Saltatory Conduction: single AP or not?

[granpa]

those are actual measurements of an actual ap by electrodes placed 3 to an internode along a single axon. one by the node. another in the middle of the internode. the third by the node at the opposite end. this is repeated for several consecutive nodes.

they even go against what was expected. look at the backward propagating signal in curve c

notice the phrase 'from the same records as fig 6'

 

[somasimple]

granpa,
we don't care at all.
If an AP has a duration and a speed then it has a "length".
This last value determines the # of active nodes and their values (curve fitting).
you can't mix nodes with internodes if you respect a constant interval = internode lenght.

 

[somasimple]

they even go against what was expected. look at the backward propagating signal in curve C

This is not really a backward propagation since the peak stays at its place but a shortening of the falling phase.

 

[granpa]

This is not really a backward propagation since the peak stays at its place but a shortening of the falling phase.

absolutely. exactly right. its not the peak that's moving backward. its the falling phase. a nort of anti-ap that is moving backward (from the next node at coincidentally exactly the same time that that node fires its ap forward) returning the axon to its resting state.

 

[somasimple]

absolutely. exactly right. its not the peak that's moving backward. its the falling phase. a nort of anti-ap that is moving backward (from the next node at coincidentally exactly the same time that that node fires its ap forward) returning the axon to its resting state.

Hmm, it is now, impossible to find a passive and electrical solution...

 

[granpa]

Hmm, it is now, impossible to find a passive and electrical solution...

not if the node from which from which the anti-ap propagates becomes (just before it fires) completely impassable to all ap's and anti-ap's. then its very simple

 

[atyy]

so more myelin or larger axon=less capacitance=greater voltage difference in signal=less delay at the node. (which kinda somehow makes sense)

The part I don't understand about this is membrane capacitance seems to always appear with membrane resistance in the equations: RmCm.

Myelin decreases capacitance, but increases resistance, so it does nothing to RmCm.

It would make a lot more sense to me if the standard explanation emphasized that myelin increases Rm to increase the length constant, in which case decreased Cm is needed to keep RmCm the same.

 

[granpa]

I don't know anything about the standard explanation. and very little about time and length constants. (just a little about rlc circuits)

all i know is that myelin (and increased axon diameter) increases net speed of conduction which is apparently (http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8) mainly controlled by the delay at the node. I'm assuming passive conduction through the internode and virtually no leakage (cells can't be that leaky. they wouldn't survive). the only reason for the myelin then would be to increase capacitance and that means that fewer ions moving across the membrane produces a larger voltage difference.

 

[somasimple]

Hmm, it is now, impossible to find a passive and electrical solution...

Two currents are added in this configuration and it can't give such a solution, Granpa.
I insist.
see:
www.somasimple.com/flash_anims/node_01.swf

Myelin decreases capacitance, but increases resistance, so it does nothing to RmCm.

A Nothing that increases speed is THE explanation.

 

[granpa]

Two currents are added in this configuration and it can't give such a solution, Granpa.
I insist.

I'm afraid I have no idea what you mean by that.

 

[granpa]

I'm thinking more in terms of voltages than currents. I don't think there is much current. someone said that very few ions actually move at anyone time. and the cell can fire thousands of times even after all active pumping stops

reminds me again of modern microprocessors. their transistors use voltage not current. very little current flows in a modern microprocessor. per instruction at least.

 

[somasimple]

I'm thinking more in terms of voltages than currents. I don't think there is much current. someone said that very few ions actually move at anyone time. and the cell can fire thousands of times even after all active pumping stops

reminds me again of modern microprocessors. their transistors use voltage not current. very little current flows in a modern microprocessor. per instruction at least.

Voltage or current, it doesn't matter and if neuron is not a microprocessor it is largely better.

 

[Dale]

your messages have a tendency to be something more than cryptic.

I am glad it isn't just me.

DaleSpam,
Are you masochist?

Trying to follow your convoluted illogic is rather painful.

There is a quite soliton solution for unmyelinated axons and the function has a derivative at any portion => Continuity.
The case is totally different for myelinated axons => A discontinuity exists in regard of x.

How do you infer on the t variable? Are you able to rewind time or stop it...?
That is the fate of a temporal function: Time that inexorably flows without...discontinuity.

