# Saltatory Conduction: single AP or not?

• somasimple

#### somasimple

Gold Member
Hi All,
http://en.wikipedia.org/wiki/Saltatory_conduction

Because the cytoplasm of the axon is electrically conductive, and because the myelin inhibits charge leakage through the membrane, depolarization at one node of Ranvier is sufficient to elevate the voltage at a neighboring node to the threshold for action potential initiation. Thus in myelinated axons, action potentials do not propagate as waves, but recur at successive nodes and in effect "hop" along the axon, by which process they travel faster than they would otherwise. This process is outlined as the charge will passively spread to the next node of Ranvier to depolarize it to threshold which will then trigger an action potential in this region which will then passively spread to the next node and so on. This phenomenon was discovered by Ichiji Tasaki[1][2] and Andrew Huxley[3] and their colleagues.

If at node N1, an AP is generated and then the passive spread initiates another AP at node N2, is there 2 APs existing at the same time?
In fact, the second AP is ever initiated before the first has ended. It seems it contradicts the theory?

If at node N1, an AP is generated and then the passive spread initiates another AP at node N2, is there 2 APs existing at the same time?
At least 2.

In fact, the second AP is ever initiated before the first has ended. It seems it contradicts the theory?
AFAIK the theory doesn't predict that the first AP will end before the second is initiated. In fact, according to cable theory, when the first has ended then there is no depolarization to propagate passively.

At least 2.
How is a cable able to contain, at least two APs, when only one was initiated?

if a cable is passive then wouldn't it only apply to the part of the axon between the nodes?

A very good question!
If a cable is passive then you may have problem to connect the two existing APs.

How is a cable able to contain, at least two APs, when only one was initiated?
Cable theory uses only linear circuit elements, so superposition applies.

At anyone time there are action potentials at more than one location along the axon, but each action potential is at a different point in its time course. At three successive locations with an AP, one AP has just passed its peak, another AP is at its peak, and the third AP has not reached its peak.

The above description is only approximate because APs at different points in the axon do not have identical time courses. In the internode, the AP changes shape, but retains enough shape that an onset, peak and end can be reasonably defined.

At anyone time there are action potentials at more than one location along the axon, but each action potential is at a different point in its time course. At three successive locations with an AP, one AP has just passed its peak, another AP is at its peak, and the third AP has not reached its peak.

The above description is only approximate because APs at different points in the axon do not have identical time courses. In the internode, the AP changes shape, but retains enough shape that an onset, peak and end can be reasonably defined.

Cable theory uses only linear circuit elements, so superposition applies.
So you expect;
1. decay?
2. delay?
3. decay+delay?
4. other?

At anyone time there are action potentials at more than one location along the axon, but each action potential is at a different point in its time course. At three successive locations with an AP, one AP has just passed its peak, another AP is at its peak, and the third AP has not reached its peak.

The above description is only approximate because APs at different points in the axon do not have identical time courses. In the internode, the AP changes shape, but retains enough shape that an onset, peak and end can be reasonably defined.

At anyone time there are action potentials at more than one location along the axon, but each action potential is at a different point in its time course. At three successive locations with an AP, one AP has just passed its peak, another AP is at its peak, and the third AP has not reached its peak.

The above description is only approximate because APs at different points in the axon do not have identical time courses. In the internode, the AP changes shape, but retains enough shape that an onset, peak and end can be reasonably defined.
Echo? That is a good perspective.

The above description is only approximate because APs at different points in the axon do not have identical time courses. In the internode, the AP changes shape, but retains enough shape that an onset, peak and end can be reasonably defined.
A traveling wave depends entirely of his past history. That is a good new since you can construct its future.

So you expect;
1. decay?
2. delay?
3. decay+delay?
4. other?
For a sub-threshold neuron I expect:
$$\lambda ^2 \frac{\partial ^2v}{\partial x^2}=-i r+v+\tau \frac{\partial v}{\partial t}$$

DaleSpam,
You're funny. An equation without parameters and conditions... Just funny!
Is it decay like this since you insist on the light speed propagation?
or decay + delay?
it cant' be delay only.

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I had assumed that you would be familiar with the cable equation since it is the basic equation of the cable theory that we have been discussing, and I wrote it using standard notation. So I didn't think it was necessary to explain the terms any more than I would explain the terms of "f=ma" in the physics section. I apologize for my unwarranted assumption and I will gladly describe it in detail now.

