Saltatory Conduction: single AP or not?

[somasimple]

Hi All,
from this page:
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?

[DaleSpam]

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.

[somasimple]

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

[granpa]

if a cable is passive then wouldnt it only apply to the part of the axon between the nodes?

[somasimple]

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

[DaleSpam]

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.

[atyy]

At any one 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.

[atyy]

At any one 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.

[somasimple]

Cable theory uses only linear circuit elements, so superposition applies.
So you expect;

decay?
delay?
decay+delay?
other?


At any one 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 any one 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. :approve:

[somasimple]

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.

[DaleSpam]

So you expect;

decay?
delay?
decay+delay?
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}

[somasimple]

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.

[DaleSpam]

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?

[somasimple]

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...

[DaleSpam]

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.

[somasimple]

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

Really? :rolleyes:
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:
http://www.physicsforums.com/showthread.php?t=258168
Where is the component implied by the missing capacitor?
Where is the internal axonal resistance?

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!
http://www.physicsforums.com/showthread.php?t=260444

[granpa]

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?

[somasimple]

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.

[granpa]

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

[somasimple]

I'm not exactly sure what you mean by 'decay' but isnt 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.

[somasimple]

And we have demonstrated that your cable theory miss, at least, 2 points:
http://www.physicsforums.com/showthread.php?t=258168
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 =>

[atyy]

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.

[somasimple]

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!

[somasimple]

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.
http://www.physicsforums.com/showpost.php?p=1894462&postcount=12

[DaleSpam]

Really? :rolleyes:
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?

[somasimple]

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...
Language barrier? I do not think so.

[granpa]

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 cant determine the exact point where it reached this threshold?

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

[granpa]

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 theres 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 doesnt seem to require active pumping.

[somasimple]

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 cant 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.

[atyy]

See the red curves.
http://www.physicsforums.com/showpost.php?p=1894462&postcount=12

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?

[atyy]

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...."

[granpa]

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, wouldnt 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.

[somasimple]

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

[somasimple]

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.

[somasimple]

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, wouldnt 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.

[granpa]

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

you mean delay at the nodes?

[somasimple]

A delay at nodes may be the result of combined delays:


Latency (but I suspect that an axon skips it.)
Delay in the internode (from records).
Delay implied by decay.

[granpa]

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

it appears to me based on this that the ap from one node passes right through the next node without delay but has become by that time so spread out that it just appears to be the onset/upstroke of the next ap which actually occurs (at that next node) after a 0.1 ms delay.

[somasimple]

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

it appears to me based on this that the ap from one node passes right through the next node without delay but has become by that time so spread out that it just appears to be the onset of the next ap which actually occurs (at that next node) after a 0.1 ms delay.
The B curve shows stairs that aren't horizontal => Delay.

[granpa]

further the speed through the internode appears to be so fast that it cant even be determined from the graphs. the measured 20 m/s being due almost entirely to the delay at each node.

[granpa]

The B curve shows stairs that aren't horizontal => Delay.
what do you figure the speed is?

[somasimple]

further the speed through the internode appears to be so fast that it cant even be determined from the graphs. the measured 20 m/s being due almost entirely to the delay at each node.
A speed may be seen as fast when you compare it with a slow one.
The delay is around 20 µs (internode to internode). You have not records from nodes so you can't extrapolate that way.

[somasimple]

what do you figure the speed is?
800 to 1300 ms-1
perhaps less.

[granpa]

800 to 1300 ms-1
perhaps less.
sounds about right. speed of sound in water being 1500 m/s

[granpa]

The B curve shows stairs that aren't horizontal => Delay.

whoa. I totally misunderstood you. I thought you were saying the horizontal parts of the B curve werent really horizontal.

you also misundrestood me. when I said it (the B curve) seems to pass through without delay I mean it seems to become the A curve

[somasimple]

whoa. I totally misunderstood you. I thought you were saying the horizontal parts of the B curve werent really horizontal.

you also misundrestood me. when I said it (the B curve) seems to pass through without delay I mean it seems to become the A curve

The A curve is based upon rising phases that vary with decays.
Average speed must be < 1500 ms-1 because of the dampening (decay).

Edit: I said it => I thought you were saying the horizontal parts of the B curve werent really horizontal.

[granpa]

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, wouldnt 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.


notice what I said about the C curve too.

[somasimple]

which actually seems to move backward.
This?

[granpa]

The A curve is based upon rising phases that vary with decays.
Average speed must be < 1500 ms-1 because of the dampening (decay).

Edit: I said it =>

I dont see your first point.

so it cant be a sound wave becaise it decays? hmmmm.

[granpa]

This?

this what?

[somasimple]

this what?
which actually seems to move backward.
so it cant be a sound wave becaise it decays? hmmmm.
Sound is a wave and it strength decays with distance.
A wave is a wave, so...

[somasimple]

If the node is purely passive as expected you must have a backward effect:

Here is a simple working hypothesis:
The movie is not completed.
www.somasimple.com/flash_anims/node_01.swf

[granpa]

oh. yes, that is what I was referring to.

I'll try to watch your animation but my competer tends to freeze whenever I do.