Yes, for the full cable+HH model in unmyleinated axons the solution is a continuous soliton. I never said differently. I only said that there are no continuity constraints for signals in cables and gave an example of a simple signal, H(x-ct), which is discontinuous in x and t.

You seem to think that finding a discontinuity in the model for myleinated axons would be some sort of valid argument against the model. But Maxwell's equations, the wave equation, and circuit theory all admit discontinuous solutions, so there is nothing wrong with discontinuities in the HH and cable theory.

 

[somasimple]

I only said that there are no continuity constraints for signals in cables and gave an example of a simple signal, H(x-ct), which is discontinuous in x and t.

You affirm that a temporal signal (where time can't be stopped) and flowing in a wire/cable from an end to the other one may be discontinuous in t?

Trying to follow your convoluted illogic is rather painful.

I'm rather pleased to see your constant affirmations ever contested by Science.
I must thank you, the model is less robust than before with your help.

 

[granpa]

I assume that somasimple is saying that the signal moves from one node to the next then stops at the node for a short delay before continuing on. I actually tend to agree with him here. the graph here:
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8
seems to support this idea.
but I don't see what the big deal is. the signal is transported passively through the internode but the nodes themselves are active. so why not a delay? its 2 different mechanisms.

 

[somasimple]

granpa,
I said apparent .
It look like a traveling wave at nodes but it can't travel in such a tiny space.

 

[granpa]

granpa,
I said apparent .
It look like a traveling wave at nodes but it can't travel in such a tiny space.

apparent?
traveling wave at nodes?
cant travel in such a tiny space?

 

[granpa]

so its only an apparent delay? its still a traveling wave at the nodes? what do you mean 'cant travel in such a tiny space'?

 

[somasimple]

granpa;
a delay is a delay (it's a duration).
it is an apparent traveling wave.
Edit: That's why, in myelinated axons the soliton has no solution. Nodes are like little windows wher you can see only a little bit of an AP. You see an AP through a so little window that it appears as traveling but it doesn't.
The movie I provided show this. the blue regions are nodes where voltage grows ans decays at the same place but if we record (introducing a t variable) these variations you will obtain the shape of the AP (caution: the movie is just an example)

 

[Dale]

You affirm that a temporal signal (where time can't be stopped) and flowing in a wire/cable from an end to the other one may be discontinuous in t?

Yes. And I have given a very simple specific example: H(x-ct). It is discontinuous at t=x/c since $$\lim_{t\to \frac{x}{c}^-} \, H(x-c t)\neq \lim_{t\to \frac{x}{c}^+} \, H(x-c t)$$ and at x=tc since $$\lim_{x\to (c t)^-} \, H(x-c t)\neq \lim_{x\to (c t)^+} \, H(x-c t)$$.

 

[somasimple]

Once again you reply...at left of the question.
I'm asking if the function is discontinous in t and your example has little to see with a real cable carrying a real electrical signal.

And what is the value of x in your example?

 

[Dale]

DaleSpam,
Are you masochist?

The more I think about this question the more I realize you are right. My posts to you are obviously futile. You are clearly not interested in anything I say, only in pushing your weird anti-HH agenda. Your posts to me are equally futile. I generally cannot even understand your ideas due at least in part to the language barrier. The only remotely useful thing of any of your posts are the interesting references, but I can get those from Google with much less hassle.

Anyway, goodbye somasimple. I expect that you will find other people willing to continue the conversation.

 

[somasimple]

No, DaleSpam
You're only taking me for an idiot.
http://www.myreckonings.com/wordpress/Images/EllipticNomogram/LowerCurveEquations.jpg
Please are you able to record such a signal in a cable or an axon? Just no!
Every time you are faulty you bring an obscure statement or function that has no relation with the discussion.
As I said it earlier you are not obliged to try to reply systematically in opposition: That is not a scientific behavior...
Goodbye you had already proved your... talent.

 

[granpa]

I'm afraid dale is right. this has become tiresome. you shoot down anything I say while making vague cryptic references to some theory of yours that you never bother to explain. I don't even know what it is that you are arguing and this is page 9. really enough is enough.

