Action potential and Na+

[somasimple]

Hi All,

It is a fact that Na+ ions cross the membrane and enter the cell during the rising phase of the action potential. The process happens because Na ions channels are open.
Then the ions channels becomes inactivated/closed for a while.

What happens to the Na+ ions that entered the cell?

[Renge Ishyo]

The sodium ions stay there for the time being until they are actively pumped back out of the cell by the Na/K ATPase pump.

What happens during an action potential is sodium atoms briefly flood into the cell down their concentration gradient which makes the inside of the cell a bit more positive than normal. To restore the membrane potential back to normal, potassium channels are opened shortly after the sodium ion channels are opened and potassium flows out of the cell down its concentration gradient (carrying its positive charge with it, hence putting the inside of the cell back to its original negative state after it leaves). The sodium is then pumped out, and the potassium is pumped back in using the ATP dependent pumps which completes the cycle.

[somasimple]

This explanation contradicts twice the facts:

Na K pumps are not involved in AP and it is a slow process.
The graph doesn't lie, the decay is also... fast.

[Andy Resnick]

Hi All,

It is a fact that Na+ ions cross the membrane and enter the cell during the rising phase of the action potential. The process happens because Na ions channels are open.
Then the ions channels becomes inactivated/closed for a while.

What happens to the Na+ ions that entered the cell?

Lots of things happen during an action potential- a transient regenerative spike in the resting membrane potential that changes from around - 60 mV to +20 mV. Some ion channels cause the spike, some channels respond to the spike.

The resting potential is caused by a concentration imbalance between sodium (high outside, low inside) and potassium (low outside, high inside) and is maintained by the Na-K ATPase combined with a potassium channel.

The action potential is caused by changes to the sdium and potassium conductance, leading to a small influx of sodium and efflux of potassium, corresponding to depolarization. It's important to note that small Na and K ion currents are sufficient to cause large changes in the membrane potential.

The channels that allow depolarization and repolarization are voltage-gated ion channels- channels do not use ATP to move ions, but allow passive diffusion of ions through the membrane as a function of the membrane potential. Hodgkin and Huxley,in 1952 using squid axons, generated a model system demonstrating how an action potential is generated by having voltage-gated changes to ion conductance.

Briefly, the rapid increase in sodium conductance causes the depolarizing phase as sodium influxes. Opposing this is hyperpolarizing potassium (and chloride) channels, which must be overcome in order to initiate an action potential. The delayed potassium conductance change is what brings about repolarization. Potassium channels determine the resting potential and terminate the action potential.

So the big picture is that the action potential is caused by movements of small numbers of sodium and potassium via ion channels.

Calcium channels are also involved, as they are also voltage-gated, and play a role in muscle contraction. There, the calcium influx causes calcium-mediated calcium release from the sarcomplasmic reticulum, which is then pumped back in by the SERCA pump.

[somasimple]

So the big picture is that the action potential is caused by movements of small numbers of sodium and potassium via ion channels.

I fully accept this explanation but if the rising is done by an influx then the decay must be done the same way in opposite direction (efflux) but all papers speak about Na ions channels inactivated or closed.
How is it possible to get a rapid decay when gates are closed?

[Andy Resnick]

Not all the papers. Have you read the original Hodgkin-Huxley papers? Potassium channels are a key player.

There are a few concepts required to understand what is going in:

1) reversal potential. This is the potential at which no ions flow through the channel.

2) Voltage dependence of the open probability. This is what is meant by voltage-gating

3) Inactivation of a channel. I don't fully understand this, but it means the channel is open but does not conduct ions.

4) channels can be rectifying channels- ions are allowed to move in one direction only.

The reversal potential of outwardly rectifying potassium channels (Shaker-type) is about -80 mV. The reversal potential of sodium channels is around + 50mV. The 50% open probability for K+ channels is around -30 mV, that for Na+ channels around -50 mV. The ~ 0% open probability is about -50 and -70 mV, respectively and the ~100% open probability is about -10 and -30 mV, respectively.

The voltage-gated Na+ channels produce the initial depolarization (ignore Ca+ for now). Shaker-type K+ channels are outwardly rectifying and also *delayed* in opening, and is responsible for repolarization. Now remember, the action potential is generated by changes in the *conductance* of a channel, meaning the open probability. The actual currents are quite small. The K+ channels, because of the low reversal potential, act to oppose the Na+ channel and maintain the resting state.

Again recall that small numbers of ions moving across the membrane will produce large changes in membrane potential: 0.004% of the K+ in a cell moving across the membrane will produce a potential of -61.5 mV.

[Renge Ishyo]

1. Na K pumps are not involved in AP and it is a slow process.
2. The graph doesn't lie, the decay is also... fast.


Perhaps the confusion here is caused by my sloppiness so let me clarify one point; the reinstatement of the Na/K gradients via the Na/K pump is NOT part of the action potential (as you mention). This part of the process happens after the fact.

The influx of Na accounts for the change in membrane potential and the efflux of K accounts for the restoration of the original membrane potential (as described in satisfying detail by Mr. Resnick in his posts above). I was including the Na/K pump as part of the description only to give the full picture of how the cycle works.

[Andy Resnick]

Renge,

I've never seen a reasonable discussion of Cl- transport in all this stuff: most of what I've read is that Cl- merely maintains cell volume (via osmotic balance). What's your presepective?

[Renge Ishyo]

From my understanding the Cl ion channel is somewhat of an oddity which is why it often gets completely bypassed in these discussions (it is sort of like that weird half brother that nobody likes to talk about...), but it does serve a purpose in the above process in that it can protect against overly negative membrane potentials (such as if too much potassium leaves the cell during the efflux after an action potential).

As with the sodium and calcium ions, Chloride ion is kept at a higher concentration outside the cell than that of chlorine ion inside the cell. But unlike the previous two ions, when the gate for this channel is open, chlorine ion moves spontaneously *against* its concentration gradient and even more chlorine flows out of the cell (it is for this reason that I believe it is usually ignored...its easier to ignore this behavior than it is to try and explain it, but I will do my best below ^^).

The only time this sort of thing can happen is when the membrane potential (Vm) is more negative than the normal desired amount (and my guess is the chlorine channel is not even opened unless triggered by this overly negative potential although I have yet to see this hunch "officially" confirmed). To see how this can happen, the formula that describes the Gibbs free energy criterion (or change in Gibbs, dG) for all of the above mentioned ion channel processes (borrowed from the text "Principles of Biochemistry" by Nelson, Cox) is:

dG = RTln(Cin/Cout) + ZF(Vm)

The logarithmic term in this equation describes the effect of concentration on membrane transport for ions. If the concentration on the inside (Cin) is lower than (Cout), as it is for sodium, calcium, and chlorine, then "RT ln (Cin/Cout)" as a whole will always be negative and ions will move spontaneously from a higher concentration outside to a lower concentration inside. However, this is not the only factor...the right term ZF(Vm) also determines the direction of ion flow. For chlorine, Z = -1....so in this case, if Vm is also large and negative then "ZF(Vm)" as a whole can be positive. If this term is positive and larger than the logarithmic term, then the movement will be against the concentration gradient and even more chlorine ion will move out as the Gibbs moves towards zero for the overall process.

This is how the chlorine ion channel works. The effect is much the same as the sodium and calcium channels (it makes the inside of the cell less negative). However, it does so by removing the negatively charged chlorine ions until Vm reaches the proper resting potential.

So then, the question might be "why bother with the chlorine ion channel? If the membrane becomes too negative, why not just let in more sodium and calcium to make things positive and normal again?" Well, it makes sense to do it this way as both sodium and calcium channels are directly part of the signal transduction process (as opposed to the potassium and chlorine channels which to the best of my knowledge merely transfer ions and not signals). Letting more of either sodium or calcium ions flow in could affect the membrane potential signal sent from these channels in a negative way (or have some other damaging effect such as creating unwanted additional signals to be propagated). In contrast, there is no action potential generated at the Chlorine ion channels, and so this channel allows the membrane potential inside the cell to become more positive without affecting the signal transduction process at all.

Or at least, that is my understanding of this at the present. Of all of the ion channels mentioned in this thread, the chlorine channel is by far the least studied of the bunch and may also serve some additional purpose that I am neglecting...

[somasimple]

http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-97602006000300005

I was extremely excited and honored when Guayo admitted me in his lab to work on my doctoral thesis. He first suggested measuring chloride fluxes during voltage clamp (36Cl was an isotope we could get, unlike 42K), but we found that their contribution to the resting conductance was quite small, indicating that in the squid axon the leakage current was mainly cationic.

The simultaneous measurement of ionic currents and fluxes allowed us to test directly whether Na currents were carried exclusively by Na after blocking the K currents. These experiments, done in collaboration with Illani Atwater, confirmed that the transport number of Na was, indeed, very close to one (Atwater et al., 1969) and also demonstrated that by interrupting the Na current before it inactivated, the large current tail also was transported exclusively by Na (Bezanilla et al., 1970a).

[Renge Ishyo]

Yeah Soma, we know these things (no need to bold!)...that's why I wrote in my post above:

...both sodium and calcium channels are directly part of the signal transduction process (as opposed to the potassium and chlorine channels which to the best of my knowledge merely transfer ions and not signals).

The problem is that your original question about what happens to sodium cannot be answered without considering what happens a short (very short) while *after* the signal has been sent.

I know the process as a whole is somewhat confusing, and I also know many Cell Bio texts (including the one that I read a few years ago) ONLY mention the sodium and calcium channels when talking about signal transduction and ignore discussion of the "cleanup" process involving the potassium and chlorine channels altogether (or they put the description of these channels in a completely different place)...my guess is this probably lies at the root of your original question about what happens to sodium after the action potential?

