Information

Why Is Action Potential Propagation Not Described by Telegrapher's But Cable Equation?


In modelling the propagation of action potential in an axon, why is the partial differential equation the cable equation rather than the telegrapher's equation? The difference between the two is that the former does not have inductance while the latter has. Does an axon not have inductance whether it is myelinated or unmyelinated? This is related to my previous question. There the only answer I obtained attributes this choice not to experimental evidence but the deficiency on the part of biologists in mathematical sophistication in dealing with the complication of electromagnetism arising from including inductance.


I am the individual who answered your earlier question. The answer remains much the same. The Cable Equation is inappropriate. It was developed originally as the Heat Equation of Thomson, While Thomson disowned its application to the axon as a cable, Herman continued to promote the solution within the Biology community. The problem is the Cable Equation requires as an initial condition that the stimulation of the cable continues until the signal reaches the terminus of the axon by conduction (diffusion).

When exploring the myelinated axon, the Telegrapher's equation must be used. The formal name for this equation is the General Wave Equation, GWE, of Maxwell. It involves an initial condition that is much more lenient. The stimulus must only be applied to the axon for long enough to ensure the desired full waveform is represented. Thus the GWE involves propagation and not conduction (or diffusion). See section 7.4 of Chapter 7 of "Processes in Biological Hearing," PBH, on my website.

Cole & Baker, "Longitudinal Impedance of the Squid Giant Axon", Journal of General Physiology, (1941) vol 24(6) pp 771-783 present their initial measurements of inductance within the large axon of a small squid. This axon generated "swim waveforms" and not "Action Potentials" as currently defined. The inductance is much smaller in a non-myelinated axon than in a myelinated axon. It remains calculable in either case.

I have reviewed the two papers by Lieberstein & Mahrous you cited for my benefit. The authors are apparently two very good mathematicians without much knowledge of biophysics or the biophysics literature. They quote a diffusion velocity from Hodgkin & Huxley (1952) that is several orders of magnitude slower than the phase velocity along an axon that is very well documented by Cole and more recently by Smith et al. I have uploaded a more complete analysis in Section 9.1.1.4.3 of the above citation to chapter 9 of my work, 9SignalTransmission.pdf.

These two papers should not be relied upon until reviewing Section 9.1.1.4.3


Action potential

This Wikipedia selection is available offline from SOS Children for distribution in the developing world. Before you decide about sponsoring a child, why not learn about different sponsorship charities first?

In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, and endocrine cells, as well as in some plant cells. In neurons, they play a central role in cell-to-cell communication. In other types of cells, their main function is to activate intracellular processes. In muscle cells, for example, an action potential is the first step in the chain of events leading to contraction. In beta cells of the pancreas, they provoke release of insulin. Action potentials in neurons are also known as "nerve impulses" or "spikes", and the temporal sequence of action potentials generated by a neuron is called its "spike train". A neuron that emits an action potential is often said to "fire".

Action potentials are generated by special types of voltage-gated ion channels embedded in a cell's plasma membrane. These channels are shut when the membrane potential is near the resting potential of the cell, but they rapidly begin to open if the membrane potential increases to a precisely defined threshold value. When the channels open, they allow an inward flow of sodium ions, which changes the electrochemical gradient, which in turn produces a further rise in the membrane potential. This then causes more channels to open, producing a greater electric current, and so on. The process proceeds explosively until all of the available ion channels are open, resulting in a large upswing in the membrane potential. The rapid influx of sodium ions causes the polarity of the plasma membrane to reverse, and the ion channels then rapidly inactivate. As the sodium channels close, sodium ions can no longer enter the neuron, and they are actively transported out of the plasma membrane. Potassium channels are then activated, and there is an outward current of potassium ions, returning the electrochemical gradient to the resting state. After an action potential has occurred, there is a transient negative shift, called the afterhyperpolarization or refractory period, due to additional potassium currents. This is the mechanism that prevents an action potential from traveling back the way it just came.

In animal cells, there are two primary types of action potentials, one type generated by voltage-gated sodium channels, the other by voltage-gated calcium channels. Sodium-based action potentials usually last for under one millisecond, whereas calcium-based action potentials may last for 100 milliseconds or longer. In some types of neurons, slow calcium spikes provide the driving force for a long burst of rapidly emitted sodium spikes. In cardiac muscle cells, on the other hand, an initial fast sodium spike provides a "primer" to provoke the rapid onset of a calcium spike, which then produces muscle contraction.


BIOELECTRIC PHENOMENA

Electromotive Force Properties

The three major ions K + , Na + , and Cl − are differentially distributed across the cell membrane at rest and across the membrane through passive ion channels as illustrated in Figure 11.5 . This separation of charge exists across the membrane and results in a voltage potential Vm as described by the Goldman Equation 11.33 .

Across each ion-specific channel, a concentration gradient exists for each ion that creates an electromotive force, a force that drives that ion through the channel at a constant rate. The Nernst potential for that ion is the electrical potential difference across the channel and is easily modeled as a battery, as is illustrated in Figure 11.11 for K + . The same model is applied for Na + and Cl − with values equal to the Nernst potentials for each.

Figure 11.11 . A battery is used to model the electromotive force for a K + channel with a value equal to the K + Nernst potential. The polarity of the battery is given with the ground on the outside of the membrane, in agreement with convention. From Table 11.1 , note that the Nernst potential for K + is negative, which reverses the polarity of the battery, driving K + out of the cell.


Contents

The article is extremely confusing, there is a lot of material and definitions which are, however, poorly organized. A lot of repetitions and the flow of argument is completely absent. I'll see what i can do.
It is incredible that it is a FEATURED ARTICLE with so many problemsRvfrolov (talk) 18:32, 2 January 2009 (UTC) 2 January 2009

There are three articles now which discuss very much the same things with numerous repetitions and description of the same material in different terms.

As it was already suggested by Methoxyroxy 12:37, 2 November 2006 (UTC), it needs a really big clean-up and optimization. There is a lot of confusion there so I will do this albeit not at once. I will move different parts between these three articles, edit and unify their style etc. At later stage I will need someone who is native English speaker to do spellcheck.Rvfrolov (talk) 20:52, 2 January 2009 (UTC)

I have replied at Talk:Membrane potential. Looie496 (talk) 22:01, 2 January 2009 (UTC) Hi Rvfrolov. The problem is that explaining an action potential, without first describing what the 'mV' part of membrane potential is, can lead to a whole lot of problems down the road. I'm all for reorganizing it, just very carefully Paskari (talk) 15:41, 24 June 2009 (UTC)

The current version of the article mixes action potentials with propagation of potentials creating excessive complexity and inaccuracies.

Potential propagation is not a required property of an action potential. Most textbooks first define the action potential in an isopotential cell. In Hodkin and Huxley's experiments, for example, a wire was strung along a squid giant axon to shunt axial currents effectively producing an isopotential membrane compartment. With this preparation, current-clamp experiments still produce action potentials along the entire fiber, without a "wave of electrochemical activity." Neither does a cell need to carry APs over a distance to make use of action potentials (e.g. electrocyte action potentials in electric fish, and many other cell types produce action potentials for other reasons than long-distance signaling).

The current definition is also missing a key defining component: the key role of voltage-sensitive conductances.

Propagating action potentials may be more consistently described as a continuous succession of local action potentials triggering action potentials in the adjacent sections. This distinction would help avoid some of the current inaccuracies in the article.

For example, the current article describes saltatory conduction as follows "Since the axon is insulated, the action potential can travel through it without significant signal decay." In reality, myelinated stretches of axons do not produce action potentials and the action potential does not "travel through it." It would be more accurate to state that depolarization from an action potential at one node propagates passively to the next node and triggers an action potential at the next node. The signal may decay significantly between nodes and still trigger an action potential at the next node. The same section seems to imply that the action potential must be generated at the synapse for the release of neurotransmitter, which is also inaccurate. Any depolarization of sufficient magnitude (passive or active) will have a similar effect.

In summary, to make the article more useful, I recommend providing a complete and general definition of the action potential with minimal extraneous detail. The adjacent topics such as "Electrotonic propagation of potentials", "Neurotransmitter release", "Cable theory", "Saltatory conduction", probably belong in separate articles or sections.

Thank you for your attention to this, and for your very thoughtful analysis. In large part, I agree with you. Your analysis of propagation seems to me to be correct. I have felt for some time that the lead section of the page is too long and rambling, and should be shortened, and I think it would be an improvement to simplify it per WP:LEAD and per your comments. I also think errors in the explanation of action potentials, of the sort you identified, should be corrected as they come up throughout the text. However, I'm not so sure about splitting off separate articles. The topics you list are not all sections in the current page, and the sections related to these topics do begin with main article links already, and it is appropriate to discuss each of those topics in this page (with the possible exception that discussion of the passive propagation of subthreshold graded potentials should be limited to their relevance to action potentials). Therefore, I would tend to favor simplifying the lead, and correcting errors elsewhere, but not necessarily splitting off any new pages or merging material here to other existing pages. --Tryptofish (talk) 15:44, 27 July 2009 (UTC) I'm pretty much in line with that response. On one side, this article has become much too large and disorganized, probably because of the lack of anybody actively maintaining it. So simplifying the article would be a good thing. On the other side, propagation is probably the reason why action potentials exist, so omitting any discussion of it at all would be bad. Neurotransmitter release, however, might not belong here beyond a brief sentence or two to explain what happens when an action potential arrives. Looie496 (talk) 21:41, 27 July 2009 (UTC) Just to clarify: what both I and Yatsenko agree is that propagation of the action potential, in the sense of an intact action potential just traveling along, is presented misleadingly. On the other hand, propagation in the sense of passive propagation of a depolarization which then brings membrane potential to threshold, activating voltage-sensitive ion channels and regenerating an action potential, is correct, and nobody wants to omit that. (Did that clarify, or make it worse? (smile)) --Tryptofish (talk) 21:51, 27 July 2009 (UTC) Propagation is not a necessary feature of an action potential and should be relegated to a later section. Otherwise the definition is simply incorrect because it would not apply to the phenomenon that was described by Hodgkin and Huxley. Action potentials can be and are produced without propagation in many experimental preparations. Voltage-gated channels (active conductances) are a required part of an action potential and should be included in the primary definition. I would first define the action potential in the case of an isopotential compartment. Dimitri Yatsenko 00:58, 28 July 2009 (UTC) Although the lead is now more accurate, it is way too long and too technical for a general readership. We need to look at ways to make the wording less technical, and to move parts of the lead into other parts of the page. --Tryptofish (talk) 19:02, 28 July 2009 (UTC)

I am removing "nerve spikes" from the first sentence.

I do not believe that the term "nerve spike" could be generally applied to all action potentials. Action potentials are transient membrane voltage events in individual cells or their compartments. They happen in many cell types. Nerves are bundles of axons in the peripheral nervous system (no nerves in the brain or spinal cord). Thus "nerve spikes" are but one specific manifestation of action potentials. The same could be said about MUAPs (motor unit action potentials), for example. This does not make them synonymous with action potentials. Dimitri Yatsenko 01:25, 28 July 2009 (UTC)

I don't have much of an objection to removing the mention of spikes, which is a bit colloquial. However, I reverted your deletion of "nerve impulse." I did that because, first, it is a widely-used synonym (even though not all action potentials are in neurons), and secondly, because nerve impulse is an existing redirect to this page, and therefore the phrase needs to be bolded in the lead sentence. --Tryptofish (talk) 19:00, 28 July 2009 (UTC) I have not seen the term "nerve spike" or "nerve impulse" used as a general synonym for action potentials in any modern scientific literature. An axon is not a nerve. Neurons are sometimes called nerve cells in less technical usage, but this is inaccurate and would not pass in a scientific paper. So I am conflicted between being precise or catering to general nontechnical usage of terms. I think we should strive to be technically accurate and, in so doing, influence the popular understanding of these natural phenomena. Dimitri Yatsenko 19:23, 28 July 2009 (UTC) I wasn't disagreeing with you about spikes. Impulse is used widely in English. Besides: WP:R#PLA and number 7 of WP:NOTGUIDE. --Tryptofish (talk) 19:32, 28 July 2009 (UTC) What if we separate the article for "nerve spike" and "nerve impulse" and explain that it is but one special case of action potential that is recorded from nerves in the PNS? Dimitri Yatsenko 19:31, 28 July 2009 (UTC) No, not needed, and WP:CFORK. --Tryptofish (talk) 19:34, 28 July 2009 (UTC) I defined "spikes" and "impulses" in separate sentences in the first section. What do you think? Dimitri Yatsenko 20:36, 28 July 2009 (UTC)

The current wording in the second paragraph states that depolarization "increases both the inward sodium current (depolarization) and the balancing outward potassium current (repolarization/hyperpolarization)". I question the accuracy of that statement.

As the membrane depolarizes, the membrane potential moves toward the reversal potential for sodium. This reduces the electrochemical driving force for sodium. Unless the sodium conductance increases by a greater factor to compensate, the sodium current will decrease, not increase. So the statement is not generally accurate. I propose rewording it to state that both conductances increase and only when the net current is negative and leads to further depolarization, a positive feedback loop is generated to precipitate the action potential. Dimitri Yatsenko 21:07, 28 July 2009 (UTC) —Preceding unsigned comment added by Yatsenko DV (talk • contribs)

Sorry to disagree, but the present text you quoted is accurate, and the changes you propose are way too technical for this project. --Tryptofish (talk) 21:35, 28 July 2009 (UTC) Fair enough. I agree that this simplification is accurate for relevant time scales, membrane potential ranges, and channel types. Dimitri Yatsenko 22:05, 28 July 2009 (UTC) —Preceding unsigned comment added by Yatsenko DV (talk • contribs) Thank you for understanding. A lot of this is just a matter that we (Wikipedia) are writing for a general audience, and that puts limits on how technical or scholarly we can get. --Tryptofish (talk) 22:56, 28 July 2009 (UTC)

In the "Quantitative models" section there are many references to things being simple or a simplification. While this section does have many references attached to it, there is no mention in the article of what these things are simpler than. That is, why are these things simple, and compared to what, and what would be more complex.