[granpa]

but the backward effect is the opposite of what you would expect. it returns the axon to its resting state.

[somasimple]

oh. yes, that is what I was referring to.

I'll try to watch your animation but my competer tends to freeze whenever I do.
Update your flash player;
http://www.adobe.com//downloads/

[somasimple]

but the backward effect is the opposite of what you would expect. it returns the axon to its resting state.
Hmmm, no, it implies an effect we do not see on curves. :wink:

[granpa]

thanks. I did get to see it. I watched for about 20 seconds. it just repeats doesnt it?

[somasimple]

Update your flash player;
http://www.adobe.com//downloads/
or download it on your computer.

[granpa]

that is exactly what I would have expected but like I said the backward effect is exactly the opposite.

[somasimple]

thanks. I did get to see it. I watched for about 20 seconds. it just repeats doesnt it?
Yes it repeats. Just a working hypothesis to see the transition phases.

[somasimple]

that is exactly what I would have expected but like I said the backward effect is exactly the opposite.
If you do not see the expected prediction of a theory, change the facts or theory.

[granpa]

If you do not see the expected prediction of a theory, change the facts or theory.


hmm. facts or theory. hmmm

:tongue2:

[granpa]

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

imagine this: four nodes. nodes 1,2,3 and 4. nodes 3 and 4 would be locked (all nodes would normally be locked). meaning they wont pass signals. the first signal that reaches node 3 is from node 1. it has the effect of unlocking the node. this would take time so there would be a delay before node 2 fires. node 2 then fires and the ap passes through node 3 (without delay) to node 4 which it unlocks. there is a delay while node 4 is being unlocked. then node 3 fires.

just before each node fires it locks itself again. so when it does fire the ap can only go in one direction.

so the sequence for each locked node would be:
1 receive a weak signal from 2 nodes away that unlocks it
2 pass, without delay, a stronger signal from 1 node away to unlock the next node.
3 lock itself and then fire its own ap.

the point of course would be to prevent misfiring. this would explain why there is such a long and seemingly needless delay at each node.
and after each node locks itself the previous internode can begin to return to its resting state. hence the backward moving anti-action-potential I mentioned. (anti not because it is moving backword but because it returns the axon to its resting state)

[atyy]

We disagree how is the passive section and what is happening.

What is the disagreement? Model #2 in your post 21, and DaleSpam's cable equation seem to be basically the same, and Huxley and Stämpfli seem to mention both for the internode:

HS p329 cf Model #2: "length of a fibre which does not include a node is closely similar to ... a resistance and capacity in parallel...".

HS's p333 cf cable equation: the bottom equation has a second order derivative in space, and first order derivative in time.

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.[/url]

Don't RC circuits have frequency dependent phase shifts? Also, the time course of a signal depends on the presence of all its Fourier frequencies, so wouldn't a frequency dependent reduction in amplitude (even without a phase shift for each Fourier component) produce a shape change in the time course anyway?

The passives sites must exhibit what the active are doing in both directions because they are passive.
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.
If the node is purely passive as expected you must have a backward effect

HS discusses how the backward effect is seen in their data (p323): "surprising feature that the descending phase occurs earlier at the distal than at the proximal end of the internode ... Graph C in one internode and Graph B in the next more distal internode represent different aspects of the same disturbance spreading symmetrically from the node separating them.

[somasimple]

What is the disagreement?
Delay in the internode propagation.
a resistance and capacity in parallel....
This does not tell us how they are connected.
Why the capacity is omitted since it is 40 time greater than at node?

Don't RC circuits have frequency dependent phase shifts? Also, the time course of a signal depends on the presence of all its Fourier frequencies, so wouldn't a frequency dependent reduction in amplitude (even without a phase shift for each Fourier component) produce a shape change in the time course anyway?
Phase shift is not equal to delay.
BTW, the better way to test such models is sinusoidal signals.
surprising feature that the descending phase occurs earlier at the distal than at the proximal end of the internode
Graph it! It seems normal with a decay. (see the pictures I provided)

Granpa,
Make a drawing: I'm lost.

[somasimple]

http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=9#page
This comes from page 323:
This spread takes place with a finite velocity (not necessarily constant) so that graph B becomes later, and graph C earlier towards the distal end of each internode.
Ditto!
An attenuation that occurs with distance must take time.

[somasimple]

Granpa,
Make a drawing: I'm lost.

imagine this: four nodes. nodes 1,2,3 and 4. nodes 3 and 4 would be locked (all nodes would normally be locked).
Hmmm, no: It is better to lock something to ensure the transmission. Locking something before the transmission will be the best source of problem and no transmission.

[DaleSpam]

A theory must describe all facts and make logical links between them. ... 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. This is completely wrong. Each scientific theory has some limited domain of applicability. For example, Maxwell's equations do not model the orbits of planets nor does it model the photoelectric effect, such things are outside of its domain. Maxwell's theory of EM does not need to "describe all facts", it only needs to describe and link facts within its domain. The search for a "Grand Unified Theory" or "Theory of Everything" is ongoing, and even if such a theory were available it would likely be too cumbersome to apply to neurons.

