https://doi.org/10.36866/pn.113.6

For science to thrive, we must always be willing embrace and facilitate substantive debate. Even the long established and most well-regarded of our theories must be open to challenge and withstand constant experimental scrutiny. “Mysteries of the action potential” in Physiology News 111 stoked such a debate, and we received several letters to the editor which we have published together with responses from the authors.

Action potential conduction is not a mystery

James A Fraser
Department of Physiology, Development and Neuroscience, University of Cambridge, UK

Ron R Horgan
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK

The article “mysteries of the action potential” (Physiology News 111, p.38-41) suggests that action potential propagation cannot be understood by cable theory. We are pleased to reassure readers that it can be; instead, the problem appears to be that the article’s authors do not understand cable theory.

At the heart of Johnson and Winlow’s article is a complete misunderstanding of how electrical conduction works. Thus, the authors repeatedly claim that the mechanism of action potential propagation as described by cable theory is either impossible or too slow to account for nerve conduction. They state, for example, that “the physical properties of Na+ ions cannot allow flow of charge from one ion channel to the next in the time available” and “a conservative simple Speed-Time calculation suggests that the maximum speed Na+ ions can travel between channels is less than a thousandth of what is necessary for propagation.” These statements are simply wrong, and it is surprising that they have been published.

Na+ ions do not quickly diffuse from one ion channel to the next, but nor do they need to. Instead, as Na+ ions enter the axon they cause an increase in local net positive charge density. This generates an electric field (a voltage gradient) that drives a current along the axon. Johnson and Winlow’s statements above appear to refer to the drift velocity of the injected Na+ ions; to correctly understand how one ion channel might trigger the next, they must instead consider the electrical current that results from this Na+ entry. The current is carried by all mobile ions in the electrolyte and, just as in any conductor, the nature of the charge carrier is immaterial except in how it determines the electrical conductivity. This conductivity may be measured or calculated easily. As it happens, K+ is the most prevalent intracellular ion and hence the principle charge carrier. The K+ concentration is many orders of magnitude larger than that of the newly injected Na+ ions, perhaps explaining why Johnson and Winlow’s calculations based on Na+ mobility are incorrect by a similar margin.

Cable theory then derives from similar statements of very basic physics that apply to transmission lines in general: put simply, ionic charges produce an electric field; ionic solutions are electrical conductors; conductors separated by thin insulators have a capacitance. The axon is, in this respect, a high loss coaxial cable. The theory that describes such cables has been known for well over 100 years. Its application to nerve conduction can be derived fairly straightforwardly (e.g. Rall, 2011). Indeed, more recent work has demonstrated that extensions of cable theory reproduce and predict excitability and conduction velocity even in the more complex membrane architecture of skeletal muscle (Pedersen et al., 2011; Fraser et al., 2011).

Thus, the proposed soliton model is unnecessary. It is not described in sufficient detail to be fully understood or analysed. However, there are some obvious flaws in the theory. What roles do K+ channels play? Would these sound-like waves not decay in amplitude where cable diameters increased, such as from a nerve dendrite to its soma? Why do action potentials travelling in opposite directions cease at the point of collision, when sound waves would pass through one another?

In conclusion, conduction in biological tissues is well described by cable theory. There is certainly more to learn about excitable tissues under physiological and pathological conditions. However, those studying these systems should seek to understand, rather than reinvent, the relationships between voltage, conductance, capacitance and current.

References

Fraser JA, Huang CL-H, Pedersen TH (2011). Relationships between resting conductances, excitability, and t-system ionic homeostasis in skeletal muscle. Journal of General Physiology 138, 95–116.
Pedersen TH, Huang CL-H, Fraser JA (2011). An analysis of the relationships between subthreshold electrical properties and excitability in skeletal muscle. Journal of General Physiology 138, 73–93.
Rall W (2011). Core Conductor Theory and Cable Properties of Neurons. In Comprehensive Physiology. Hoboken, NJ, USA: John Wiley & Sons, Inc.