Reply to unsigned comment: What it means is that mathematical equations do not capture all the complexity of a living cell. I've tried to make it a little clearer, but I'm not sure whether there is any way of saying it better. --Tryptofish (talk) 23:25, 3 September 2009 (UTC)

The refractory period section seems like it was copy pasted from a text book which was written by a high school teach held at gun point. Perhaps we should consider updating it Paskari (talk) 23:30, 6 October 2009 (UTC)

I've taken a shot at rewriting it. Cellular stuff is not really my strength, so if I got anything wrong, I hope somebody will correct it. Looie496 (talk) 00:10, 7 October 2009 (UTC) I'm just about to sign off, but I'll take a look at it tomorrow. --Tryptofish (talk) 00:14, 7 October 2009 (UTC) That is much better, great job. Paskari (talk) 11:02, 7 October 2009 (UTC) Yes, much better, thanks. I tweaked it a little further, not much. --Tryptofish (talk) 18:34, 7 October 2009 (UTC)

I've just attempted a pretty major rewrite of the lead, which I hope won't offend anybody. I thought the existing version was too hard for readers to understand -- it also contained a couple of minor errors. I also added a paragraph about the distinction between sodium and calcium spikes, which seems to me to be a very important point. Regards, Looie496 (talk) 20:08, 23 February 2010 (UTC)

I note that the lead from the last FAR was moved some time ago to the overview section. If this persists, we should justify the need for both a lead and overview section, and ensure that they are not redundant to each other. Geometry guy 20:39, 23 February 2010 (UTC) The Overview section needs revision too, but it seemed to me that these changes to the lead were sufficiently "bold" that it would be better not to pile other changes on top of them before discussion. Looie496 (talk) 20:48, 23 February 2010 (UTC)

I have removed a reference from the lede that was to:

  • Miller FP, Vandome AF, McBrewster J (2009). Cardiac action potential. Beau Bassin Mauritius: Alphascript Publishing. ISBN6130098685 . CS1 maint: multiple names: authors list (link)

Alphascript Publishing republished Wikipedia content. And the book in question republishes this article. The cover of the book can be seen [http://www.amazon.com/Cardiac-action-potential-Frederic-Miller/dp/6130098685/ref=sr_1_1?ie=UTF8&s=books&qid=1267362547&sr=1-1 on Amazon]. This article is named on the front cover. (The format for Alphascript books is to list the WP articles contained therein on the front cover as part of the name.)

The person who owns the book can verify that this is republished Wikipedia content by looking at the copyright information inside the book itself. -- RA (talk) 13:16, 28 February 2010 (UTC)

The other danger is Alphascript also publishes academics' thesis if they convince them to sign their terms. Was the source republishing of wiki article or a thesis. So always double check before removing any references about whether they are wikipedia article or a thesis. Generally a quick way to check is searching product description in wikipedia. Kasaalan (talk) 13:29, 28 February 2010 (UTC) It is VDM that also publishes academics' thesis if they convince them to sign their terms. All alphascript titles are wikipedia articles. My mistake. Kasaalan (talk) 19:14, 5 March 2010 (UTC) Note: I have edited the previous comment, because it was added by altering the comment above it in a way that made this section impossible to understand without going back through the history. I hope that my revision has not changed the message. Looie496 (talk) 19:26, 5 March 2010 (UTC)

The region with high concentration will diffuse out toward the region with low concentration. To extend the example, let solution A have 30 sodium ions and 30 chloride ions. Also, let solution B have only 20 sodium ions and 20 chloride ions. Assuming the barrier allows both types of ions to travel through it, then a steady state will be reached whereby both solutions have 25 sodium ions and 25 chloride ions. If, however, the porous barrier is selective to which ions are let through, then diffusion alone will not determine the resulting solution. Returning to the previous example, let's now construct a barrier that is permeable only to sodium ions. Since solution B has a lower concentration of both sodium and chloride, the barrier will attract both ions from solution A.

There is not a single citation about osmosis. Osmosis tells us exactly the contrary. Facts tells us the same thing as osmosis: The cited diffusion doesn't occur. The concentrations may be equilibrated by water movement and membrane is permeable to water through aquaporins or directly. Somasimple (talk) 05:28, 3 June 2010 (UTC)

If solution A is electroneutral THEN 30n+30p=0 (where n stands for negative and p for positive). If solution B is also electroneutral THEN 25n+25p=0. Considering an action from a compartment onto another one orders to consider all positive and negative charges that exist in the compartments.

So, there is NO electric flux OR electric field BECAUSE EACH compartment is neutral at start. Saying a compartment is neutral is saying that it can't exert any electric "thing" at all.

Conclusion: You can't get something that is the result of k(25p/30p) or k(30p/25p). That is mathematically and physically incorrect because you arbitrarily remove the negative charges without any scientific explanation. Somasimple (talk) 09:27, 3 June 2010 (UTC)

Can you fix it, or should that part be removed? Looie496 (talk) 00:52, 4 June 2010 (UTC) Are you asking me to change the way how biology is taught ? This page remains for historical reason (Nobel prizes) but its contents is far from actual and accepted knowledge in Biochemistry for example. If the goal of wikipedia is to promote science then you must re-write the page but it will against the Biology community.Somasimple (talk) 06:10, 4 June 2010 (UTC) Wikipedia articles are written by people like you and me. If you see errors in an article, and can back up the claim that they are errors by referring to reputable scientific publications, then you should feel free to rewrite the section in a way that makes it more correct. In this case, if you don't fix it, it's likely that nobody else who reads this will be able to. I certainly can't. Regards, Looie496 (talk) 17:04, 4 June 2010 (UTC) This is my area of expertise more than it is Looie's, so I think I can help here. I think the page is correct about this, as it is written. There are several errors in what Somasimple has said here. First, this is not an osmotic phenomenon, in that we are not dealing with H2O molecules moving along with the ions. Second, there are two factors driving ionic movement: electroneutrality or like-charge repulsion, as mentioned, but also entropy. Entropy will cause, in the quoted example, the ions to move from A to B. When they do, electroneutrality will be achieved when there are 25 plus 25 in A, and 25 plus 25 also in B. --Tryptofish (talk) 18:23, 4 June 2010 (UTC) Several errors? Did I say it was an osmotic phenomenon? No! I just said there was NOT a single citation about it. Osmosis exists whenever there is a concentration change, just whenever! THEN OSMOSIS EXISTS WHENEVER SOME IONS MOVE. There must be some osmosis because it's a reverse diffusion. If you put a cell (neuron is a cell) in an hypotonic solution, osmosis happens and the cell expands because the internal concentration decreases by water flux. It is a fact. This fact creates an error in "your" silent diffusion that occurs in the other direction. I like, again, your "entropic electroneutrality". It is the first time I heard/read that a charge vanishes by entropy. A citation, a reference? In our example, it was clear (at least for me) that the membrane was semipermeable thus the result is not the one you gave. "Returning to the previous example, let's now construct a barrier that is permeable only to sodium ions. Since solution B has a lower concentration of both sodium and chloride, the barrier will attract both ions from solution A." The difference remains because negative ions remain in one side. It creates the membrane potential but you're right, it raises another big problem. You have now, a side that is negative and another that is positive and diffusion will have some problem to be achieved -( Somasimple (talk) 05:19, 5 June 2010 (UTC) I never said that entropy makes a charge disappear. I said that it can make it move. The reason that excitable cells do not shrink or swell due to hyper- or hypo-tonicity is that the ions that move across the membrane represent a very small fraction of all of the ions that are present (in real cells, though not in the example). You also might want to familiarize yourself with the Nernst equation. --Tryptofish (talk) 14:24, 5 June 2010 (UTC) You do not reply at all. Where do the negative charge move in our example (the membrane is only permeable to Sodium)? Somasimple (talk) 10:14, 6 June 2010 (UTC) If the membrane is permeable only to sodium cations, then anions do not cross the membrane at all. Consequently, there is a separation of charge, giving rise to a transmembrane voltage difference. --Tryptofish (talk) 15:17, 6 June 2010 (UTC) If it was so simple. As you know, at molecular level (the level we are speaking of), distances are of importance. The electrochemical force you created comes between 2 compartments separated by a membrane which thickness is known as 5 to 7 nm. It means that anions and cations must be separated, in all compartments, by a distance that is always superior to the membrane thickness. If the distance is lower in any compartment then you have an "entropic" problem (in fact I call it a simple Coulomb force): anions or cations can't be attracted by the other side since the strength of the force coming from the other side is not sufficient. This limits the process to concentrations < to 5 mmol. Far from the concentrations that exists in cells. I think you might NOT consider the Nernst equation because it will give you some headaches with charge density and Conservation of Energy. Somasimple (talk) 05:32, 7 June 2010 (UTC) Somasimple, consider a parallel-plate capacitor, which is how the cell membrane is represented in the Hodgkin-Huxley model. Note that the capacitance C is proportional to the area of the charged plates divided by their separation[1]. For a membrane thickness of about 5nm, you still have a significantly large area in which the ions are able to arrange themselves (even an impossible miniscule cell with a central body length only ten times the width of the membrane will have a "plate" area 100 times larger). The point is that capacitance will be very large, such that even if 5nm were a very large distance for Coulomb attraction (which it very much is not), it won't matter because there are so many ions able to line up along the membrane, just like in an ordinary circuit-board capacitor. And from there, depolarization occurs when you suddenly open the ion gates and sodium floods in, etc etc etc. SamuelRiv (talk) 17:21, 14 June 2010 (UTC) I'm considering effectively a capacitor and you do not consider the distances that effectively exist between the ions in presence (here is link to physics principles). Even if the surface is enlarged then you decreases the charge density and it matters for capacitance : the less charge density you have the less tension you'll get. In our case ions can't be attracted from the other side: TOO FAR! --Somasimple (talk) 06:04, 15 June 2010 (UTC)

The inward movement of sodium ions and the outward movement of potassium ions are passive

Let's describe all the events that happen simultaneously:

1/ Sodium movement balanced with chloride

sodium is inward and Na ions stick to the internal membrane, chloride ions stay out, and balance the Na charge, across the external membrane

2/ Potassium movement balanced with chloride

potassium is outward and K ions stick to the external membrane, chloride ions stay in, and balance the K charge, across the internal membrane

Now let's see what happens on each side:

sodium is inward and Na ions stick to the internal membrane, chloride ions stay in, and balance the K charge, across the internal membrane

chloride ions stay out, and balance the Na charge, across the external membrane, potassium is outward and K ions stick to the external membrane

Result: a membrane voltage that is. quite null.

Osmosis: Since there are concentrations changes there is water flux through aquaporins:

1/ from int to ext for sodium

2/ from ext to int for potassium

Result : How is it possible to make a bidirectional and simultaneous water movement in aquaporins? Somasimple (talk) 05:57, 5 June 2010 (UTC)

Sorry, but you misunderstand. Ion channels are not aquaporins, and they are not permeable to water molecules. In vertebrate animals, aquaporins are mainly expressed in the kidneys, and there is relatively little water transport during an action potential. Ion channels are selectively permeable to ions, so chloride does not move together with cations also there is a differential distribution across the membrane of impermeable anions. The reason there is a membrane potential at all, is that there is a separation of charge. If you continue to disagree about all of this, please cite sources. --Tryptofish (talk) 14:21, 5 June 2010 (UTC) Ions channels are not permeable to water molecules? Really? Molecular dynamics of the KcsA K(+) channel in a bilayer membrane Somasimple (talk) 10:22, 7 June 2010 (UTC)

About this section Myelin and saltatory conduction It is said:

  1. "The evolutionary need for the fast and efficient transduction of electrical signals in nervous system resulted in appearance of myelin sheaths around neuronal axons."
  2. "Myelin prevents ions from entering or leaving the axon along myelinated segments."

The first assertion is false since every axon is covered by myelin compact or not, leaving no room (<20 nm) around the axon. See the excellent book, page 128 [http://www.amazon.com/Neurocytology-Structure-Neurons-Processes-Neuroglial/dp/313781801X/ref=sr_1_1?ie=UTF8&s=books&qid=1276061846&sr=1-1 Neurocytology: Fine Structure of Neurons, Nerve Processes and Neuroglial Cells]

The second becomes, in that case, not true since it assumes that unmyelinated axons are bare. --Somasimple (talk) 05:43, 9 June 2010 (UTC)

Well, this topic I do know about. Myelin appears only in vertebrates (although some other groups have similar substances), and even in vertebrates only a subset of axons are myelin-coated. I don't have that specific book on hand, but every basic neuroscience book covers this point very thoroughly. Looie496 (talk) 06:44, 9 June 2010 (UTC) Here is a link to the book Ennio Pannese Google book There are citations on page 119 and following ones about evolutionary aspects. On page 128, if vertebrates have always axons that are insulated, how do they function since the ions exchanges can't happen? --Somasimple (talk) 07:28, 9 June 2010 (UTC) From this one The Biology of Schwann Cells The Biology of Schwann Cells: Development, Differentiation and Immunomodulation Edited by Patricia Armati: "All neurons in the PNS are in intimate physical contact with Schwann and satellite cells, regardless of whether they are myelinated or unmyelinated, sensory or autonomic. All axons of the peripheral nerves are ensheathed by rows of Schwann cells, in the form of either one Schwann cell to each axonal length, or in Remak bundles, formed when an individual Schwann cell envelopes lengths of multiple unmyelinated axons (Figures 1.2, 1.3 and 1.4b). There is now a large body of evidence that defines a multitude of Schwann cell functions that are not related to myelination (Lemke 2001). This uncoupling of myelin-associated functions from other Schwann cell roles emphasises the essentially symbiotic relationship between nerve cells and Schwann cells, where each is dependent on the other for normal development, function and maintenance." Here is the link to the excerpt --Somasimple (talk) 10:07, 9 June 2010 (UTC) You raised a lot of points that need to be addressed so I'll try to hit them all, in no particular order. I must have missed your quotes above (#1 & #2) in the original wikipedia article as number 2 is incorrect (it's mostly due to capacitance changes, there would have been other ways of just removing channels from the membrane to minimize ionic current. but then there's still all that capacitative loss with no regenerative ionic current). Regarding number 1, this is true, though as mentioned in the book to which you linked other organisms have attained similar sorts of results in other ways (e.g. the squid giant axon). I should note that being in intimate contact and being ensheathed are VERY different (and really when we say myelinated what's meant is compact ensheathment, which is somewhat different still). Regarding ion movement, see the discussion of the Node of Ranvier. I don't work on invertabrates, so I don't know how they deal with such things, presumably there's either enough space (This is the case for skeletal muscle, where the fibers are packed like sardines but there's still enough space for things to work. There are some computational modeling studies of these sorts of things on pubmed.) or there are random holes/gaps similar to nodes of Ranvier. The important points from that is that the picture of unensheathed axons in a swimming pool of ions of constant concentration isn't really correct (but normally a close enough approximation) and Schwann cells aren't a one-hit wonder. --Dpryan (talk) 20:56, 10 June 2010 (UTC) From the excerpt: "In a mixed peripheral nerve unmyelinated fibres outnumber myelinated fibres by a ratio of three or four to one (Jacobs and Love 1985). For example, a transverse section of a human sural nerve contains approximately 8000 myelinated fibres per mm2, whereas the unmyelinated axons number 30 000 per mm2". I think that the approximation you made about the pool is quite far from the reality of anatomy? The constant concentration is perhaps not achieved at all! --Somasimple (talk) 06:28, 11 June 2010 (UTC) For comparison, a t-tubule is often 20-40nm in diameter and even then the ion concentrations don't change that much (you'll get a plateau after a few stimulations in a prolonged train, and the change will only be a few mM). You really don't need a lot of ions to move for an AP to occur, otherwise we would have very different anatomy! So, as I said, the approximation usually works for non-extreme cases (a square mm is a fair bit of space). --Dpryan (talk) 17:43, 11 June 2010 (UTC) I TOTALLY agree with you. Saying that concentrations remain unchanged may be reformulated that way Only, a tiny fraction, acts and creates all the effects. It may be refined in another way The unchanged big portion isn't involved in any manner in the process. --Somasimple (talk) 05:18, 12 June 2010 (UTC)