For a more complete view of the process that integrates the roles of the various channels into one discussion, I suggest having a look at the description given in the above mentioned "Lehningers Principles of Biochemistry" by Nelson, Cox (4th or I guess now 5th ed.) as it gives what I consider to be the most clear description of the interplay between all these channels that I have seen in a text (or at least it has a really good graphic of the ion channels, see Chapter 12).

[somasimple]

Well,
the K conductance is lower than the Na one and the number of K channel is 10 time lower than the Na one.
How is it possible that in quite the same time (because you excluded all other ions species) the voltage decays like it grew...quickly (but Na ions are confined inside and Na channels closed or inactive)?

[somasimple]

http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=neurosci.section.201

The depolarization that produces Na+ channel opening also causes delayed activation of K+ channels and Na+ channel inactivation, leading to repolarization of the membrane potential as the action potential sweeps along the length of an axon

The delay makes trouble in a fast decay. :smile:

[somasimple]

For a more complete view of the process that integrates the roles of the various channels into one discussion, I suggest having a look at the description given in the above mentioned "Lehningers Principles of Biochemistry" by Nelson, Cox (4th or I guess now 5th ed.) as it gives what I consider to be the most clear description of the interplay between all these channels that I have seen in a text (or at least it has a really good graphic of the ion channels, see Chapter 12)

I ordered the book.

[Cincinnatus]

Somasimple seems to have some kind of axe to grind against the Hodgkin-Huxley theory of how action potentials are generated from electrochemical gradients and propagated down an axon.

Here is a previous thread on physicsforums where we discused this similarly: http://www.physicsforums.com/showthread.php?t=182840

If you google somasimple and action potential you will find many hits with him talking about the same things on many forums. As I recall when I looked him up last time, he had a long discussion about this on a wikipeda talk page as well.

[Andy Resnick]

From my understanding the Cl ion channel is somewhat of an oddity which is why it often gets completely bypassed in these discussions (it is sort of like that weird half brother that nobody likes to talk about...), but it does serve a purpose in the above process in that it can protect against overly negative membrane potentials (such as if too much potassium leaves the cell during the efflux after an action potential).

As with the sodium and calcium ions, Chloride ion is kept at a higher concentration outside the cell than that of chlorine ion inside the cell. But unlike the previous two ions, when the gate for this channel is open, chlorine ion moves spontaneously *against* its concentration gradient and even more chlorine flows out of the cell (it is for this reason that I believe it is usually ignored...its easier to ignore this behavior than it is to try and explain it, but I will do my best below ^^).

<snip>

Nice post- it took me a while to work through the whole thing.

My understanding (which appears to be similar to your explanation) is that movement of sodium or potassium changes the membrane potential not by adjustments to the concentration, but by movement of charge- that way small numbers of ions have a large effect on the membrane potential. Conversely, calcium movement does operate by concentration, because the intracellular Ca++ concentration is so low.

Chloride is intermediate- as you point out, the concentration gradient is small, so ions can flow either way depending on the details of the membrane potential. Plus, paracellular transport of Cl- is usually invoked to "complete the circuit" and maintain overall charge neutrality. So, just as the rule of thumb is that "water follows sodium", I guess "chloride follows charge".

I mostly work on the kidney- in the renal tubule, specifically the juxtaglomerular apparatus, Cl- is the rate-limiting ion for the Na/K/Cl cotransporter, which translates into a cell volume trigger back to the glomerulus: Increasing chloride concentration leads to a decrease in the glomerular filtration rate as a feedback mechanism for salt and water homeostasis.

Also, Cystic Fibrosis is purely a defect of cloride transport (CFTR). One hypothesis is that defective chloride transport leads to excessive and unregulated sodium absorption- it's not clear to me if the Cl- is absorbed or excreted- but the result is the same: dehydrated mucus, leading to problems in the lung and digestive system.

[Renge Ishyo]

Somasimple seems to have some kind of axe to grind against the Hodgkin-Huxley theory of how action potentials are generated from electrochemical gradients and propagated down an axon.

It is in the spirit of science to question things. My take is that so long as nobody kills or harms each other over differences in ideas then I see disagreement as a very very good thing (in fact, it is the horrible necessity of progress). Of course, people DO kill and harm each other over differences in opinion...so *ahem ahem*, in light of that observation, 95% of the time when I encounter someone with a different opinion, my response is to simply keep my ideas to myself. You would be amazed at how many times I have typed out these long posts here on PF only to delete them before posting, because I did not want to risk my ideas provoking a negative response in the person on the other end...

I ordered the book.

You will not be disappointed. I haven't had a chance to really look at the 5th edition yet, but the 4th did a better job on the cell bio topics than pretty much every other dedicated cell bio text that I have seen.

My understanding (which appears to be similar to your explanation) is that movement of sodium or potassium changes the membrane potential not by adjustments to the concentration, but by movement of charge- that way small numbers of ions have a large effect on the membrane potential. Conversely, calcium movement does operate by concentration, because the intracellular Ca++ concentration is so low.

Chloride is intermediate- as you point out, the concentration gradient is small, so ions can flow either way depending on the details of the membrane potential. Plus, paracellular transport of Cl- is usually invoked to "complete the circuit" and maintain overall charge neutrality. So, just as the rule of thumb is that "water follows sodium", I guess "chloride follows charge".

As for the role of chloride in osmotic processes, I am sure all these ions and their individual concentrations have to be very carefully regulated to ensure proper balance. As far as signal transduction processes go, I don't see osmotic balance as too much of an issue per say, because of the rapid way with which the concentration gradients are manipulated and restored to balance, and the small size of the concentration changes with respect to the cytosol as a whole. Certainly in the case of a defective ion channel (such as in CF) where balance cannot be restored properly and the mistake "piles up" over time, the importance of establishing osmotic balance for these channels becomes readily apparent.

As far as the movement of charge itself being the dominating force (at least for external plasma membrane ion channels) as opposed to concentration, everything I have read lately points to that idea being right on. In my understanding, the 2nd term of that above equation dealing with the impact of charge on the process is THE critical contributor to the functioning of the voltage gated ion channels that appear on the external plasma membrane (intracellular channels such as the calcium channel in the ER lack a strong membrane potential and can be an exception, which I will get to in a minute). This is further reinforced when you consider that chloride is generally NOT kept with a small concentration gradient (yes, one of the many puzzling things about it); in fact, in most cases the concentration gradient is the same for chloride as it is for sodium. For example, in squid axon sodium is 440 mM outside and 50 mM inside whereas chloride is at 560 mM outside and 40-150mM inside. Yet, it is known that at least in neurons, chloride moves against the concentration gradient in its ion channels. My thinking is that the concentration gradients are set up to create, maintain, and tweak the membrane potential while the rapid changes in the membrane potential itself (created by opening or closing channels a bit too long compared with the norm) control the actual movement of ions and initiate the main responses (this is sort of clouded by the fact that sodium has *both* an inward concentration gradient and an inward electrochemical gradient for it that together "push" sodium into the cell when its channel opens, prompting explanations to focus on either one or the other).

Indeed the sensitive membrane potential, and not concentration, now seems to be the main driving force for the proton channels used in the production of ATP, at least for eukaryotes (plants do seem to use the "old pH model" that gets taught in schools which I won't get into here). This became apparent once they found out that the eukaryotic membrane wasn't "hording" protons in a little comparment like it does for intracellular calcium or in plants, but that hydrogen ions were free to diffuse away from the plasma membrane and become diluted throughout the cytosol. It is like dropping a bottle of concentrated hydrochloric acid into the ocean (which I should mention here is something that nobody should do); ten minutes later, if you stick a piece of pH paper into the same spot of oceanwater you will get the pH of the ocean and not the acid. External pH cannot be the driving force in such a situation. Yet, protons are driven through the proton ion channel to make ATP just the same...so the conclusion was reached that it actually was the negative membrane potential (with a small effect in proton concentration differences) that largely seems to pull the protons in. Of course, if you gave that answer in your typical college class on a test you will probably be marked wrong (even if some of the more recent cell bio texts such as "The Cell" by Albert, Johnson, Lewis, etc. do implement this somewhat more modern view).

The steep concentration gradient for calcium can be an exception to this as calcium channels are also used on internal membranes (such as the ER) that do not have the same strong membrane potential as the external plasma membrane does. Thus, two additional things are done so that the concentration term can dominate in the Gibbs for Ca in this instance: 1) Calcium is kept in a small sealed compartment (preventing the "ocean diffusion" idea from above and keeping the Ca concentration in the region of the channel very high), and 2) the concentration of Ca in the cytosol is kept extremely low. Of course, calcium can also function with ion channels on the external plasma membrane, and I suspect that as with Na,K, and Cl channels that in this instance once again the membrane potential become the dominant force over concentration, even for calcium.

These sort of ideas about the electrical potential are out there now, but they do not seem to get the same amount of "press" as the concentration concept because concentration differences DO still contribute and it is simply much more easy to understand than a more full picture that takes into account electrical potentials from Physics (and hence, the poor poor chloride ion channel, which then runs counter to the "easy model" about concentration gradients and ion movement, gets regulated to the "zit" status as the tendency seems to be more about covering it up and hoping it will just go away rather than probing deeper into its function...).

[somasimple]

Somasimple seems to have some kind of axe to grind against the Hodgkin-Huxley theory of how action potentials are generated from electrochemical gradients and propagated down an axon.