Classical experiments had already “demystified” the action potential

David Miller
School of Life Sciences, University of Glasgow, UK; History and Archives Committee, The Physiological Society

The electrical nature of the action potential is nothing like so “mysterious” as Johnson and Winlow suggest (PN 111, p.38-41). James Fraser and Ron Horgan have addressed one aspect, explaining the true nature of electrotonic conduction in nerve or muscle fibres. Here, I detail further physiological phenomena that contradict the “soliton” concept of action potential
(AP) propagation.

The authors perhaps overlooked long-known observations such as the macroscopically detectable intra- and extra-cellular local circuit currents that spread ahead of the AP. Thus, reducing extracellular resistance (ro) increases the AP propagation speed, just as cable theory predicts. Hodgkin (1939) showed this by placing a nerve prep (crab or squid single axons) on platinum plates to reduce ro, whereas increasing ro by oil bath immersion or air exposure slowed the AP. None of this is explicable with the mechanical “soliton” that would proceed unaffected by these “remote” extracellular modifications having only electrical “relevance”.

A “soliton” account of saltatory conduction in myelinated fibres (see Johnson & Winlow, 2018) is also unpersuasive. Their model offers no obvious role for axoplasmic resistance and thus in explaining how a greater diameter increases conduction velocity (CV) in myelinated and unmyelinated fibres. Cable Theory accurately predicts the linear relationship of diameter to CV in myelinated axons as against the square-law relationship for unmyelinated fibres. Such modelling predicts the evolutionarily optimised ratio of 0.6 of conducting “core” to overall insulating “sleeve” diameter, as observed in peripheral myelinated axons. And last, myelination theoretically becomes disadvantageous in the smallest axons (Rushton, 1951, Fig. 5): indeed, below that predicted size, myelination is not observed. Rushton (1951) detailed all this: it cannot be accounted for by the “soliton”.

The ‘soliton’ model also fails to account for liminal length considerations. Again, Cable Theory reveals why a minimum area of membrane must be activated to sustain propagation. Sufficient current – thus a cylindrical length of axon membrane with
its complement of activated channels – is required to discharge the capacitance of the neighbouring region sufficiently to bring it above threshold: the liminal length for an excitable cell.

A final twist is that the authors perhaps overlooked one of the very first observations relevant to our understanding of the intrinsically electrical nature of activity in nerve and muscle. This is the phenomenon of “ephaptic” excitation first described by Galvani (e.g. 1794), as used to be demonstrated by some of us to junior Physiology and Medicine students. I refer to the experiment where extrinsic current flow around an activated frog gastrocnemius muscle, triggered via its sciatic nerve, is sufficient to excite a second sciatic- gastrocnemius preparation: the second nerve is merely draped over the first muscle. The first sciatic can be activated by a squeeze with forceps: the resulting injury potential accounts for the activation in that nerve, thence the first muscle and the second sciatic and gastrocnemius activate in turn. None of this need involve batteries and electrodes. Galvani’s observation contributed to contemporary consideration of whether “animal electricity” was intrinsically different from that produced by physico-chemical means (“Voltaic piles” etc.). Any “mechanical” soliton propagation/excitation between the anatomically separate first muscle and second nerve can obviously be discounted.

None of these long-established phenomena can plausibly be accounted for in the “soliton” scheme. By contrast, Cable Theory provides a coherent, testable and quantifiable account of all of them.

I suggest that any mechanical disturbance of the transmembrane channel proteins that accompanies the AP is itself an epiphenomenon. One expects the deformation of activated channels that allows ions to pass through would have mechanical sequelae. Channel proteins sit in a voltage field of 100 mV expressed across 10 nm, or 100 kV/cm: a huge field strength. Deformation upon voltage change is very understandable. But expecting such nanometre-scale perturbations to propagate over a millimetre or more of internode in larger myelinated axons surely stretches credulity. (The internodal length in larger axons is some 100,000 times the axonal membrane thickness, or more). That a mechanical wave generated at nm dimensions can propagate over such distances would require a “stiffness” of the lipid bilayer – itself a dynamic, fluid, physical phase – that cannot be credible.