The cable equation is:
$$\lambda ^2 \frac{\partial ^2v}{\partial x^2}=-i r+v+\tau \frac{\partial v}{\partial t}$$
where v is the transmembrane voltage, x is the distance along the axon or dendrite, i is the current through the membrane, r is the transmembrane resistance, and t is time. $$\lambda$$ is known as the space constant and $$\tau$$ is known as the time constant. They are free parameters that depend on the electrical properties of the specific neuron with typical values from tens to hundreds of micrometers for the space constant and from tens to hundreds of microseconds for the time constant.

I have a fundamental question for you: if you do not even recognize the cable equation in standard notation then on what basis are you objecting to cable theory?

I have a fundamental question for you: if you do not even recognize the cable equation in standard notation then on what basis are you objecting to cable theory?

Does a cable is able to expand or shrink?
Does a cable exhibit heat changes in both directions?
Does a cable swells?
Does a cable uses ions?

The cable theory is unable to integrate this fate.
BTW, the simulator produces curves. These curves are produced upon models. They must fit facts.
Once again, it is easy to test your model but you obstinately refuse to give any value.
If you're true then the curves will show the predictions of the cable theory and I'll shut my mouth...

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Does a cable is able to expand or shrink?
Does a cable exhibit heat changes in both directions?
Does a cable swells?
Does a cable uses ions?
I assume by these questions you are talking about industrial cables such as the underseas telegraph cables that originally inspired the cable equation rather than biological cables where the cable equation is more commonly used now. Even with industrial cables the answer is yes to all of these.

Industrial cables expand (swell) and shrink, particularly in response to changes in temperature (in both directions). In addition industrial cables are designed to a specific size, the cable equation is generally important in determining the optimal size. During the design process a wide variation of size can be considered (much wider than would occur thermally). The cable equation can even handle changes in size and temperature even that are not uniform simply by including the appropriate terms (e.g. tau becomes a function of x). That covers your first three points.

Your last point, about using ions, is interesting. I assume that you think there is something fundamentally different between electrical currents where the charge carriers are free electrons in a metal and ones where the charge carriers are free ions in an electrolyte. Interestingly, the original cable equations were for a metal cable immersed in sea-water, so both electronic and ionic currents were considered. The purely ionic currents in neurons are actually simpler than the mix of ionic and electronic currents in industrial cables.

The cable theory is unable to integrate this fate.
BTW, the simulator produces curves. These curves are produced upon models. They must fit facts.
Once again, it is easy to test your model but you obstinately refuse to give any value.
If you're true then the curves will show the predictions of the cable theory and I'll shut my mouth...
There is a wealth of experimental evidence going back several decades supporting neuronal cable theory. The models do fit the facts as you well know from your studies.

DaleSpam said:
Even with industrial cables the answer is yes to all of these.

Really?
A cable that exudes water when a message travels?
A cable where ions are going in and out of the cable at the same speed but having different atomic size?
A cable that is hot when the message arrives and makes cold when he goes?
A cable where the diameter is enlarged when the message runs?

Does the cable theory describe all these points?

And we have demonstrated that your cable theory miss, at least, 2 points:
Where is the component implied by the missing capacitor?
Where is the internal axonal resistance?

DaleSpam said:
The purely ionic currents in neurons are actually simpler than the mix of ionic and electronic currents in industrial cables.
That is why I brought that one!

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someone in another thread said that neuron membranes are normally permeable to k. is that true. I thought there were k gates that opened during an ap.

is it just sodium gates that open?

Sodium gates are at nodes.
Potassium gates are at paranodes (under myelin).
Myelin is impermeable to sodium and potassium.
The two kind of gates are functional in sequence.

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I'm not exactly sure what you mean by 'decay' but isn't the fact that the ap decays over time the reason for having nodes in the first place.

I'm not exactly sure what you mean by 'decay' but isn't the fact that the ap decays over time the reason for having nodes in the first place.
The cable theory implies a dampening of the signal. I agree.
Edit: I want to know if there is a delay or not.

And we have demonstrated that your cable theory miss, at least, 2 points:
Where is the component implied by the missing capacitor?
Where is the internal axonal resistance?
You have to choose (or propose one) between these models =>

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someone in another thread said that neuron membranes are normally permeable to k. is that true. I thought there were k gates that opened during an ap.

is it just sodium gates that open?

The resting membrane potential is set in large part by a potassium "leak" channel, so the neuron membrane is normally permeable to K. When the AP occurs, voltage-gated sodium channels open, sodium comes in, then sodium channels close. Even with only the potassium "leak" present, the membrane potential would eventually re-set, since that is the only channel that is open. During an AP, voltage-gated potassium channels open after the voltage-gated sodium channels to increase the rate at which the resting membrane potential is restored. Or at least that's my current story.