In this article [Cable Theory] the conduction velocity depends greatly of the time constant that is result of τm=Cm*Rm
It is said that myelin decreases the membrance capacitance. That's seems OK but what happens to the membrane resistance in case of myelinization?
Computation of the the time constant with reasonable values leads to an increase of the time constant:
You may see a discussion about this problem.--Somasimple (talk) 10:55, 11 June 2010 (UTC)

The discussion you linked to sets it clearly: membrane capacitance decreases while membrane resistance increases, so there is no charge dispersed through the membrane. Think of a capacitor - the plates have their charged particles line up on each end which drops the voltage through the circuit, so to maximize voltage propagation we need to maximize the time constant *across the membrane* and minimize the time constant *through the axon*. That's probably where your confusion lies - you need variables for each direction. Each node can change direction of propagation by depolarizing sequentially, with the potential difference propagating along a straight line each time. SamuelRiv (talk) 23:06, 13 June 2010 (UTC) Vey. My confusion comes from the [http://www.amazon.com/Biophysics-Computation-Information-Computational-Neuroscience/dp/0195181999 book of Koch]. pages 10 and 167. The text is clearly speaking of the τm=Cm*Rm, nothing else. BTW, your comment contradicts the comments below (next section) where internal current becomes negligible. --Somasimple (talk) 05:15, 14 June 2010 (UTC) Okay, I might have gotten confused, but here's what I was saying before (hopefully clearer): there are two R-C-I's here: one for the current between the inside of the axon and the salt medium outside the cell (across the membrane), and the other through the axon from one node to the next. In the first case (across the cell membrane), R is big, C is small, and I is minimal. In the second case (through the axon between nodes), R is small, C is big-to-infinite (as a wire), and I is V/R from the depolarization. Note that charge carriers do not actually flow with appreciable speed through the axon, the same as in electric conductivity through a wire where electrons flow at about 0.1mm/s - rather, the current propagates as a potential difference from one node to the next (as a big capacitor with the dielectric having conductive properties in the cations that I don't know of and should look up). SamuelRiv (talk) 08:20, 14 June 2010 (UTC) That's NOT OK at all: Please give a reference about this second internal capacity. How is it connected with the internal R? In parallel or serial?. Here is mine Koch circuit Secondly, if you exchange electrons then you have an electric current that travels at light-speed even if the electrons themselves don't (Electric circuit). The internal resistance is BTW higher than you tell us. --Somasimple (talk) 10:11, 14 June 2010 (UTC) In the Koch pdf (I have the same book btw, though in a box somewhere), there are two separable circuits. One is bracketed and labeled "node", while the other lies over the internode and none of the circuit elements are labeled. The first one represents the membrane potential between the inside of the axon and the outside cations, while the other models the internal resistance through the myelinated portion of the axon between nodes. Those are what I was referring to before as "two separate R-C-I's", the first being across the membrane and the second being through the axon. Yes, the current does effectively travel at light-speed as it simply is electric polarization between two points, same as a metal wire (which I used as an example to illustrate that electrons move extremely slowly compared to light-speed current). Another illustration similar to Koch is in this review (section: Active properties of nerve fibers) where Ra is the resistance of the "wire" that is the myelinated internode portion of the axon. So I think we're just mixed up here - it's the difference between resistance through the metal wire and the resistance of the rubber insulation - membrane resistance increases with myelination allowing effective axon "wire" resistance to decrease. SamuelRiv (talk) 16:48, 14 June 2010 (UTC) Are you saying that Sodium current intake (physical displacement) is followed by an electronic exchange (No displacement) with the next node? If so, then you have some problems: 1/ The next node becomes positive with this exchange and the sodium intake at this site will do not happen. 2/ The electric current you create with this electronic exchange has not the good direction. 3/ If an electronic exchange exists, when does it start and when/where does it stop? 4/ The worst problem remains the law of the least resistance. An electric current flows following mostly the least resistance and because AP uses only a very tiny quantity of ions in presence then there is not enough current that flows to the next node triggering another AP. --Somasimple (talk) 05:04, 15 June 2010 (UTC)

This page is not a forum for general discussion about Action potential. Any such comments may be removed or refactored. Please limit discussion to improvement of this article. You may wish to ask factual questions about Action potential at the Reference desk, discuss relevant Wikipedia policy at the Village pump, or ask for help at the Help desk.

Everyone know this limitation. Does that mean that errors must NOT be discussed and thus articles, NOT improved?
I brought in the previous section a computation that contradicts the notion of velocity improvement by capacitance reduction of myelin. You get any rigth to bring another computation that tells something else or you MUST accept the fact that article formulation is wrong even if it contradicts your actual conviction. Here is a quote at the bottom of the edition page "Encyclopedic content must be verifiable." That seems clear. --Somasimple (talk) 05:06, 12 June 2010 (UTC)

The point of the comment above is that the article needs to follow the published literature as directly as possible. If you make objections without pointing to reputable major-league publications that make those objections, it isn't useful. In this case I believe the reason you won't find major publications making this objection is that the assumptions underlying cable theory don't apply to myelinated axons, because the conductance at the nodes is so dominant. Looie496 (talk) 17:45, 12 June 2010 (UTC) I don't understand what you said Looie. Among many other things (like modeling bifurcation and propagation in unmyelinated dendrites), cable theory is used to represent nontrivial capacitance structure which changes the threshold current from the usual "spherical cow" capacitance model in, for example, the original Hodgkin-Huxley. No insulation is perfect, especially not myelin, so I don't see how one can argue that myelination would make such corrections in threshold current inapplicable, but maybe it's because I do theory? SamuelRiv (talk) 18:17, 13 June 2010 (UTC) Let me try again. Cable theory says that signal propagation is determined by two key parameters, the time constant and the length constant. But in a myelinated axon, the distance between nodes is a small fraction of the length constant, which means that the assumptions of cable theory don't apply and therefore the cable theory time constant is irrelevant. The fraction of current that flows through the myelin is too small to matter it is dominated by the current that flows across the membrane at the nodes. At least that's my understanding. Looie496 (talk) 19:04, 13 June 2010 (UTC) I didn't read the full conversation beforehand. I hope I cleared up confusion for OP in my response in the previous section. Now, I'm not sure how general a term Cable theory is, but I would suspect it's applicable everywhere, though in the axon once the proper approximations are made I'm sure you get to ignore most of it as you say above. I was thinking about it in terms of other areas, so yeah, you're right. SamuelRiv (talk) 23:09, 13 June 2010 (UTC)
Thanks Looie for this explanation.
Since an axon is a 3 dimensional thing (a cylinder,)
Since electrical propagation is omni-directional,
Since the external milieu has a lower resistance than the axolemna
Since the electric law of the least resistance implies and orders a shorter circuit (any node of every axon that is closer than the next node of the active one). Remember that axons do not travel alone but packed in nerves.
Then, there is NOT a chance that the current flows to the following node. It is to far. Here you try to limit the theory to a longitudinal propagation where Electricity has not this limitation. --Somasimple (talk) 05:31, 14 June 2010 (UTC)

From the Peak and Falling Phase" section:

However, the same raised voltage that opened the sodium channels initially also slowly shuts them off, by closing their pores the sodium channels become inactivated. This lowers the membrane's permeability to sodium, driving the membrane voltage back down.

How? If some sodium is still flowing into the cell, the membrane voltage would continue to go up. Wouldn't it be the rate of increase that goes down. And if the sodium flow is blocked completely, then how does this change the voltage at all? If the only thing driving down the voltage is the potassium outflow, then the last part of the quoted statement is misleading and needs to be fixed.

The relationship between ion movement and voltage is not as direct as you apparently think. It is possible to have ion flow without any change in membrane potential, and it is possible to have a change in membrane potential without any ion movement. The rules that govern membrane potential are outlined in the membrane potential article -- this is complicated stuff, though, and it might be better to consult a textbook. Looie496 (talk) 06:37, 12 January 2011 (UTC) Agreed, it's a complicated subject and perhaps there is a critical concept I have yet to understand. But just for the record, if you got the impression that I was equating sodium flow with membrane potential, that's incorrect. I was only talking about sodium flow's individual contribution to membrane potential. Thanks for your input though. I'll check that link out. 184.96.106.141 (talk) 22:10, 12 January 2011 (UTC) 184, I think you raise a valid point. The problem is with the imprecise "up/down" language, and I'll fix it on the page. As Looie said, the information is correct, but I have to admit that it is worded less helpfully than it could have been. Thanks! --Tryptofish (talk) 20:14, 12 January 2011 (UTC)

Let me leave a note that I'm going to try to do some serious work on this article. The main thing I've done so far is to move a bunch of material to the membrane potential article, so that this article doesn't repeat a lot of stuff that more properly belongs there. It needs instead to have a detailed discussion of voltage-gated ion channels and their effects on membrane potential. Looie496 (talk) 19:17, 14 October 2011 (UTC)

Hey everyone! I did a lot of writing on this article in the distant past - half a dozen years ago or so, and kind of moved on to other things. I'm happy to see all that has been done to it since then! The article is much improved in many ways. I was kind of astonished when I scanned the history to see just how many changes have been made and how many people have made contributions. Having said that, having skimmed through the present article, I feel like there is still room for improvement, which seems kind of hard to believe, given how many people have toiled over this for the past few years. I'm a little hesitant to jump back in. One of the reasons I hesitate is that don't really want to 'undo' any of the great things that have been done, but there is so much history, I can't take it all in. I've not re-read the whole article in detail yet, and of course I would do that before I proposed any changes. But the introduction, in particular seems kind of muddy to me. I feel like a naive reader could get through the first couple of paragraphs and still not have any idea of what an action potential is. There are also things in the intro paragraphs that are basically inaccurate. The trouble is that the 'inaccuracies' are more in the technical detail rather than in concept. This may be appropriate for the intro paragraphs. For example, the intro talks about how the membrane potential "rises" during the action potential, when really, during most of the "rising phase" of the AP, the membrane potential is approaching zero. It is more accurate to say that the membrane is 'depolarizing', although even this only describes it's relationship to membrane potential up until the rising phase crossed 0 volts (after which it's then polarizing again, but in the opposite polarity). In the sense that during the rising phase of the action potential, the membrane potential is moving in a positive direction, it could be said to be 'rising'. So it's not wrong, it just seems. muddy. In the second paragraph, it says: "(ion channels) rapidly begin to open if the membrane potential increases to a precisely defined threshold value." This is just wrong. The threshold does not determine when ion channels open. It's the other way around. The probability that a channel will be open as the membrane potential changes, determines, in part, the threshold for the action potential. The relationship between membrane potential and channel open probability is a smooth curve without threshold. What really determines the threshold of the action potential is the balance between sodium and potassium current. At the membrane potential where the sodium current exceeds the potassium current, depolarization of the membrane becomes regenerative (i.e the AP threshold is the membrane potential where INa > IK). The state of the channels determines the threshold, not the other way around. Even to say that the threshold is "precisely defined" is wrong, at least in the sense that the membrane potential value of threshold is precisely defined. The membrane potential value of threshold changes all the time, depending on the recent history of the membrane potential (e.g. the refractory period is basically a change in AP threshold). The threshold *IS* precisely defined in terms of it being at the precise membrane potential where INa exceeds IK. I had a fairly detailed explanation of this is a long-ago version of this article, but it's been long-since removed. I presume the reason that it got taken out was that it was too technical. I appreciate that the article needs to be readable by a large audience and thus probably shouldn't get too technical, but does it have to be dumbed down to the point where it's not correct? Do you think there might be a way to have it be both understandable and correct?

Well, there's huge room for improvement, no doubt about it, and I hope you will feel free to work on the article. I'm not keen on using "depolarize" in place of "rise". Success for this article means getting the reader to have a visual image of what happens during an action potential, and the word "rise" is a lot more visually evocative than "depolarize". Regards, Looie496 (talk) 14:48, 23 October 2011 (UTC) A lot of us, myself included, would like to make the lead more accessible to the general reader, but also find the task a bit daunting. As for threshold, it's true that it's the threshold for the action potential itself, rather than of the ion channels, but nonetheless voltage-sensitive ion channels have precise voltages at which they start to open (and below which they do not open), and those "thresholds" generate the threshold of the action potential. --Tryptofish (talk) 19:49, 24 October 2011 (UTC)

So I would, maybe not so much as dispute that, but modify it a bit. I find it more useful to think of the relationship between voltage and channel opening in terms of probability. The actual functions that describe this relationship are exponentials or sums of exponentials, so they don't really have a distinct 'starting point'. Rather, they asymptote as they approach zero probability. So no, they really don't have a threshold or a precise voltage where they open. They have a precise probability for being open at a given voltage - and that's different because it's a smooth function without threshold. Even a voltage-gated sodium channel will open every now and aqain, even at a very hyperpolarized potential. As for the threshold of the action potential, it is determined only indirectly by the voltage-dependence of sodium channel opening. The single proximate basis of the AP threshold is the voltage where the sodium current becomes larger than the potassium current. This is, of course, influenced by how many sodium channels are open, but you can't ascribe the threshold solely to Na because it also depends on K. If you made a whole-cell current/voltage plot, you could pick out the threshold precisely as the voltage where the slope of the plot becomes negative. I tried to describe threshold this way (with a diagram) in an earlier version of this article, but it was clearly too technical for people's taste. Synaptidude (talk) 01:24, 25 October 2011 (UTC)

. and just in case this horse is still breathing, even though precise, the probability function that describes the relationship between channel opening and voltage is not fixed. It depends on other things, such as the inactivation state of the channel. In the extreme case (and in a population of channels, since a single channel behaves stocastically) the probability of a channel in a population opening can be zero at all potentials, if they are all inactivated. So the probability that sodium channels will open at a given voltage depends on the history of the voltage, how long it's been since the voltage changed, etc. So basically, if you want to be accurate, you can't even say that the action potential threshold happens at a precise voltage, because that threshold is changing all the time because of the recent history of the membrane potential. Yes, if you hold the membrane at precisely the same potential for long enough for the channel to reach a steady state, then the threshold will be at the same place every time you test it. The only thing you can say with precision is that the action potential will fire at precisely the voltage where INa > IK - whatever the size of those currents are in a particular set of circumstances. Synaptidude (talk) 05:12, 25 October 2011 (UTC)

. and sorry, but in all my verbosity, I forgot the main point I wanted to make. Because the threshold for the action potential is at the point where INa becomes larger than Ik, the sodium current can actually grow quite large before the threshold is reached. So even if you wanted to (incorrectly ) say that sodium channel opening has a threshold, the threshold for the action potential occurs at some votage-distance from that 'threshold'. Obviously, the larger is Ik the farther along the voltage scale, and thus the farther from the sodium channel 'threshold', is the threshold for the AP. Thus, even if there was a true threshold for sodium channel opening, it is not directly related to the action potential threshold.