Here is a previous thread on physicsforums where we discused this similarly: http://www.physicsforums.com/showthread.php?t=182840

If you google somasimple and action potential you will find many hits with him talking about the same things on many forums. As I recall when I looked him up last time, he had a long discussion about this on a wikipeda talk page as well.

Cincinnatus,

I ask questions that seem important for the science community and it seems true that often I do not get any response. That is strange. I pointed out some basic violations of physics laws and the "faulty" drawings were removed from wikipedia because my argument was sufficiently strong.

The question of this thread is of a similarly importance since sodium, that is a major contributor to action potential, enters the cell but do not go out before a long delay. That contradicts curves and curves do not lie. Na entered and just returned out. That is a lesson of conductances. If you make a derivation of the curve you obtain an internal shift immediately followed by an external motion.

The theory must be refined. I have a theory that explains the fact, have you one that may explains this?

I have many respect for Hodgkin and Huxley (the scientists) and they were pioneers in the domain and I remind some great words from them: Our theory is a very simplified way to explain how the things really happen. And it is true that some huge but necessarily truncations have been made because it wasn't impossible at the time to compute anything.
Remember that a single pico second of a realistic ion channel computation takes several hours... Actually!

[Cincinnatus]

Renge Ishyo, I read your recent post but I'm not sure how what you are describing is any different from our usual formalism for talking about these questions. That is, we calculate the reversal potentials of the various ions by the Nernst equation (or some variant thereof). Once you know the reversal potential and the concentrations of the various ions then for any voltage you know which direction the ions will be flowing. This is what you said a few posts up.

This much was known before Hodgkin and Huxley. Their contribution can be viewed as the extension of this same formalism to the case where we have voltage gated ion channels. That is, the permeability of the ion is a function of the voltage.

---
Somasimple, are you asking about the (mostly) k-channel mediated hyperpolarization that brings the membrane voltage back down after an action potential? Or are you asking about how the electrochemical gradients themselves are maintained? This occurs by pumps like the Na-K pump.

---
I like what you said about the chlorine channel "completing the circuit" and maintaining charge neutrality. The AMPA channel has a reversal potential very close to 0 mV because it fluxes K, Na and Cl with differing permeabilities for each.

[somasimple]

Somasimple, are you asking about the (mostly) k-channel mediated hyperpolarization that brings the membrane voltage back down after an action potential? Or are you asking about how the electrochemical gradients themselves are maintained? This occurs by pumps like the Na-K pump.
Neither the primer nor the later. I just want to know where the Na ions go when they entered the cell (since we suppose Na channels are closed/inactive). The Na/K pumps are too slow to reverse the situation and it is proved than blocking them do not implies an increase in internal Na+.

The Na conductance gives matter to reflexion but we are in a condition where ions fluxes are supposed constant by the GHK equation (but not realistic).

[Cincinnatus]

Neither the primer nor the later. I just want to know where the Na ions go when they entered the cell (since we suppose Na channels are closed/inactive). The Na/K pumps are too slow to reverse the situation and it is proved than blocking them do not implies an increase in internal Na+.

Well this depends on how much the internal Na concentration actually changes during an action potential. I don't have these numbers available but maybe someone else does?

It could be that the change in concentration is negligible with respect to the concentration gradient. If that is the case then the future firing of the neuron will be unaffected and there is no need to have some other process removing Na ions from the cell on a fast timescale. The slower Na-K pump is enough to maintain the concentration gradient over longer timeframes.

[somasimple]

If that is the case then the future firing of the neuron will be unaffected and there is no need to have some other process removing Na ions from the cell on a fast timescale

Yes but it will automatically affect the resting potential and you must see its growing with future firing. Experiment show that several thousand APs may occur before any change occur....

[somasimple]

Here is an image about the Na conductance:

[Renge Ishyo]

Renge Ishyo, I read your recent post but I'm not sure how what you are describing is any different from our usual formalism for talking about these questions.

Correct you are sir; these ideas are very well rooted in classical experiments and (though contested and often misunderstood) the ideas I have presented are hardly revolutionary (that is why I am referring to their presence in certain textbooks as opposed to research papers).

My descriptions are attempts to try and understand the wheel, rather then reinvent it (although my willingness to actually talk about the chloride ion channel may have led you to believe otherwise :wink:).

[somasimple]

these ideas are very well rooted in classical experiments and (though contested and often misunderstood) the ideas I have presented are hardly revolutionary
You're welcome.

A theory that explains the underlying mechanisms of:

refractory periods
propagation without "passive spread"
inactivation of Na channel
branching, acceleration...


and respects facts and laws of physics may be of some interest?

[somasimple]

Well, is there some evidence about the Na/K pump? I found some evidences that disprove it but none that support it?

[Andy Resnick]

You're welcome.

A theory that explains the underlying mechanisms of:

refractory periods
propagation without "passive spread"
inactivation of Na channel
branching, acceleration...


and respects facts and laws of physics may be of some interest?

Soma,

Several times in this thread you have alluded to some idea you have but have yet to present it. I think it's time you at least presented what you have in mind, rather than trying to claim other (well-established, well verified, well studied) models are invalid.

[somasimple]

Andy,

I have a full respect to your position and it's sure that such a novice like me may irritate such authority like you.

BTW, I'm not sure that someone gave me a satisfying response about the Na within this thread. Of course, I have an explanation but I'm querying all current hypothesis to see if the wheel is not already turning.

Well studied?
Is there a plausible explanation about refractory periods? Only a simple affirmation => The membrane stays in a refractory state (how?)
How do you explain that Na channel becomes inactive after some delay? I brought a graph showing a high permeability during the falling phase => a high permeability contradicts a closed gate.
What is the mechanism that makes the propagation unidirectional? Yes, because the membrane is refractory! (How?)
The action potential is propagated with an electrotonic current! When this current happens?
Where is the energy to maintain the Na/K pump?
Where is the delay in the cable theory?
What about the water that fills the channels sequences?
Have Na and K the same speed or size?
How is it possible to a ion to make an instant translation?
...

[Cincinnatus]

Is there a plausible explanation about refractory periods? Only a simple affirmation => The membrane stays in a refractory state (how?)
How do you explain that Na channel becomes inactive after some delay? I brought a graph showing a high permeability during the falling phase => a high permeability contradicts a closed gate.
What is the mechanism that makes the propagation unidirectional? Yes, because the membrane is refractory! (How?)
The action potential is propagated with an electrotonic current! When this current happens?
Where is the energy to maintain the Na/K pump?
Where is the delay in the cable theory?
What about the water that fills the channels sequences?
Have Na and K the same speed or size?
How is it possible to a ion to make an instant translation?

Soma, have you tried playing around with the NEURON simulation environment that Hines and Carnevale wrote? Here's a link to their forum: http://www.neuron.yale.edu/phpBB2/index.php
You should be able to answer all these questions for yourself that way. For example, you can use their NMODL tool to change around the properties of the sodium channel making them as realistic or phenomenological as you like and you can see how this affects the properties of the membrance excitability, refractoriness etc.

You ask how the sodium channel becomes inactive after some delay. The Hodgkin-Huxley theory does not address this question. Hodgkin and Huxley simply modeled the sodium channel with an "inactivation" parameter fit from experimental data. However, you can replace their phenomenological model with a more realistic model incorporating what we know about the kinetics of the channel. There are many different states that the channel can be in, each associated with different permeabilities. We can define rate constants that determine how the channel changes states. For details on how to do this simulation check out the following books:

Johnston and Wu, Foundations of Cellular Neurophysiology.
and
Koch and Segev, Methods in Neuronal Modeling: From Ions to Networks,

The latter is a collection of articles describing useful methods that you could use in conjunction with the NEURON software (or any other programming environment) to examine these questions yourself.

The Johnston and Wu book is the "bible" of cellular neurophysiology from a quantitative perspective. I recall they have a chapter early on in the book that describes kinetic models of ion channels and discusses how this reductionist view recapitulates the Hodgkin-Huxley formalism.

For your questions about cable theory there is no better reference (to my knowledge) than Cristof Koch's book called Biophysics of Computation.

[somasimple]

Cincinnatus,

I'm already registered on their forum. I'm not in agreement with the NEURON software that is fully electric and thus unable to mimic a single ion.
BTW, this software doesn't respect any SPICE model...

About Na channel => Experiments shows this delayed "inactivation" => I do not contest a fact.

About a cable theory: Is a real cable functions with ions? Is an axon shows some inductance?

Just try to get an open mind and try to reply to the question for yourself:
If the entering Na ions create a passive current spread thus it means that every entering positive ion will be associated with an electron or a negative ion but this will contradicts the HGK computing and how the interior may be more positive as the ions enter since they are immediately balanced ?

[Cincinnatus]

Cincinnatus,

I'm already registered on their forum. I'm not in agreement with the NEURON software that is fully electric and thus unable to mimic a single ion.
BTW, this software doesn't respect any SPICE model...


I don't understand what you mean here. NEURON assumes almost nothing for itself. You can build in whatever you like. Its just an easy way to keep track of conductances ie. solve the partial differential equations of cable theory. You can build in the particular form of all the currents yourself. The only real thing that NEURON assumes is Ohms law.

I don't know why you would be interested in a single ion anyway. The movement of one single ion has a negligible effect on the membrane potential.


About a cable theory: Is a real cable functions with ions? Is an axon shows some inductance?


I think now that English must not be your native language. I have no idea what you mean by "is a real cable functions with ions?".

