membrane potential dependency from ion concentrations?

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Bonic
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membrane potential dependency from ion concentrations?

Post by Bonic » Mon Nov 26, 2018 4:07 pm

Hello everybody,

In my thesis i will work with NEURON. In order to understand the NEURON simulations better, i refresh my neurophysiology knownledge. Thereby, some questions came up, i stuck with. May you can help me.

For example, if i increase the internal potassium concentration (for example by current injection), the cell will hyperpolarize according to Goldman Equation (and the increased chemical gradient). My problem is that i would assume the increased potassium concentration in the cell would have depolarized the cell in the first place. Is there any way i can visualize this? Same problem with injection of potassium outside the cell but vice versa.

My second question might can help elucidate my first question: The Goldman Equation only considers Ions for which the membran has permability. What If i would increase for example the outside calcium concentration (or the concentration of any other ion the cell has little/no permability for)? Would the change in concentration of this ion affect the membrane potential?

I have not discovered any features of NEURON, which considers ion concentrations directly (only the ion-conductancies and potentials). Is there no need for it? Is the cell described sufficiently by specification of the membrance conductance and the equilibrium potential of this neuron?

I would really appreciate help as i am stucked.

With kind regards,

Bonic

ted
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Re: membrane potential dependency from ion concentrations?

Post by ted » Mon Nov 26, 2018 5:29 pm

i would assume the increased potassium concentration in the cell would have depolarized the cell in the first place . . .
What If i would increase for example the outside calcium concentration (or the concentration of any other ion the cell has little/no permability for)?
It would be very useful to take a good course in physical chemistry, or at least a course in biophysics that addresses experiments that involve semipermeable membranes. That will require time and effort, so in the meantime you might find it helpful to probe the web for instructional material about the origin of membrane potential.
I have not discovered any features of NEURON, which considers ion concentrations directly (only the ion-conductancies and potentials).
Read chapters 8 and 9 of The NEURON Book. Also see the Programmer's Reference documentation of ion_style and related keywords.

Bonic
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Re: membrane potential dependency from ion concentrations?

Post by Bonic » Mon Nov 26, 2018 7:23 pm

ted wrote:
Mon Nov 26, 2018 5:29 pm
i would assume the increased potassium concentration in the cell would have depolarized the cell in the first place . . .
What If i would increase for example the outside calcium concentration (or the concentration of any other ion the cell has little/no permability for)?
It would be very useful to take a good course in physical chemistry, or at least a course in biophysics that addresses experiments that involve semipermeable membranes. That will require time and effort, so in the meantime you might find it helpful to probe the web for instructional material about the origin of membrane potential.
I have not discovered any features of NEURON, which considers ion concentrations directly (only the ion-conductancies and potentials).
Read chapters 8 and 9 of The NEURON Book. Also see the Programmer's Reference documentation of ion_style and related keywords.
Thanks for the answer. I appreciate the reference to the NEURON book and i will read the adviced chapters.

I honestly think that i understand the origin of the membrane potential. In all the books i have read, the explanation for how it builds up is basically the same and i can comprehend. Also i have good training in (bio)physical chemistry. From the point of the electrochemical gradient (and the Nernst-equation) i can understand why the cell behaves like it does after injecting current.

In my on words the theory is as following, assuming the membrane is only permeable for potassium:

1. After injecting potassium current in the cell, potassium will first, due to the increased inside-outside concentraion gradient, diffuse out of the cell and therby carry charge
2. This will charge the membrane until the equilibrium potential for this specific potassium concentration ratio is reached (It is assumed that the potassium concentration on both sides of the membrane stays the same as the amount of potassium diffusing through the membran is negligible small in relation to the total potassium).
3. The equilibrium potential that is reached (and calculated by the Nernst equation) will contrast the potassium diffusion out of the cell. A point of thermodynamic equilibrium has adjusted when you assume the membrane is just permeable fo potassium.


After google search i found similary question to mine in the internet ("Why does an injected potassium current in a cell not charge the membrane and depolarize the cell?"). In the answers to these question it is always refered to the Goldman equation and the electrochemical gradient.

When i visualizing injecting potassium current in the cell i could think of something like the 3 points i described above.
My problem is that i do not understand why an injected current of potassium (which is charged) is able to diffuse in the first place (unlike it is contrasted by an anion (is it contrasted by an anion?). When the potassium is not contrasted by an anion, i would assume that after a potassum current is injected within the cell, it will directly settle down to the negativly charged membrane within the cell...