Edit: Actually, APs in different neurons are generated by different combinations of channels. In the thalamus, the same neuron can at times fire mainly single APs, and at other times mainly bursts of several APs. Take a look at this abstract on pubmed: Steriade M, McCormick DA, Sejnowski TJ. Thalamocortical oscillations in the sleeping and aroused brain. Science. 1993 Oct 29;262(5134):679-85. Or this guy's site, which has good movies and other stuff: http://info.med.yale.edu/neurobio/mccormick/mccormicknew/Index.html.

Edit: Wow, David McCormick's site seems to have his publications available free! He is one of the very best cortical electrophysiologists, so you will not regret it if you choose to study his work.

Sodium gates are at nodes.
Potassium gates are at paranodes (under myelin).
Myelin is impermeable to sodium and potassium.
The two kind of gates are functional in sequence.

Koch makes the most interesting comments about APs at nodes. He says that there are no voltage-gated potassium channels at the node, and the membrane potential is quickly reset because the (potassium?) leak is abnormally large at the node. He says the function of the potassium channels under the myelin is unknown!

But I just saw an abstract on pubmed saying that there are voltage-gated potassium channels at nodes - I think - but I don't remember the exact source. Different species? Different parts of the nervous system? Experimental error?

The cable theory implies a dampening of the signal. I agree.
Edit: I want to know if there is a delay or not.

I'm not sure how to calculate a velocity, but the dampening, together with the change in shape from the filtering, could effectively "delay" the signal.

Suppose at a patch in the internode, the voltage sequence is Va=(0,20,40,30,20,10,0)

Because of decay (ignoring shape change) at the next patch of internode Vb=(0,10,20,15,10,5,0)

Suppose we say that the AP "begins" once it reaches 20. Then the time slot at which it "begins" has shifted from time slot 2 to time slot 3, and this will appear as a "delay".

When I used this method to estimate internode speed on your re-plotting of Huxley and Stämpfli's data, my value was too slow. I think that is because the estimation effectively assumed that the time constant is zero in the internode, ie. that the voltage decays immediately. If the voltage in one time slot doesn't decay completely, then the voltage from the next time slot can build up on it, decreasing the apparent delay.

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He says that there are no voltage-gated potassium channels at the node, and the membrane potential is quickly reset because the (potassium?) leak is abnormally large at the node.
Why are they (K+ Channels) under myelin at paranode sites? Look at the anatomical configuration!

I'm not sure how to calculate a velocity, but the dampening, together with the change in shape from the filtering, could effectively "delay" the signal.

Suppose at a patch in the internode, the voltage sequence is Va=(0,20,40,30,20,10,0)

Because of decay (ignoring shape change) at the next patch of internode Vb=(0,10,20,15,10,5,0)

Suppose we say that the AP "begins" once it reaches 20. Then the time slot at which it "begins" has shifted from time slot 2 to time slot 3, and this will appear as a "delay".
See the red curves.
https://www.physicsforums.com/showpost.php?p=1894462&postcount=12

Really?
A cable that exudes water when a message travels?
A cable where ions are going in and out of the cable at the same speed but having different atomic size?
A cable that is hot when the message arrives and makes cold when he goes?
A cable where the diameter is enlarged when the message runs?

Does the cable theory describe all these points?
Yes, all of these effects can easily be described by modern cable theory. As the cable exudes water, changes temperature, and changes diameter its electrical properties may change. So instead of having $$\lambda$$ we would have $$\lambda(d,T,[H2O],...)$$ etc.

Have you any evidence to support the idea that the cable equation is not a good approximation to the behavior of sub-threshold neural activity?

Yes, all of these effects can easily be described by modern cable theory. As the cable exudes water, changes temperature, and changes diameter its electrical properties may change. So instead of having $$\lambda$$ we would have $$\lambda(d,T,[H2O],...)$$ etc.
Easily?! You're certainly kiddin'
The theory may describe, eventually, the electrical perturbations created by physical events. Ions are physically moving and carry electrical fields, so... you can record these electrical events.

A theory must describe all facts and make logical links between them. The cable theory try to describe electrical events that occur in neurons. It doesn't describe how are linked the physical events but only restricted electrical consequences.
The cable theory is very static.

Have you any evidence to support the idea that the cable equation is not a good approximation to the behavior of sub-threshold neural activity?

Why are you reducing the field of discussion?
Sub-threshold activity, as the whole cable theory, describes a facet of a thing that has many others. Please choose the electric model that mimics this activity and give us some values?
I understand why you continuously refuse...
Langauge barrier? I do not think so.

