# Membrane potential explained: Nernst potential

Good evening,

I got a seriously problem at understanding the membrane potential for ions in a cell. Particulary, i dont understand the case for example for ions with a charge of 2 or higher. I take a look on two scenarios: If you got an ion like calium and got a concentration ratio of 1:10 (inside utside) in a cell you get a voltage of -58mV. If you then just change the ion with calzium (its charge is +2) and got the same concentration ration, then you will have exactly the half of the potential. And this is what i dont get. Why is that so????

For me, potential is a quantity that is depending from the amount of charge you have there. As far as i understand the potential, i thought there will be the same amount of charge for both cases (calium und calzium). But it seems its not, why is that so?

Hope someone can help me i really struggle with that question and it wont let me rest haha
Best Regards

• atyy and Delta2

atyy
You have to remember that the bulk of the solution is electrically balanced, because if you use KCl or CaCl2, the chloride will balance the charge of the K+ or Ca2+. So it is not the concentration difference that is "directly" producing the membrane potential.

The concentration difference drives ions from the side with higher concentration to the side with lower concentration. Because of the selective permeability, a charge difference is produced (there is a tiny change in the concentration, but a huge change in the membrane potential). The charge difference will tend to cause ions to move against the concentration gradient, and the steady state will come when the tendency to move down the concentration gradient is balanced by the tendency to move against the potential gradient.

• JanSpintronics
You have to remember that the bulk of the solution is electrically balanced, because if you use KCl or CaCl2, the chloride will balance the charge of the K+ or Ca2+. So it is not the concentration difference that is "directly" producing the membrane potential.

The concentration difference drives ions from the side with higher concentration to the side with lower concentration. Because of the selective permeability, a charge difference is produced (there is a tiny change in the concentration, but a huge change in the membrane potential). The charge difference will tend to cause ions to move against the concentration gradient, and the steady state will come when the tendency to move down the concentration gradient is balanced by the tendency to move against the potential gradient.
Yeah it is a electrical neutral solution but i dont see how this effect the potential or the voltage...
I mean, the Ca+2 will drive to the side of less concentration and in case of chloride i thought i cant go through the membran, so it will stay on one side.
I understand what you write about the origin but what you meant that the concentration difference is not directly producing the potential? What else it is?

Ygggdrasil
Gold Member
Good evening,

I got a seriously problem at understanding the membrane potential for ions in a cell. Particulary, i dont understand the case for example for ions with a charge of 2 or higher. I take a look on two scenarios: If you got an ion like calium and got a concentration ratio of 1:10 (inside utside) in a cell you get a voltage of -58mV. If you then just change the ion with calzium (its charge is +2) and got the same concentration ration, then you will have exactly the half of the potential. And this is what i dont get. Why is that so????

For me, potential is a quantity that is depending from the amount of charge you have there. As far as i understand the potential, i thought there will be the same amount of charge for both cases (calium und calzium). But it seems its not, why is that so?

Hope someone can help me i really struggle with that question and it wont let me rest haha
Best Regards

The Nernst potential is not calculating the voltage resulting from a conentration gradient of ions across a membrane. Rather, the Nernst potential (also called the reversal potential) is the membrane potential at which there will be no net movement of ions across the membrane, given a certain concentration gradient of ions (i.e. where the system will be at equilibrium).

Consider your example of a 1:10 inside to outside ratio of a monovalent Na+ ion versus a divalent Ca2+ ion. Both will have a similar drive to enter the cell to equalize the concentration across the membrane. Which ion would require a larger membrane potential to counteract that drive to move down the concentration gradient?

• JanSpintronics and atyy
atyy
The Nernst potential is not calculating the voltage resulting from a conentration gradient of ions across a membrane. Rather, the Nernst potential (also called the reversal potential) is the membrane potential at which there will be no net movement of ions across the membrane, given a certain concentration gradient of ions (i.e. where the system will be at equilibrium).
I think the OP is thinking that although the Nernst equation only gives the equilibrium potential, if one has a model of the dynamics, that model has more information, and we should be able to derive the equilibrium situation from the dynamics.

A (presumably wrong) heuristic model of the dynamics might be: For a divalent ion, each ion that goes over will feel twice the electrical force pulling it back, for the same number of ions that have gone over. So overall, only half the number of ions will be able to go over, compared to the monovalent case. Since half the ions go over, but each ion has twice the charge, the voltage should be the same.

We know this is wrong, and your post shows a simple way to understand the right answer. But in terms of the above model, presumably the part that is wrong is: for each ion that goes over, the electrical force pulling it back is twice?

• JanSpintronics
The Nernst potential is not calculating the voltage resulting from a conentration gradient of ions across a membrane. Rather, the Nernst potential (also called the reversal potential) is the membrane potential at which there will be no net movement of ions across the membrane, given a certain concentration gradient of ions (i.e. where the system will be at equilibrium).
Im sorry, correct me if im wrong but isnt that the same? Or you mean its a potential and not a voltage?