The domain of cable theory is sub-threshold activity, it always has been. Did you not understand that? The HH model describes supra-threshold activity and does not include any propagation mechanism. The cable model includes a propagation mechanism, but does not describe supra-threshold behavior. I thought that was understood, perhaps this is the real problem.

Please choose the electric model that mimics this activity and give us some values?
I understand why you continuously refuse...
Language barrier? I do not think so.I have told you the model I support several times: the standard HH model and cable equation. Since these are the standard models used my mainstream scientists there are plenty of references describing in exhaustive detail their use and their experimental validation. You know that perfectly well since you have read many of these papers. What could I possibly put in a post than would be more informative that what you already have read? I have neither the time nor the inclination for such a pointless pursuit.

[somasimple]

I have neither the time nor the inclination for such a pointless pursuit.
That is not a problem. I have the same inclination.

[somasimple]

The HH model describes supra-threshold activity and does not include any propagation mechanism.

http://en.wikipedia.org/wiki/Hodgkin-Huxley_model
The Hodgkin–Huxley model is a scientific model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear ordinary differential equations that approximates the electrical characteristics of excitable cells such as neurons and cardiac myocytes.
(sic)!

[granpa]

Hmmm, no: It is better to lock something to ensure the transmission. Locking something before the transmission will be the best source of problem and no transmission.

the idea is to prevent misfirings. so yes the idea is to create no transmission at all until everything is ready and the first few nodes are unlocked.

at any one time no more than 3 nodes would be unlocked

[granpa]

every ap is initiated at one node (which had just locked itself so the ap con only go in one direction) passes without delay through the next node (which then gets ready to fire) and finally the by now much weakened ap strikes the third node which is locked so the signal ends there. but in striking the third node it unlocks it so the next ap can pass.

when each node fires it first locks itself so the normal state of all nodes is to be locked

[somasimple]

Suppose a node remains locked => no transmission.
We have seen that APs are overlapping.
If a locking mechanism exists (high probability) it may function when a node is already firing and initiating an AP at the next node. It may avoid node interactions.

[somasimple]

when each node fires it first locks itself so the normal state of all nodes is to be locked
contradiction: nodes are locked at firing and at rest.

[granpa]

contradiction: nodes are locked at firing and at rest.
to signals coming from one direction.

each node is unlocked by one signal
it then passes a second signal
at then locks itself and then fires. it doest need to be unlocked to fire because it isnt passing a signal. its creating a signal which only goes one way from the node.

here is a very good picture of what I am talking about:
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8

[somasimple]

here is a very good picture of what I am talking about:
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8
Elaborate!

[granpa]

contradiction: nodes are locked at firing and at rest.
locked means it wont pass a signal. not that it cant initiate one. but if it does initiate one then the ap can only go in one direction.

[granpa]

curve B after the delay at the node fires. this is the firing of the node. it travels to the next node (which does not yet fire) and passes straight through without delay becoming the horizontal part of curve A and finally ending at the second node which is locked. while that node is being unlocked there is a delay. then the next node fires and repeats the process. as each node fires a backward propagating anti-action-potential (curve C) restores the previous internode to its resting state. that is why the node must lock itself before firing.

[granpa]

so each node receives 2 signals. a weaker one that unlocks it and a stronger one that causes it after a short delay to fire.
a single signal alone isnt enough to cause it to fire. this also helps to prevent misfiring.

[somasimple]

curve B after the delay at the node fires. this is the firing of the node. it travels to the next node and passes straight through without delay becoming the horizontal part of curve A and finally ending at the second node which is locked. while that node is being unlocked there is a delay. then the next node fires and repeats the process. as each node fires a backward propagating anti-action-potential (curve C) restores the previous internode to its resting state. that is why the node must lock itself before firing.

The A curve shows rising phases of APs
The B curve shows peaks
The C one: falling phases.

Since there is decay in internode then all is OK.
Your process is too complicated and threshold + delay explains fully the process.

[somasimple]

a single signal alone isnt enough to cause it to fire.
No, a single is largely sufficient.

[granpa]

No, a single is largely sufficient.

the first signal is small (decayed). and in fact is usually just considered to be part of the rising phase of a single ap which is in fact 2 aps. the older decayed one followed rapidly by a newer more intense one. so it would appear that one signal was sufficient to trigger it but its actually 2

[granpa]

The A curve shows rising phases of APs
The B curve shows peaks
The C one: falling phases.

Since there is decay in internode then all is OK.
Your process is too complicated and threshold + delay explains fully the process.

I know what ABand C are supposed to show. but I think they are wrong. A is the older decayed signal from further away. B is the actual signal from a freshly opend gate. and C is the backward propagating anti-action-potential.

I dont understand why you think thats complicated. is it any more complicated than a human eye? or the human brain? seems well within the capability of evolution. moreover it explains the seemingly needless delay at each node. it has to wait for the node down the line to become unlocked. and the whole process is to prevent noise and misfirings.

seems pretty reasonable to me.

not to mention supported visually by this:
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8

[somasimple]

taking two signals implies a delay and AP that is larger in duration.
Since there is a delay, it would be very easy to verify your hypothesis: axon elongation => enlarges or shrinks the AP duration...
I keep the single signal processing.

