Talk:Hodgkin–Huxley model

"obsolete" vs "incomplete" assumptions of synapse function

Reading the paper, I'd go with "obsolete". The new findings of Naundorf et al. suggest a difference in quality, not in quantity (context-sensitive differential regulation vs. a simple all-or-nothing concept). The title basically say it all - for the vertebrate (mammalian?) cerebral cortext, Hodgkin-Huxley dynamics is a behavior that can as it seems only be achieved in vitro and does not occur in a natural state. Note that not all models are "obsolete" unless proven obsolete, but rather preliminary or tentative. Dysmorodrepanis 14:57, 9 June 2006 (UTC)

This paper is interesting, but saying that it invalidates the Hodgkin-Huxley model is really kind of off-base. The HH model should be viewed as basically an inter-spike interval model -- it was generated as a model of when a neuron would throw a spike that had more biochemical plausibility than a simple leaky integrate-and-fire neuron. The temporal response sharpening the article discusses an is interesting example of the general phenomenon of cortical response nonlinearities; it probably does point out something useful about one of the many things that the HH model either doesn't or can't replicate. But at this point there's no widely accepted biochemical model of spiking behavior that doesn't describe the same basic mechanisms and time-course as the HH model. saccade 10, June 2006.

The point is that the paper suggests cortical neurons work differently, and such behavior seems crucial in understanding what exactly happens up there (nonlinear behavior seems the key; at any rate, our understanding of cerebral function seems to run into a barrier when viewed from a linear standpoint). Suffice to say that in mammalian cerebral cortices (as opposed to squid giant axons), the HH model doesn't really seem to be a particular adequate description. Dysmorodrepanis 12:08, 11 June 2006 (UTC)

It does raise an intriguing point, but it doesn't abandon most of the machinery of the HH model -- it suggests a change in the behavior of voltage gated ion channels, but doesn't question that they exist. Granted, the HH model does imply statistically independent stochastic gate behavior, which they are suggesting might not be a good assumption in cortical neurons. But bear in mind that most of the molecular machinery implied by the HH model has actually been found and independently observed -- it's a very well-validated model as far as what it was intended to model goes. Anyway, until the consensus in the molecular neuroscience community is that the HH model isn't really useful anymore, I think it would be kind of premature for Wikipedia to declare it obsolete. I know people who still do actual work with it, so I doubt it's on its way out just yet. saccade 11, June 2006.

Okay, to get technical on you guys, the original HH model is of type II excitability, where spikes occur through a Hopf bifurcation, while cortical APs are type I excitable, so spikes occur through a saddle-node bifurcation. So we know that the original HH model is not an accurate model of spike generation in cortical neurons, and no one would claim that it is. However, modified versions (that include A-type potassium currents) are believed to be accurate. Dysmorodrepanis, all of these models are fundamentally nonlinear, including the original HH model. The Naundorf et al. paper that claims to show cooperativity between Na+ channels is a controversial result, and in my opinion is likely an artifact. IIRC, the same results can be obtained using a standard HH model, if one takes into account the action potential being initiated at axon initial segment, which has been experimentally observed (I don't have the refs offhand). I don't know the full details, but I know of a group that will be publishing a rebuttal of Naundorf et al. soon (as of Dec. 2006). In any case, it's a recent paper, and it's a controversial result, so I don't think it belongs here in Wikipedia. evilrobotxoxo Dec 19, 2006.

So I actually have a reference to back this up-- http://jacknife.med.yale.edu/spikeclub/mc_resp.pdf -- in the mean time, I removed the references to the Naundorf paper entirely.Evilrobotxoxo 19:51, 19 December 2006 (UTC)

Link to FitzHugh-Nagumo model

I added a link to the FitzHugh-Nagumo model, this article does not exist yet in the English wikipedia. A German article is available at http://de.wikipedia.org/wiki/FitzHugh-Nagumo-Modell.