By probing the web (and books) for the question of the effect of ion-concentration-changes, the membrane has no permability for, i have found nothing...An injected charge should settle to the membrane immediatly. This is because ions without a cation or anion as counterpart can not diffuse freely in the cell or extracellular. So changes in the calcium concentrations should change the membrane potential unlike the same amount of an anion which contrast the calcium will be injected at the same time.

ted
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Re: membrane potential dependency from ion concentrations?

Post by ted » Tue Nov 27, 2018 1:19 am

Quoting from your original post:
if i increase the internal potassium concentration (for example by current injection), the cell will hyperpolarize according to Goldman Equation (and the increased chemical gradient). My problem is that i would assume the increased potassium concentration in the cell would have depolarized the cell in the first place.
Start by thinking about the simplest case. For the time being, forget about current injection--it just introduces a confounding factor that interferes with understanding. Instead, suppose you attach a patch electrode filled with a high concentration of K gluconate or K citrate to a cell, and break the cell membrane. What do you suppose happens next? (FYI neither gluconate nor citrate can pass through the cell membrane).
The equilibrium potential that is reached (and calculated by the Nernst equation) will contrast the potassium diffusion out of the cell.
Contrast? You mean "oppose"?
i found similary question to mine in the internet ("Why does an injected potassium current in a cell not charge the membrane and depolarize the cell?")
Interesting. Where?
In the answers to these question it is always refered to the Goldman equation
No mention of the Nernst equation?

I do not understand what you mean by the word "contrast" in this sentence, or the one that follows it:
i do not understand why an injected current of potassium (which is charged) is able to diffuse in the first place (unlike it is contrasted by an anion
When the potassium is not contrasted by an anion, i would assume that after a potassum current is injected within the cell, it will directly settle down to the negativly charged membrane within the cell
Do you imagine that intracellular potassium is plastered up against the inner surface of the cell membrane? What about intracellular sodium? Why would that happen?
By probing the web (and books) for the question of the effect of ion-concentration-changes, the membrane has no permability for, i have found nothing
Even so, "how do impermeant ions (ions to which a membrane is impermeable) affect membrane potential?" is still a good question. The answer is: they don't. Facts:
1. Intracellular and extracellular fluid is full of impermeant ions.
2. If an ion can't pass through a membrane, a concentration gradient can't force it through that membrane, and that means it can't produce the charge imbalance that is needed to contribute to a transmembrane electrical potential gradient.

FYI: most proteins are negatively charged, but very few can pass through healthy cell membranes. As far as I know, there are no reports of such movements having any detectable effect on on membrane potential.

Bonic
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Re: membrane potential dependency from ion concentrations?

Post by Bonic » Tue Nov 27, 2018 5:13 pm

Again, thanks for your patience and help Ted. I really appreciate your inputs and you effort in order to help me.
if i increase the internal potassium concentration (for example by current injection), the cell will hyperpolarize according to Goldman Equation (and the increased chemical gradient). My problem is that i would assume the increased potassium concentration in the cell would have depolarized the cell in the first place.
Start by thinking about the simplest case. For the time being, forget about current injection--it just introduces a confounding factor that interferes with understanding. Instead, suppose you attach a patch electrode filled with a high concentration of K gluconate or K citrate to a cell, and break the cell membrane. What do you suppose happens next? (FYI neither gluconate nor citrate can pass through the cell membrane).
Hopefully, i understand the experimental set-up correctly. For simplification, i will additionally assume that i have blocked any other channels except the Kalium-channels. In this case, the K+ would flow out of the cell until the equilibrium potential for the concentration
[K]o/([K]i+[K gluconate]), calculated by the Nernst equation, is reached.
The gluconate, which is the corrosponding anion to the K+ which left the cell, will remain in the cell as anions (somehow?) and might stick to the cell-membrane.

The equilibrium potential that is reached (and calculated by the Nernst equation) will contrast the potassium diffusion out of the cell.
Contrast? You mean "oppose"?
Yes, i mean "oppose". I am not an english-native-speaker. That is why i might sometimes use words accidentally in the wrong context.
I do not understand what you mean by the word "contrast" in this sentence, or the one that follows it:
i do not understand why an injected current of potassium (which is charged) is able to diffuse in the first place (unlike it is contrasted by an anion
I just meant unlike it is an kation-anion-pair, like K+gluconate or K+citrate