[somasimple]

I know what ABand C are supposed to show. but I think they are wrong.
Facts are facts: They were recorded and these curves are results of simple computations.

[granpa]

taking two signals implies a delay and AP that is larger in duration.
Since there is a delay, it would be very easy to verify your hypothesis: axon elongation => enlarges or shrinks the AP duration...
I keep the single signal processing.


none of that makes any sense. axon elongation wouldnt have any effect on the ap duration. you have apparently misunderstood something i said. and what delay are you talking about. the only delay is the one that is apparent in the graph. about 0.1 ms at each node.

[granpa]

Facts are facts: They were recorded and these curves are results of simple computations.

I dont contest the facts. those curves are the basis of everything i am saying. why would i contest them?

look at one node on the axon. first it receives the A signal then the B signal then then it fires then receives the C signal. i think the A signal is the ap from 2 nodes away. the B signal before the delay is the ap from 1 node away. the B signal after the delay is the node itself firing. the C signal is the backward propagating anti-action-potential which is resetting the previous internode to its resting state.

[granpa]

taking two signals implies a delay and AP that is larger in duration.
Since there is a delay, it would be very easy to verify your hypothesis: axon elongation => enlarges or shrinks the AP duration...
I keep the single signal processing.


i'm not sure i understand you but you appear to be forgetting that each ap passes through 2 internodes before being stopped by a locked node. so a single node con receive 2 signals just as fast as before. there is no delay.

the first signal is decayed and doest cause the node to fire. it just unlocks it. the second one causes it to fire (after a short delay).

[somasimple]

Facts are facts: These curves are results of simple computations.
Computations may distort the facts in that case. But I cant' how you compute your two signals => They must be added and there is a delay.

[granpa]

Computations may distort the facts in that case. But I cant' how you compute your two signals => They must be added and there is a delay.

i already told you in post 87. the only delay is the one everyone already agrees on. there are 2 signals because the ap passes through the first node it reaches (which after a short delay fires) and continues on without delay to the next node which it unlocks.

i dont understand what it is that you dont understand. please ask more specific questions.

[granpa]

this is just an idea that I am presenting. it isnt established fact. the facts are here:
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8

nodes 1234. nodes 3 and 4 and all further nodes are locked. meaning that they will not pass signals.
ap=action potential

t0 node 1 fires producing ap1 which moves at the speed of sound in water. 1500 m/s
t1 ap1 almost instantly reaches node 2 and passes through WITHOUT DELAY
t2 ap1 almost instantly reaches and ends at node 3 and unlocks node 3 (which takes some time)
t3 after 0.1 ms node 2 fires producing ap2 which moves at the speed of sound in water. 1500 m/s
t4 ap2 almost instantly reaches node 3 and passes through WITHOUT DELAY
t5 ap2 almost instantly reaches and ends at node 4 and unlocks node 4 (which takes some time)
t6 after 0.1 ms node3 fires producing ap3 which moves at the speed of sound in water. 1500 m/s

t0 node 1 fires producing ap1
t1 ap1 almost instantly reaches node 2
t1-t3 delay of 0.1 ms at node 2 before it fires
t3 node 2 fires producing ap2
t4 ap2 almost instantly reaches node 3
t4-t6 delay of 0.1 ms at node 3 before it fires

there is therefore only one delay and it is the 0.1 ms one that everyone already agrees on. so it takes 0.1 ms for an action potential at one node to create an action potential at the next node which is typically 1 or 2 mm away. that gives a net speed of 10-20 m/s. if there were no delay at each node then the signal would move at 1500 m/s. the speed of sound in water. (thats just a guess but its certainly at least a good fraction of that speed)

just before each node fires its ap it relocks itself so the ap can only go in one direction and the previous internode can immediately begin to return to its resting state. this is seen in curve C:
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8

[somasimple]

http://www.physicsforums.com/showpost.php?p=1897614&postcount=66

This spread takes place with a finite velocity (not necessarily constant) so that graph B becomes later, and graph C earlier towards the distal end of each internode.
finite => delay
+ delay to initiate the next AP since there is a decay in internode.

So I reject, one more time, your point of view. Sorry.

[granpa]

i thought we agreed that the speed of the ap through the internode was around 1000 m/s and all the delay came at the node as is suggested by the data here:
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8

[somasimple]

i thought we agreed that the speed of the ap through the internode was around 1000 m/s and all the delay came at the node.
It gives 1~2µs for the internode and since the decay is quite 1/3 => total delay around 20 µs.

[granpa]

according to this:
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8
the delay at the node is about 0.1 ms or 100 microseconds. a 20 microsecond delay would be almost negligible

[granpa]

travelling at 1000 m/s an ap will travel the 1-2 mm from node to node in about 1 or 2 microseconds. so i guess we agree on that. whether decay results in a delay i dont know but i dont see what it matters. the inherent delay at the node swamps it out anyway.

i fail to see what any of this has to do with the idea that nodes lock and unlock

[somasimple]

whether decay results in a delay i dont know but i dont see what it matters.
A lot, since the threshold will be reached later at next node. o:)

[atyy]

HH model for unmyelinated axon:
-Describes AP at a point and its propagation.
-Considers active and passive circuit components uniformly distributed along the axon.
-Is a wave equation with a well-defined propagation velocity which matches experiement.
-Reduces in a certain limit to the linear passive cable equation which does not have a well defined velocity.

