great, you have introduced the notion of Continuity. I take it.

About extrapolations;
At node: What is the speed of an event that has a duration of 0.3 ms and travels 1 µm?
For internode : What is the speed of an event that has a duration of 10 µs (or less if you want) and travels 2 mm?

 

[Dale]

Before we continue can you clearly state which part of the standard theory you disagree with?

This is now the third time I have had to ask this question just since you began this new thread. It is pointless to continue until you clearly define your objection.

 

[atyy]

At node: What is the speed of an event that has a duration of 0.3 ms and travels 1 µm?
For internode : What is the speed of an event that has a duration of 10 µs (or less if you want) and travels 2 mm?

The "event" that you define to travel in the internode would correspond roughly to a fixed "phase" of the AP. Because the AP is changing shape and decaying in the internode, and also because a passive cable has no traveling wave solutions, the "phase" of an AP in the internode in cable theory can only be indirectly defined.

I think we shouldn't compute the "real" travel speed in the node - at least not from (AP duration)/(node length) because that would use different phases of the AP.

In one of your one of your posts on the orginal thread, you treated the node as a point, which seems a reasonable approximation (https://www.physicsforums.com/showthread.php?t=254044).

So a rough picture could be as follows:
1. AP speed across nodes and internodes is about 20 mm/ms.
2. Nodes are spaced 2 mm apart.
3. In the internodes, travel is passive and very fast, so we may take the travel time in the internodes to be roughly 0 ms.
4. However, the AP changes shape and decays in the internodes.
5. The AP has to be actively re-boosted at nodes.
6. Most of the "travel time" is actually time spent re-boosting the AP at a node ~ 2/20 ms = 0.1 ms.
7. In your post #5, the brown line representing the "internode event" begins at ~0.1 ms after the start of an AP, in accord with the above.

 

[somasimple]

Electrical signals are not massive, they are not rigid, they do not have momentum, and they do not have inertia. Their velocity can change without force and their shape can change without stress. Your continued analogies in this direction are not helpful to your argument.

http://www.greenandwhite.net/~chbut/conservation_of_momentum.htm

It holds true no matter what kind of forces the bodies exert on each other. They may be gravitational forces, electric or magnetic forces, tension in strings, compression in springs, attraction or repulsion.

Example: compute the necessary energy to promote an electric signal from 0 mV to 0.001mV within 0 ms! A short event duration hides often a high energy...

so we may take the travel time in the internodes to be roughly 0 ms.

NO! Electric signals may have work and power. Your statement implies an infinite velocity => d/t

Before we continue can you clearly state which part of the standard theory you disagree with?

Energy/momentum and the graph I provide (where you agreed) implies a solution of continuity (discontinuity) in the electric signal. I can demonstrate it.
Please give me some values for a simulation as I asked already earlier. (unmeylinated and myelinated axons).

The AP has to be actively re-boosted at nodes.

Thanks, you confirm my point of view.

 

[atyy]

5. The AP has to be actively re-boosted at nodes.

Thanks, you confirm my point of view.

Good.

So was the question about why the AP must be actively re-boosted but some people say that it isn't an active process?

It is important to note that there are different uses of the word "active":
1) Biochemists mean "using ATP".
2) Electricians mean "not modeled by passive elements such as resistors and capacitors whose properties don't change with voltage".

An AP is active in both senses
-It is obviously true in the second sense of needing voltage-dependent channels.
-Let me comment on the first sense. The re-boosting of the AP at the node uses the energy built up in the concentration differences of sodium and potassium ions across the cell membrane.
-The concentration difference is due ultimately to biochemical pumps which use ATP, and which operate much more "slowly" compared to the voltage dependent channels in the node.
-The concentration difference in sodium and potassium ions across the cell membrane is very large (100+ mM), and a single AP changes it, but only minutely. You would need about 1000 APs to change the concentration difference by 10%. A single AP changes the concentration difference by 0.01%.
-So if you poison the biochemical pumps that set up the concentration difference, or remove ATP from the neuron, the neuron will have to fire at least 1000 APs before you detect a significant change in AP amplitude.
-Thus an AP uses ATP only very indirectly, and is accordingly often not considered "active" in the first sense, but that would be debatable if one were to require the statement to be true in a very strict sense.

 

[somasimple]

The "event" that you define to travel in the internode would correspond roughly to a fixed "phase" of the AP. Because the AP is changing shape and decaying in the internode, and also because a passive cable has no traveling wave solutions, the "phase" of an AP in the internode in cable theory can only be indirectly defined.

That is a problem: Since the axon exists and records were made, a solution must exist because the signal was recorded.
You are facing to some alternatives;

1. A problem without solution implies to change the hypothesis.
2. A force that is changed during the transmission.
3. A milieu that is different.
4. An error in computation.

 

[somasimple]

http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=4647244
Internode duration is quite in agreement with my computation: 20 µs.

 

[granpa]

I see what you mean by 'bagpipes' now.

can you give me a ballpark number for how many microtubules are in a mylenated axon? 10 100 1000?

I've been googling but everything decent is nonfree.

 

[atyy]

I see what you mean by 'bagpipes' now.

can you give me a ballpark number for how many microtubules are in a mylenated axon? 10 100 1000?

I've been googling but everything decent is nonfree.

'Bagpipes' was someone else's analogy on a different thread - I like it, but only because I like the sound of bagpipes - now I shall have to find out how bagpipes actually work

Sorry, have no idea about microtubules - ask Roger Penrose

 

[granpa]

'Bagpipes' was someone else's analogy on a different thread - I like it, but only because I like the sound of bagpipes - now I shall have to find out how bagpipes actually work

Sorry, have no idea about microtubules - ask Roger Penrose

whoops. I assumed this was a continuation of the same discussion. my mistake. it was bunburryist that mentioned it.