--193.175.8.13 13:13, 28 November 2006 (UTC)

a few problems with this article

This article has a few things that are not clearly explained and a few mistakes. I'm pretty sure the role of the Na+/K+ transporter was not modeled by H and H as a current. Basically, it was only reflected in the reversal potentials of the different conductances. Also, this article should explicitly mention what the main conductances were, etc. I'll make some changes when I get a chance, but I wanted to notify first. Evilrobotxoxo 03:54, 20 December 2006 (UTC)

• The role of the NaK transporter was not modeled in the original paper. The article, I guess, is about Hodgkin-Huxley type models in use today. Should we change the title to reflect that? Today, when we hear someone mention HH models, they most likely mean HH-type models (as indicated in the figure caption).--Zyryab 16:30, 12 April 2007 (UTC)

Scrambled references & solitons?!?

It seems that the references are a bit scrambled. I'm too much of a Wikipedia n00b to know why and fix them.

Also, this business about the soliton model of nerve conduction seems a bit out of place seeing as how it's completely outside of mainstream neuroscience. —Preceding unsigned comment added by 76.167.214.133 (talk) 09:51, 24 November 2007 (UTC)

I agree, the soliton model is not part of mainstream neuroscience, and it does not belong on this page. Science articles in wikipedia should reflect the current consensus, not controversial ideas that are not yet accepted. Even if the idea eventually turns out to be correct, I don't think it's well-supported enough to be included here.Evilrobotxoxo (talk) 01:04, 9 December 2007 (UTC)

The more I think about it, that soliton stuff really doesn't belong here, so I'll delete it. If anyone objects, I think they can reverse the changes and we can discuss it.Evilrobotxoxo (talk) 01:07, 9 December 2007 (UTC)

HH isn't perfect - that's what most of what you deleted is about (a criticism section, if you will). The soliton model is a passing reference, and you can delete that passing reference if you like. Alternative models can be found in the main article:Biological neuron models link, so we don't need to discuss every single one here, particularly not a rather brand new one like the soliton model. By the way, the soliton model is pretty awesome (it has actually been proposed in a minor way in the 80s, but nobody seemed to take note - more work on melting transitions of the membrane was needed) and has supporting evidence in both invertebrate and mammalian, myelinated and unsheathed neurons. But I agree that it doesn't belong here. In summary, I reverted and removed the soliton reference. SamuelRiv (talk) 01:15, 9 December 2007 (UTC)

Come to think of it, the direct link to Fitzhugh-Nagumo bothers me, mainly because the profs at CWRU seemed to prefer Morris-Lecar as a simplified model, as it preserved most direct biological circuit analogues. Maybe that section should be merged into problems and alternatives. I will do that next. SamuelRiv (talk) 01:23, 9 December 2007 (UTC)

On the topic of HH vs. FitzHugh-Nagumo and Morris-Lecar, I don't think was appropriate that those were listed as "improvements." They're simplifications, which is not the same thing, so I'm glad you fixed that part. As far as the HH criticism section, I honestly don't think that's appropriate either. The HH model is a simplified, macroscopic model. It doesn't attempt to explain everything going on at the level of exact mechanisms with individual lipid and channel molecules. The idea that it's a "problem" that the HH model doesn't take into account local thickening of the membrane in its capacitance term is flat out absurd--did you know that something like 20% of membrane capacitance in biological membranes is derived from reorientation of charged/polar groups on membrane proteins, and is therefore nonlinear? The HH model doesn't take that into account either! Even more significantly, the HH model didn't get the kinetics of Na+ channel inactivation quite right. It's also deterministic, not taking into account stochastic effects of single channel openings and closings. The point is, it doesn't claim to perfectly capture all phenomena below its level of abstraction; it's a model that captures the major features of membrane excitability in compact mathematical form. As far as the criticisms listed, they are not the most valid criticisms one could make, and they're not even really criticisms at all because they simply operate at a different level of abstraction than the HH model. They're also thinly veiled plugs for the soliton model, which I just don't think is appropriate. There are actual flaws with the soliton model that are far more serious than the pseudoflaws listed here. If you or someone else wanted to put together a more comprehensive, balanced discussion of the merits and drawbacks of the HH model that included the soliton stuff, that might be appropriate. You could start with this: http://linkinghub.elsevier.com/retrieve/pii/S0166223602022786