Now the question is, can we find a way to accurately describe the threshold without confusing everyone. Synaptidude (talk) 05:28, 25 October 2011 (UTC)

As an electrophysiologist myself in real life, I partly enjoy these kinds of discussions, but for Wikipedia's purposes, we are writing for the non-specialist general public, and one can over-think these things. It's important to be accessible. Poor horse! --Tryptofish (talk) 14:20, 25 October 2011 (UTC) Yes. Our audience here is not neuroscience students, much less neuroscience professionals -- they have much better sources of information. If this article is not accessible to "outsiders", it serves no purpose. Looie496 (talk) 15:02, 25 October 2011 (UTC) I don't disagree with that. But one pet peeve I often have with scientific writing for the lay public, is that it in the quest to make it accessible, it is made inaccurate. All I'm saying is that we should strive to make it both accessible AND accurate. The stuff I wrote about above is obviously too advanced for this article. That's why I'm having this discussion in the talk with you experts, so we can agree on the 'truth' before we agree on the presentation in the article. What is, after all, the point of making it understandable if the understanding is wrong? I'm sure if we put out heads together, we can figure out a wording that will be accessible and correct. Synaptidude (talk) 17:22, 25 October 2011 (UTC) Good, I think we actually all agree about that. --Tryptofish (talk) 17:35, 25 October 2011 (UTC) Great! Now I'm going to go back on it, just a little ). I just want to float an idea with you guys. What if we just alter the wording in the intro, on the subject of threshold, just a little bit to make it accurate, and then include farther down in the article or more technical description of threshold? I think that it could be made completely accurate and accessible kind of on a 'Scientific American' level challenging, but not impossible. That way, those who just want, and can grasp, the simple explanation get that right up front, and those who want more detail can get that too. Do you think that would be consistent with the mission of WikiPedia and useful as well? Just a thought - interested in your opinion. Synaptidude (talk) 18:01, 25 October 2011 (UTC) I'm fine with that. I'm also better at taking the electronic equivalent of a red pen to something that's already written, than I am at visualizing what this will look like before a first version is written. So I'd say WP:BE BOLD and go for it with the understanding that you can't break anything, and anything you write will end up getting changed by me and others in any case. --Tryptofish (talk) 18:08, 25 October 2011 (UTC)

I'd like to suggest a reorganization of this article to make it more readable and less repetitive. I'm prepared to do it over the next few weeks myself or with help, if there are no objections. In my eyes, there are 3 parts to this article, and most of my suggestions are for the 2nd.

1. The Lead/Overview - a lot of entries in the Talk agree this needs to be changed to be more coherent and accessible to the lay reader. I think we should make the 2nd paragraph of the lead a much shorter description, just the basic idea of what it means for an AP to be an AP (I know, harder than it sounds). The info currently in the 3rd paragraph should be later in the article - in it's place, we could put a paragraph that takes a quick introductory walk through the later sections. The Overview is okay, but I think voltage changes and threshold potential will make more sense if the explanation walks the reader through an image like Figure 1A, although one that is a little clearer. That is usually how the action potential is taught, with constant reference to a graph.

2. Current sections 2 through 6 - Here's where the article is a bit messy. How I think it could be organized:

Biophysical basis Phases Propagation Termination

I think Phases should be included in the Biophysical Basis section. Besides including a lot of similar information, the phases are described using the same mechanisms that are being talked about in 'Biophysics'. And the 'Biophysics' section currently has no structure - going through mechanisms phase-by-phase would give it that. The new section would have general information up front, then subsections for each phase.

The Neurotransmission section should be removed, and its contents sorted into the other sections. First of all, neurotransmission is about the release and reception of neurotransmitters - this is related to APs and should be referred to, but that can go in the 'Termination' section and be primarily links to relevant articles. Second, a lot of what's in this section rambles about things other than neurotransmission anyway. I'm not suggesting any particular content be removed, only moved. Some of that will be clear, some not - I don't know where the bit about sensory neurons and pacemaker potentials should go, though I do agree they should be in the article.

3. The miscellaneous sections - I have no issue with their organization.

So broadly speaking, the changes are to fix the beginning of the article for the lay reader, and then reorganize the middle sections so that they walk through the AP from how it starts, to how it moves, to what it does when it gets where it's going.

Twodarts (talk) 02:21, 18 December 2011 (UTC)

Go for it! One of the things I have tried to do, in the limited work I've done on this article, is to leave most of the basic biophysics for the membrane potential article, and focus this article on the biophysics that are specifically relevant to excitability. But if you're interested in doing major work on the article, you should feel free to do whatever seems appropriate to you. The article is definitely full of redundancy and extraneous material at the moment, so I think you should feel free to get rid of stuff if you don't think it belongs. Regards, Looie496 (talk) 17:29, 18 December 2011 (UTC)

The article states (emphasis mine):

"To be specific, myelin wraps multiple times around the axonal segment, forming a thick fatty layer that prevents ions from entering or escaping the axon. This insulation prevents significant signal decay as well as ensuring faster signal speed. This insulation, however, has the restriction that no channels can be present on the surface of the axon. There are, therefore, regularly spaced patches of membrane, which have no insulation. These nodes of ranvier can be considered to be 'mini axon hillocks', as their purpose is to boost the signal in order to prevent significant signal decay."

First it says that the insulation prevents signal decay. Then it says that it's the gaps in the insulation that prevent signal decay (i.e., it's not the insulation itself), which implies to me that the insulation may even contribute to the decay (or why else would there be signal boosters needed?). Could someone do a bit of rewrite to clarify the intended meaning here? DMacks (talk) 06:19, 12 January 2012 (UTC)

From what I understand, all-or-none signals should be digital. Unless I'm missing something here.--Miracleman123 (talk) 06:58, 4 July 2012 (UTC)

I don't think either "digital" or "analog" encompasses the full truth. The amplitude is essentially all-or-none, but the waveform is smooth and the timing is not discretized. Looie496 (talk) 16:10, 4 July 2012 (UTC) This question has come up before, and I wonder whether we should simply delete the description as "analog" (in other words, say nothing, neither analog nor digital). As Looie correctly says, action potentials are continuous variations in the value of the membrane potential, and therefore, their waveform shapes are analog, rather than digital bits. (In fact, strictly speaking, even their amplitudes can vary, depending on the resting potential that serves as a baseline. But that's not the same thing as graded subthreshold potentials.) What is all-or-none is whether they occur or not. They are nothing like what we generally consider to be digital signals, so I think that it's technically correct to describe them as analog. But it gets real confusing to say that in the same sentence that calls them "all-or-none". I've just moved the link to analog signals to another place on the page. Is this better? --Tryptofish (talk) 19:43, 4 July 2012 (UTC) Also the "purely" digital signals in electronics have a waveform ascending and descending and slight voltage variations,that limit their usability (think of high temperatures where chips start behaving erratically. The notion that an action potential has a definite waveform is irrelevant to it's digtial character. Only the frequency of action potentials passing by contains the relevant information from for instance a sensory organ.Viridiflavus (talk) 13:18, 13 January 2013 (UTC)

I popped in here because this article was in an error category (invalid LCCNs) and one thing I immediately noticed was that the references were /very/ messy. For one thing, only about half the books in the 'bibliography' section were actually cited, and there were a number of books that weren't in that section. I've been doing quite a bit of work on reorganizing how they are laid out, with the goal of trying to get them all into some kind of 'uniform' appearance, and laid out in a way that's actually useful.

Though I am changing the format of the book references to use |ref=harv, it's not out of any intention to violate CITEVAR, or force something like list-defined references on the article. the format as it existed was, like I said, very confused, and moving the books into a separate section and using <> and <> seemed like the best way to hammer this into something more usable, and less messy.

I would ask, though, that if there is a problem with how I'm doing this, you just poke me and say 'hey dummy', do this instead. I'm not changing the content, but I think where I am now would be a better 'starting point' to get this to something decent that the regular content editors of this can deal with (and that's not ugly) than where it was, even if it means moving in a different direction. If anyone wants to comment, please do so. Revent talk 11:17, 27 August 2014 (UTC)

Just to make it extremely clear, I'm being very careful to not damage the referencing, checking each edit multiple times, every citation 'points' at exactly the same source, it's just the formatting of the reference section (and completing the metadata on all the references) that I'm changing. I am using harvard references for the books, but the same 'visual' change can be done without that if people want me to change it back, it was just easier for sorting out the 'bundling'. Revent talk 02:26, 28 August 2014 (UTC) Ok, I'm finally done sorting all the books out. this is actually, for the books, more like the 'original' citation format, which was 'manual' short footnotes and a list just now they are actually using the template. I think it would make sense (especially for editability in parts) to also do the same thing with the journals, but I'm not going to do that unless people express that they want me to. If that does turn out to be desirable, please ping me and I will do it. Revent talk 07:37, 28 August 2014 (UTC)

Is it accurate to understand that an action potential is what can happen at a place, position or point on a cell's membrane, as indicated or measured by a point probe, rather than the succession of AP along, say, a neuron's axon? That is, that an AP is not the traveling of an event (the "spike train"?), but just the occurrence of the voltage event at a point?

If so, could it be appropriate to amend and add to the first sentence in the intro, from, "In physiology, an action potential is a short-lasting event in which the electrical membrane potential of a cell rapidly rises and falls, following a consistent trajectory.",

to, "In physiology, an action potential is a short-lasting event at a position in a cell in which the electrical membrane potential rapidly rises and falls, following a consistent trajectory. An action potential at one position may initiate another following action potential in a nearby continuous part of the membrane, such that an impulse signal made up of a sequence of action potentials travels along the cell membrane." ? (Without the boldface used here to make the phrase stand out, and 'spike train & impulse struck out and signal replaced impulse.)UnderEducatedGeezer (talk) 03:53, 26 June 2016 (UTC)

What I'm trying to get at is, which of these two is most like an AP: 1. a CANNON FUSE, burning from where it's lit, then on along its whole length & finally to its end where it causes something to explode, or, 2. a single POINT on a cannon fuse which point was initially not burning but is ignited by a burning point just before it and then it burns out? UnderEducatedGeezer (talk) 02:37, 29 June 2016 (UTC) This is a very good question that took me aback, as I can immediately see how this can be so non-obvious. I think your analogy of the canon fuse is not a good one. The AP itself happens as soon as the neuron is stimulated (i.e. due to ion channels opening suddenly somewhere on a dendrite causing a sudden rush of ions, sorta like blowing the hatch on a spaceship) (though of course in some exceptions it doesn't have to be stimulated at a point or externally). This sudden rush of ions makes the charge at that particular dendrite of the neuron different from the undisturbed other end(s) of the neuron (in the canonical pyramidal neuron, this would be the axon). That charge difference is "felt" as an electric field inside the neuron and can be measured at any point inside the neuron – if the cell is relatively simple that field alone will be enough to trigger the release of neurotransmitters at the end of the axon (or whatever signalling body). That release is probably what you are thinking of as the cannon "blast", and the propagation of the electric field is what you are thinking of as the "fuse". The electric field in the neuron indeed is a bit messy/slow to propagate since the "wire" along which it travels is just a soup of ions held together by a rather leaky membrane, but that is not a good analogy to a "fuse". I should add that while the strength of the electric field as it propagates matches the shape of the voltage of the original action potential, it should not itself be called an action potential at any point inside the cell, even though the propagation of the electric field is often referred to as the "propagation of the action potential" (with the important exceptions at the Nodes of Ranvier, where new APs are triggered to "boost the signal", so to speak, and probably other exceptions as well that I don't recall because there's always exceptions). In summary, in the most basic case, the AP itself happens once at the point at which a neuron is stimulated a charge difference is created between the stimulated end of the neuron and the signalling end, which is expressed as an electric field that "propagates" in a lossy manner in the ion soup of the cell (not an AP) and the charge difference felt at the signalling end causes it to release neurotransmitters into the synapse to signal the next neuron (not an AP). SamuelRiv (talk) 20:40, 30 June 2016 (UTC) @SamuelRiv, Looie496, Tryptofish, and Lova Falk: Thanks Samuel, for your lengthy response, and for putting it up under my real AP question, I appreciate it! However, I'm none the less deeply confused by your answer, so I have some questions about it. And please bear in mind that my nom-de-plume is accurate, I am under-educated (& it could be said that I'm slow, too)! (& I added notification to Looie496 & Tryptofish & Lova Falk in hopes for any possible further info on the subject.) You said, "The AP itself happens as soon as the neuron is stimulated. ". As far as I understand, some stimulations do not cause an AP, because their total contributions to the potential at the axon hillock are too small. Since the AP in a neuron is essentially what happens after neurotransmitters cause ligand-gated pores to open allowing a rush of ions into the neuron, which then passively spread along the neuron membrane (electrotonus), down the dendrites, across the soma, and toward the axon hillock, getting weaker as they spread out, and the AP will then at the point of the axon hillock either happen or not happen, depending on the strength/quantity of the input(s), I cannot see how the AP can happen as soon as the neuron is stimulated. The typical waveform describing an AP often shows small voltages that have reached the axon hillock which do not reach the necessary trigger voltage & consequently fail to initiate an AP there. Is this understanding not somewhat accurate? Here is a graph which shows failed initiations of the AP (although the indication of the refractory period is not quite right, I think): https://en.wikipedia.org/wiki/File:Action_potential.svg UnderEducatedGeezer (talk) 02:45, 4 July 2016 (UTC) Now, your suggestion that the rush of ions into the neuron from stimulation causes a difference in potential between that initial entry point and the axon terminals at the end of the neuron makes sense to me, but since the movement of that potential is passive & graded, and if I'm right consequently diminishes with distance, even though it can be presumably be measured at the axon terminals, I would think that by itself without an active propagation of a stimulated action potential, it would be vanishingly small & almost always too small to open voltage-gated calcium pores at those endings to allow the release of neurotransmitter vesicles into a synapse. Am I misunderstanding something here? UnderEducatedGeezer (talk) 03:10, 1 July 2016 (UTC) And here is one site that leads me to think that the AP is a point event that is then propagated, and also uses a kind of a 'fuse' analogy http://neuroscience.uth.tmc.edu/s1/chapter03.html UnderEducatedGeezer (talk) 21:25, 3 July 2016 (UTC)

Is a 'spike train' the succession of action potentials along axon (like a gunpowder fuse burning from start to finish along the length of the fuse), or a rapid repeated firing of the neuron itself (like a machine gun firing some number of rounds one after another rapidly from one trigger pull)?UnderEducatedGeezer (talk) 04:00, 26 June 2016 (UTC)

It is the latter. If this is unclear then it should definitely be spelled out in the article. SamuelRiv (talk) 00:32, 30 June 2016 (UTC) Thanks. I kinda thought it was as you said, such as it meaning repeated outputs over a short period of time, and the article may or may not actually be unclear, depending on my question above about what actually is the AP, point event or linear one. Current related text in article says, ". the temporal sequence of action potentials generated by a neuron is called its "spike train" (bolding added). Now, if an AP is the whole event like the fuse in example above burning from start to end, then 'spike train' would clearly be repeated events in time of 're'burnings (or resetting) of the fuse, ie, repeated signals. But if AP is the event at a point on the neuron membrane manifesting the typical waveform of resting, rise, maximum, falling, overshoot, & return to resting potential, then the 'spike train' would be sequential AP's along the length of the axon over a (very short) period of time, or just one 'signal'. So even though I thought 'spike train' really referred to a sequence in time of repeated signals, as you said, it still seems that both from some other readings and at least quasi-logic, an AP would just be the measured event at a point (unless people are using the term for both events, the measured response at a point and the sequential firings of that AP along the whole length of an axon?).UnderEducatedGeezer (talk) 02:55, 30 June 2016 (UTC)

I have just modified 3 external links on Action potential. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at <> ).