HS model for myelinated axon
-Nodes active, internodes passive
-Internodes considered as resistor and capacitor in parallel (I think I know what they mean, but agree with somasimple it's not obvious), and apparently equivalently with an equation that resembles the linear passive cable equation.
-Expected backwards propagation from node into internode is apparently seen in the data and discussed.
-No explicit calculation of internode velocity, but heuristic and dimensional arguments are given for its form.

FH model data for myelinated axon
-FH model is standard reference for myelinated axon
-Only FH 1964 seems to be available to me, and does not describe propagation, but there may be other FH papers.

[granpa]

not much later. not enough to make any difference. the delay at the node is already 100 microseconds anyway. i dont see what internode delay has to do with anything at all much less whether nodes lock or unlock.

[granpa]

-Expected backwards propagation from node into internode is apparently seen in the data and discussed..
http://www.pubmedcentral.nih.gov/pagerender.fcgi?artid=1392492&pageindex=8
but the backward propagation that is seen (at least in the data i saw) isnt a backward propagating ap. its an anti-ap. it doesnt depolorize the axon. it returns it to its resting state.

but thats not the issue at the moment.

[atyy]

Why the capacity is omitted since it is 40 time greater than at node?

Capacity is not omitted - they are discussing resistor and capacitor in parallel as a model for the internode.

[DaleSpam]

HH model for unmyelinated axon:
-Describes AP at a point and its propagation.
-Considers active and passive circuit components uniformly distributed along the axon.
-Is a wave equation with a well-defined propagation velocity which matches experiement.
-Reduces in a certain limit to the linear passive cable equation which does not have a well defined velocity.Hi atyy, do you by any chance have a link for this? None of the variants of the HH models that I have seen have any spatial terms, but it has been years since I studied this stuff. I would be very interested to see a single model that includes the voltage-gated channels and spatial terms.

[atyy]

Hi atyy, do you by any chance have a link for this? None of the variants of the HH models that I have seen have any spatial terms, but it has been years since I studied this stuff. I would be very interested to see a single model that includes the voltage-gated channels and spatial terms.

The HH paper discussing AP propagation in an unmyelinated axon doesn't seem to be free online, unlike the others. I learnt about this from somasimple, haven't read it, but looks sensible on a quick scan: http://butler.cc.tut.fi/~malmivuo/bem/bembook/.

I'll summarise the argument presented by Koch (Biophysics of Computation, OUP 1999) [Vxx is second partial of V wrt x, I haven't bothered about correct signs]:

1. im~Vxx

2. im~Vt+F(V), where F(V) represents the HH model for the AP at a point, including terms that look like dp/dt~f(p)

3. So Vt~Vxx+F(V)

"no general analytical solution is known ... Hodgkin and Huxley only had access to a very primitive hand calculator ... Instead they considered a particular solution to these equations ... postulated the existence of a wave solution ... Vxx~Vtt ... [more steps until an ordinary DE is also obtained] ... Hodgkin and Huxley iteratively solved this equation until they found a value of u leading to a stable propagating wave solution. In a truly remarkable test of the power of their model, they estimated 18.8 m/s at (18.3oC) ... a value within 10% of the experimental value of 21.2 m/s ..."

" ... more than 10 years later that Cooley, Dodge and Cohen solved the full partial differential equation numerically ..."

It boggles my mind they did that with a "primitive hand calculator"?! :smile:

[atyy]

I think I may finally understand somasimple's "discontinuity" objection - it makes sense to me if "discontinuous" means "non-analytic".

Linear passive cable equation: Vxx~Vt, which is a linear parabolic partial differential equation.

HH equation: Vxx~Vt+F(V,p,dp/dt), where p are the HH point conductance parameters. The considerations in its derivation are the same as in deriving the cable equation, but it is not parabolic. This is usually called the HH equation only if p is not a function of x, but I will refer to it as the HH equation even for p(x).

For an unmyelinated axon, some parameter like the density of sodium channels pn is spatially constant.

For a myelinated axon, the spatial distribution of sodium channels can presumably be modelled by pn(x), which if analytic will approach zero only asymptotically, and the equation will not be exactly parabolic for any axon segment, and we cannot do an exact separation into "active" and "passive" compartments (HS discuss this, but in different language, they say the internode may be active, but not active enough for current to lead voltage).

If pn(x) is smooth but not analytic, then it can be exactly zero over some internode segment, and the equation will reduce exactly to the cable equation. In this case we can do an exact separation into "active" and "passive" compartments.

Presumably since the full analytical solution is not known, whether one chooses the parameter to be smooth and analytic, or smooth but not analytic, will be a matter of numerical convenience, since the difference will probably not be experimentally detectable.