But in its current state, I think it's just more appropriate if it were left out entirely.Evilrobotxoxo (talk) 15:14, 9 December 2007 (UTC)

Maybe it's just conflicting philosophies, but could you please stop deleting relevant information, like the end bit about more computationally or analytically simple models, when you make these judgements. Deleting an entire section shows up in bold on our watchlists for a reason. See also comments on clash of disciplines in Talk:Soliton model. Finally, I fully intend to restore what you deleted once I get to the office and can add a few criticisms that aren't directly tied to the soliton model. SamuelRiv (talk) 18:35, 9 December 2007 (UTC)

I apologize for deleting stuff without agreement first--I'm new to editing stuff on wikipedia, and I don't know how all the etiquette works. However, I'm not new to neurophysiology or biophysics, which I have been studying for over 12 years, including a PhD. I'm even in the unenviable position of being able to recite a significant portion of the shaker channel sequence from memory, a fate I wish on no one ;) So I understand your perspective in the "clash of disciplines" section on the other page, though I actually have a different interpretation of what's going on. However, I don't want to be antagonistic on this--I think we should work together to improve this article, so I won't just edit things without discussion first. That said, several of the points you raise contain factual errors, and there are other things I think should be altered stylistically.

The Hodgkin-Huxley model is widely accepted in the scientific community. However some problems remain:

I think calling them "problems" is overstating things. I think it's more appropriate to use the phrase "limitations" or something along those lines. This comes down to your idea of what models are in science. The HH model does not claim to reflect the immutable laws of the universe--it's explicitly fit to data. It's simply a false comparison to compare it to Newton's laws, Maxwell's equations, or whatever other things were "overthrown" by 20th-century physics. In this case, it's a question of scale. Everybody knows that we could model things at a smaller scale, and people have done molecular dynamics simulations of ion channels, etc. I have personally done modeling work at smaller scales than HH. But the existence of models at those scales is not a "problem" for the HH model.

* The shape of a neuron is modeled as a perfect sphere, whereas real neurons will usually have multiple input dendrites and a cylindrical axon, which changes the electrodynamics.

That's simply not true. Remember the original HH model was of a squid axon, not a neuron, and HH-type models are all about the "isopotential compartment." There are whole suites of modeling software to generate HH-type models in all sorts of complex geometries.

* Ion channel dynamics in the model do not usually describe experimental results and generally cannot be adapted to model the stochastic nature of an ion current.

Actually, channel dynamics in modern HH-type models typically are fit to data, and people have done modeling with stochastic single-channel currents. Of course, then you're getting outside the scope of HH models, but the typical solution in practice is just to introduce a random noise term into your model.

* It can be experimentally observed that a signal traveling along a neuron results in a slight local thickening of the membrane and a force acting outwards; this should lead to a change in capacity which is not captured by the model.

The question is, is this relevant? Remember, the HH model is an approximation. As I said before, there are more significant problems than this with the treatment of protein-containing lipid bilayers as capacitors in general. If you've ever done numerical simulations of the HH equations, try changing the capacitance term a little. I think you'll be surprised how little the solutions differ when capacitance is altered pretty significantly.

* The circuit model of a neuron cannot usually describe thermodynamic and temperature-dependent anomalies that occur during an action potential.

That may be true, but models at the HH scale don't claim to be able to. It's fair to describe this as a limitation of the model, but describing it as a "problem" suggests that you think the model should be able to, implying that you don't really understand the scale of the model very well.

Furthermore, the effects of many drugs and external stimuli on the nervous system have not been fully explained in this circuit model of the neuron. Research is ongoing to resolve these discrepancies.

That's a very, very bold claim to make, that holes in our understanding of anesthetic action somehow imply phenomena that can't be explained by HH-type models. If we want to be serious here, how do you distinguish between something that doesn't fit the model and something that fits the model in a way that we haven't figured out yet? There are so many places that a given small molecule agent could act that it's practically impossible to rule them all out. As far as membrane-intercalating agents disrupting voltage-dependent gating, that's been experimentally demonstrated. So there's no obvious reason why we need to resort to more exotic ideas to explain their action.