As of February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot . No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template <> (last update: 15 July 2018).

  • If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
  • If you found an error with any archives or the URLs themselves, you can fix them with this tool.

I have just modified one external link on Action potential. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

As of February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot . No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template <> (last update: 15 July 2018).

  • If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
  • If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Recently a video explaining the action potential has been deleted (and it was the case for MANY medical articles on the same day). I do not know why it has been deleted but I am guessing that it was considered too "simple". I will not undo this deletion since I don't feel I'm entitled to but it does raise the question : are wikipedia article made for the people already in the medical field or for everyone ? If the answer is the former, it would be disappointing but I would understand the video deletion. If it's the latter. why has the video been removed? Simplification will always be made (even when expert talk to each other). I do not understand this choice that goes against a popular use of wikipedia. — Preceding unsigned comment added by Alouzi (talk • contribs) 20:50, 16 April 2018 (UTC)

@Alouzi: Those videos were not removed for that reason, and Wikipedia is written for the general public. What happened with those videos is that, following a very extensive discussion, editors decided that they violated some Wikipedia policies (and some of them also contained factual errors). You can see the discussion at Wikipedia:WikiProject Medicine/Osmosis RfC. --Tryptofish (talk) 22:35, 16 April 2018 (UTC) @Tryptofish: Thank you for your answer, it is greatly appreciated. — Preceding unsigned comment added by Alouzi (talk • contribs) 13:54, April 17, 2018 (UTC)

I have temporarily reverted a very large addition to the section on plant action potentials. For reference, here it is:

Plant action potentials Edit

Plant and fungal cells [a] are also electrically excitable. The action potential observed in vascular plants is better observed than those of vegetative [1] [2] because the diffusion of electrical signals occurs primarily in the phloem sieve tube – a distinctive characteristic of higher plants [3] . [4]

The general progression of plant action potentials is the same as animal action potentials, however, plants possess alternate mechanisms.

Resting Phase Edit

Plant cells are commonly observed to have more negative resting membrane potentials and rising phase membrane potentials. For example, the Dionaea’s resting membrane potential is approximately -120mV [5] , whereas neurons are regularly between -40mV to -90mV [6] .

To attain understanding regarding plant action potentials, Opritov et al. recorded the electric potentials of maize leaves. To do so, they cut the leaf accordingly to allow aphids to attach for a long period to feed in efforts to expose the sieve. Once exposed, the researchers removed the aphids carefully with a laser to access the contents released by the leaf. This liquid-like substance was then measured with a microelectrode that was previously calibrated with a control of water. [7] The recorded values were similar to those that were expected when reviewing a study of Mimosa pudica [8] which indicated that the resting membrane potential measured was significant.

Stimulation and Rising Phase Edit

Stimulation also induces action potentials within plant cells, the most commonly mentioned stimulation is touch [5] . Unlike animals, the plant’s action potentials will not register any information regarding the characteristics of the interaction. [2] Upon stimulation, the depolarization in plant cells is not accomplished by an uptake of positive sodium ions, but but rather the influx of calcium. [4] Logically, one can understand the plant’s lack of dependence on sodium ions to initiate depolarization because too many sodium ions lead to detrimental outcomes. [9] Together with the following release of positive potassium ions, which is common to plant and animal action potentials, the action potential in plants infers, therefore, an osmotic loss of salt (KCl), whereas the animal action potential is osmotically neutral, when equal amounts of entering sodium and leaving potassium cancel each other osmotically. The interaction of electrical and osmotic relations in plant cells [b] indicates an osmotic function of electrical excitability in the common, unicellular ancestors of plants and animals under changing salinity conditions, whereas the present function of rapid signal transmission is seen as a younger accomplishment of metazoan cells in a more stable osmotic environment. [10] It must be assumed that the familiar signalling function of action potentials in some vascular plants (e.g. Mimosa pudica) arose independently from that in metazoan excitable cells.

Peak Edit

As calcium influxes towards the cytoplasm, they activate calcium-dependent anion channels, causing negatively charged ions, like chloride, to flow out of the cell thus further depolarizing the membrane. Similarly to the resting membrane potentials of plants and animals, the peaks correspond in a similar manner: they are commonly more negative. Dionaea’s action potential usually maximizes at -20mV, approximately 60mV less than an average nerve cell. [3]

Falling Phase and After-hyperpolarization Edit

Unlike the rising phase and peak, the falling phase and after-hyperpolarization seem to depend primarily on cations that are not calcium. To initiate repolarization, the cell requires movement of potassium out of the cell through passive transportation on the membrane. This differs from neurons because the movement of potassium does not dominate the decrease in membrane potential In fact, to fully repolarize, a plant cell requires energy in the form of ATP to assist in the release of hydrogen from the cell – utilizing a transporter commonly known as H+-ATPase. [7] [3]

Although there is a lot of debate regarding the refractory period of a plant cell, what is not up to speculation is the fact that their refractory periods are much longer than those in animals, [8] and that in order to fire and action potential again, they require more sources for electrical current. [3]

Although animals and plants both possess action potentials, those of plants are often overlooked or ignored due to the plants’ lack of nerves and nervous system. The deficiency of a brain or a specified location to integrate information makes it difficult to believe that action potentials of plants create a response however, plants definitely do perceive stimuli (without information regarding it) that can develop into an (generic) effector response. [2]

  1. ^ Holsinger, Kent E. “Holsinger.” Reproductive Systems and Evolution in Vascular Plants, vol. 97, no. 13, 20 June 2000, pp. 7037–7042.
  2. ^ abc
  3. Pyatygin, S. S. (February 13, 2007). "Signaling Role of Action Potential in Higher Plants" (PDF) . Russian Journal of Plant Physiology 2008. 55: 312–319.
  4. ^ abcd Hedrich, Rainer, and Erwin Neher. “Venus Flytrap: How an Excitable Carnivorous Plant Works.” Trends in Plant Science, vol. 23, no. 3, Mar. 2018, pp. 220–234., https://doi.org/10.1016/j.tplants.2017.12.004.
  5. ^ ab Hedrich, Rainer. “Ion Channels in Plants.” Physiology, vol. 92, Oct. 2012, pp. 1777–1811., doi:10.1152.
  6. ^ ab Hedrich, Rainer, and Erwin Neher. “Venus Flytrap: How an Excitable Carnivorous Plant Works.” Trends in Plant Science, vol. 23, no. 3, Mar. 2018, pp. 220–234., https://doi.org/10.1016/j.tplants.2017.12.004.
  7. ^ Purves D, Augustine GJ, Fitzpatrick D, et al., editors. Neuroscience. 2nd edition. Sunderland (MA): Sinauer Associates 2001. Electrical Potentials Across Nerve Cell Membranes.Available from: https://www.ncbi.nlm.nih.gov/books/NBK11069/
  8. ^ ab Opritov, V A, et al. “Direct Coupling of Action Potential Generation in Cells of a Higher Plant (Cucurbita Pepo) with the Operation of an Electrogenic Pump.” Russian Journal of Plant Physiology, vol. 49, no. 1, 2002, pp. 142–147.
  9. ^ ab Fromm, Jörg, et al. “Electrical Signaling along the Phloem and Its Physiological Responses in the Maize Leaf.” Frontiers in Plant Science, vol. 4, no. 239, 4 July 2013, pp. 1–7., doi:10.3389/fpls.2013.00239.
  10. ^ Pardo, Jose M, and Francisco J Quintero. “Plants and Sodium Ions: Keeping Company with the Enemy.” Genome Biology, vol. 3, no. 6, 24 May 2002, pp. 1–4., genomebiology.com/2002/3/6/reviews/1017.
  11. ^ Gradmann, D Mummert, H in Spanswick, Lucas & Dainty 1980, Plant action potentials, pp. 333–344. harvnb error: no target: CITEREFSpanswickLucasDainty1980 (help)

In part, there are formatting problems, but I also am concerned that this material fails WP:DUE. Plants just aren't that big a part of the topic, and it seems to me to be inappropriate to have so many subsections that recapitulate the descriptions of action potential stages higher on the page. --Tryptofish (talk) 22:33, 22 May 2018 (UTC)

A lot of it seems to have been reincorporated at Action_potential#Plant_action_potentials, and I added back a bit more. Specifically, the resting potential values for plants vs animals and some more specific info on the role of potassium in the post-peak phases. — Wug·a·po·des​ 00:09, 2 May 2021 (UTC)


Answers and Replies

1. Now, do these potentials travel in the same way as action potential in the axon?

In case of an EPSP, say for example, a ligand-gated sodium channel got opened and Na rushed into the cytoplasm. As a result, the local positive charges (that were already in the cytoplasm) will experience a strong repulsive force and will travel away from the channel. This local flow of current will depolarise (make the membrane potential less negative) the adjacent membrane and if the potential reaches the threshold potential only then an Action Potential will be generated. But an EPSP usually doesn't generate a threshold potential. EPSPs from different synapses generate a total current which depolarises the axon hillock/ initial segment to reach the threshold potential, and an Action potential is generated.

In case of IPSP, the influx of negative charge cause the adjacent membrane to hyperpolarize in a similar way, inhibiting stimulation, as the membrane potential at Axon hillock drops far from the threshold potential.

PSPs do not travel in the same way as action potentials. Action potential travel is described by the Hodgkin-Huxley equations. In contrast, as a first approximation, PSPs can be described by passive travel using the cable equation. The way in which velocity is defined in the Hodgkin-Huxley equations and passive cable equations is different. See for example the discussion of both equations in https://www.amazon.com/dp/0195181999/?tag=pfamazon01-20.

PSPs do not always travel purely passively. However, the voltage-dependent channels in the dendrites are different from those in the axon, eg.
https://www.nature.com/articles/nn0900_895
https://www.researchgate.net/public. pse_location_in_hippocampal_pyramidal_neurons

Yes and no. Yes, in the sense that in passive travel, there is no inactivation to prevent the PSPs from travelling backward. However, in practice, you will find that it is not a useful concept.

There can be backpropagating action potentials that travel from the cell body into the dendrites, eg. https://www.ncbi.nlm.nih.gov/pubmed/7658365

#2: Yes, normally the action potentials don't travel backwards. However, this can be done experimentally by stimulating an axon, but not after it has just propagated an action potential (when the Na-channels are inactive).

Action potentials are often said to be actively propagated because additional Na-channels are recruited to their open state by the change on membrane potential in an ever enlarging region of the cell membrane.
The IPSPs and EPSPs effects on membrane potential are often said to spread passively. They open where the receptors are stimulated and the neighboring membrane potential is affected but additional channels of the same type are not opened.
All of these membrane potential changes can go in all directions. Only the action potentials are actively conducted by recruiting additional neighboring channels to open so it can travel to distant locations.

#3: The axon hillock, where the cell body joins the axon, is a transition between the two. The channel proteins (including receptors and other channels) can differ between the two locations. This results in different membrane properties (electro-physiologically speaking) for the two areas. The axon hillock itself may have its own set of special channels, I don't know.
Voltage gated Na-channels (used in action potentials) are not usually located in the cell body, so Na based action potentials are not usually propagate there. That would start at the axon hillock.
After an action potential is initiated, additional unopened Na-channels open, injecting new current into the cell, making the signals propagation more robust. This may account for the impression that the nodes of Ranvier have a different threshold of activation. Not sure if that is true.
Not all axons that can generate action potentials have myelin and nodes of Ranvier. Some just have the neuronal membrane with voltage gated channels in it. This can also conduct action potentials, just not as fast.

Besides voltage gated Na-channels there can be voltage gated Ca-channels which can also produce action potentials, but usually with a slower longer time course. Among other places they are found in synapses and heart muscle.


Abstract—Recently, Spach et al (Circ Res. 199883:1144–1164) measured the transmembrane action potential 150 to 200 μm below the tissue surface during longitudinal and transverse propagation. They found that “during longitudinal propagation there was initial slowing of Vm [action potential] foot that resulted in deviations from a simple exponential… ” (p 1144). They attributed this behavior to the effects of capillaries on propagation. The purpose of this commentary is to show that the perfusing bath plays an important role in determining the time course of the action potential foot, even when the transmembrane potential is measured 150 μm below the tissue surface. Using numerical simulations based on the bidomain model, we find that the action potential foot for transverse propagation is nearly exponential (τfoot=314 μs). For longitudinal propagation, the action potential foot is not exponential because of an initial slowing (best-fit τfoot=483 μs). We conclude that the perfusing bath must be taken into account when interpreting data showing differences in the shape of the action potential foot with propagation direction, even if the transmembrane potential is measured 150 μm below the tissue surface. The full text of this article is available at http://www.circresaha.org.

In 1981, Spach et al 1 observed a smaller maximum rate of rise of the action potential, V̇max, and a larger time constant of the action potential foot, τfoot, during propagation parallel to the myocardiac fibers (longitudinal) than during propagation perpendicular to the fibers (transverse). They attributed these differences to the discrete cellular structure of the myocardium. Their research has been cited widely and is often taken as evidence for discontinuous propagation in cardiac tissue. 2

Several researchers 3 4 5 6 7 8 9 10 11 have suggested that the observations of Spach et al 1 may be caused by the bath perfusing the tissue rather than the discrete nature of the tissue itself. Recently, Spach et al 12 presented additional evidence supporting their earlier data, but instead of measuring the transmembrane potential (Vm) at the tissue surface, as they did in 1981, they measured Vm 150 to 200 μm below the surface to eliminate bath perfusate effects. In their study, they emphasized the time course of the action potential foot. The purpose of this commentary is to model the experiment of Spach et al 12 using a numerical simulation and to show that the perfusing bath plays an important role in determining the time course of the action potential foot, even when Vm is measured 150 μm below the tissue surface.

Materials and Methods

The simulation is similar to that described by Pollard et al 7 a slab of cardiac tissue is superfused by a conductive bath (Figure 1 ). The bidomain model 13 represents the anisotropic electrical properties of the cardiac tissue. This model is a continuum description that does not take into account the discrete nature of individual myocardial cells. The electrical potential in the isotropic perfusing bath obeys Laplace’s equation. At the interface between the tissue and the bath, the boundary conditions are continuity of the extracellular (bath and interstitial) potential, continuity of the normal component of the extracellular current density, and the vanishing of the normal component of the intracellular current density. 14 All other boundaries are sealed.

A planar wavefront propagates in the x direction, and the z direction is perpendicular to the tissue-bath surface (Figure 1 ). Fibers are aligned in either the x direction (longitudinal propagation) or the y direction (transverse propagation). The tissue parameters are given in the Table . The common scale factor of the 4 bidomain conductivities 15 is selected so that the resulting propagation speed of the action potential is typical of that observed in experiments. 12

The ionic current through the membrane is described as a passive leak term plus an active sodium channel. 12 16 The sodium channel gates obey Ebihara-Johnson kinetics. 17 We restrict our attention to the depolarization phase of the action potential.