[DaleSpam]

3. So Vt~Vxx+F(V) OK, that makes sense. The Vt~Vxx part is the cable equation and the F(V) part is what I knew as the HH model. I just hadn't seen them put together like that, but it is pretty obvious when someone else points it out for you :smile:

[granpa]

just thought this was interesting:

http://www.ncbi.nlm.nih.gov/pubmed/314337

Using a special albumin technique, nodes of Ranvier have been examined within frog skeletal muscle, sciatic nerve and rat and frog cerebrum. Initial segments have been examined in cerebrum of frog and rat. Mictotubules usually run longitudinally through these regions, but within the bare area of the intramuscular node of Ranvier, annular or helical bundles of microtubules run in a marginal band at right angles to the more centrally placed longitudinal microtubules. These nodal bare areas show a pronounced convexity and it is suggested that the annular microtubules serve to maintain this convexity during muscle contraction.

http://www.ncbi.nlm.nih.gov/pubmed/1869882?ordinalpos=1&itool=EntrezSystem2.PEntrez.Pubmed.Pubmed_ResultsPanel.Pubmed_DiscoveryPanel.Pubmed_Discovery_RA&linkpos=2&log$=relatedarticles&logdbfrom=pubmed


The relationship between the degree of nodal narrowing and the changes in the structure of the axonal cytoskeleton was studied in 53 fibres of mouse sciatic nerve. Nodal narrowing increased with increasing fibre calibre to reach about 20% of the internodal area in the thicker fibres. The narrowing corresponded quantitatively to a decreased number of nodal neurofilaments. Nodal microtubule numbers varied greatly, and a majority of fibres had considerably (approximately 55%) more microtubules in their nodal profile than in the internode

[somasimple]

Capacity is not omitted - they are discussing resistor and capacitor in parallel as a model for the internode.

http://butler.cc.tut.fi/~malmivuo/bem/bembook/21/21.htm
Sorry, but I do not see it.

Granpa,
It is.

[granpa]

you do realize that the attached image in your last post, the one from the website here:
http://butler.cc.tut.fi/~malmivuo/bem/bembook/21/21.htm

(in the case of dc, and neglecting the fh at the node, and using the water analogy for current) is just a description of a long empty and leaky pipe. you turn on the water and it takes a while before any comes out the other end.

it says the internode is just modeled as a resistor. the capacitors are for the nodes. doesnt make much sense to me.

[somasimple]

I think I may finally understand somasimple's "discontinuity" objection - it makes sense to me if "discontinuous" means "non-analytic".


Not at all.
Continuity (http://www.sosmath.com/calculus/limcon/limcon05/limcon05.html) is a prerequisite for an electrical signal in a wire/cable.
There is discontinuities at internode/node junctions when the signal leaves the internode entering in the node and when it leaves the node entering to the next internode.

[somasimple]

it says the internode is just modeled as a resistor. That is the problem I'm pointing out.
Normally the nodes are connected to external milieu.

[atyy]

http://butler.cc.tut.fi/~malmivuo/bem/bembook/21/21.htm
Sorry, but I do not see it.

The above doesn't even model most nodes as active. HS discuss resistance and capacitance of the internode, and it is very important for them to come to the conclusion that the internode is passive, or at least much less active than the nodes (p328 bottom paragraph through p329).

There is discontinuities at internode/node junctions when the signal leaves the internode entering in the node and when it leaves the node entering to the next internode.

In the data or in someone's model?

[somasimple]

The above doesn't even model most nodes as active. HS discuss resistance and capacitance of the internode, and it is very important for them to come to the conclusion that the internode is passive, or at least much less active than the nodes (p328 bottom paragraph through p329).
Adding a capacitor doesn't change the passivity but it is missing (I added the table 2)
In the data or in someone's model?
Both.
Edit: In the model a node is connected to 2 internodes and must be at the same potential.
In data: the end of an internode is not at the same potential than the beginning of the next internode.

[somasimple]

HS discuss resistance and capacitance of the internode, and it is very important for them to come to the conclusion that the internode is passive, or at least much less active than the nodes (p328 bottom paragraph through p329).
I agree.
Edit:
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1473353
see figure 1 for a more appropriate electric model.

[granpa]

" The conduction velocity also is relatively insensitive to the internodal length"

i like that.

[somasimple]

Here is the problem:
And, active node or not, it does not change the passive internodes, does it?

[somasimple]

" The conduction velocity also is relatively insensitive to the internodal length"

i like that.
Me too. It is normal in a body that moves and thus stretches or shrinks nerves: The message must be delivered (safety factor) and insensitivity to internal motion.

[granpa]

if the impulse does indeed move at or just below the speed of sound in water or is even just limited by the speed of sound in water then that would mean that significant amounts of water are being moved. the mass of the water would add an inductance to the equivalent circuit. or so it seems to me.

[somasimple]

if the impulse does indeed move at or just below the speed of sound in water or is even just limited by the speed of sound in water then that would mean that significant amounts of water are being moved. the mass of the water would add an inductance to the equivalent circuit. or so it seems to me.
Why an inductance?

[granpa]

because inductance is the electrical equivalent of mass.