References

Galvani L (1794). Dell’uso e dell’attività dell’arco conduttore nelle contrazioni dei musoli. San Tommaso d’Aquino, Bologna.
Hodgkin AL (1939). The relation between conduction velocity and the electrical resistance outside a nerve fibre. Journal of Physiology 94, 560-570.
Johnson AS, Winlow W (2018). The soliton and the action potential – primary elements underlying sentience. Frontiers in Physiology 9, 779.
DOI: 10.3389/fphys.2018.00779.
Rushton WAH (1951). A theory of the effects of fibre size in medullated nerve. Journal of Physiology 115, 101-122.

Responses from the feature authors

Andrew Johnson
Neuroscience & Physiology Consultants (NPC) Newton, France
Bill Winlow
University of Naples Federico II, Italy; University of Liverpool, UK & NPC Newton, UK

Our general response to the letters above is as follows. Point-by-point specific responses to each letter are given below.

At issue is not whether the action potential can be understood by Cable Theory but is it correct to do so. A correlation with Cable Theory is not evidence, unless the underlying molecular activity matches the model and it does not.

The APPulse is a soliton pulse synchronised with the action potential; it will therefore have many of the same attributes, because any model of the nerve impulse must account for the activity produced at the molecular level of the membrane. In either the APPulse or Cable Theory the ion channel properties are identical and opening of the channels takes place in both models.

However, the Hodgkin and Huxley (HH) model does not include a modern understanding of either the membrane or the ion channels because this knowledge was unknown at that time and our article presented evidence unavailable to them. In particular, we now have detailed knowledge of the ion channel structure and function, as well as channel reconfigurations and subsequent shape changes and the mechanical changes that can cause them to open. In the HH model, the absence of closely aligned ion channels gives no coherent mechanism for them to be sequentially activated or to explain the refractory period of single ion channels. In contrast, in the APPulse a detailed description is given of the electrostatic and geometric changes that match precisely the entropy changes, the morphology changes and the “electrical” changes.

What is not explained by HH is the destiny of the entropy derived from the opening of the ion gates – if they are attached to the membrane then the membrane will move and it is logical to conclude that this entropy is transferred to the ever-present soliton accompanying the action potential. In Cable Theory and during the APPulse the membrane would inevitably move. Only the APPulse explains the entropy change. Furthermore, the mathematics and properties of solitons are now much better understood. We now know that a soliton always accompanies an action potential and solitons have recently been visualised using interferometric imaging
(Ling et al., 2018).

Thus, there is now overwhelming evidence that a soliton travels with the action potential. Movement of ion channels will therefore cause movement in the membrane in both models. We know the soliton is synchronised to the action potential, arriving just before the ion channel opens. The major difference between the APPulse and Cable Theory is the mechanism of activation of the ion channels – mechanical or electrical. Given that there will always be a soliton present it is therefore logical that this is the mechanism for activation.

The APPulse satisfies the requirements of entropy and transmission according to the knowledge we now possess of the mechanisms available at the membrane (for more detail, see Johnson and Winlow, 2018). Because the APPulse is based upon the action potential, it contains many of its elements with the addition of the synchronised soliton and its activation of ion channels by mechanical force.
In scientific research there are often conflicts between groups of scientists supporting opposing theories, but quite often the opposing theories unify and a composite hypothesis emerges later. For example, in the 1950s it had just become widely accepted that synaptic transmission was by chemical rather than electrical means when electrical transmission was conclusively demonstrated in the crayfish by Furshpan and Potter (1957; 1959). We have therefore used current data to illuminate the older and well-verified HH model and have combined those ideas into the concept of the APPulse – a useful working model – although others may suggest that no such compromise is possible and that nerve cells communicate with mechanical pulses, not electrical pulses (see Fox, 2018 for background).