We solve the bidomain equations for the tissue and Laplace’s equation for the bath by approximating the differential equations by finite differences. 5 The time step is 2 μs. The space step in the z direction is 20 μm, and in the x direction is 50 μm for longitudinal propagation and 20 μm for transverse propagation. The boundary-value problem is solved iteratively using overrelaxation 5 the iteration is terminated when the residual is <1 μV.

The membrane is at rest initially (Vm=−80 mV). At t=0, Vm along the left edge (x=0) is raised to 0 mV, initiating the action potential. Measurements of Vm and its derivative are made at the midpoint of the slab, where the action potential wavefront has reached a steady shape. The length of the slab is 15 mm for longitudinal propagation and 6 mm for transverse propagation (301 nodes in both cases). The slab is 0.5 mm thick, and its bottom surface is sealed. The transmembrane potential is measured at 3 depths: the tissue-bath surface, 150 μm below the tissue-bath surface, and at the bottom of the tissue. The bath is 1 mm thick.

The time constant of the action potential foot is calculated by fitting a straight line to the phase-plane plot of dVm/dt versus Vm over the range of Vm from –79 to –65 mV (approximately the first 15 mV of depolarization). The reciprocal of the slope of this line is τfoot.

Results

Figure 2 shows the transmembrane potential as a function of x and z, for longitudinal and transverse propagation. In both cases, the wavefront is curved, with the action potential at the surface leading the action potential at the center. The spreading of the contours indicates that the rate of rise of the action potential is lower at the surface than in the bulk. The speed of longitudinal propagation is 0.552 m/s, and of transverse propagation is 0.203 m/s. The peak-to-peak interstitial potential, measured 150 μm below the surface is 23.0 mV for longitudinal propagation and 11.6 mV for transverse propagation.

Figure 3A contains a phase-plane plot of the action potential during longitudinal and transverse propagation, for Vm measured at the tissue surface. The rate of rise is 15% lower during longitudinal propagation (V̇max=149 V/s) compared with transverse propagation (V̇max=175 V/s). The inset shows a magnified view of the action potential foot. For propagation in either direction, the action potential foot is not exponential (an exponentially rising action potential foot would appear as a straight line in a phase-plane plot). The best-fit value of τfoot is 706 μs for propagation in the longitudinal direction and 486 μs for propagation in the transverse direction.

The dotted curve in Figure 3A represents the action potential calculated when the bath is not present. In this case, the wavefront is not curved. The speed of longitudinal propagation is 0.505 m/s, and the speed of transverse propagation is 0.202 m/s. The time course of the action potential is independent of the direction of propagation. The action potential foot is exponential (τfoot=294 μs), and V̇max (201 V/s) is greater than when the bath is present.

Figure 3B contains similar data, but Vm is measured 150 μm below the tissue surface. As in Figure 3A , V̇max is less for longitudinal propagation (196 V/s) than for transverse propagation (201 V/s), although the difference between the two (2.5%) is smaller than when Vm is measured at the surface. The action potential foot for transverse propagation is nearly exponential (τfoot=314 μs), although it contains a slight “initial slur.” 12 For longitudinal propagation, the action potential foot is clearly not exponential because of an initial slowing (best-fit τfoot=483 μs).

At the bottom of the tissue (Figure 3C ), V̇max is larger, and τfoot is smaller, for longitudinal propagation (V̇max=214 V/s, τfoot=272 μs) than for transverse propagation (V̇max=203 V/s, τfoot=292 μs). The action potential foot is nearly exponential, although there is a slight initial slur for propagation in the longitudinal direction. Note that V̇max is greater than, and τfoot is smaller than, if the bath were not present.

Discussion

The data of Spach et al 1 are cited widely as evidence for discontinuous propagation in cardiac tissue. 2 Their hypothesis of discontinuous propagation is supported by the following logic: (1) During 1-dimensional propagation in a tissue with continuous electrical properties, the time course of the action potential (including V̇max and τfoot) does not depend on the intracellular and interstitial conductivities 18 (2) experiments indicate that in cardiac tissue V̇max and τfoot differ with the direction of propagation and therefore with conductivity 1 and (3) therefore, the conductivity of cardiac tissue is not continuous. A flaw exists in this line of reasoning: when a conductive bath perfuses the tissue, the propagation is not 1-dimensional. The extracellular conductivity is higher for the tissue near the surface (adjacent to the bath) than it is for the tissue far from the surface (deep within the bulk). Therefore, gradients in Vm exist not only in the direction of propagation, but also in the direction perpendicular to the tissue surface. Reasoning based on the 1-dimensional cable model (such as used in the first premise of the syllogism above) is not applicable.

Several researchers 3 4 5 6 7 8 9 10 11 have shown theoretically that the presence of the perfusing bath may account for the difference in the rate of rise with direction that was observed by Spach et al. 1 The high-conductivity bath causes the wavefront to be curved (surface leading bulk) and the surface rate of rise to be slowed. This effect is more dramatic for longitudinal propagation than for transverse propagation because of the unequal anisotropy ratios of the tissue. For longitudinal propagation, the intracellular and interstitial conductivities are approximately the same, 15 so large interstitial potentials exist in the bulk, although the potential in the high-conductivity bath is small. For transverse propagation, the interstitial conductivity is ≈4 times greater than the intracellular conductivity, 15 so the extracellular potentials are small both at the tissue surface and deep in the bulk. The smaller gradients of the extracellular potential result in smaller gradients in the transmembrane potential during transverse propagation compared with longitudinal propagation. Our calculated changes in propagation speed, V̇max, and τfoot measured at the tissue surface are qualitatively consistent with previous numerical models 3 4 5 6 7 8 9 10 11 and with experimental data. 1

Recently, Spach et al 12 measured Vm ≈150 μm below the tissue surface, where they claim “there should be minimal effects of the superfusate solution.” (p 1146). Although Spach et al 12 recorded the action potential rate of rise, their main goal was to present “a detailed experimental analysis of the time course of the foot of the cardiac action potential (Vm foot) during propagation in different directions in anisotropic cardiac muscle.” (p 1144). They observed that “during longitudinal propagation there was initial slowing of Vm foot that resulted in deviations from a simple exponential corollary changes occurred at numerous sites during transverse propagation.” 12 (p 1144). They attributed these results to an effect of capillaries on conduction.

The results in Figure 3B show that the influence of the perfusing bath extends at least 150 μm below the tissue surface. Furthermore, the bath causes the action potential foot to rise more slowly than exponentially, and this slowing is greater for longitudinal propagation than for transverse propagation. These results agree qualitatively with the recent experimental data of Spach et al. 12 The action potential foot is particularly sensitive to the perfusing bath, more so than other features of the action potential. 9 10 11 12 13 14 15 16 17 18 19

Quantitatively, the biggest discrepancy between our calculations and the data of Spach et al 12 lies not in the action potential foot, but instead in V̇max. Our calculations indicate that V̇max 150 μm below the tissue surface is only 2.5% less for longitudinal propagation than for transverse propagation, whereas the experimental data show an average difference of 22%. The source of this discrepancy is unclear. It may arise from the discrete nature of the tissue, from capillary effects, from incorrect parameter values in the simulation, or from of the presence of dead tissue 200 to 300 μm below the tissue surface 12 Our model does not incorporate a dead core of tissue. According to Spach et al, 12 the dead core has an enlarged interstitial space, which might increase the interstitial conductivity and cause the core to function approximately in the same manner as the perfusing bath.

Spach et al 12 supported their theory of capillary effects by comparing their data with that measured by Fast and Kléber 20 in monolayers of neonatal cardiac myocytes. They suggested that because such monolayers are devoid of capillaries, the action potential foot should be exponential. The action potentials measured by Fast and Kléber 20 do indeed have an exponential foot. However, the monolayers of Fast and Kléber 20 are also devoid of “deep” tissue far from the perfusing bath, so there can be no gradients of Vm with depth. Therefore, the data of Fast and Kléber 20 are also consistent with the hypothesis that the purfusing bath determines the shape of the action potential foot. Thus, data from monolayers does not distinguish between the capillary mechanism and the purfusing bath mechanism for slowing the action potential foot.

One way to distinguish between the 2 mechanisms (capillaries versus perfusing bath) would be to repeat the experiments of Spach et al 1 12 with and without a perfusing bath present. The tissue would have to be kept alive when the perfusing bath was absent, perhaps by arterial perfusion. The results in Figure 3A indicate that when the bath is eliminated, the action potential foot should become exponential, with no differences between longitudinal and transverse propagation. Furthermore, the maximum rate of rise of the action potential should increase and become independent of propagation direction. Although this experiment is easy to conceive, it would be susceptible to several sources of error. If Vm were measured optically, the data would represent an average over a depth of a few hundred microns. Because the model predicts that Vm changes dramatically over such distances, the data would be difficult to interpret. Microelectrode measurements, on the other hand, are sensitive to capacitative coupling to the perfusing bath, and the degree of such coupling depends on the bath depth. The rapid depolarization phase of the action potential is particularly sensitive to electrode capacitance. Although it is possible to correct the data for the influence of electrode capacitance, these corrections would be crucial when comparing data measured at different bath depths.

We cannot conclude from our study that capillaries are not important during action potential propagation. Nor can we conclude that discontinuous propagation does not occur (particularly in diseased tissue). These factors may well play a role in propagation. We can conclude, however, that the influence of a perfusing bath must be taken into account when interpreting data showing differences in the shape of the action potential foot with propagation direction, even if Vm is measured 150 μm below the tissue surface. Therefore, differences in action potential shape with direction 1 12 cannot be taken as definitive evidence supporting discontinuous propagation or capillary effects if a perfusing bath is present. Finally, without additional experiments, we cannot exclude the possibility that in healthy tissue the difference in the shape of the action potential upstroke with propagation direction is simply an artifact of the way the tissue was perfused.

Figure 1. Schematic diagram showing the geometry of the tissue slab and the perfusing bath.

Figure 2. Isocontours of the transmembrane potential as a function of x and z for an action potential propagating in the longitudinal (A) and transverse (B) directions. z=0.5 mm is the tissue-bath interface.

Figure 3. Phase-plane plots of the action potential during longitudinal (L) and transverse (T) propagation, measured at the tissue-bath surface (A), 150 μm below the tissue-bath surface (B), and at the bottom of the slab (C). Dotted curve in panel A represents the action potential when the bath is not present. Insets show a magnified view of the action potential foot.

Table 1. Tissue Parameters for the Model

This research was supported by NIH Grant RO1HL57207. We thank the School of Engineering and Computer Science at Oakland University for their computational support.


Modelling in vivo action potential propagation along a giant axon

A partial differential equation model for the three-dimensional current flow in an excitable, unmyelinated axon is considered. Where the axon radius is significantly below a critical value (R_) (that depends upon intra- and extra-cellular conductivity and ion channel conductance) the resistance of the intracellular space is significantly higher than that of the extracellular space, such that the potential outside the axon is uniformly small whilst the intracellular potential is approximated by the transmembrane potential. In turn, since the current flow is predominantly axial, it can be shown that the transmembrane potential is approximated by a solution to the one-dimensional cable equation. It is noted that the radius of the squid giant axon, investigated by (Hodgkin and Huxley 1952e), lies close to (R_) . This motivates us to apply the three-dimensional model to the squid giant axon and compare the results thus found to those obtained using the cable equation. In the context of the in vitro experiments conducted in (Hodgkin and Huxley 1952e) we find only a small difference between the wave profiles determined using these two different approaches and little difference between the speeds of action potential propagation predicted. This suggests that the cable equation approximation is accurate in this scenario. However when applied to the it in vivo setting, in which the conductivity of the surrounding tissue is considerably lower than that of the axoplasm, there are marked differences in both wave profile and speed of action potential propagation calculated using the two approaches. In particular, the cable equation significantly over predicts the increase in the velocity of propagation as axon radius increases. The consequences of these results are discussed in terms of the evolutionary costs associated with increasing the speed of action potential propagation by increasing axon radius.

This is a preview of subscription content, access via your institution.


This work has been supported by Linköping University, and the Swedish Research Council (Grant No. 621-2013-6078). This work comprises an appendix, paper I, from Malcolm Latorre's thesis titled �tion Potential Generator and Electrode Testing.” The authors would like to thank Research Engineer Bengt Ragnemalm at the Department of Biomedical Engineering, Linköping University for his support in the programming of this microcontroller, and help with the design of the printed circuit board, Professor E. Göran Salerud the Department of Biomedical Engineering, Linköping University for his guidance and support, and Professor Rejean Munger at the Ottawa Hospital Research Institute, University of Ottawa for his valuable early contributions to this project.

Andreasen, L. N. S., Struijk, J. J., and Haugland, M. (1997). 𠇊n artificial nerve fiber for evaluation of nerve cuff electrodes,” in Proceedings of the 19th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vol. 5 (Chicago, IL), 1997�. doi: 10.1109/iembs.1997.758734

Aregueta-Robles, U. A., Woolley, A. J., Poole-Warren, L. A., Lovell, N. H., and Green, R. A. (2014). Organic electrode coatings for next-generation neural interfaces. Front. Neuroeng. 7:15. doi: 10.3389/fneng.2014.00015

Åström, M., Diczfalusy, E., Martens, H., and Wårdell, K. (2015). Relationship between neural activation and electric field distribution during deep brain stimulation. IEEE Trans. Biomed. Eng. 62, 664�. doi: 10.1109/TBME.2014.2363494

Buschbacher, R. M., and Prahlow, N. D. (2006). Manual of Nerve Conduction Studies. New York, NY: Demos Medical Publishing LLC.

