Action Potential: Passive Spread Current

[somasimple]

but I want to know whether you would also predict 50 APs arriving at the axon terminal

Fact: Only one arrives. Nature plays with us!
Prediction:When an AP is initiated at a next node then the previous one must be lost. There is a simple and anatomical explanation.
I'm was actually working on the drawing...

 

[somasimple]

I'll bring another schema that proves the existence of multiple APs at the same time.

 

[atyy]

Fact: Only one arrives. Nature plays with us!
Prediction:When an AP is initiated at a next node then the previous one must be lost. There is a simple and anatomical explanation.
I'm was actually working on the drawing...

Good, that's fine. I think the APs are lost mainly through the same thing that destroys colliding APs.

There are backpropagating APs, but from the soma/axon (I'm not sure which) into the dendrites, and these are hypothesized to cause the synapse to strengthen, and thus to underlie memory formation.

I'll bring another schema that proves the existence of multiple APs at the same time.

I think this is reasonable from your rough calculation - I only wonder whether the number is 1 or 10 or 50 or 100 - so I'm not debating this point.

Edit: The reason why I don't know whether the multiple APs at one time are 1 or 100 is because first of all you have used a rough calculation, and one would need to do a fuller calculation on the HH model of AP propagation to know what that predicts. Actually I'd be surprised if that wasn't known. Secondly, your calculation involved parameters from many different sorts of neurons, which is completely reasonable for a rough calculation. However, different neurons have different sets of ion channels, and the HH equations cannot be applied to all neurons - they must be modified depending on which part of the brain you are in. For example, in the cortex, some neurons seem to only fire one spike in response to a stimulus, but other neurons fire with many spikes in response to the same stimulus. So I think we are at the limits of what a rough calculation can do here.

Edit: Experimental evidence may already exist about the number of "events" (what you're calling APs, but I'm avoiding that term for technical reasons) along an axon at one point in time. Koch mentions Waxman et al, "The Axon: Structure, Function and Pathophysiology", OUP, 1995.

 

[somasimple]

I think the APs are lost mainly through the same thing that destroys colliding APs.

It's simpler: the delay is constant => The previous AP lasts before the one that exists at next node.

I think this is reasonable from your rough calculation - I only wonder whether the number is 1 or 10 or 50 or 100 - so I'm not debating this point.

Its depends of AP duration and speed.

The model is universal but derivations are possible. As you said, channels are different and functions, too...

Experimental evidence may already exist about the number of "events"

Yes, plenty! Just look closer at this one (fig 7)
http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=16991863

 

[atyy]

Yes, plenty! Just look closer at this one (fig 7)
http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=16991863

The bottom panel shows the location of one AP along the axon at different times.

The top panel seems to be amplitudes of one AP along the axon at different times.

What we need is a plot of voltage or current along the axon at one time (not different times).

Edit: Perhaps Fig 6. In the 1 ms window, there are APs (each with a slightly different phase) at different positions along the axon. This remains true even for a 0.5 ms window. So that's in accord with the time resolution you used in your calculation - nice job! It also shows that although at fixed time there are multiple APs along the axon, as time is varied, only one AP propagates.

 

[somasimple]

The two figures are linked and give us many lessons?

 

[Dale]

I do not agree with theory but accept facts.

I also accept the facts, but I agree with the theory. Your disagreement with the cable theory is irrational since you have not yet demonstrated that the accepted facts contradict the theory. However, you are certainly free to have irrational opinions.

 

[somasimple]

I also accept the facts, but I agree with the theory. Your disagreement with the cable theory is irrational since you have not yet demonstrated that the accepted facts contradict the theory. However, you are certainly free to have irrational opinions.

https://www.physicsforums.com/showpost.php?p=1874067&postcount=14
Where is the propagated delay within these graphs?

 

[Dale]

https://www.physicsforums.com/showpost.php?p=1874067&postcount=14
Where is the propagated delay within these graphs?

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.

This is in agreement with the measured experimental data (aka facts) as shown in http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=16991863" . 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.

 

[somasimple]

This figure 7 is the proof I need.
It shows at nodes a quite stationary speed (quite = 0)
And a very high speed during under myelin.
Unfortunately, the AP shape remains quite the same.
As we said the AP duration is 0.5 ms (Huxley shows 0.3 but shrinks the curves by computation).

So we have, during a single AP, a speed that varies with a shape that do not!
They recorded the same duration! It is a fact.

You may replace the AP by a train.
Put three observers at Node 1, A1, in the middle of the internode, A2 and then at Node2, A3.

A1 sees the train normally at speed 23 m/s and the observation duration is 0.5 ms.
A2 sees the train normally at speed >> 23 m/s and the observation duration is 0.5 ms.
A3 sees the train normally at speed 23 m/s and the observation duration is 0.5 ms.

You violate some laws of physics for sure. A2 can't see the train during 0.5 ms.