When the potassium is not contrasted by an anion, i would assume that after a potassum current is injected within the cell, it will directly settle down to the negativly charged membrane within the cell
Do you imagine that intracellular potassium is plastered up against the inner surface of the cell membrane? What about intracellular sodium? Why would that happen?
Honestly, yes i did think so. Its because after injecting current (K+ for example) the cytoplasm is not electroneutral anymore (as it should be). So i imagine the excess of K+ will plaster up against the inner surface so that the cytoplasm remains electroneutral...That may lead to the misconception of me that the cell will depolarize at first.
By probing the web (and books) for the question of the effect of ion-concentration-changes, the membrane has no permability for, i have found nothing
Even so, "how do impermeant ions (ions to which a membrane is impermeable) affect membrane potential?" is still a good question. The answer is: they don't. Facts:
1. Intracellular and extracellular fluid is full of impermeant ions.
2. If an ion can't pass through a membrane, a concentration gradient can't force it through that membrane, and that means it can't produce the charge imbalance that is needed to contribute to a transmembrane electrical potential gradient.

FYI: most proteins are negatively charged, but very few can pass through healthy cell membranes. As far as I know, there are no reports of such movements having any detectable effect on on membrane potential.

What i do not understand is this: When i inject an amount of impermeant ions into the cell, what happens to the excess charge of the injected impermeant ions ? The cytoplasm is supposed to stay electroneutral, so where does the charge go? In my mind, the membrane potential just have to change due to the injection of charge.
The impermeant ions, you are talking about, are already in the cell and are already neutralised. So they do not affect the membrane potential. But if i would inject imperment ions (for example Ca2+) with an electrode they are not neutralised, right?

ted
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Re: membrane potential dependency from ion concentrations?

Post by ted » Wed Nov 28, 2018 10:55 am

The proper setting for discussions like this would be a graduate seminar with a small number of students. It doesn't seem likely to occur in a typical classroom.
For simplification, i will additionally assume that i have blocked any other channels except the Kalium-channels
The assumption is unnecessary, but if it helps avoid confusion, OK. The cell will do the right thing.

Both K and gluconate will diffuse into the cell. The increase of ki will make ek more negative, and v (membrane potential) will also become more negative. gluconate will have no effect on membrane potential, and is unlikely to associate itself with the cell membrane because of its negative charge (the molecules that comprise the cell membrane are presumably negatively charged).

Don't worry about vocabulary. If I run into a word or phrase I don't understand, or "slovenliness of language," I will ask what is intended.
Orwell, G. "Politics and the English Language." 1946. See https://en.wikipedia.org/wiki/Politics_ ... h_Language

Most intracellular elemental ions are surrounded by water molecules, not bound to membranes. Otherwise, cytoplasmic resistivity would be much higher than ~100 ohm cm. The only intracellular ionic species that is likely to associate with membrane is calcium, but most intracellular calcium is either buffered (associated with hydroxyl i.e. OH-, or with non-membrane organic molecules) or "free" and not closely associated with cell membranes at all.

Even if membrane potential is "large", intracellular charge imbalance is so small that cytoplasm is for all practical purposes electroneutral--the difference between total charge attributable to anions and total charge attributable to cations lies well below the resolution of analytical chemical methods.
When i inject an amount of impermeant ions into the cell, what happens to the excess charge of the injected impermeant ions ?
It stays in the cell. But you can't inject impermeant ions by themselves, either by bulk injection or simple diffusion, because they will be accompanied by counterions. And it doesn't matter whether the counterions are permeant or impermeant. The cytoplasm remains essentially electroneutral. Time to read about Donnan equilibrium.

One situation in which it might be possible to "inject" some impermeant species X into a cell is via an electrode filled with an ion exchange resin. The resin, which is immobile and remains in the electrode, would be the counterion for X in the electrode. One could attach such an electrode to a cell and use it to pass a current that forces X into the cell. Remove the electrode and X stays in the cell. What do you think happens to such a cell if the cell membrane has no ionic permeability at all? What happens if the cell membrane is permeable to one or more other ions that are in the intracellular and extracellular fluids?

Bonic
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Re: membrane potential dependency from ion concentrations?

Post by Bonic » Sat Dec 01, 2018 10:02 am

Hey Ted, Thanks again for your detailed response. This thread helped me to a great degree to develop a visual concept of what is happening in the cell so far.