Just try to get an open mind and try to reply to the question for yourself:
If the entering Na ions create a passive current spread thus it means that every entering positive ion will be associated with an electron or a negative ion but this will contradicts the HGK computing and how the interior may be more positive as the ions enter since they are immediately balanced ?

Are you trying to argue that the Goldman-Hodgkin-Katz equation is not being correctly applied when we use it to calculate the resting membrane potential? However it has been experimentally verified at least for the squid axon the numbers are quite well known... You must be trying to say something else, but I'm not sure what.

[Renge Ishyo]

If the entering Na ions create a passive current spread thus it means that every entering positive ion will be associated with an electron or a negative ion but this will contradicts the HGK computing and how the interior may be more positive as the ions enter since they are immediately balanced ?

If the ion charge were immediately balanced, it is correct that no significant current will flow due to a membrane potential (concentration gradient movement would still take place somewhat), but it is known that this is not the case. The charge imbalance is created by the nature of the Na/K pump. Both Na and K ions have the same charge (+1), but the pump brings in only two K ions for every 3 Na ions it expels. Assuming that the chloride ion channels are kept closed to simplify the thinking, this means that a "net positive" charge leaves the cell every time the Na/K pump operates (leaving the inside of the cell necessarily more negative with an ion imbalance as per the law of conservation of charge).

Accepting that the Na/K pump is used to establish membrane potentials helps to explain a lot of things such as the rather large amount of energy the body reserves for using these particular pumps. It makes sense to have to use all this energy if the Na/K pump is needed to do something very important that each and every cell needs such as establishing the ion flow for that cell as is postulated by the current theory...it doesn't make sense to devote a lot of energy to this process if this pump merely serves some other minor purpose.

I have a full respect to your position and it's sure that such a novice like me may irritate such authority like you.

Any respectable scientist is going to go with well supported logical theories when they go about explaining the universe around them. Don't take it personally; it is part of our training to learn the benefits of approaching things this way. I am not against those theories being challenged at all (in fact, I find it exciting when some new wrinkle adds a new understanding to an old familiar concept), but I see *no reason* to disregard well established views *until* I see some experiment, observation, or explanation that forces me to do so. If you believe you have that explanation and observation that forces the issue go ahead and publish it. I will evaluate whether I need to readjust my views at that time.

[somasimple]

As mentioned by Renge, I will apply logic and its correlate;
"All things being equal"

Validity domain of GHK equation (and thus the HH model) ?
Several assumptions are made in deriving the GHK current equation:

* The membrane is a homogeneous substance
* The electrical field is constant so that the transmembrane potential varies linearly across the membrane
* The ions access the membrane instantaneously from the intra- and extracellular solutions
* The permeant ions do not interact
* The movement of ions is affected by both concentration and voltage differences

Membrane is homogenous ? NO
The electrical field is constant so that the trans membrane potential varies linearly across the membrane? NO
The ions access the membrane instantaneously from the intra- and extracellular solutions? NO

Exercise of Logic:
1/ I may apply the GHK equation even if the validity domain is rejected
2/ I can't apply a ionic current theory or the ohm law for the same reasons.

I take logically the second reply.

I don't know why you would be interested in a single ion anyway.
Facts:
Neuron cannot make a complex electrostatic interaction (That's not its domain).
ions are involved in Action potential.

Logic:
If NEUTON is unable to mimic a ion, it can't for millions.

I think now that English must not be your native language. I have no idea what you mean by "is a real cable functions with ions?".
I'm French.
A real coaxial cable is made of metal and it has electric properties;
inductance
http://en.wikipedia.org/wiki/Inductance
A real cable works with electric current (electrons). The atoms do not really move.
In an axon, atoms move from outside to inside.

[somasimple]

Renge,

Theory:
A Na/K pump functions all the time and maintains the ionic imbalance.

Facts;
When ATP is blocked the ionic imbalance is maintained for several hours.

Logic:

Na/K pumps work even if they are blocked.
They do not work all the time.


I take logically the second explanation.

When the Na/K pump reaches the "good" ionic level:

Na/K pumps continue to work
They stop.

I take logically the second take.

Just logic.

[Cincinnatus]

As mentioned by Renge, I will apply logic and its correlate;
"All things being equal"

Validity domain of GHK equation

Several assumptions are made in deriving the GHK current equation:

* The membrane is a homogeneous substance
* The electrical field is constant so that the transmembrane potential varies linearly across the membrane
* The ions access the membrane instantaneously from the intra- and extracellular solutions
* The permeant ions do not interact
* The movement of ions is affected by both concentration and voltage differences

Membrane is homogenous ? NO
The electrical field is constant so that the trans membrane potential varies linearly across the membrane? NO
The ions access the membrane instantaneously from the intra- and extracellular solutions? NO


These are all quite reasonable assumptions despite not being true "strictly speaking". The fact that the model predicts experiments quite well validates our choice of premises. If the model did not agree with experiment then you could look to the premises to see what went wrong. The fact that the model does agree with experiment tells us that the assumptions we made are ok.

This tells us that the inhomogeneity of the membrane is a relatively minor contributor to the value of the resting potential.


I'm French.
A real coaxial cable is made of metal and it has electric properties;
inductance
http://en.wikipedia.org/wiki/Inductance
A real cable works with electric current (electrons). The atoms do not really move.
In an axon, atoms move from outside to inside.

So what? I don't know a damn thing about these so-called electrons, who am I? a chemist?

To understand cable theory all I need to know about are currents, conductances and voltages. It doesn't matter one bit if the currents are caused by a flow of electrons or a flow of ions. In fact I don't even need to believe in ions to understand cable theory. The only notions I need are Ohms law and some idea of current as something that "flows".

Theory:
A Na/K pump functions all the time and maintains the ionic imbalance.

Facts;
When ATP is blocked the ionic imbalance is maintained for several hours.

Logic:

1. Na/K pumps work even if they are blocked.
2. They do not work all the time.


I take logically the second explanation.

When the Na/K pump reaches the "good" ionic level:

1. Na/K pumps continue to work
2. They stop.

I take logically the second take.

No one claimed that Na/K pumps work all the time. They are not involved in maintaining the cell's resting potential. I don't see where you are going with this.

[somasimple]

They are not involved in maintaining the cell's resting potential. I don't see where you are going with this.
hHere or there =>
http://en.wikipedia.org/wiki/NaKATPase
http://advan.physiology.org/cgi/content/full/28/4/139

[Cincinnatus]

You are quoting me out of the context of the conversation.

In the short term, Na ions are flowing into the cell balanced by K ions flowing out. Several other ions are also crossing the membrane in this charge balanced manner. This and this alone is sufficient to maintain the resting potential for short periods.

In the long term, something else is necessary to move the ions back to the appropriate side of the membrane. These are the various pumps like the Na/K pump.

This explanations is consistent with the experiment you mentioned where lack of ATP leads to a loss of ion imbalance after a period of hours. That is, in the short term the Na/K pumps are unnecessary. After several hours without ATP (and thus without functional Na/K pumps) the concentrations of the ions becomes equilibriated and the electrochemical gradient is destroyed.

[somasimple]

About cable
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/part7/page1.html
www.geocities.com/ve2_azx/CoaxialCableDelay.pdf
http://www.ivorcatt.com/4_6.htm
http://users.encs.concordia.ca/~trueman/bounce/demos.htm
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/skineffect/page5.html

In the short term, Na ions are flowing into the cell balanced by K ions flowing out. Several other ions are also crossing the membrane in this charge balanced manner. This and this alone is sufficient to maintain the resting potential for short periods.
We are in the first milliseconds, and I want to know what happens to Na ions once they entered? The hypothesis is that ions channels are closed/inactivated. I contest it since the graph shows a high permeability/conductance! I do not care they are balanced. It does not change anything to my asking!!!

ps: The ohm law works with definite electrical circuits: Please, draw me one?

[somasimple]

These are all quite reasonable assumptions despite not being true "strictly speaking". The fact that the model predicts experiments quite well validates our choice of premises. If the model did not agree with experiment then you could look to the premises to see what went wrong. The fact that the model does agree with experiment tells us that the assumptions we made are ok.

This tells us that the inhomogeneity of the membrane is a relatively minor contributor to the value of the resting potential.

You're focused by results that are computations of integrations. That makes very good average values but... Averages are averages.

Ions cross membranes through ions channels! Do you expect that every ion get the same chance or velocity in this process?

[Cincinnatus]

We are in the first milliseconds, and I want to know what happens to Na ions once they entered? The hypothesis is that ions channels are closed/inactivated. I contest it since the graph shows a high permeability/conductance! I do not care they are balanced. It does not change anything to my asking!!!


What graph are you referring to here?

You're focused by results that are computations of integrations. That makes very good average values but... Averages are averages.

Ions cross membranes through ions channels! Do you expect that every ion get the same chance or velocity in this process?

The HH theory does not address what happens when a single ion crosses. The theory is phrased in terms of voltages, conductances and currents.

We have other techniques we can use to describe the motion of a single ion. Typically we do this by assuming the ion's motion is described by a Wiener process (Brownian motion). Then we can calculate the mean first passage time for the brownian particle to hit a channel, pass through the channel etc. You haven't explained why you think this should be relevant though.

You have been alluding to your own theory for some time. I agree with Andy, now it is time for you to tell us what it is... Though as per the rules of this forum, you may need to submit to the independent research forum. We can read it there though.

[somasimple]

What graph are you referring to here?
This one:
http://www.physicsforums.com/showpost.php?p=1824723&postcount=23

If the sodium channels are inactivated (and I agree that we see an "inactivation") then the conductance may fall towards 0, immediately. It does, quickly but it express a Na ions movement.