Other versions of the Hodgkin-Huxley model have also been developed. Some of these take into account new knowledge of the workings of neurons, while others were developed to be computationally more efficient, either through mathematical abstraction or simplifications of the circuit model.

I think it should be rephrased to stress that the HH model was developed for modeling biophysical phenomena in a single cell, but people who model populations of cells tend to use more abstract models, both in terms of the model of membrane excitability and cell geometry.

Anyway, let's figure out what we both think would be appropriate to list in the article.Evilrobotxoxo (talk) 14:44, 10 December 2007 (UTC)

Welcome, then! I'm fairly new myself, but I've learned a lot in the past month by seriously involving myself in editing. Anyway, as far as etiquette goes, the only thing that needs to be taken seriously is to avoid "edit wars", where people revert other people's contributions/deletions in an endless cycle. My philosophy has been that if it's factual and relevant, it deserves to stay, and if people make good points, then incorporate those in to your next edit. So with your edits, I felt that you had deleted factual and relevant information, but made good points, so I reverted and then changed things to hopefully make them acceptable.

The other rule that you have used well is to be bold in editing, which you have done and I think should continue to do. Just know that flat deletions of entire sections, from my perspective, would require a bit more justification on scientific articles.

Now as far as this goes, I have no problems with changes in vocabulary - I basically just tried to keep things as close to the original wording as possible while making edits, as this article is slightly beyond my expertise as I don't use HH regularly (I'm a networks guy). So feel free to edit wording as you see fit.

In terms of claims, if HH were trying to simply fit data, it would be FitzHugh-Nagumo or some polynomial regression. But HH also provides a theoretical underpinning that the circuit model is in reality what occurs, which is why a criticism section must have some critiques of the circuit model itself.

Shape of neuron: I specified that a standard circuit model doesn't account for geometry, but it should be clarified that it can be made to. A lot of the information, anyway, is in the biological neuron models article (which I created mostly from Koch's book, and would love some input on).

I have no problem if you delete the reference to "drugs and external stimuli". I don't know what I was thinking when I wrote that (maybe I'll do it myself).

Go ahead and rephrase the computation section, but note that HH combined with neurotransmitter dynamics is used in network computations with computer arrays. I'm not familiar with this area of research, but it's definitely done. SamuelRiv (talk) 16:44, 10 December 2007 (UTC)

I'll do some editing later on when I have more time, which will unfortunately be next week. Also, John Rinzel (who knows more about HH models than either of us) is writing an article for scholarpedia.org...I don't know how it works, but maybe that can be borrowed from? Anyway, you're correct that HH does make some specific claims about what's going on in that it's a conductance-based model and some others are not, but the actual behavior of the channels is entirely fit to data. I think that soliton-type stuff is part of the underlying mechanism of how the channels operate, so if anything, those effects are already taken into account by the model fitting. They're simply not explained mechanistically. On geometry, a standard circuit model actually approximates a neuron as a point, not a sphere. I think the best approach for the time being is for me to simply delete anything that I think is inappropriate, and just leave the section incomplete until someone can fill it in later. Evilrobotxoxo (talk) 18:13, 10 December 2007 (UTC)

Bit more explanation please

I doubt if anyone could understand this article unless they were already an expert in neural physiology, in which case they would not need to read it in the first place. I find it odd that there are batteries and ion pumps all in the same direction. Is the idea that charge is being pushed backward through the batteries? Tuntable (talk) 07:39, 28 June 2013 (UTC)

I guess I would qualify as an expert in the source material, and this is a tough page even for me. I'm not even sure that I understand the question you asked, but I think the answer is that the batteries represent a voltage difference, and ions go through the ion channels down the voltage gradient (forwards through the batteries, as it were), unless the concentration gradient (the difference in the concentration of the ion, between one side of the membrane and the other) is large enough to move the ions backwards through the batteries, as it were. --Tryptofish (talk) 19:26, 28 June 2013 (UTC)