Carnevale, N. T., and Hines, M. L. (2006). The NEURON Book. Cambridge: Cambridge University Press. doi: 10.1017/CBO9780511541612

Chen, C. Y., Chang, C. L., Chang, C. W., Lai, S. C., Chien, T. F., Huang, H. Y., et al. (2013). A low-power bio-potential acquisition system with flexible PDMS dry electrodes for portable ubiquitous healthcare applications. Sensors (Basel) 13, 3077�. doi: 10.3390/s130303077

Golestanirad, L., Elahi, B., Molina Arribere, A., Mosig, J. R., Pollo, C., and Graham, S. J. (2013). Analysis of fractal electrodes for efficient neural stimulation. Front. Neuroeng. 6:3. doi: 10.3389/fneng.2013.00003

Hemm, S., and Wårdell, K. (2010). Stereotactic implantation of deep brain stimulation electrodes: a review of technical systems, methods and emerging tools. Med. Biol. Eng. Comput. 48, 611�. doi: 10.1007/s11517-010-0633-y

Hodgkin, A. L., and Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500�. doi: 10.1113/jphysiol.1952.sp004764

Kelly, R. C., Smith, M. A., Samonds, J. M., Kohn, A., Bonds, A. B., Movshon, J. A., et al. (2007). Comparison of recordings from microelectrode arrays and single electrodes in the visual cortex. J. Neurosci. 27, 261�. doi: 10.1523/JNEUROSCI.4906-06.2007

Kip, A. L., Nicholas, B. L., Mike, D. J., Sarah, M. R.-B., Jeffrey, L. H., and Daryl, R. K. (2011). Poly(3,4-ethylenedioxythiophene) (PEDOT) polymer coatings facilitate smaller neural recording electrodes. J. Neural Eng. 8:014001. doi: 10.1088/1741-2560/8/1/014001

Lewis, E. R. (1968a). An electronic model of neuroelectric point processes. Kybernetik 5, 30�. doi: 10.1007/BF00288896

Lewis, E. R. (1968b). Using electronic circuits to model simple neuroelectric interactions. Proc. IEEE 56, 931�. doi: 10.1109/PROC.1968.6445

Marozas, V., Petrenas, A., Daukantas, S., and Lukosevicius, A. (2011). A comparison of conductive textile-based and silver/silver chloride gel electrodes in exercise electrocardiogram recordings. J. Electrocardiol. 44, 189�. doi: 10.1016/j.jelectrocard.2010.12.004

Martens, H. C., Toader, E., Decre, M. M., Anderson, D. J., Vetter, R., Kipke, D. R., et al. (2011). Spatial steering of deep brain stimulation volumes using a novel lead design. Clin. Neurophysiol. 122, 558�. doi: 10.1016/j.clinph.2010.07.026

McIntyre, C. C., Mori, S., Sherman, D. L., Thakor, N. V., and Vitek, J. L. (2004). Electric field and stimulating influence generated by deep brain stimulation of the subthalamic nucleus. Clin. Neurophysiol. 115, 589�. doi: 10.1016/j.clinph.2003.10.033

Meziane, N., Webster, J. G., Attari, M., and Nimunkar, A. J. (2013). Dry electrodes for electrocardiography. Physiol. Meas. 34, R47–R69. doi: 10.1088/0967-3334/34/9/R47

Pedrosa, P., Alves, E., Barradas, N. P., Fiedler, P., Haueisen, J., Vaz, F., et al. (2012). TiNx coated polycarbonate for bio-electrode applications. Corros. Sci. 56, 49�. doi: 10.1016/j.corsci.2011.11.008

Ravichandran, R., Sundarrajan, S., Venugopal, J. R., Mukherjee, S., and Ramakrishna, S. (2010). Applications of conducting polymers and their issues in biomedical engineering. J. R. Soc. Interface 7(Suppl. 5), S559–S579. doi: 10.1098/rsif.2010.0120.focus

Rieger, R., Schuettler, M., and Chuang, S. C. (2014). A device for emulating cuff recordings of action potentials propagating along peripheral nerves. IEEE Trans. Neural Syst. Rehabil. Eng. 22, 937�. doi: 10.1109/TNSRE.2014.2300933

Roy, G. (1972). A simple electronic analog of the squid axon membrane: the NEUROFET. Biomed. Eng. IEEE Trans. 19, 60�. doi: 10.1109/TBME.1972.324161

Rushton, W. A. (1951). A theory of the effects of fibre size in medullated nerve. J. Physiol. 115, 101�. doi: 10.1113/jphysiol.1951.sp004655

Searle, A., and Kirkup, L. (2000). A direct comparison of wet, dry and insulating bioelectric recording electrodes. Physiol. Meas. 21, 271�. doi: 10.1088/0967-3334/21/2/307

Tathireddy, P., Krummenacker, S., Kammer, S., Hoffmann, K., Solzbacher, F., Hoffmann, K., et al. (2008). “Towards high aspect ratio tungsten Micro Electrode Array for neural recording and stimulation applications,” in 13th Annual Conference of the International Functional Electrical Stimulation Society, Freiburg Concert Hall, IFESS_2008 (Freiburg).

Tortora, G. J., and Grabowski, S. R. (2000). Principles of Anatomy and Physiology. San Francisco, CA: Benjamin Cummings.

Wang, X., Larsson, O., Platt, D., Nordlinder, S., Engquist, I., Berggren, M., et al. (2012). An all-printed wireless humidity sensor label. Sens. Actuators B Chem. 166, 556�. doi: 10.1016/j.snb.2012.03.009

Yoshida, K., Kurstjens, G. A., and Hennings, K. (2009). Experimental validation of the nerve conduction velocity selective recording technique using a multi-contact cuff electrode. Med. Eng. Phys. 31, 1261�. doi: 10.1016/j.medengphy.2009.08.005

Keywords: action potential, biomedical electrode, electronic nerve model, nodes of Ranvier, ulnar nerve

Citation: Latorre MA, Chan ADC and Wårdell K (2015) A physical action potential generator: design, implementation and evaluation. Front. Neurosci. 9:371. doi: 10.3389/fnins.2015.00371

Received: 26 February 2015 Accepted: 22 September 2015
Published: 20 October 2015.

Michele Giugliano, University of Antwerp, Belgium

Pascal Darbon, Strasbourg University, France
Adolfo E. Talpalar, Karolinska Institutet, Sweden

Copyright © 2015 Latorre, Chan and Wårdell. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.


Abstract—Recently, Spach et al (Circ Res. 199883:1144–1164) measured the transmembrane action potential 150 to 200 μm below the tissue surface during longitudinal and transverse propagation. They found that “during longitudinal propagation there was initial slowing of Vm [action potential] foot that resulted in deviations from a simple exponential… ” (p 1144). They attributed this behavior to the effects of capillaries on propagation. The purpose of this commentary is to show that the perfusing bath plays an important role in determining the time course of the action potential foot, even when the transmembrane potential is measured 150 μm below the tissue surface. Using numerical simulations based on the bidomain model, we find that the action potential foot for transverse propagation is nearly exponential (τfoot=314 μs). For longitudinal propagation, the action potential foot is not exponential because of an initial slowing (best-fit τfoot=483 μs). We conclude that the perfusing bath must be taken into account when interpreting data showing differences in the shape of the action potential foot with propagation direction, even if the transmembrane potential is measured 150 μm below the tissue surface. The full text of this article is available at http://www.circresaha.org.

In 1981, Spach et al 1 observed a smaller maximum rate of rise of the action potential, V̇max, and a larger time constant of the action potential foot, τfoot, during propagation parallel to the myocardiac fibers (longitudinal) than during propagation perpendicular to the fibers (transverse). They attributed these differences to the discrete cellular structure of the myocardium. Their research has been cited widely and is often taken as evidence for discontinuous propagation in cardiac tissue. 2

Several researchers 3 4 5 6 7 8 9 10 11 have suggested that the observations of Spach et al 1 may be caused by the bath perfusing the tissue rather than the discrete nature of the tissue itself. Recently, Spach et al 12 presented additional evidence supporting their earlier data, but instead of measuring the transmembrane potential (Vm) at the tissue surface, as they did in 1981, they measured Vm 150 to 200 μm below the surface to eliminate bath perfusate effects. In their study, they emphasized the time course of the action potential foot. The purpose of this commentary is to model the experiment of Spach et al 12 using a numerical simulation and to show that the perfusing bath plays an important role in determining the time course of the action potential foot, even when Vm is measured 150 μm below the tissue surface.

Materials and Methods

The simulation is similar to that described by Pollard et al 7 a slab of cardiac tissue is superfused by a conductive bath (Figure 1 ). The bidomain model 13 represents the anisotropic electrical properties of the cardiac tissue. This model is a continuum description that does not take into account the discrete nature of individual myocardial cells. The electrical potential in the isotropic perfusing bath obeys Laplace’s equation. At the interface between the tissue and the bath, the boundary conditions are continuity of the extracellular (bath and interstitial) potential, continuity of the normal component of the extracellular current density, and the vanishing of the normal component of the intracellular current density. 14 All other boundaries are sealed.

A planar wavefront propagates in the x direction, and the z direction is perpendicular to the tissue-bath surface (Figure 1 ). Fibers are aligned in either the x direction (longitudinal propagation) or the y direction (transverse propagation). The tissue parameters are given in the Table . The common scale factor of the 4 bidomain conductivities 15 is selected so that the resulting propagation speed of the action potential is typical of that observed in experiments. 12

The ionic current through the membrane is described as a passive leak term plus an active sodium channel. 12 16 The sodium channel gates obey Ebihara-Johnson kinetics. 17 We restrict our attention to the depolarization phase of the action potential.

We solve the bidomain equations for the tissue and Laplace’s equation for the bath by approximating the differential equations by finite differences. 5 The time step is 2 μs. The space step in the z direction is 20 μm, and in the x direction is 50 μm for longitudinal propagation and 20 μm for transverse propagation. The boundary-value problem is solved iteratively using overrelaxation 5 the iteration is terminated when the residual is <1 μV.

The membrane is at rest initially (Vm=−80 mV). At t=0, Vm along the left edge (x=0) is raised to 0 mV, initiating the action potential. Measurements of Vm and its derivative are made at the midpoint of the slab, where the action potential wavefront has reached a steady shape. The length of the slab is 15 mm for longitudinal propagation and 6 mm for transverse propagation (301 nodes in both cases). The slab is 0.5 mm thick, and its bottom surface is sealed. The transmembrane potential is measured at 3 depths: the tissue-bath surface, 150 μm below the tissue-bath surface, and at the bottom of the tissue. The bath is 1 mm thick.

The time constant of the action potential foot is calculated by fitting a straight line to the phase-plane plot of dVm/dt versus Vm over the range of Vm from –79 to –65 mV (approximately the first 15 mV of depolarization). The reciprocal of the slope of this line is τfoot.

Results

Figure 2 shows the transmembrane potential as a function of x and z, for longitudinal and transverse propagation. In both cases, the wavefront is curved, with the action potential at the surface leading the action potential at the center. The spreading of the contours indicates that the rate of rise of the action potential is lower at the surface than in the bulk. The speed of longitudinal propagation is 0.552 m/s, and of transverse propagation is 0.203 m/s. The peak-to-peak interstitial potential, measured 150 μm below the surface is 23.0 mV for longitudinal propagation and 11.6 mV for transverse propagation.

Figure 3A contains a phase-plane plot of the action potential during longitudinal and transverse propagation, for Vm measured at the tissue surface. The rate of rise is 15% lower during longitudinal propagation (V̇max=149 V/s) compared with transverse propagation (V̇max=175 V/s). The inset shows a magnified view of the action potential foot. For propagation in either direction, the action potential foot is not exponential (an exponentially rising action potential foot would appear as a straight line in a phase-plane plot). The best-fit value of τfoot is 706 μs for propagation in the longitudinal direction and 486 μs for propagation in the transverse direction.

The dotted curve in Figure 3A represents the action potential calculated when the bath is not present. In this case, the wavefront is not curved. The speed of longitudinal propagation is 0.505 m/s, and the speed of transverse propagation is 0.202 m/s. The time course of the action potential is independent of the direction of propagation. The action potential foot is exponential (τfoot=294 μs), and V̇max (201 V/s) is greater than when the bath is present.

Figure 3B contains similar data, but Vm is measured 150 μm below the tissue surface. As in Figure 3A , V̇max is less for longitudinal propagation (196 V/s) than for transverse propagation (201 V/s), although the difference between the two (2.5%) is smaller than when Vm is measured at the surface. The action potential foot for transverse propagation is nearly exponential (τfoot=314 μs), although it contains a slight “initial slur.” 12 For longitudinal propagation, the action potential foot is clearly not exponential because of an initial slowing (best-fit τfoot=483 μs).

At the bottom of the tissue (Figure 3C ), V̇max is larger, and τfoot is smaller, for longitudinal propagation (V̇max=214 V/s, τfoot=272 μs) than for transverse propagation (V̇max=203 V/s, τfoot=292 μs). The action potential foot is nearly exponential, although there is a slight initial slur for propagation in the longitudinal direction. Note that V̇max is greater than, and τfoot is smaller than, if the bath were not present.

Discussion

The data of Spach et al 1 are cited widely as evidence for discontinuous propagation in cardiac tissue. 2 Their hypothesis of discontinuous propagation is supported by the following logic: (1) During 1-dimensional propagation in a tissue with continuous electrical properties, the time course of the action potential (including V̇max and τfoot) does not depend on the intracellular and interstitial conductivities 18 (2) experiments indicate that in cardiac tissue V̇max and τfoot differ with the direction of propagation and therefore with conductivity 1 and (3) therefore, the conductivity of cardiac tissue is not continuous. A flaw exists in this line of reasoning: when a conductive bath perfuses the tissue, the propagation is not 1-dimensional. The extracellular conductivity is higher for the tissue near the surface (adjacent to the bath) than it is for the tissue far from the surface (deep within the bulk). Therefore, gradients in Vm exist not only in the direction of propagation, but also in the direction perpendicular to the tissue surface. Reasoning based on the 1-dimensional cable model (such as used in the first premise of the syllogism above) is not applicable.

Several researchers 3 4 5 6 7 8 9 10 11 have shown theoretically that the presence of the perfusing bath may account for the difference in the rate of rise with direction that was observed by Spach et al. 1 The high-conductivity bath causes the wavefront to be curved (surface leading bulk) and the surface rate of rise to be slowed. This effect is more dramatic for longitudinal propagation than for transverse propagation because of the unequal anisotropy ratios of the tissue. For longitudinal propagation, the intracellular and interstitial conductivities are approximately the same, 15 so large interstitial potentials exist in the bulk, although the potential in the high-conductivity bath is small. For transverse propagation, the interstitial conductivity is ≈4 times greater than the intracellular conductivity, 15 so the extracellular potentials are small both at the tissue surface and deep in the bulk. The smaller gradients of the extracellular potential result in smaller gradients in the transmembrane potential during transverse propagation compared with longitudinal propagation. Our calculated changes in propagation speed, V̇max, and τfoot measured at the tissue surface are qualitatively consistent with previous numerical models 3 4 5 6 7 8 9 10 11 and with experimental data. 1

Recently, Spach et al 12 measured Vm ≈150 μm below the tissue surface, where they claim “there should be minimal effects of the superfusate solution.” (p 1146). Although Spach et al 12 recorded the action potential rate of rise, their main goal was to present “a detailed experimental analysis of the time course of the foot of the cardiac action potential (Vm foot) during propagation in different directions in anisotropic cardiac muscle.” (p 1144). They observed that “during longitudinal propagation there was initial slowing of Vm foot that resulted in deviations from a simple exponential corollary changes occurred at numerous sites during transverse propagation.” 12 (p 1144). They attributed these results to an effect of capillaries on conduction.

The results in Figure 3B show that the influence of the perfusing bath extends at least 150 μm below the tissue surface. Furthermore, the bath causes the action potential foot to rise more slowly than exponentially, and this slowing is greater for longitudinal propagation than for transverse propagation. These results agree qualitatively with the recent experimental data of Spach et al. 12 The action potential foot is particularly sensitive to the perfusing bath, more so than other features of the action potential. 9 10 11 12 13 14 15 16 17 18 19

Quantitatively, the biggest discrepancy between our calculations and the data of Spach et al 12 lies not in the action potential foot, but instead in V̇max. Our calculations indicate that V̇max 150 μm below the tissue surface is only 2.5% less for longitudinal propagation than for transverse propagation, whereas the experimental data show an average difference of 22%. The source of this discrepancy is unclear. It may arise from the discrete nature of the tissue, from capillary effects, from incorrect parameter values in the simulation, or from of the presence of dead tissue 200 to 300 μm below the tissue surface 12 Our model does not incorporate a dead core of tissue. According to Spach et al, 12 the dead core has an enlarged interstitial space, which might increase the interstitial conductivity and cause the core to function approximately in the same manner as the perfusing bath.