We have other techniques we can use to describe the motion of a single ion. Typically we do this by assuming the ion's motion is described by a Wiener process (Brownian motion). Then we can calculate the mean first passage time for the brownian particle to hit a channel, pass through the channel etc. You haven't explained why you think this should be relevant though.
I know that but they extremely simplify the reality... In fact, simplification is quite a mandatory process in theory generalization. The problem is that one may simplify the wrong fact.

You have been alluding to your own theory for some time. I agree with Andy, now it is time for you to tell us what it is... Though as per the rules of this forum, you may need to submit to the independent research forum. We can read it there though.
Too soon but I suspect you're interested...

[Andy Resnick]

Andy,

I have a full respect to your position and it's sure that such a novice like me may irritate such authority like you.

<snip>


Soma,

Firstly, I wouldn't say I am irritated, exactly. I choose to participate in this thread or not. At some point I will reach diminishing returns and drop out. Second, I'm not sure I would consider myself an authority on the subject, either. Hopefully I'm not merely quoting doctrine- I am trying to provide evidence.

[Andy Resnick]

<snip>

Is there a plausible explanation about refractory periods? Only a simple affirmation => The membrane stays in a refractory state (how?)
How do you explain that Na channel becomes inactive after some delay? I brought a graph showing a high permeability during the falling phase => a high permeability contradicts a closed gate.
What is the mechanism that makes the propagation unidirectional? Yes, because the membrane is refractory! (How?)
The action potential is propagated with an electrotonic current! When this current happens?
Where is the energy to maintain the Na/K pump?
Where is the delay in the cable theory?
What about the water that fills the channels sequences?
Have Na and K the same speed or size?
How is it possible to a ion to make an instant translation?
...

I agree with the hypothesis that a channel can be open and inactive is an odd one; I also have problems with waving the magic wand of "conformational changes" to explain things. Nonetheless, I have nothing better to add and the concept has explanatory power- calmodulin, for example.

Rectifying channels, either inward or outward directed, are not so difficult to think about- I picture it as one reaction is favored over the other. For example, Na-K-ATPase can either consume ATP to transport ions against the electrochemical gradient, or can generate ATP by running in reverse- both can occur under test-tube conditions, but the forward reaction is (highly) energetically favored in a cell.

Note I haven't really drawn a distinction between a channel, a transporter, co-transporter, pump, etc. Conceptually, there's not that much of a difference- some are 'active' (requiring ATP), some are passive, some are modulated by some mechanism, etc.

Not sure what you mean by "water that fills the channels sequences".... there are water channels, and most ion channels are highly specific. Na+ and K+ are not the same size (different hydration radius), and that is the key to understanding the selectivity. The transit time for an ion across a 10 nm membrane, subject to a 60 mV driving potential, is likely to be small.

Where is the energy required to maintain the membrane potential? Better to ask where is the setpoint. How is the membrane potenial set to a particular value? What are the feedback and feedforward mechanisms to stably maintain the membrane potential?

[somasimple]

Not sure what you mean by "water that fills the channels sequences"...
The channel can't "pass" ions without water as you know. It has been confirmed by Prof R MacKinnon. These sequences (ion/water/ion...) may have profound consequences.

Where is the energy required to maintain the membrane potential? Better to ask where is the setpoint. How is the membrane potenial set to a particular value? What are the feedback and feedforward mechanisms to stably maintain the membrane potential?

I learnt a lot from this site.
http://www.lsbu.ac.uk/water/kosmos.html
http://www.lsbu.ac.uk/water/cell.html

[Mike H]

We are in the first milliseconds, and I want to know what happens to Na ions once they entered?

You're focused by results that are computations of integrations. That makes very good average values but... Averages are averages.

Ions cross membranes through ions channels! Do you expect that every ion get the same chance or velocity in this process?

I haven't entirely been able to keep track of all of the details of this conversation (I napped through the neuro section of my one cell bio class as an undergraduate during the Clinton administration), but I can't but help wonder about a few questions after reading the above quoted material.

What is the status of single molecule methods as applied to ion channel function? As a physical chemistry/biophysics sort, I tend to think in terms of optical spectroscopic/microscopy methods, which - from the last time I was digging around in this topic - only gramicidin had been subjected to such investigations with any degree of publishable success. I've heard of such things as doing electrophysiological measurements on single ion channels - are the results from such measurements consistent with larger-scale measurements? My impression is that they are, but I know that drawing such conclusions can be a somewhat non-trivial affair.

I'm also curious as to what is meant by "what happens to Na ions once they enter" the cell. Do they not just hydrate and dive into the cytoplasm, waiting to be pumped out or eventually used as a cation to bind to some biological macromolecule in due time? I know that, for example, copper ions are carefully chaperoned after transport into the cell, but I was not aware of any suggested similar mechanisms for sodium.

somasimple - I would be very interested in reading your theory (although it looks like we'll have to wait for it), particularly if it involves any material not yet in the literature regarding kinetics of single ions being transported across a biological membrane (actual cell or model system) and/or being able to track single inorganic ions upon entry into a cell and their fate, esp. if there's an as-yet-unidentified sodium chaperoning/trafficking pathway.

[Renge Ishyo]

Soma, it is expected that the current would decay slowly over time after the channel is shut off. The reason why there is a "sharp" change at first is that the gradient was established prior to the opening of the channel (thus, this part of the cycle will not show on the graph anymore than it does on a discharge graph for a DC capcitor). After the ions flow in, in a short period of time there will be a lot of positive ions in the vicinity of the membrane and the Vm will be affected at its peak at this point locally on the membrane (but I should mention that it will affect only a very small area of the membrane as this ion increase is negligible at this point compared to the ion content in the cell at large). A brief time later if the channel is closed so that no more sodium ions rush in, the Vm in the vicinity of the membrane will gradually decrease back towards the predominating membrane potential in most of the cell all on its own. Why? It is because the ions are mobile and are in an aqueous solution. The sodium ions will diffuse away from the membrane, and the positive charge density will spread out as much as possible. This *slowly* dilutes the effect of the positive charge increase on that small region of the inner membrane over time.

This is the same thing as the "ocean diffusion" example given earlier; if the strong acid is dumped into the ocean and you are measuring this area with a pH meter, you will see an immediate "spike" to a pH of 1 after dumping. This would then gradually decay to the pH of the ocean as the hydrogen ions diffuse away from the place where the bottle was emptied.

The cell couldn't keep this up for ever (and neither could the ocean; in theory if I kept on dumping acid into the ocean like this, after a long period of time the pH of the entire ocean would eventually be altered). The long term accumulation of positive charges would build to a point to where the membrane potential of the entire cell was altered, and at this point the cells function would be altered. The Na/K pump prevents this "global" problem from taking place long term, which is why you can't shut it off forever and expect the ion gradients to survive indefinitely (although as you mention, it is reasonable to expect the gradient to hold up for some time before enough ions build up in the cell to change the entire membrane potential permanently).

Soma, I am confused as to which part of the theory you are questioning. Is it the mechanism by which the ion channel shuts off ion flow that interests you? Or is it the nature of an exponential decay of the residual current flow? The former is still being worked out and will likely need at least some knowledge of the protein structure to answer, but the latter would probably lend itself better to a physical analysis using diffusion based ion models and I don't see any clear reason why this model would have to contradict anything that came before it.

[somasimple]

I've heard of such things as doing electrophysiological measurements on single ion channels - are the results from such measurements consistent with larger-scale measurements? My impression is that they are, but I know that drawing such conclusions can be a somewhat non-trivial affair.

Thanks for the interest, Mike.
I already said that we need a simplification for a better understanding of the phenomenon.
The dynamics involved in a single realistic channel is far out of our computation possibility.
A single channel is unable to grasp the whole process, they work in a "collective" manner.
You need to simulate art least thousand and thousand of ions channels: I'm unable to do such a magical trick.
Here is a single ion channel within its natural environment.

[somasimple]

Renge,

I must thank you, once again to bring another subject of contradiction about membrane properties:

This marvelous membrane capacitor.
A single cm˛ that carries 1µF. That is clearly extraordinary and may make a furious envy to many electronics suppliers.
I attached a little piece of "membrane" it is only 0.5 µm long and has only 0.48 µm of diameter.
I put some ions channels on its surface with a reasonable density. Of course, it is just a point of view since it is too "regular" but it is the best arrangement for energy.

It looks like a sieve (and it is) but I may have some hard to fix a boundary of a single pFcapacitor.

Experiment:

Take a real capacitor http://www.interq.or.jp/japan/se-inoue/e_capa.htm
Charge it at will (It doesn't matter).
take a cm3 of saline water
put the wires into the water


Does the capacitor maintains any charge?
Does the water is polarized?

Second experiment:

Let the capacitor wires in the water
try to charge it (at will)

Have you any success?
Be careful and good luck!

I may have a similar reasoning with a resistor that works like an interrupter (ion channel).
The only possible solution is to insulate totally the wires from the medium => No wires => no circuit => no component => no current.

[Andy Resnick]

The channel can't "pass" ions without water as you know. It has been confirmed by Prof R MacKinnon. These sequences (ion/water/ion...) may have profound consequences.

I think Rod would be rather upset to hear his work so misrepresented- ion channels do not pass water. Read the history of aquaporin: prior to the discovery of the water channel, it was assumed that water diffused through the lipid bilayer.

Ions are stripped of their hydration shell upon entry into the channel; that is one reason they traverse the membrane so fast- to get re-hydrated on the other side.