Responses to James A Fraser & Ron R Horgan

Paragraph 1: No, we do not agree that Cable Theory can provide the explanation of propagation and we think there is still some mystery to the underlying mechanism, best explained with soliton theory.

Paragraphs 2 & 3: We dispute that inter-ionic charge effects at the site of ion release would make any difference. Local charge activity could not affect the ion channels. When Cable Theory was proposed inter-channel distances and activity were not known as they now are. Charged Na+ ions exiting from an ion gate produce a local field. This field will affect nearby ions (any ions) but it is not directional along the axon but into the cytoplasm and any resultant field would dissipate quickly because of entropy lost. For charge to propagate along a membrane, anions would have to move correspondingly and directionally without interaction of cations as in near-adiabatic processes. The only other forces are diffusional.

Paragraph 4: This is not an argument, as once again both models would almost certainly apply. In cardiac muscle one of the more important aspects is to consider how the elements that compose the excitation-contraction coupling synchronise. In the APPulse all elements are synchronised by the mechanical activation of the ion channels to the contraction of the muscle. In accepting Cable Theory the basic mechanical action of the heart muscle to be synchronised to the cardiac action potential is overlooked.

Paragraph 5: There is substantial evidence in the biophysical literature to describe solitons. In answer to the question “Why do action potentials travelling in opposite directions cease at the point of collision, when sound waves would pass through one another?”, solitons lose entropy to their surroundings. Collision of two APPulses results in areas around the collision in both directions becoming refractory and the entropy of the soliton will decay without entropy recharge from the ion channels. Cancellation of the APPulse by another is not therefore a property of the soliton itself.

Hodgkin and Huxley only suggested Cable Theory as a model not as the mechanism it has become in accepted orthodoxy. We now know the most likely configurations of the ion channels and the selector site for activation of Na+ channels. The horizontally directed expansion of the activated channels is the only mechanism that can add entropy to the always present soliton. There is no evidence indicating that charge can spread from one ion channel to the next in the timing required. Cable Theory does not explain the soliton nor the entropy changes but the APPulse does.

Responses to David Miller

Paragraphs 1 & 2: Ion channels open on membrane potential change and this is not disputed. There would be no difference between the two models in this case.

Paragraph 3: Rushton himself describes the relationship as a coincidence and in any case the rules would apply similarly to a pulse.

Paragraph 4: This would apply equally to a soliton flow along a cylinder. The activation of a pulse in a cylinder requires sufficient entropy – the same entropy provided by the ion gates.

Paragraph 5: As stated, ion channels are opened by both change in potential and mechanics. This is exactly the same in both HH and the APPulse. Any stimulation would cause contraction in either model.

Paragraph 6: All these long-established phenomena can be accounted for by the APPulse as explained above.

Paragraph 7: The soliton is a pulse travelling along the surface of a cylinder in which entropy is directed only in the direction of propagation. This is an entropy-closed system due to the surface linking of the impulse around the circumference during propagation. Loss of entropy in such a situation is minimal. In addition our knowledge of membranes indicates that a soliton can propagate very long distances. Contrast this with the situation in Cable Theory where charge is proposed to spread this same distance – no local currents could achieve this. For propagation of the impulse between ion channels the soliton is the best candidate.

References

Fox D (2018). The brain, reimagined. Scientific American 318(4), 60-67.
Furshpan EJ, Potter DD (1957). Mechanism of nerve-impulse transmission at a crayfish synapse. Nature 180, 342-343.
Furshpan EJ, Potter DD (1959). Transmission at the giant motor synapses of the crayfish. Journal of Physiology 145(2), 289-325.
Johnson AS, Winlow W (2018). The soliton and the action potential – primary elements underlying sentience. Frontiers in Physiology 9, 779. DOI: 10.3389/fphys.2018.00779.
Ling T et al. (2018). Full-field interferometric imaging of propagating action potentials. arXiv:1807.03269 [physics.bio-ph].