Spach et al 12 supported their theory of capillary effects by comparing their data with that measured by Fast and Kléber 20 in monolayers of neonatal cardiac myocytes. They suggested that because such monolayers are devoid of capillaries, the action potential foot should be exponential. The action potentials measured by Fast and Kléber 20 do indeed have an exponential foot. However, the monolayers of Fast and Kléber 20 are also devoid of “deep” tissue far from the perfusing bath, so there can be no gradients of Vm with depth. Therefore, the data of Fast and Kléber 20 are also consistent with the hypothesis that the purfusing bath determines the shape of the action potential foot. Thus, data from monolayers does not distinguish between the capillary mechanism and the purfusing bath mechanism for slowing the action potential foot.

One way to distinguish between the 2 mechanisms (capillaries versus perfusing bath) would be to repeat the experiments of Spach et al 1 12 with and without a perfusing bath present. The tissue would have to be kept alive when the perfusing bath was absent, perhaps by arterial perfusion. The results in Figure 3A indicate that when the bath is eliminated, the action potential foot should become exponential, with no differences between longitudinal and transverse propagation. Furthermore, the maximum rate of rise of the action potential should increase and become independent of propagation direction. Although this experiment is easy to conceive, it would be susceptible to several sources of error. If Vm were measured optically, the data would represent an average over a depth of a few hundred microns. Because the model predicts that Vm changes dramatically over such distances, the data would be difficult to interpret. Microelectrode measurements, on the other hand, are sensitive to capacitative coupling to the perfusing bath, and the degree of such coupling depends on the bath depth. The rapid depolarization phase of the action potential is particularly sensitive to electrode capacitance. Although it is possible to correct the data for the influence of electrode capacitance, these corrections would be crucial when comparing data measured at different bath depths.

We cannot conclude from our study that capillaries are not important during action potential propagation. Nor can we conclude that discontinuous propagation does not occur (particularly in diseased tissue). These factors may well play a role in propagation. We can conclude, however, that the influence of a perfusing bath must be taken into account when interpreting data showing differences in the shape of the action potential foot with propagation direction, even if Vm is measured 150 μm below the tissue surface. Therefore, differences in action potential shape with direction 1 12 cannot be taken as definitive evidence supporting discontinuous propagation or capillary effects if a perfusing bath is present. Finally, without additional experiments, we cannot exclude the possibility that in healthy tissue the difference in the shape of the action potential upstroke with propagation direction is simply an artifact of the way the tissue was perfused.

Figure 1. Schematic diagram showing the geometry of the tissue slab and the perfusing bath.

Figure 2. Isocontours of the transmembrane potential as a function of x and z for an action potential propagating in the longitudinal (A) and transverse (B) directions. z=0.5 mm is the tissue-bath interface.

Figure 3. Phase-plane plots of the action potential during longitudinal (L) and transverse (T) propagation, measured at the tissue-bath surface (A), 150 μm below the tissue-bath surface (B), and at the bottom of the slab (C). Dotted curve in panel A represents the action potential when the bath is not present. Insets show a magnified view of the action potential foot.

Table 1. Tissue Parameters for the Model

This research was supported by NIH Grant RO1HL57207. We thank the School of Engineering and Computer Science at Oakland University for their computational support.


The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Abbott, B. C. (1958). The positive and negative heat production associated with a nerve impulse. Proc. R. Soc. B Biol. Sci. 148, 149�. doi: 10.1098/rspb.1958.0012

Anishkina, A., Loukinb, S., Tengb, J., and Kung, C. (2014). Feeling the hidden mechanical forces in lipid bilayer is an original sense. Proc. Natl. Acad. Sci. U.S.A. 111, 7898�. doi: 10.1073/pnas.1313364111

Appali, R., van Rienen, U., and Heimburg, T. (2012). 𠇊 comparison of the Hodgkin-Huxley model and the soliton theory for the action potential in nerves,” in Advances in Planar Lipid Bilayers and Liposomes, Vol. 16, ed. A. Iglic (Elsevier: Advances in Planar Lipid Bilayers and Liposomes), 275�. doi: 10.1016/B978-0-12-396534-9.00009-X

Brd, C., and Destexhe, A. (2013). Generalized cable theory for neurons in complex and heterogeneous media. Phys. Rev. E 88:022709. doi: 10.1103/PhysRevE.88.022709

Brd, C., and Destexhe, A. (2016). “Generalized cable models of neurons and dendrites,” in Neuroscience in the 21st Century, eds D. W. Pfaff and N. D. Volkow (New York, NY: Springer), 1�.

Berg, R. W., Tving-Stauning, M., Balslev-Sørensen, J., and Jahnsen, H. (2017). Penetration of action potentials during collision in the median and lateral giant axons of invertebrates. Phys. Rev. X 7, 028002. doi: 10.1103/PhysRevX.7.028001

Bestel, R., Appali, R., van Rienen, U., and Thieleman, C. (2017). Effect of morphologic features of neurons on the extracellular potential: a simulation study using cable theory and electro-quasi-static equations. Neural Comput. 29, 2955�. doi: 10.1162/neco_a_01019

Brohawn, S. G., Campbell, E. B., and MacKinnon, R. (2014). Physical mechanism for gating and mechanosensitivity of the human TRAAK K+ channel. Nature 516, 126�. doi: 10.1038/nature14013

Bullock, T. H. (1958). 𠇎volution of neurophysiological mechanisms,” in Behavior and Evolution, eds A. Roe and G. G. Simpson (New Haven, CT: Yale University Press), 165�.

Bullock, T. H., Orkand, R., and Grinnell, A. (1977). Introduction to Nervous Systems. San Francisco, CA: W. H. Freeman and Co., 559.

Catterall, W. A. (2012). Voltage-gated sodium channels at 60: structure, function and pathophysiology. J. Physiol. 590, 2577�. doi: 10.1113/jphysiol.2011.224204

Catterall, W. A. (2013). Structure and function of voltage-gated sodium channels at atomic resolution. Exp. Physiol. 99, 35�. doi: 10.1113/expphysiol.2013.071969

Diesmann, M., Gewaltig, M. O., and Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature 402, 529�. doi: 10.1038/990101

Dowling, J. E. (1975). “LCNs in the vertebrate retina,” in Local Circuit Neurons, Vol. 13, ed. P. Rakic (Cambridge, MA: MIT press), 334�.

Dowling, J. E. (1992). Neurons and Networks – An Introduction to Neuroscience. Cambridge, MA: Belknap Press, 447.

El Hady, A., and Machta, B. B. (2015). Mechanical surface waves accompany action potential propagation. Nat. Commun. 6:6697. doi: 10.1038/ncomms7697

Follmann, R., Rosa, E., and Stein, W. (2015). Dynamics of signal propagation and collision in axons. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 92:032707. doi: 10.1103/PhysRevE.92.032707

Goodman, J. A., Kroenke, C. D., Bretthorst, G. L., Ackerman, J. J., and Neil, J. J. (2005). Sodium ion apparent diffusion coefficient in living rat brain. Magn. Reson. Med. 53, 1040�. doi: 10.1002/mrm.20444

Grundfest, H. (1959). 𠇎volution of conduction in the nervous system,” in Evolution of Nervous Control from Primitive Organisms to Man, ed. A. Bass (Washington, DC: American Association for the Advancement of Science), 43�.

Hamill, O. P., Marty, A., Neher, E., Sakmann, B., and Sigworth, F. J. (1981). Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflugers Arch. 391, 85�. doi: 10.1007/BF00656997

Haydon, P. G., and Winlow, W. (1982). Multipolar neurones of Lymnaea stagnalis – I. Multiple spike initiation sites and propagation failure allow neuronal compartmentalization. J. Comp. Physiol. 147, 503�. doi: 10.1007/BF00612016

Heimburg, T., and Jackson, A. D. (2005). On soliton propagation in biomembranes and nerves. Proc. Natl. Acad. Sci. U.S.A. 102, 9790�. doi: 10.1073/pnas.0503823102

Hille, B. (1992). Ion Channels of Excitable Membranes. Sunderland, MA: Sinauer.

Hodgkin, A. L. (1975). The optimum density of sodium channels in an unmyelinated nerve. Philos. Trans. R. Soc. Lond. B 270, 297�. doi: 10.1098/rstb.1975.0010

Hodgkin, A. L., and Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500�. doi: 10.1113/jphysiol.1952.sp004764

Holden, A. V., and Yoda, M. (1981). The effect of ionic channel density on neuronal function. J. Theor. Neurophysiol. 1, 60�.

Howarth, J. V. (1975). Heat production in non-myelinated nerves. Philos. Trans. R. Soc. B Biol. Sci. 270, 425�. doi: 10.1098/rstb.1975.0020

Howe, J. F., Loeser, J. D., and Calvin, W. H. (1977). Mechanosensitivity of dorsal root ganglia and chronically injured axons: a physiological basis for the radicular pain of nerve root compression. Pain 3, 25�. doi: 10.1016/0304-3959(77)90033-1

Johnson, A. S. (2015). The coupled action potential pulse (APPulse)–neural network efficiency from a synchronised oscillating lipid pulse hodgkin huxley action potential. EC Neurol. 2, 94�.

Johnson, A. S., and Winlow, W. (2017a). Computing action potentials by phase interference in realistic neural networks. EC Neurol. 5, 123�.

Johnson, A. S., and Winlow, W. (2017b). Shortcomings of current artificial nodal neural network models. EC Neurol. 4, 198�.

Ledergerber, D., and Larkum, M. E. (2012). The time window for generation of dendritic spikes by coincidence of action potentials and EPSPs is layer specific in somatosensory cortex. PLoS One 7:e33146. doi: 10.1371/journal.pone.0033146

Marban, E., Yamagishi, T., and Tomaselli, G. F. (1998). Structure and function of voltage-gated sodium channels. J. Physiol. 508, 647�. doi: 10.1111/j.1469-7793.1998.647bp.x

Marrero, H. G., and Lemos, J. (2007). “Loose-patch-clamp method,” in Patch Clamp Analysis: Advanced Techniques, ed. W. Walz (New York City, NY: Humana Press), 325�. doi: 10.1007/978-1-59745-492-6_11

Martinac, B. (2012). Mechanosensitive ion channels: an evolutionary and scientific tour de force in mechanobiology. Channels 6, 211�. doi: 10.4161/chan.22047

McCusker, E., Bagnéris, C., Naylor, C., Cole, A., D𠆚vanzo, N., Nichols, C., et al. (2012). Structure of a bacterial voltage-gated sodium channel pore reveals mechanisms of opening and closing. Nat. Commun. 3:1102. doi: 10.1038/ncomms2077

Moens, A. (1878). Die Pulscurve. Leiden: E. J. Brill.

Moujahid, A., d𠆚njou, A., Torrealdea, F. J., and Torrealdea, F. (2011). Energy and information in Hodgkin-Huxley neurons. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 83:031912. doi: 10.1103/PhysRevE.83.031912

Mussel, M., and Schneider, M. F. (2018). Similarities between action potentials and acoustic pulses in a van der Waals fluid. arXiv:1801.01367v1 [Preprint].

Poznanski, R. R. (2013). Mathematical Neuroscience. San Diego, CA: Academic Press.

Rall, W. (1962). Electrophysiology of a dendritic neuron model. Biophys. J. 2, 145�. doi: 10.1016/S0006-3495(62)86953-7

Rall, W. (1995). The Theoretical Foundations of Dendritic Function. Cambridge, MA: MIT Press.

Ritchie, J. M., and Keynes, R. D. (1985). The production and absorption of heat associated with electrical activity in nerve and electric organ. Q. Rev. Biophys. 18, 451�. doi: 10.1017/S0033583500005382

Roberts, A., and Bush, B. (1981). Neurones Without Impulses: Their Significance for Vertebrate and Invertebrate Nervous Systems. Society for Experimental Biology Seminar Series, 6. New York, NY: Cambridge University Press, 290.

Shannon, R. D. (1976). Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides. Acta Cryst. 32, 751�. doi: 10.1107/S0567739476001551

Shen, H., Zhou, Q., Pan, X., Li, Z., Wu, J., and Yan, N. (2017). Structure of a eukaryotic voltage-gated sodium channel at near-atomic resolution. Science 355:eaal4326. doi: 10.1126/science.aal4326

Shepherd, G. M. (1975). “Models of LCN function in the olfactory bulb,” in Local Circuit Neurons, Neurosciences Research Program Bulletin, Vol. 13, ed. P. Rakic (Cambridge, MA : MIT Press), 343�.

Shepherd, G. M. (1988). Neurobiology, 2nd Edn. Oxford: Oxford University Press, 689.

Stuart, G. J., and Sakman, B. (1994). Active propagation of somatic action potentials into neocortical pyramidal cell dendrites. Nature 367, 69�. doi: 10.1038/367069a0

Takahashi, K., Yusuke, M., and Keiji, N. (2016). Mechanosensitive ion channels. AIMS Biophys. 3, 63�. doi: 10.3934/biophy.2016.1.63

Tasaki, I., and Byrne, P. M. (1992). Heat production associated with a propagated impulse in bullfrog myelinated nerve fibers. Jpn. J. Physiol. 42, 805�. doi: 10.2170/jjphysiol.42.805

Tasaki, I., and Iwasa, K. (1982). Rapid pressure changes and surface displacements in the squid giant axon associated with production of action potentials. Jpn. J. Physiol. 32, 69�. doi: 10.2170/jjphysiol.32.69

Walz, W. (2007). Patch-Clamp Analysis. Totowa, NJ: Humana Press. doi: 10.1007/978-1-59745-492-6

Waxman, S. G., and Bennett, M. V. L. (1972). Relative conduction velocities of small myelinated and non-myelinated fibres in the central nervous system. Nat. New Biol. 238, 217�. doi: 10.1038/newbio238217a0

Winlow, W. (1990). “The “typical” neuron,” in Neuronal Communications, ed. W. Winlow (Manchester: Manchester University Press), 1𠄴.

Yu, F. H., and Catterall, W. A. (2003). Overview of the voltage-gated sodium channel family. Genome Biol. 4:207.

Zhang, X. C., Liu, Z., and Lie, J. (2016). From membrane tension to channel gating: a principal energy transfer mechanism for mechanosensitive channels. Protein Sci. 25, 1954�. doi: 10.1002/pro.3017

Keywords : sentience, action potentials, soliton, phase ternary computation, brain neural networks

Citation: Johnson AS and Winlow W (2018) The Soliton and the Action Potential – Primary Elements Underlying Sentience. Front. Physiol. 9:779. doi: 10.3389/fphys.2018.00779

Received: 31 January 2018 Accepted: 04 June 2018
Published: 25 June 2018.

Peter John Fraser, University of Aberdeen, United Kingdom

Tibor Kiss, Hungarian Academy of Sciences, Hungary
Fenglian Xu, Saint Louis University, United States

Copyright © 2018 Johnson and Winlow. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.