I learnt a lot from this site.
http://www.lsbu.ac.uk/water/kosmos.html
http://www.lsbu.ac.uk/water/cell.html

Ah- now I see what your motivation is. The water structure field is interesting, I suppose (I've read Pollack's book 'Cells, Gels, ..."), but there is no good experimental demonstration that requires structured water. Does it exist? Given the large field strengths present near a membrane, it would seem likely that the water is polarized. However, large-scale ordering of water molecules does not appear to exist.

[Andy Resnick]

<snip>

What is the status of single molecule methods as applied to ion channel function? As a physical chemistry/biophysics sort, I tend to think in terms of optical spectroscopic/microscopy methods, which - from the last time I was digging around in this topic - only gramicidin had been subjected to such investigations with any degree of publishable success. I've heard of such things as doing electrophysiological measurements on single ion channels - are the results from such measurements consistent with larger-scale measurements? My impression is that they are, but I know that drawing such conclusions can be a somewhat non-trivial affair.
<snip>

Single-channel patch clamping is reasonably routine here- it's tricky, to be sure- but really cool once it works. The data is usually a measurement of the open-channel probability as a function of whatever chemicals or votages are present.

In terms of optics, it's like dialing the intensity down and using a single-photon detector.

[somasimple]

I think Rod would be rather upset to hear his work so misrepresented- ion channels do not pass water. Read the history of aquaporin: prior to the discovery of the water channel, it was assumed that water diffused through the lipid bilayer.
http://nobelprize.org/nobel_prizes/chemistry/laureates/2003/mackinnon-lecture.pdf
The K+ ion pair could diffuse
back and forth between 1,3 and 2,4 configurations (bottom pathway), or
alternatively an ion could enter the filter from one side of the membrane as
the ion-water queue moves and a K+ exits at the opposite side (the top pathway).
Movements would have to be concerted because the filter is no wider
than a K+ ion or water molecule.
I think too.

[somasimple]

Ah- now I see what your motivation is.
I do not understand the hidden sense of your sentence.
See references =>
http://www.lsbu.ac.uk/water/ref.html

[Andy Resnick]

I do not understand the hidden sense of your sentence.
See references =>
http://www.lsbu.ac.uk/water/ref.html

http://www.chem1.com/CQ/clusqk.html

[Mike H]

Well, now, I'm a bit more confused at this point. Probably should have paid more attention in cell bio way back when....

The dynamics involved in a single realistic channel is far out of our computation possibility.
A single channel is unable to grasp the whole process, they work in a "collective" manner.
You need to simulate art least thousand and thousand of ions channels: I'm unable to do such a magical trick.

OK, am I correct in understanding this as follows – the behavior of a particular single ion channel is dependent on its environment in the membrane, namely surrounded by many other ion channels? That is, there is some sort of collective behavior among many ion channels that is not observable by single channel studies, where a single ion channel of interest will have noticeable differences in its behavior whether it's alone or if it's surrounded by many other ion channels. This sounds perfectly reasonable to me in principle, but then I have to wonder something. It was stated earlier that

You're focused by results that are computations of integrations. That makes very good average values but... Averages are averages.

Ions cross membranes through ions channels! Do you expect that every ion get the same chance or velocity in this process?

If the important behavior to consider is of a collective nature (see the first quote in this post), why would it be important that not every ion might pass through the ion channel in exactly the same manner? You're interested in the collective effect of many ions passing through many ion channels, not just one ion through one ion channel. And why would it matter then that the Hodgkin-Huxley theory is one of averages and macroscopic/whole-cell behavior, and not single ion channels? Wouldn't it be rather appropriate then, as it describes (I'm figuring) the collective effect of many ion channels, which – according to the quote I have at the start of this post – is preferable to just focusing on a single ion channel which does not capture the full complexity of the process?

I understand the difficulties in carrying out large-scale biological simulations of membrane proteins and their surrounding lipid environment. However, I'm thinking that if the important effects only arise in the limit of thousands of ion channels (BTW, how firm of a limit is this threshold? Can you capture the emergence of collective effects for an ion channel surrounded by, say, 50 to 100 ion channels?), maybe a coarse-grained model based on more detailed single ion channel studies might be appropriate. That is, you plug the data/results from the best simulations you can run on a single channel into some sort of simulation where you're looking at a less-detailed array of many ion channels. I know people have done molecular dynamics studies on systems such as KcsA where they've simulated some of the bilayer and solvent, but I have the impression that sort of work is not directly relevant to the questions at hand.

Andy Resnick – Thank you for the response regarding single-channel patch clamping. It is greatly appreciated.

[somasimple]

I feel you're irritated there, Andy.

I do not "sustain" at any moment the content of your link.
Please, avoid the confusion.
I'm speaking about well known water bonds...

[Andy Resnick]

http://nobelprize.org/nobel_prizes/chemistry/laureates/2003/mackinnon-lecture.pdf

I think too.

Ok, now we are getting somewhere. Again, this discussion would be a lot more efficient if you would simply put your ideas out there first, rather than requiring extensive back-and-forth to try and deduce your ideas.

From:

http://www.nature.com/nature/journal/v414/n6859/full/414023a0.html

'The structure sketched out the molecular basis of this specificity: a narrow 'selectivity filter' in the shape of an oxygen-lined electronegative tunnel in which dehydrated K+ (but not Na+) fits precisely. This structure rationalized why a K+ ion is so willing to leave its thermodynamically comfortable home in aqueous solution to enter the pore in a largely dehydrated form; the channel interior mimics the embrace of the water molecules in the inner hydration shell surrounding the ion in solution.

[...]

'Potassium ions are now seen in seven distinct sites along the pore-axis (Fig. 1a). Four of these reside in the narrow selectivity filter, and one in the wider hydrated cavity, as described earlier. By solving structures at varying ion concentrations, MacKinnon and colleagues argue that the four selectivity-filter sites are not all occupied simultaneously; rather, a pair of K+ ions separated by a single water molecule shifts in a concerted fashion between two configurations within the filter — inner and outer — occupying each about half the time (Fig. 1b).

[...]

'Most dramatically, in the position closest to the pore entrance a K+ ion is caught in flagrante, coordinated in front by four protein carbonyl groups reaching outwards, and behind by solvent; this must represent the long-postulated 'dehydration transition state' in which the ion sheds its water while entering the pore. It is now seen not to be a high-energy transition-state at all, but rather a true intermediate, an integral part of the flat landscape.'

This is all well and good, but I don't what this has to do with Sodium channels, which you consider to be the sole driver of an action potential spike, nor does it have to do with 'collective behavior' of thousands of channels, nor does it have anything to do with properties of lipid bilayers.

Consequently, now it's entirely unclear exactly *what* question you are trying to answer; we started with a discussion of the electrical dynamics of an action potential, to talking about sodium channel dynamics, and now you are discussing potassium channels.

Please take a moment to write out a coherent post discussing *your ideas*. Because right now I feel like I am chasing a moving target.

[somasimple]

Mikz,

Some numbers about the original experiments on the giant squid axon;

1/ its diameter is 0.5 mm => 500 µm
2/ its speed is 20 ms-1
3/ Action potential length is 40,000 µm => 40 mm.
4/ Surface of this patch is 62,800,000 µm˛
5/ it contains 20,700,000,000 ions channels
6/ its circumference is 1,571 µm
7/ this circumference has an average of 28,535 ion channels.
8/ each slice of 1 µm contains 518,000 ions channels.

I said thousand and thousands...

Andy, you're picky there. We know that membrane has K and Na channels.

[somasimple]

Ionic contrast terahertz near-field imaging of axonal water fluxes.

Masson JB, Sauviat MP, Martin JL, Gallot G.

Laboratoire d'Optique et Biosciences, Ecole Polytechnique, Centre National de la Recherche Scientifique Unité Mixte de Recherche 7645, Institut National de la Santé et de la Recherche Médicale U696, 91128 Palaiseau, France.

We demonstrate the direct and noninvasive imaging of functional neurons by ionic contrast terahertz near-field microscopy. This technique provides quantitative measurements of ionic concentrations in both the intracellular and extracellular compartments and opens the way to direct noninvasive imaging of neurons during electrical, toxin, or thermal stresses. Furthermore, neuronal activity results from both a precise control of transient variations in ionic conductances and a much less studied water exchange between the extracellular matrix and the intraaxonal compartment. The developed ionic contrast terahertz microscopy technique associated with a full three-dimensional simulation of the axon-aperture near-field system allows a precise measurement of the axon geometry and therefore the direct visualization of neuron swelling induced by temperature change or neurotoxin poisoning. Water influx as small as 20 fl per mum of axonal length can be measured. This technique should then provide grounds for the development of advanced functional neuroimaging methods based on diffusion anisotropy of water molecules.

PMID: 16547134 [PubMed - indexed for MEDLINE]

[somasimple]

Is the mobility of the pore walls and water molecules in the selectivity filter of KcsA channel functionally important?

Kraszewski S, Yesylevskyy SO, Boiteux C, Ramseyer C, Kharkyanen VN.

Institut UTINAM, Laboratoire de Physique Moléculaire, UMR CNRS 6213, Faculté des Sciences et Techniques, Université de Franche-Comté, 16 route de Gray, 25030 Besançon Cedex, La Bouloie, France.