 

[atyy]

So we have, during a single AP, a speed that varies with a shape that do not!
They recorded the same duration! It is a fact.

You may replace the AP by a train.
Put three observers at Node 1, A1, in the middle of the internode, A2 and then at Node2, A3.

A1 sees the train normally at speed 23 m/s and the observation duration is 0.5 ms.
A2 sees the train normally at speed >> 23 m/s and the observation duration is 0.5 ms.
A3 sees the train normally at speed 23 m/s and the observation duration is 0.5 ms.

You violate some laws of physics for sure. A2 can't see the train during 0.5 ms.

An observer at a single point cannot measure a speed. We must have observers at at least two points to measure a speed. So two observers in the internode will measure a higher speed than two observers who are placed several nodes apart.

I think it's quite ok for a shape to remain constant while the speed changes - like a car - it can accelerate and decelerate but its shape remains the same.

 

[somasimple]

I think it's quite ok for a shape to remain constant while the speed changes

No it is not possible at all.
If the length of the train is well defined then the duration of its observation must be shortened with speed.

A train isn't elastic at all. The cable theory expects the contrary but fig 7 denies it. You can't have a portion of a train that runs at 23 m/s then some wagons that runs at a higher speed and finally some others at the original speed.

 

[atyy]

No it is not possible at all.
If the length of the train is well defined then the duration of its observation must be shortened with speed.

A train isn't elastic at all. The fig 7 expects the contrary. You can't have a portion of a train that runs at 23 m/s then some wagons that runs at a higher speed and finally some others at the original speed.

In your rough calculation, you calculated that APs must exist simultaneously over several nodes of Ranvier. The time window you used in that calculation was 1 ms, and depended on AP duration and speed. The data in Huxley and Stämpfli show that your calculation was good.

I think the next step should be to try to think of it on a finer time scale. Referring to Huxley and Stämpfli's Figure 6, you will see that in fact the simultaneous APs in the 1 ms window are not strictly simultaneous. At any instant of time, they are all at slightly different phases of their time course. So there is only a single AP propagating down the axon when you conceive of it on a fine time scale. So it is not like a train and and many wagons, it is really just like a single car.

 

[somasimple]

They are in line (arranged in a linear fashion) but the traveled distance is different at node vs internodes.
I'll bring a better graph.

 

[atyy]

They are in line (arranged in a linear fashion) but the traveled distance is different at node vs internodes.
I'll bring a better graph.

If it's a single action potential I don't see the problem. A single car can accelerate and decelerate any way it wants.

Which part is problematic? Do you think it's not a single AP? Or do you think a car cannot accelerate and decelerate any way and still stay the same shape?

 

[somasimple]

Which part is problematic?

The duration of the AP that remains constant.

A single car can accelerate and decelerate any way it wants.

You can't see these things during the same event (the first AP) since you observe a low speed at nodes and a fast at internodes. There is no interruption during the observations.

Here you're abused by the apparent velocity (23 m/s).

 

[somasimple]

A single car can accelerate and decelerate any way it wants.

Yes and no. You need transitions between speeds. You have not any transition in that cases.

 

[atyy]

The duration of the AP that remains constant.

Good point. The car analogy doesn't work.

Cable theory predicts that the AP should change shape while traveling in the internode - it should get smaller, and its peak should become broader. I wonder why we don't see that in the data. Is the change simply too small to see?

Edit: looking at Fig 7, lower panel, comparing trace A and C from distance 1 mm to 7 mm, they are not exactly parallel, so there is some change in shape.

Edit: Also the top panel of Fig 7 shows that the peak changes in the internode. However it is maximum at the centre - not my naive expectation - what's their explanation?

 

[Dale]

This figure 7 is the proof I need.
It shows at nodes a quite stationary speed (quite = 0)
And a very high speed during under myelin.
Unfortunately, the AP shape remains quite the same.
As we said the AP duration is 0.5 ms (Huxley shows 0.3 but shrinks the curves by computation).

So we have, during a single AP, a speed that varies with a shape that do not!
They recorded the same duration! It is a fact.

You are clearly mistaken about http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pubmed&pubmedid=16991863" 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.

You may replace the AP by a train.
Put three observers at Node 1, A1, in the middle of the internode, A2 and then at Node2, A3.

A1 sees the train normally at speed 23 m/s and the observation duration is 0.5 ms.
A2 sees the train normally at speed >> 23 m/s and the observation duration is 0.5 ms.
A3 sees the train normally at speed 23 m/s and the observation duration is 0.5 ms.

You violate some laws of physics for sure. A2 can't see the train during 0.5 ms.

The action potential is an electrical signal, not some massive rigid object like a train or a car. If you understood the data at all it would be clear to you that the shape does, in fact, change. It is not a massive body that resists acceleration (so you see saltatory conduction) nor does it resist deformation (so you see shape changes). The whole point of saltatory conduction is that the AP jumps and does not move at a steady speed like a train.

Get your facts correct.