 

[atyy]

Points in this post are my interpretation of: Ritchie, Physiology of Axons in "The Axon: Structure, Function and Pathophysiology" ed. Waxman, Kocsis and Stys, OUP 1995.

1. Myelinated axons conduct faster (v~d) than unmyelinated axons (v~sqrt(d)), where v is the speed across nodes and internodes. The key for this is the length constant, as I suspected from dimensional considerations in earlier posts. (Lussier and Rushton 1951).

2. There are references for the computation of velocity in axons, but I do not know whether this is across nodes and internodes, or whether they can also compute a separate internode velocity. (Blight 1985, Brill et al 1978, Dodge 1963, Fitzhugh 1962, Goldman and Albus 1968, Hardy 1973, Hutchinson et al 1970, Koles and Rasinsky 1972, Moore et al 1978, Ritchie and Stagg 1982, Schauf and Davis 1974, Waxman and Brill 1978, Wood and Waxman 1982)

3. There is criticism of the "classical" passive internode model and the neglect of a conduction pathway beneath the myelin, especially for mammalian myelinated axons. (Barrett and Barrett 1982, Blight 1985, Blight and Someya 1985, Bowe et al 1987). Quote for somasimple: "The internodal membrane not only has a capacitance two to three orders of magnitude greater than that of the node, but also contains a repertoire of ionic conductances...".

4. There is criticism of Rushton's analysis for small myelineated axons: "Rushton's belief that conduction velocity of PNS myelinated nerve fibers falls off markedly ... may be correct, but perhaps for a different reason from the one he proposed..."

5. "The studies of Moore et al (1978) show that internodal parameters control the conduction velocity far more than does the node itself. They help account for the insensitivity to the nodal constriction that is characteristic of myelinated fibers."

6. "[referring to activation rate constants] Why this should be so is unclear. Indeed it should be pointed out that the conduction velocity of a mammalian nerve fiber at 37^oC can be simulated reasonably well only if these activation constants are brought into line with the squid giant axon value of 3 (Ritchie and Stagg 1982)."

 

[atyy]

Hi somasimple, I'm done with the discussion too - but I think your points are excellent. This is really getting into specialist territory, and I'm not personally inclined to pursue the details further. Much luck on your studies!

 

[somasimple]

I'm afraid dale is right. this has become tiresome. you shoot down anything I say while making vague cryptic references to some theory of yours that you never bother to explain. I don't even know what it is that you are arguing and this is page 9. really enough is enough.

The content of this thread was started to elucidate if 2 or more nodes are active during a single message propagation. This is a complex subject and solitons are much more complex.
You question about inductance, water... are far out the subject.

Atyy,
Thanks for the support.
I'll take a closer look at references.
ps: the Koch's book is disappointing: it contains quite nothing on the subject.
BTW, it gives more numbers and some graphs show strange results...

 

[granpa]

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

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

 

[somasimple]

Interesting concepts but what is the relation with the current subject?

 

[granpa]

no particular relation. just showing that ions and electric fields can and do interact with phonons. hence the possibility of an electrical signal propagating at the speed of sound.

 

[somasimple]

But we're working, here, in a wet and hydrated environment, not a crystalline one.

 

[somasimple]

http://stbb.nichd.nih.gov/role_pot_wave52.pdf

The action current of a conducted nerve impulse changes its shape when the
recording partition is shifted along the nerve fiber. Within an internodal segment,
the rising phase of the action current is shortest and the maximum is attained earliest
when the recording partition is located at the proximal end of the internode. The
rising phase is retarded, within an internodal stretch, continuously with increasing
distance of the recording partition from the proximal node. This fact is also ascribed
to the distributed capacity of the myelin-covered portion of the nerve fiber.
The difference between the time-course of the action current (flowing through
the axis-cylinder) and that of the action potential (recorded from the surface of the
nerve trunk) is shown to be due to the capacity distributed along the surface of the
nerve fiber.
The latent period of the action potential of a conducted nerve impulse varies
continuously as the distance along the fiber. The steepnes so f the rising phases hows
a sharp maximum at each node of Ranvier regularly. This result was correlated
with the measurements of action currents recorded by the partition method.
Conduction of the nerve impulse in myelinated fibers is saltatory with respect to
space but not, in general, with respect to time.