We performed in-depth analysis of the forces which act on the K(+) ions in the selectivity filter of the KcsA channel in order to estimate the relative importance of static and dynamic influence of the filter wall and water molecules on ion permeation and selectivity. The forces were computed using the trajectories of all-atom molecular dynamics simulations. It is shown that the dynamics of the selectivity filter contributes about 3% to the net force acting on the ions and can be neglected in the studies focused on the macroscopic properties of the channel, such as the current. Among the filter atoms, only the pore-forming carbonyl groups can be considered as dynamic in the studies of microscopic events of conduction, while the dynamic effects from all other atoms are negligible. We also show that the dynamics of the water molecules in the filter can not be neglected. The fluctuating forces from the water molecules can be as strong as net forces from the pore walls and can effectively drive the ions through the local energy barriers in the filter.

PMID: 18404233 [PubMed - indexed for MEDLINE]

[Andy Resnick]

Mikz,

Some numbers about the original experiments on the giant squid axon;
<snip>

Andy, you're picky there. We know that membrane has K and Na channels.

Really...

Hi All,

It is a fact that Na+ ions cross the membrane and enter the cell during the rising phase of the action potential. The process happens because Na ions channels are open.
Then the ions channels becomes inactivated/closed for a while.

What happens to the Na+ ions that entered the cell?

I fully accept this explanation but if the rising is done by an influx then the decay must be done the same way in opposite direction (efflux) but all papers speak about Na ions channels inactivated or closed.
How is it possible to get a rapid decay when gates are closed?

Well,
the K conductance is lower than the Na one and the number of K channel is 10 time lower than the Na one.
How is it possible that in quite the same time (because you excluded all other ions species) the voltage decays like it grew...quickly (but Na ions are confined inside and Na channels closed or inactive)?

Cincinnatus,

I ask questions that seem important for the science community and it seems true that often I do not get any response. That is strange. I pointed out some basic violations of physics laws and the "faulty" drawings were removed from wikipedia because my argument was sufficiently strong.

<snip>

The theory must be refined. I have a theory that explains the fact, have you one that may explains this?
<snip>

You're welcome.

A theory that explains the underlying mechanisms of:

refractory periods
propagation without "passive spread"
inactivation of Na channel
branching, acceleration...


and respects facts and laws of physics may be of some interest?


This is not really a discussion anymore- please put forth your ideas in a coherent manner now.

[Renge Ishyo]

This marvelous membrane capacitor.
A single cm˛ that carries 1µF. That is clearly extraordinary and may make a furious envy to many electronics suppliers.

Most of natures inventions are far superior to our own in design, function, and economy. Let's face it, God (or if you prefer, "Random Mutation Man") is simply a better engineer than we are.


Please take a moment to write out a coherent post discussing *your ideas*. Because right now I feel like I am chasing a moving target.

I noticed a post or so ago that it seemed as if the target of the debate isn't always the same thing. I don't think the conversation is exactly moving in circles though, the randomness of the conversation has definitely increased from page to page indicating that the conversation is evolving in a quite natural way.

Of course, I should mention at this point that I DO have a bottle of special mineral water for sale if anyone is interested...

[somasimple]

The chase is prohibited. I belong to a protected specie.
Unable to give the results about simple experiments? Some reasonable doubt insinuated into your mind?
Perhaps you need some more:
Did they remove the ions channels when they measured the membrane capacitance? No, because they didn't know they were there. But you know it!
Electroneutrality: Even Roderick MacKinnon is aware of ions hydration (just see the pictures provided in the Nobel Lecture). That makes a big problem to a polarized membrane as a capacitor since you must solve its boundaries limits: Does the violation stops at 0.5 nm, more, less but how? What is the effect of hydration on charged particles?

Please forget your cynicism and re-adopt a scientific profile: examine the facts and conclude by yourself.

[DaleSpam]

Did they remove the ions channels when they measured the membrane capacitance? No, because they didn't know they were there. But you know it!
Why do you think the presence or absence of the ion channels would significantly change the capacitance of a membrane?

[somasimple]

Capacitance was measured with voltages/currents and there is voltage gated ions channels embedded in membrane.

[DaleSpam]

So what? That would change the conductance, not the capacitance. Conductance is a current which is proportional to a voltage, capacitance is a current which is proportional to the derivative of a voltage.

[somasimple]

And does a capacitor have latency? :biggrin:
So what?
And our conductances aren't linear at all!!!

[DaleSpam]

Your statement is unclear. The conductance of the membrane is a non-linear function of time and voltage. But conductance itself is a linear relationship between voltage and current. Do you understand the distinction? If not I will try again since I know there is some language barrier.

Also, what is the relevance to measuring the capacitance?

[DaleSpam]

This marvelous membrane capacitor.
A single cm˛ that carries 1µF. That is clearly extraordinary and may make a furious envy to many electronics suppliers.By the way, this is rather silly. We make phospholipid bilayers synthetically all the time and they regularly approach this capacitance. In fact, the capacitance is used as an easy metric to test the quality of the synthetic membrane.

Electronics suppliers are in no way furious or envious. They know about this technology and could generate as much phospholipid membrane as they like. The reason they don't is because such capacitors would be rather delicate and temperature sensitive as well as having low maximum-voltage ratings.

[somasimple]

I understand clearly the differences but I do not understand why you refuse to reply to previous questions and give results from experiments that costs less than 1$ each.

OK, lets suppose that membrane is a capacitor:
1/ Where are the metal planes?
2/ Where are the wires?
3/ In a capacitor, current flows through wires and circuit, is it the same with membrane?
4/ In a capacitor, dielectric insulates the two metal plates. In membrane, dielectric allows the whole currents fluxes, why?
5/ In a capacitor current is made from electrons, is it the same?
6/ In a capacitor, the distributed charges are symmetric, is it the same?
7/ in a capacitor, exchanges occur exclusively (except leakage current) through wires and are vertical, how are you able to enable also (in propagation) a transversal one and what rules does it follow?
8/ In your schematic, capacitor is associated with ions channels (resistances). Since wires are in both cases situated in the "capacitor plates", how do you connect them?
9/ since AP requires only a tiny 0.04 % of available ions, why do they choose to be associated to their far neighbors from the right or the left since there is closer ones just under their entry point?

[somasimple]

Perhaps the last question is a bit rude, sorry: You have to work around the well known electric law: current always takes the path of least resistance. (Of course, you may find an alternative explanation that may explain that laws may be violated... (sic)).
http://en.wikipedia.org/wiki/Path_of_least_resistance

[DaleSpam]

current always takes the path of least resistance.This is a commonly-repeated phrase, but it is not true. Current always takes all paths.

give results from experiments that costs less than 1$ each.I have no idea what you are trying to say. Why should an experiment cost less than $1?

OK, lets suppose that membrane is a capacitor:
1/ Where are the metal planes?
2/ Where are the wires?In an electronic circuit the charge carriers (electrons) are are free to move in the metal. In the neuron the charge carriers (cations) are are free to move in the electrolyte. The electrolytical fluid takes the place of the metal.
3/ In a capacitor, current flows through wires and circuit, is it the same with membrane?Yes. However there is also leakage current which occurs across the membrane as well as in commercial capacitors4/ In a capacitor, dielectric insulates the two metal plates. In membrane, dielectric allows the whole currents fluxes, why?What do you mean?5/ In a capacitor current is made from electrons, is it the same?No, the charge carriers are primarily cations as I mentioned above.6/ In a capacitor, the distributed charges are symmetric, is it the same?Yes.7/ in a capacitor, exchanges occur exclusively (except leakage current) through wires and are vertical, how are you able to enable also (in propagation) a transversal one and what rules does it follow?Please try again, there is a language problem and I didn't understand what you are asking. What are you trying to say with the word "vertical"?8/ In your schematic, capacitor is associated with ions channels (resistances). Since wires are in both cases situated in the "capacitor plates", how do you connect them?No, the capacitor represents the capacitance of the membrane. The resistors represent the concudtance of the ion channels. And the batteries represent the Nernst potential of the bulk concentration gradients.9/ since AP requires only a tiny 0.04 % of available ions, why do they choose to be associated to their far neighbors from the right or the left since there is closer ones just under their entry point?What do you mean by "associated to"? And what do you mean by "under their entry point"? Is this somehow related to the "vertical" from above?

Please try to take things slowly. Your questions don't seem to be unanswerable, but there is a considerable language barrier. I know it is hard to express things in a forigen language, and your English is much better than my French, but even so it is probably better to spend the effort to make one clear major question than to make 9 confusing or minor questions.

In any case, the bottom line is that the HH model works quite well. You are certainly free to propose a model which works even better, but in the absence of a better model it is somewhat silly to object so strenuously to this one.

[somasimple]

This is a commonly-repeated phrase, but it is not true. Current always takes all paths.
I will reply to the first statement because the subsequent responses will be useless if you do not solve this one.
Yes, current flows in all paths but prefers the least resistances.
So you admit the situation but I said I wasn't kind and it was a rude question.

So we said that entering ions are associated with their opposite counterions. The most of them are just under and some will make the job onto the right and onto the left.

NO! It can't work at all.

If I accept that a ion is associated in the internal milieu of the cell, I must also accept it was also the case, outside. That makes a big problem. You must, now, consider, that ions were also associated, outside.

Then, you must also fill the gap of initial conditions (IC); A solution where energy is low and where the model may function.
Of course, there is one with the hypothesis:
All ions are associated, on each side!
You solve the problem of electronegativity but you may encounter some bigger ones:
You have now salt crystals on each side of the cell.
Bad new for diffusion and too bad for currents: It is also a well known thing that crystals are effectively neutral but very good... insulators for the same reason.

This point of view has not my preference: I prefer water bondings for salts...

[DaleSpam]

I will reply to the first statement because the subsequent responses will be useless if you do not solve this one.
Yes, current flows in all paths but prefers the least resistances. I don't like using human psychological terms like "prefers" to describe inanimate objects. I would say that current goes through all paths, but more current goes through the path of least resistance than through the other paths. This makes it clear that current is going through all paths and still covers the essence of the "path of least resistance" concept.

