Why does altering permeability of an ion affect equilibrium potential

[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.

 

[SW VandeCarr]

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.

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.

 

[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

 

[sodium.dioxid]

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.

The equilibrium potential between the two compartments, not between the two cationic species. My confusion comes from reading this paragraph in my textbook:

What would happen
if 10 mM K+ and 1 mM Na + were present in compartment 1, and 1 mM K+ and 10
mM Na + were present in compartment 2? If the membrane were permeable only
to K+, the membrane potential would be -58 mV; if the membrane were perme -
able only to Na •, the potential would be +58 mV. But what would the potential be
if the membrane wer e permeable to both K+ and Na +? In this case, the potential
wou ld depend on the relative permeability of the membrane to K+ and Na +. If it
were more permeable to K•, the potential would approach - 58 mV, and if it were
more permeable to Na •, the potential would be closer to +58 mV.

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?

 

[atyy]

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?

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.

 

[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?

 

[atyy]

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?

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

 

[Pythagorean]

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

 

[sodium.dioxid]

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

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.