Im asking because I saw an experiment with exactly the example below for KCl and CaCl2. The voltage we meassure for KCl was 58 and for CaCl2 it was 29, the half.
Consider your example of a 1:10 inside to outside ratio of a monovalent Na+ ion versus a divalent Ca2+ ion. Both will have a similar drive to enter the cell to equalize the concentration across the membrane. Which ion would require a larger membrane potential to counteract that drive to move down the concentration gradient?
Okay if i understand the concept of a potential it is the potential energy of one charge. if we say 2 Calium and 1 Calzium ion is moving on the other side then it should be the same because we have the same amount of charges on both sides in both cases
I know its not right but i dont find my mistake.

A (presumably wrong) heuristic model of the dynamics might be: For a divalent ion, each ion that goes over will feel twice the electrical force pulling it back, for the same number of ions that have gone over. So overall, only half the number of ions will be able to go over, compared to the monovalent case. Since half the ions go over, but each ion has twice the charge, the voltage should be the same.
That is exactly my thought but i dont see where it is wrong...

We know this is wrong, and your post shows a simple way to understand the right answer. But in terms of the above model, presumably the part that is wrong is: for each ion that goes over, the electrical force pulling it back is twice?
Either im blind or dumb or both i dont see it

Ygggdrasil
Gold Member
I think the OP is thinking that although the Nernst equation only gives the equilibrium potential, if one has a model of the dynamics, that model has more information, and we should be able to derive the equilibrium situation from the dynamics.

A (presumably wrong) heuristic model of the dynamics might be: For a divalent ion, each ion that goes over will feel twice the electrical force pulling it back, for the same number of ions that have gone over. So overall, only half the number of ions will be able to go over, compared to the monovalent case. Since half the ions go over, but each ion has twice the charge, the voltage should be the same.

We know this is wrong, and your post shows a simple way to understand the right answer. But in terms of the above model, presumably the part that is wrong is: for each ion that goes over, the electrical force pulling it back is twice?

Remember that the cations are not the only ions in solution, so you'd also have to account for the effect on the movement of anions also (which is why considering the dynamics is difficult).

I'm not exactly sure about the details of the system you're talking about (are you fixing the potential across the membrane? You seem to have a situation where the voltage varies as you move ions across, which is a very complicated condition to consider). Here may be a simpler system:

Consider a membrane with a fixed potential across (i.e. you hook the two sides up to a battery). As you would expect, divalent calcium ions (Ca2+) would experience a stronger pull from that potential than monovalent potassium ions (K+). So, for a fixed voltage, you would have a higher concentration gradient of Ca2+ than K+.

Say, that the potential across the membrane is sufficient to get a concentration gradient of Ca2+ of 10:1. Because K+ is pulled less strongly by the voltage, the concentration gradient of K+ will be less that 10:1. Therefore, to get a concentration gradient of 10:1 for K+ will require a greater potential difference between the two sides of the membrane than was necessary for Ca2+.

Ygggdrasil
Gold Member
Im sorry, correct me if im wrong but isnt that the same? Or you mean its a potential and not a voltage?

Im asking because I saw an experiment with exactly the example below for KCl and CaCl2. The voltage we meassure for KCl was 58 and for CaCl2 it was 29, the half.

Okay if i understand the concept of a potential it is the potential energy of one charge. if we say 2 Calium and 1 Calzium ion is moving on the other side then it should be the same because we have the same amount of charges on both sides in both cases
I know its not right but i dont find my mistake.

See the explanation above. If you move one ion across the membrane, other ions will move as well to establish an equilibrium and you also need to consider what happens to those ions.

Remember that the cations are not the only ions in solution, so you'd also have to account for the effect on the movement of anions also (which is why considering the dynamics is difficult).

I'm not exactly sure about the details of the system you're talking about (are you fixing the potential across the membrane? You seem to have a situation where the voltage varies as you move ions across, which is a very complicated condition to consider). Here may be a simpler system:

Consider a membrane with a fixed potential across (i.e. you hook the two sides up to a battery). As you would expect, divalent calcium ions (Ca2+) would experience a stronger pull from that potential than monovalent potassium ions (K+). So, for a fixed voltage, you would have a higher concentration gradient of Ca2+ than K+.

Say, that the potential across the membrane is sufficient to get a concentration gradient of Ca2+ of 10:1. Because K+ is pulled less strongly by the voltage, the concentration gradient of K+ will be less that 10:1. Therefore, to get a concentration gradient of 10:1 for K+ will require a greater potential difference between the two sides of the membrane than was necessary for Ca2+.
But why you can say that the voltage is fixed? In reality this isnt the case.

Also i still dont understand why the nernst potential isnt the voltagedrop, caused by moving ions. I mean you cant meausure potentials and i saw a meassurement, where you could see the the voltagedrop. Was this measurement the potential or the voltage?

But why you can say that the voltage is fixed? In reality this isnt the case.

Also i still dont understand why the nernst potential isnt the voltagedrop, caused by moving ions. I mean you cant meausure potentials and i saw a meassurement, where you could see the the voltagedrop. Was this measurement the potential or the voltage?
Can maybe somebody give me an answer to this? 