[granpa]

just think of a sound wave as passing through a series of masses connectedby springs. the mass effect becomes obvious.

[atyy]

Edit: In the model a node is connected to 2 internodes and must be at the same potential.
In data: the end of an internode is not at the same potential than the beginning of the next internode.

Edit:
http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=1473353
see figure 1 for a more appropriate electric model.

The data doesn't show a discontinuity, just a quick change in voltage over distance (HS Fig. 11). But I agree that if the node and internode are each modelled as a single compartment, it looks like there will be some discontinuity. I suppose more compartments can be added for both the node and internode, or it could also be taken care of by a partial differential equation in which parameters vary continuously over space.

Moore 1978 does look more appropriate. Some papers that cite their work are:

Hartline DK, Colman DR. Rapid conduction and the evolution of giant axons and myelinated fibers. Curr Biol. 2007 Jan 9;17(1):R29-35.
http://www.pbrc.hawaii.edu/~danh/PDFs/Hartline&Colman_2007.pdf

Richardson AG, McIntyre CC, Grill WM.
Modelling the effects of electric fields on nerve fibres: influence of the myelin sheath. Med Biol Eng Comput. 2000 Jul;38(4):438-46.

McIntyre CC, Richardson AG, Grill WM.
Modeling the excitability of mammalian nerve fibers: influence of afterpotentials on the recovery cycle. J Neurophysiol. 2002 Feb;87(2):995-1006.
http://jn.physiology.org/cgi/content/full/87/2/995

Hartline's site: http://www.pbrc.hawaii.edu/~danh/
Grill's site: http://fds.duke.edu/db/pratt/BME/faculty/warren.grill/publications

[somasimple]

because inductance is the electrical equivalent of mass.
http://en.wikipedia.org/wiki/Inductance
A neutral thing (water) seems unable to create electric field or voltage by itself.

[granpa]

this all reminds me so much of the equivalent circuits of microscopic straight wires in megahertz microprocessor design. I've been trying to find a diagram but I dont even know what to google.

and if its being driven close to its limit (the speed of sound in water) then that is also similar to microprocessor wires being driven close to the speed of light.

both are semi-dc.

[granpa]

http://en.wikipedia.org/wiki/Inductance
A neutral thing (water) seems unable to create electric field or voltage by itself.

it has mass and inductance is the electrical equivalent of mass. it is an 'equivalent circuit'.

[somasimple]

I suppose more compartments can be added for both the node and internode, or it could also be taken care of by a partial differential equation in which parameters vary continuously over space.

No, because adding a compartment does not change anything: Discontinuity will be... propagated,
And No because a model may be tortured until it fits your though but it is better when it sticks facts.
ps: I'll take a closer look to papers.

Granpa: Water may be a perfect silent actor.
Edit: I received "Biophysics of computation" By C Koch (it will help.)

[granpa]

http://www.edn.com/article/CA56702.html

http://www.ece.uci.edu/docs/hspice/hspice_2001_2-2874.jpg

http://www.ece.uci.edu/docs/hspice/hspice_2001_2-269.html

It is only during the initial surge of the voltage that a transmission line behaves as a constant impedance, with a value equal to its characteristic impedance. For this reason the characteristic impedance of a line is also called the surge impedance. The surge time during which the impedance is constant is the round trip time of flight, or twice the time delay. Reflections from the far end complicate the electrical behavior of the line after the surge time.
The instantaneous impedance measured at the front end of a transmission line is a complicated function of time. It depends on the nature of the terminations at the far end. When the line is shunted to ground with a resistor of value equal to the characteristic impedance of the line, there is no reflection back, and the front end of the line behaves as a resistive load. When the termination at the far end is open, the impedance at the front end starts out at the characteristic impedance and eventually, after multiple reflections, approaches an infinite impedance. During some periods the instantaneous impedance may be zero.

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

Impedance matching is the electronics design practice of setting the output impedance (ZS) of a signal source equal to the input impedance (ZL) of the load to which it is ultimately connected, usually in order to maximize the power transfer and minimize reflections from the load. This only applies when both are linear devices.
The concept of impedance matching was originally developed for electrical power, but can be applied to any other field where a form of energy (not just electrical) is transferred between a source and a load.

To prevent all reflections of the signal back into the source, the load (which must be totally resistive) must be matched exactly to the source impedance (which again must be totally resistive)

http://www.physicsforums.com/showpost.php?p=1873931&postcount=2

[somasimple]

Granpa,
I have already stated that the cable model has no inductance so it makes problem for an eventual delay.
BTW, having a delay is not a proof of an impedance existence.

[DaleSpam]

Not at all.
Continuity (http://www.sosmath.com/calculus/limcon/limcon05/limcon05.html) is a prerequisite for an electrical signal in a wire/cable.
There is discontinuities at internode/node junctions when the signal leaves the internode entering in the node and when it leaves the node entering to the next internode.This is wrong, there is no continuity requirement.