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pardon my ignorance, but the whole point of an ap is that once a critical voltige is reached the whole thing becomes unstable and the voltage plummets. it should be quite trivial to find the point in the ap where this occurs. do you mean to say that this signal decays to the point that one literally can't determine the exact point where it reached this threshold?

if so then I guess I'm beginning to get it.

seems to me that the ideal way to send a signal from one node to another would be to run a hollow microtubule from one to the next then pack it full of potassium ions. connect one end to some voltage controlled gate and open it when a signal arrives. very few ions would have to be allowed to escape to produce a large change in voltage at the next node. plus the repulsion of the ions inside the microtubule would speed up the signal propagation.

I'm not sure how they would fill back up again. but they say there's enough ions inside the cell for it to fire 100,000 times before it runs out even with all active ion pumps disables. so it doesn't seem to require active pumping.

pardon my ignorance, but the whole point of an ap is that once a critical voltige is reached the whole thing becomes unstable and the voltage plummets. it should be quite trivial to find the point in the ap where this occurs. do you mean to say that this signal decays to the point that one literally can't determine the exact point where it reached this threshold?

if so then I guess I'm beginning to get it.
The problem is;
Two active sites: nodes (but passive under threshold).
connected by a passive one.

The passives sites must exhibit what the active are doing in both directions because they are passive. We disagree how is the passive section and what is happening.

Yes, the "decay only" idea only gives an effective delay for the onset. Some sort of filtering is needed to get an effective delay in the peak (which is also closer to how H+S defined onset), which is another reason that I should include the time constant to get the internode speed right.

Is your decay+delay curve from model #2 in post #21?

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Kole MH, Ilschner SU, Kampa BM, Williams SR, Ruben PC, Stuart GJ. Action potential generation requires a high sodium channel density in the axon initial segment. Nat Neurosci. 2008 Feb;11(2):178-86.

"...It is commonly assumed that this process requires a high density of voltage-gated sodium (Na(+)) channels. Paradoxically, the results of patch-clamp studies suggest that the Na(+) channel density at the AIS is similar to that at the soma and proximal dendrites..."

maybe you've seen this before but this is really interesting:

http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=7

and especially this:

http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8

the peak seems to move almost instantly the 2 mm from node to node (the amplitude decreasing to not quite half) with a considerable delay (slightly less than 0.1 ms) at each node which gives it a net speed of 20 m/s. (during the internode, wouldn't it have to be moving at or very close to the speed of sound?) (which is 1500 m/s in water)

after the delay, the beginning of the peak at one node coincides with the beginning of the downstroke of the previous internode. which actually seems to move backward.

the arrival of the peak at the node at the end of one internode seems to correspond to the beginning of the upstroke of the next internode.

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Yes, the "decay only" idea only gives an effective delay for the onset. Some sort of filtering is needed to get an effective delay in the peak (which is also closer to how H+S defined onset), which is another reason that I should include the time constant to get the internode speed right.

Is your decay+delay curve from model #2 in post #21?
No. These curves are only working hypothesis.
The models are two low pass filters and only the cutoff frequency will be changed without any phase change for such a signal. NO DELAY.
The #2 is closer to our Cm computations for the internode.
http://en.wikipedia.org/wiki/Cut-off_frequency

Kole MH, Ilschner SU, Kampa BM, Williams SR, Ruben PC, Stuart GJ. Action potential generation requires a high sodium channel density in the axon initial segment. Nat Neurosci. 2008 Feb;11(2):178-86.

"...It is commonly assumed that this process requires a high density of voltage-gated sodium (Na(+)) channels. Paradoxically, the results of patch-clamp studies suggest that the Na(+) channel density at the AIS is similar to that at the soma and proximal dendrites..."

Why nobody takes account of a silent phenomenon? : LATENCY. Silent doesn't mean passive. Sub-threshold, too.

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maybe you've seen this before but this is really interesting:

http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=7

and especially this:

http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8

the peak seems to move almost instantly the 2 mm from node to node (the amplitude decreasing to not quite half) with a considerable delay (slightly less than 0.1 ms) at each node which gives it a net speed of 20 m/s. (during the internode, wouldn't it have to be moving at or very close to the speed of sound?) (which is 1500 m/s in water)

after the delay, the beginning of the peak at one node coincides with the beginning of the downstroke of the previous internode. which actually seems to move backward.

the arrival of the peak at the node at the end of one internode seems to correspond to the beginning of the upstroke of the next internode.

We have had already discussed about these instructive curves but DaleSpam contests any delay in the internode.
For my own, I accept facts.