[somasimple]

The criticism is well received but the model remains still invalid.

[DaleSpam]

NO! It can't work at all.

If I accept that a ion is associated in the internal milieu of the cell, I must also accept it was also the case, outside. That makes a big problem. You must, now, consider, that ions were also associated, outside.

Then, you must also fill the gap of initial conditions (IC); A solution where energy is low and where the model may function.
Of course, there is one with the hypothesis:
All ions are associated, on each side!
You solve the problem of electronegativity but you may encounter some bigger ones:
You have now salt crystals on each side of the cell.You still haven't explained about what you mean by "associated".

I don't understand how you make the completely random jump to salt formation. It is certainly not based on any understanding of correct physics. Do you understand how a salt crystal dissolves or forms in a good polar solvent like water?

Bad new for diffusion and too bad for currents: It is also a well known thing that crystals are effectively neutral but very good... insulators for the same reason.I am sorry, but you are completely mistaken. Do you understand what it means for a salt solution to be an electrolyte? It means precisely that you get both ionic currents and diffusion even even with both cations and anions present in the solution. This isn't even a biological phenomenon, it is simple high-school level chemistry. The concentrations are way to low to get salt formation, and there is diffusion and electrical conduction via ionic currents.

[DaleSpam]

The criticism is well received but the model remains still invalid.No it is not invalid. It fits a wide range of experimental data within its domain of applicability. That is all that is required to validate a scientific model. I am having a hard time following your objections, but the simple fact remains that the HH model works. Therefore it is valid. End of story.

If you make any model (it doesn't have to have any physical inspiration as the HH model does), propose a hypothesis based on the model, perform the experiment, and get data supporting the hypothesis, then the model is validated. That is the nature of science.

As you perform more experiments you may get some experiments that don't match the model. Then you learn the limits of the domain of applicability for the model. That still doesn't make the model invalid within its already scientifically validated domain.

Some later person (like yourself) may come up with a better model that fits all the data including this new domain and, if the new model is valid, it must agree with the old model within the old model's limited domain. Such is the nature of the scientific method.

[somasimple]

I do not understand how you produce an equal charge of opposite sign when you move (i.e) a Na+ ion from outside to inside.

My attempt was clearly silly as the model.
Perhaps you think that Na+ lets a "free" electron on the opposite side?

[somasimple]

More simply,

with a simple example: KCl and water with a semi permeable membrane to K+. (High school).

IC:
The KCl is on the left (membrane at center).

Terminal conditions:

Some K+ ions are at right and
membrane is now polarized (becomes a capacitor).


Problem:
Describe how you obtain the second result?

[somasimple]

Perhaps you have been taught of something like this:

http://nerve.bsd.uchicago.edu/rp1.htm

I have an immense respect for Prof Bezanilla but I reject this model.

[DaleSpam]

I do not understand how you produce an equal charge of opposite sign when you move (i.e) a Na+ ion from outside to inside.

My attempt was clearly silly as the model.
Perhaps you think that Na+ lets a "free" electron on the opposite side?No, in an electrolyte the primary charge carriers are dissolved ions. However, I don't understand why you think moving an ion from one side to the other should "produce" an equal charge of opposite sign. Since the electrolyte is, in bulk, electroneutral you know that there is already an anion in solution for every cation. So no anion needs to be produced, they already exist in the solution.

KCl and water with a semi permeable membrane to K+. (High school).

IC:
The KCl is on the left (membrane at center).

Terminal conditions:

Some K+ ions are at right and
membrane is now polarized (becomes a capacitor).


Problem:
Describe how you obtain the second result?Do you know the concept of Ampere's Law (http://en.wikipedia.org/wiki/Amperes_Law) and displacement currents (http://en.wikipedia.org/wiki/Displacement_current)? You may also find the Goldman equation (http://en.wikipedia.org/wiki/Goldman_equation) to be useful. This is a very fundamental set of concepts that apply to many different systems, not just neurons. So I would most strongly encourage you to study this until you understand how the second result happens, but you will probably need to branch out beyond the links I have provided. Please, familiarize yourself with the fundamental concepts and post any follow-up questions that you have.

[somasimple]

I know you consider that I'm an idiot.
Consider that I'm stubborn, too!

I'm now facing with a strange behavior from your own: Every time we're close to get, at last, a reply, you change abruptly and bring a ton of useless material that has nothing to see with the current question.

So, I'll restate one more time my simple "virtual" and well known experiment:

Two compartments are separated by a semi-permeable membrane oriented to the "water" side (semi permeable for K+).
IC:
compartment one contains water.
compartment two is filled with a solution of KCl (potassium chloride). Concentration doesn't matters but we will take 40 mM.
The membrane capacitor is supposed discharged, right?
http://nerve.bsd.uchicago.edu/rp1.htm

Then,
At a time t1, since some K+ have moved and now, the membrane must carry some charges since we have a potential difference?

Please describe the charges carried on each side (if needed) of the membrane that explains it functions as a capacitor and maintains charges?
Hope the question is sufficiently clear?

[Cincinnatus]

It doesn't matter how many of his questions that you answer. He doesn't think there's something in particular wrong with our understanding of action potential generation / propagation in neurons. Instead he's sure that the theory is wrong for a priori reasons and will keep changing the subject until you get tired of arguing with him.

If you google him you'll see that he's done the same thing on many fora including this one several other times. It's really pretty useless to keep answering his questions as he's never going to stop and say "oh I get it now".

Somasimple, why don't you just explain your theory? (in the IR forum here) It may well be that you can explain the data as well as or better than the Hodgkin-Huxley model (and it's extensions). Why not let us judge your hypothesis in the only way hypotheses can be, by testing them with real data.

Until then, the fact remains that the Hodgkin-Huxley model is very very good at making testable predictions and works better than any other model we currently have. This alone is reason enough to think that the model is at least a good approximation to the truth.

[somasimple]

Cincinnatus,

The same answer may apply to you. Are you unable to describe the thing?

[somasimple]

If you google him you'll see that he's done the same thing on many fora including this one several other times.
And I got, every time, different explanations. :confused:

Until then, the fact remains that the Hodgkin-Huxley model is very very good at making testable predictions

We are currently testing the initial conditions of this model and you refuse to explain the next mandatory step of its functionning. :confused:

Then,
At a time t1, since some K+ have moved and now, the membrane must carry some charges since we have a potential difference?

Please describe the charges carried on each side (if needed) of the membrane that explains it functions as a capacitor and maintains charges?
Hope the question is sufficiently clear?
Giving a good answer is the best way to smash me down!
Come on, it's my pleasure.

[DaleSpam]

I'm now facing with a strange behavior from your own: Every time we're close to get, at last, a reply, you change abruptly and bring a ton of useless material that has nothing to see with the current question.It has everything to do with the current question. If you understood the principles I linked to then you would understand capacitors and how a membrane acts as one, as well as how a potential difference can be established by a chemical gradient. I take it then that you did not even bother to read what I provided.

So, I'll restate one more time my simple "virtual" and well known experiment:

Two compartments are separated by a semi-permeable membrane oriented to the "water" side (semi permeable for K+).
IC:
compartment one contains water.
compartment two is filled with a solution of KCl (potassium chloride). Concentration doesn't matters but we will take 40 mM.
The membrane capacitor is supposed discharged, right?
http://nerve.bsd.uchicago.edu/rp1.htm

Then,
At a time t1, since some K+ have moved and now, the membrane must carry some charges since we have a potential difference?

Please describe the charges carried on each side (if needed) of the membrane that explains it functions as a capacitor and maintains charges?
Hope the question is sufficiently clear?I will restate my answer. The concentration of K+ increases until it reaches the equilibrium potential described by the Goldman equation (http://en.wikipedia.org/wiki/Goldman_equation). That movement of K+ is a current and current always needs to make a loop so there must be a return current, but the membrane is not permeable to Cl-, so the return current is a displacement current (http://en.wikipedia.org/wiki/Displacement_current). A displacement current is associated with a change in the E-field as per Ampere's law (http://en.wikipedia.org/wiki/Amperes_Law). Since an electrolyte (http://en.wikipedia.org/wiki/Electrolyte) is a conductor it cannot sustain an internal E-field (http://hyperphysics.phy-astr.gsu.edu/Hbase/electric/gausur.html#c2), therefore all of the E-field must be across the membrane. A device which stores energy in an E-field between two conductors is called a capacitor (http://en.wikipedia.org/wiki/Capacitor). Therefore the membrane is a capacitor and a simple application of Gauss' law (http://en.wikipedia.org/wiki/Gauss_law) across the membrane shows that it must carry equal and opposite charge density on each side. Obviously, since the charge carriers in this electrolyte are K+ and Cl-, the charges will be K+ on one side and Cl- on the other.

I hope the answer is sufficiently clear. If you have some specific question about one of the above physical principles, please don't hesitate to ask. If you merely have another rant about HH not being valid, please back it up with some experimental data that HH fails to explain and present your alternative which does explain it.

Your failure to understand HH and the underlying principles is not a valid criticism.

[Cincinnatus]

For the lurkers following this thread, the Goldman equation which DaleSpam refers to in the previous post is the same as the equation we had been calling the GHK (Goldman-Hodgkin-Katz) equation earlier in this discussion. It is a variant of the Nernst equation which may be more familar to some people...

Anyway, somasimple doesn't seem to accept the GHK equation as applied to biological membranes...