But you can't inject impermeant ions by themselves, either by bulk injection or simple diffusion, because they will be accompanied by counterions. And it doesn't matter whether the counterions are permeant or impermeant. The cytoplasm remains essentially electroneutral. Time to read about Donnan equilibrium.
I think that was what i got wrong. I assumed, most probably due to a lack of experimental experience in electrophysiology, that it is possible to inject ions without their counterions. In this case however the charge of the total system would be influenced and would change. In order to apply the Goldman equation to determine if a cell will de-/hyperpolarize after current injection, it is assumed that the injected current is electorneutral as, for example, potassium is always accompained by its counterion. In order to apply Goldman/Nernst equation it is prerequisite that the total charge of the system will not change.
The proper setting for discussions like this would be a graduate seminar with a small number of students. It doesn't seem likely to occur in a typical classroom.
I think so, too and it would have helped me. A lot of people, which are new to electrophysiology, will think for example that ions will be injected not accompanied by their counterions. In books it is often presented that way.This might lead to misunderstandings like the ones i had. For people who are experient in experimental electrophysiology it is self-sufficient that injected ions are always accompanied by their counterions and so they will not mention it additionally.

Time to read about Donnan equilibrium.
I did so, now. But Donnan equation only applies in living cells when the Na+/K+-ATPase fails, right?
One situation in which it might be possible to "inject" some impermeant species X into a cell is via an electrode filled with an ion exchange resin. The resin, which is immobile and remains in the electrode, would be the counterion for X in the electrode. One could attach such an electrode to a cell and use it to pass a current that forces X into the cell. Remove the electrode and X stays in the cell. What do you think happens to such a cell if the cell membrane has no ionic permeability at all?
I think in this case, if X is a cation, the cell will depolarize.
What happens if the cell membrane is permeable to one or more other ions that are in the intracellular and extracellular fluids?
That was basically the scenario i thought of, when i started this thread at first. If the na+/k+-atpase will not work, the donnan equilibrium may arises after some time. Otherwise, i think, if the injected X is a cation, the cell will depolarize at first. After some time a dynamic equilibrium may occur, if the na+/k+-atpase will not fail.

ted
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Re: membrane potential dependency from ion concentrations?

Post by ted » Sun Dec 02, 2018 2:55 pm

The proper setting for discussions like this would be a graduate seminar with a small number of students.
I think so, too and it would have helped me.
Is it too late to ask the instructors or institution for a tuition refund?
Time to read about Donnan equilibrium.
I did so, now. But Donnan equation only applies in living cells when the Na+/K+-ATPase fails, right?
I mentioned Donnan equilibrium as an example of a situation in which there is an impermeant charged species, in order to illustrate a more general point. The impermeant ion makes no direct contribution to membrane potential, regardless of whether active transport is operating or not.
One situation in which it might be possible to "inject" some impermeant species X into a cell is via an electrode filled with an ion exchange resin. The resin, which is immobile and remains in the electrode, would be the counterion for X in the electrode. One could attach such an electrode to a cell and use it to pass a current that forces X into the cell. Remove the electrode and X stays in the cell. What do you think happens to such a cell if the cell membrane has no ionic permeability at all?
I think in this case, if X is a cation, the cell will depolarize.
True. The depolarization develops while the impermeant cation is being injected, and the depolarization at any particular time t is proportional to the total amount of charge that has been injected by that time. If the membrane is impermeable to all ionic species, the depolarization persists forever after the injection stops. If the cytoplasm is permeable to some other ionic species that is present in the cytoplasm and/or extracellular fluid, that other species may move across the cell membrane depending on its electrochemical gradient, and eventually the the cell will be at equilibrium.

Bonic
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Re: membrane potential dependency from ion concentrations?

Post by Bonic » Wed Dec 05, 2018 6:07 am

Is it too late to ask the instructors or institution for a tuition refund?
In germany (where i study) students do not pay fees for public university education. As medical students, the physiology professors did not really expect us to understand the depth of electrophysiology (most medical students are not really interested in science and lack time to go into deep). Since a lot of physiology professor here, have also undergone training in german medical schools, they might never made the effort to really understand electrophysiology on their own...exspecially when its not their field of specialisation...but of course it is hard to estimate the knownledge of a professor as a student. At the moment i attend a computational neuroscience course for medical students. I will ask the lecturer if we can discuss this topic in our group.

For now, i have found a pretty good physical chemistry book, which deals with membrane physiology. Thanks again for your responses to my questions. Your inputs have made the start in this topic a lot easier.

ted
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Re: membrane potential dependency from ion concentrations?

Post by ted » Wed Dec 05, 2018 10:25 am

students do not pay fees for public university education.
Then request a tax refund. Ask a friend from France for help.

With regard to medical school, there's too much to learn, and too little time to learn it. Besides, after students graduate (at least in this country), they're going to be spending most of their time responding to mandated checklists and dealing with compliance regulations created by bean counters and others who never really liked taking care of patients.

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