Consider the wave equation in 1 spatial dimension (e.g. an electrical signal in a wire)
c^2 \frac{\partial ^2f}{\partial x^2}=\frac{\partial
^2f}{\partial t^2} (1)

This has the solution
f = H(x-ct) (2)
where H is the Heaviside unit step function

Equation (2) is discontinuous in both time and space and it remains discontinuous even in the limit as c goes to infinity. And similarly discontinuous solutions exist for the wave equation in 3 spatial dimensions.

The above is not even including discontinuities in the medium which can lead to solutions with even more complicated discontinuities. There is simply nothing about Maxwell's equations or circuit theory that requires continuity.

[somasimple]

http://www.physicsforums.com/showpost.php?p=786028&postcount=7
A soliton is unfortunately... continuous since it is a traveling wave.
Edit;
http://en.wikipedia.org/wiki/Soliton
I'm wrong for sure...:rofl:

[granpa]

http://www.ece.uci.edu/docs/hspice/hspice_2001_2-2874.jpg

the interesting thing aboutthis model is that if yoi suddenly apply a dc voltage (turn on the water) then only the leading edge is affected. behind the leading edge the pipe is already full of water so the capacitors are irrelevant and the current isnt changing so the inductance (mass of the water. an inductor would be modelled as a constriction in the pipe) is irrelevant. only at the leading edge do these have any effect. the speed of the leading edge is v=1/√(L*C)

and as long as the inductance of one portion matches the inductance of the next then there is no reflection. it all becomes quite simple to visualize.

it also works if the pipe is emptying.

[DaleSpam]

http://www.physicsforums.com/showpost.php?p=786028&postcount=7
A soliton is unfortunately... continuous since it is a traveling wave.
Edit;
http://en.wikipedia.org/wiki/Soliton
I'm wrong for sure...:rofl:Check the definition of continuous that you cited earlier. There are no continuity constraints on solitons. H(x-ct) is a soliton (traveling wave) which is discontinuous in both x and t.

[granpa]

what is the maximum frequency at which the long myelinated axons of the spinal cord can transmit ap's?

[somasimple]

http://www.ece.uci.edu/docs/hspice/hspice_2001_2-2874.jpg

the interesting thing aboutthis model is that if yoi suddenly apply a dc voltage (turn on the water) then only the leading edge is affected. behind the leading edge the pipe is already full of water so the capacitors are irrelevant and the current isnt changing so the inductance (mass of the water. an inductor would be modelled as a constriction in the pipe) is irrelevant. only at the leading edge do these have any effect. the speed of the leading edge is v=1/√(L*C)
That is wrong. The charge of a capacitor isn't linear and its impedance changes from 0 to infinite => currunt is changing.

DaleSpam,
Are you masochist?
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.

[somasimple]

what is the maximum frequency at which the long myelinated axons of the spinal cord can transmit ap's?
In mammals the CV speed is 120~150 ms-1 but the firing rate is often < 200 HZ

[granpa]

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

the myelin doest have much effect on the speed of the wave across a single internode.

[granpa]

That is wrong. The charge of a capacitor isn't linear and its impedance changes from 0 to infinite => currunt is changing.
.


not sure what you are saying. but the capacitors behind the leading edge are already full and the voltage isnt changing (its only changing at the leading edge) so the capacitors have no further effect and can be ignored.

[somasimple]

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

the myelin doest have much effect on the speed of the wave across a single internode.

We are disagreeing on this. Computations have shown the contrary (in regard to length).

Here is another aspect of discontinuity:

[granpa]

your messages have a tendency to be something more than cryptic. its not clear to me what you mean by 'in regard to length'. if your just saying that myelin does speed ip internode travel then ok. it may speed it up some but still the internode speed is so great that it hardly matters. it seems to me that it is the delay at the node that pretty much determines the net speed of the ap over many nodes.

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

what do you mean x1 and x2 are undefined? that article you originally linked to actually measured internode values. thats what started this conversation.

[somasimple]

And here is a graph that show the number of active nodes during a single propagated AP.
It becomes obvious that the energetic cost is dependent of speed and spike duration.
It is another proof of discontinuity.

[somasimple]

your messages have a tendency to be something more than cryptic. its not clear to me what you mean by 'in regard to length'.
It was described earlier:
http://www.physicsforums.com/showthread.php?t=258168

what do you mean x1 and x2 are undefined? that article you originally linked to actually measured internode values. thats what started this conversation.

Onto the right of the picture:
x1 and x2 are taken on the apparent AP given by the apparent conduction velocity.
Thus you see an apparent AP at nodes (or wherever you want if you respect a constant interval) that is the result of synchrony of multiple firing nodes.
This apparent AP looks like an overlapping of time axis.

[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 thats 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 thats 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... :rolleyes:

[granpa]

Hmm, it is now, impossible to find a passive and electrical solution... :rolleyes:
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 dont 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 cant be that leaky. they wouldnt 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... :rolleyes:
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. :rofl:

[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 dont think there is much current. someone said that very few ions actually move at any one 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 dont think there is much current. someone said that very few ions actually move at any one 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.

[DaleSpam]

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 dont 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?

:confused:

[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)

[DaleSpam]

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? :rolleyes:

[DaleSpam]

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 dont 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 37oC 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! :smile:

[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 dont 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. :confused:

[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.