Enlarging on that: Some of our articles are about technical things that are nearly impossible to understand without background knowledge -- this is one of them. The ion pumps and batteries are really separate things. The batteries arise from passive ion channels in the presence of ion concentration differences; see our membrane potential article for at least an attempt at an explanation. The direction shown for the pump is really arbitrary, because ions are actually pumped in both directions. One could make an argument that the direction ought to be shown the opposite way, because the most important pump is the sodium-potassium exchanger, which pumps three sodiums out for every two potassiums that come in. In any case, the pump currents are often omitted when the HH model is simulated, because they are quite small in comparison to the ion-channel and capacitive currents. The pumps operate over time to set up the concentration gradients, but they don't contribute dynamically to an individual action potential. Looie496 (talk) 15:23, 29 June 2013 (UTC)

I guess there's a broader question implicit here, which is whether or not it's a good thing to have pages like this one, that require background knowledge, since we are writing for a general audience. It seems to me that a lot of science fields have pages like this (for example, many pages in physics and math), so it's not like this one is an outlier. Myself, I'm not sure what the answer really is. --Tryptofish (talk) 16:25, 29 June 2013 (UTC)

I don't think we need to write only for a general audience -- each article should be written at a level appropriate to the set of readers who are likely to want to know about the topic. My view is that there should always be at least an introductory paragraph that puts a topic in context for readers with minimal background knowledge, but beyond that, articles on specialized topics should be allowed to make greater demands than articles on broad topics. This article should do a better job of explaining in simple terms why the work was worth a Nobel prize, but I don't think the equations are out of place. Looie496 (talk) 16:43, 29 June 2013 (UTC)

As a student of physics and math trying to understand this subject, it would be excellent to have a well written version of this article. However, it is difficult to follow at the moment. I'm particularly concerned with the ionic current characterization section:

For example, it would be good to have what exactly the rate constants (alpha, beta) are explicitly.

Additionally, it would be clearer if the values were written explicitly with their dependencies.

I would make these changes, but I'm new to Wikipedia and not an expert on the subject, so I hesitate to do so Differintegral 18:50, 1 May 2014 (UTC)

Problems with the mathematical analysis section

I'm new to serious edits of important wikipedia pages, but I am a 10+ year expert on dynamical systems theory and mathematical models in physiology, especially Hodgkin-Huxley. As it stands, the math analysis section is too brief while attempting to get into too much sophistication for it to be valuable (or correct). There are some factual errors, or at least accidentally misleading implications due to being too brief, especially in the attempt to describe the Center Manifold analysis. That is an extremely advanced mathematical topic and needs a delicate treatment to be helpful. It is also missing any citations. I don't think Center Manifolds are sufficiently relevant or accessible to the existing and popular treatments of the H-H model in the literature to be appropriate for either a general audience or even a typical student of computational modeling. I'd like to suggest it is reduced to a sentence about how Center Manifold theory can be used to study the bifurcation from silence to spiking, including characterization of the limit cycle that is created; then a citation to http://en.wikipedia.org/wiki/Center_manifold. However, I can't think of a highly recognized peer-reviewed journal article or book specifically about the center manifold analysis of this particular model. I'm not sure it is as clean-cut as the author of that section suggests, and the mathematical mistakes suggest the section's author is not really an expert either. If and when this topic shows up in Scholarpedia I suggest we just link to that for more technical details. Thoughts? If no-one comments then I'll make an edit soon, myself. --Robclewley (talk) 02:18, 8 April 2014 (UTC)

Not to mention the fact that the total current equation is wrong. I think whoever wrote this got confused by trying to match the model to the schematic, which features another current, the pump current I_p, but which lack the injected current. I am not going to argue endlessly with electrophysiologists who do not understand differential equations - anyone who can do maths and wants the correct eqns can look it up in Keener and Sneyd or Weiss. 2A01:CB0C:CD:D800:FCA0:D487:955A:F4D8 (talk) 14:42, 5 February 2020 (UTC)

Modifying the Voltage Gated Ion Channels Section

I explicitly wrote out what $\alpha$ and $/beta$ are, and added a reference for the general form. If someone could double-check that the voltage conventions I used are right, since it wasn't clear to me what the conventions being used in this article are. This may be due to my lack of experience, but we may want to edit basic components to make this clearer to someone trying to understand this material for the first time Differintegral (talk 19:05, 8 May 2014 (UTC)