# Why does altering permeability of an ion affect equilibrium potential

1. Sep 8, 2013

### sodium.dioxid

It seems to me that change in permeability should not shift the equilibrium of entering and exiting ions, except how fast equilibrium is reached. Consider this: two compartments are separated by a membrane. 1st compartment holds 1mM Na+ and 10mM K+ and 2nd one holds 10mM Na+ and 1mM K+.
Let's make the membrane equally permeable to both species. Result: the species will become equally mixed on the two sides and the equilibrium potential reaches zero.
Let's rewind and start over. This time let's make the permeability of Na+ half of that of K+. My prediction: there will be equal mixture of the two species on both sides ultimately, it will just take longer for it to happen than in the first scenario. Equilibrium potential = zero.

2. Sep 8, 2013

### SW VandeCarr

Describe what you mean by the equilibrium potential between two cationic species. In time the individual concentrations of sodium and potassium ions will equilibrate across a semi-permiable membrane by passive diffusion assuming permeability to the relevant anions.

Last edited: Sep 8, 2013
3. Sep 8, 2013

### atyy

There are situations in which a steady membrane potential is reached, but it is not due to true equilibrium, rather opposing flows cancel. Since such a steady state depends on a flows, the permeability matters.

Try section 7 of http://www.st-andrews.ac.uk/~wjh/neurotut/mempot.html

4. Sep 8, 2013

### sodium.dioxid

The equilibrium potential between the two compartments, not between the two cationic species. My confusion comes from reading this paragraph in my textbook:
Why does making relative permeability go from equal to not equal make the equilibrium potential (the potential between the two compartments during equilibrium - when the rate of Na+ going from 1=>2 is equal to the rate of Na+ going from 2=>1, and when the rate of K+ going from 1=>2 is equal to the rate of K+ going from 2=>1) anything but zero?

5. Sep 8, 2013

### atyy

At steady state the fluxes must be equal, but the flux is due to permeability and the "driving force". The driving force is the difference between the membrane potential and the reversal potential. The bigger the difference, the bigger the driving force, and the bigger the flux.

If potassium permeability is big and sodium permeability is small, then to make the fluxes equal, the potassium driving force should be small and the sodium driving force should be big, so the membrane potential should be near the potassium reversal potential and far from the sodium reversal potential.

6. Sep 8, 2013

### sodium.dioxid

Oops. I was thinking in terms of "final state" rather than "steady state". So if a steady state was not maintained and the concentrations of the two ions in one compartment was not maintained relative to those in the other compartment, would membrane potential decline towards zero as a function of time?

7. Sep 8, 2013

### atyy

Yes, the concentration differences would go to zero, and so would the difference in potential across the membrane.

8. Sep 8, 2013

### Pythagorean

Basically, look at Goldman Hodgkin Katz derivation instead of Nernst resting potential.

9. Sep 8, 2013

### sodium.dioxid

Thank you atyy. With that excellent link you directed me to and your explanations, I now understand all of this...at least, for a system of Na+ and K+. I am not going to think of how Cl- would fit in the mix anytime soon (don't know if it will complicate things to a great extent). Thanks, again.