 

[atyy]

http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=4647244
Internode duration is quite in agreement with my computation: 20 µs.

Are you computing it using AP height at the node, the A value, and the length constant of the internode?

 

[atyy]

BTW, you agree with Huxley and Stämpfli's interpretation of their data, but you have some disagreement with using cable theory to describe internode propagation? What I don't understand is: how does Huxley and Stämpfli's interpretation of their data differ from the interpretation given by cable theory - aren't they basically the same?

 

[atyy]

That is a problem: Since the axon exists and records were made, a solution must exist because the signal was recorded.
You are facing to some alternatives;

1. A problem without solution implies to change the hypothesis.
2. A force that is changed during the transmission.
3. A milieu that is different.
4. An error in computation.

BTW, you agree with Huxley and Stämpfli's interpretation of their data, but you have some disagreement with using cable theory to describe internode propagation? What I don't understand is: how does Huxley and Stämpfli's interpretation of their data differ from the interpretation given by cable theory - aren't they basically the same?

OK, I understand what you mean. The full Hodgkin and Huxley partial differential equation for AP propagation in unmyelinated axons is a wave equation, which is definitely not the linear passive cable equation (which is what I meant when previously referring to the cable equation).

So in fact, the linear passive cable equation is NOT the standard model for AP propagation in unmyelinated axons and somasimple is absolutely correct on that point!

Edit: The highlighted comment will only make sense to those who have been following the discussion from somasimple's initial comments at https://www.physicsforums.com/showthread.php?t=254044.

 

[somasimple]

Well, that is a fine observation.

I have a little expertise about Digital Signal Processing and Analysis (but it not my primary job).

1. An electric signal must follow some basic but very strict rules of Physics.
2. An electric signal is temporal. Then you must have one and only one electric value per time value.
3. It is continuous because time is varying continuously. Then you cannot have blank in the recording. It has a start and an end without any gap.
4. It is unidirectional because time is varying accordingly. Then you can't have electric values that go into the past

A electric traveling wave must follow the previous strict rules more one:
A electric traveling wave must have one and only one time value per distance value because time is varying and wave moves (velocity>0).
A electric traveling wave must have one and only one electric value per time value because time is varying and wave moves (velocity>0).

Does an axon myelinated or not follow strictly these laws?

 

[somasimple]

Are you computing it using AP height at the node, the A value, and the length constant of the internode?

from the abstract;

Average internodal conduction time for normal ventral root fibres of internodal length between 0·75 and 1·45 mm is 19·7 ± 4·6 (S.D.) μsec at 37° C. Internodal conduction time appeared to show a minimum for fibres of internodal length 1·0 mm.

 

[somasimple]

Here is a graph that shows the problems with myelinated fibers.

 

[Dale]

Energy/momentum and the graph I provide (where you agreed) implies a solution of continuity (discontinuity) in the electric signal.

So as I understand what you are saying, your only objection to the cable theory is that it introduces some "discontinuity" in the signal which somehow violates the conservation of energy or conservation of momentum? Is this correct or did I misunderstand your objection?

Strictly speaking electromagnetic signals propagate at a finite speed and carry momentum, but all of circuit theory is based on the "small circuit" assumption. This is essentially the assumption that the size of the circuit is much smaller than one wavelength of the frequencies that will be used. Under that assumption the electrical signal can propagate instantaneously, or in other words for small enough circuits or low enough frequencies the speed of light is treated as infinite. Here we are talking about frequencies of a few kHz or less and distances of a few mm, so the assumption is very reasonable.

Your rejection of that assumption strikes me as rather silly. By insisting on treating the speed of light as finite in the neuron you will not improve the accuracy of anything since you will be correcting an effect that is ridiculously far below the experimental noise.

 

[somasimple]

A electric traveling wave must have one and only one time value per distance value because time is varying and wave moves (velocity>0).
A electric traveling wave must have one and only one electric value per time value because time is varying and wave moves (velocity>0).

May I rephrase these confusing assertions like this:
If a single electric traveling wave is initiated along a path (wire), there is one and only one wave that travels.

So as I understand what you are saying, your only objection to the cable theory is that it introduces some "discontinuity" in the signal which somehow violates the conservation of energy or conservation of momentum? Is this correct or did I misunderstand your objection?

Much more. If an AP is initiated along a myelinated axon then the cable theory expects one and only one AP at the time. The facts say the contrary. If there is only two then you have an energy problem.
If there is a continuity as expected in a wire you must able to draw all the transitions between a node and the next. If there is a discontuinity then the cable is cut or this is not a cable.

Under that assumption the electrical signal can propagate instantaneously, or in other words for small enough circuits or low enough frequencies the speed of light is treated as infinite. Here we are talking about frequencies of a few kHz or less and distances of a few mm, so the assumption is very reasonable.

It seems silly to violate the laws of Physics at any scale because it may provoke reasonably mistakes and false conclusions.
A computer works at the nano second scale and respects physics...

Your rejection of that assumption strikes me as rather silly. By insisting on treating the speed of light as finite in the neuron you will not improve the accuracy of anything since you will be correcting an effect that is ridiculously far below the experimental noise.

It seems irrational to contest recorded facts. Have you some references (other than theoretic) that contest the ones I brought?

 

[somasimple]

Your rejection of that assumption strikes me as rather silly. By insisting on treating the speed of light as finite in the neuron you will not improve the accuracy of anything since you will be correcting an effect that is ridiculously far below the experimental noise.

Insisting on this point increases the energetic problem and kills the cable theory because you increase the overlapping. The cable theory needs (in some way) a delay you seems to reject.
Your rejection of that assumption strikes me as rather silly.