Re: Reversing [Na+] and [K+] across a membrane, what happens?

This is an interesting question and more complex then one might assume at 
1st.

There are many ways to answer the question depending on the starting 
conditions. So lets assume it is a normal cell like a squid axon that 
usually has high intracellular K+ and high extracellular Na+ with the Rp 
at –65mV (as you had stated, but for a squid axon the Rp would normally be 
lower or more negative). Now, if one experimentally could rapidly change 
the concentrations for Na+ and K+ ions across the cell, one could simply 
plug in the values into the Goldman-Hodgkin-Katz equation. So lets do that:
 
Vm=58log  Pk[Kout] +Pna[Na out]+Pcl[Cl in]
    divided by Pk[Kin] +Pna[Na in]+Pcl[Cl out]

Rework to =58log  [Kout] +(Pna/Pk)[Na out]+(Pcl/Pk)[Cl in]
                divided by [Kin] +(Pna/Pk)[Na in]+(Pcl/Pk)[Cl out]

Lets assume : the relative permeability constants (i.e. Pk, Pna, Pcl) in 
the squid axon are  1.0:0.03:0.1

Lets assume : 
[Kin] =400 mM ; [Kout] =10 mM ; [Na in] =50 mM ; [Na out] =460 mM ; [Cl 
in] =40 mM ; [Clout] =540 mM 

These values are for squid (Page 119 of Neuron to Brain, 2nd edition, 
Kuffler, Nicholls and Martin, Sinauer Assoc. Inc, Mass.)

Now plug everything in and Vm= -70 mV. OK so it is more negative than the
-65 you were given to start with, but lets just see what happens if you 
change the values for Na and K inside and out .

I calculate Vm= + 41.58

The point is that the membrane potential changes. But recall that this 
equation is for conditions at equilibrium. So this result is what might 
happen considering the permeability (the ‘p’ ) of the cell over some time 
with out an active process resetting the values.

One should consider that since the cell is very permeable to K+ at rest 
and normally at Rp=-65mV and Equilibrium for K+ is close to this value , 
but with the new experimental change it will change. So it would depend if 
you were setting the problem up for the ions to remain altered or only for 
a temporary change and then let the cell try to "drive" itself back to 
equilibrium.

The permeability is for the most part bi-directional. This partially is 
what contributes to what is referred to as a leak current at rest. 
Normally this is what keeps the Rp close to the Ek at rest along with the 
driving gradients. So, if the Na+ and K+ were rapidly changed, K+ would 
rush into the cell and probably depolarize it even more. Over time the 
ions would reset to new values based on this factor. 

Just think what would happen to a cell with such a rapid change in ions - 
the other voltage gated channels would open up like voltage gated calcium 
channels so Ca++ rushes into the cell. Adding to the depolarization and 
likely resulting in some cellular response that might kill the cell. In 
addition voltage gated sodium and potassium channels would open at the 
values that they would normally open. I guess in the new experimental 
conditions Na+ would go out and K+ into the cell, but the problem would 
likely be if the cell is depolarized by the new conditions the voltage-
gated sodium channels would be inactivated, and will not open until the 
inactivation is removed. Wow, does this get complicated.

So what about the Na-K ATP pump ? I assume it would be working overtime to 
try to get Na+ out and K+ into the cell, but the pump is affected by 
membrane potential as far as I know. So now what would really happen ? I 
am not quite sure. I guess if such an experiment was to be done one could 
poison the pump with blockers  and see what contribution it has in the 
process of re-setting the ion gradients back to normal conditions.

Not to avoid your question about what might happen to Cl- ions, lets 
address this point. If you're considering a squid axon this is important 
since the Cl- ions move at rest. As far as I am aware most neurons in 
mammals are not that permeable at rest to Cl- so the flux of Cl- should 
not contribute at rest with the rapid Na+ and K+ experimental alteration. 
For the squid, I would think that as K rushes into the cell, causing it to 
be more depolarized that the fluxes of Cl- would be substantial and would 
decrease as the cell resets the ion balance.

I am not sure about the squid, but in many cells there are other ion 
exchangers like the Ca/Na exchanger (not ATP dependent) but driven by the 
concentrations on both sides of the membrane and can work in reverse mode 
as well. Normally if both Na+ and Ca++ are high extracellular there is not 
much drive for the exchanger, but if  Na+ is experimental made high in the 
cell that would drive Na+ to go out and Ca++ to go in. Ca++ with a 2+ 
would have an effect on the cell membrane potential. 

 In short, I think this problem helps to demonstrate that so many aspects 
are tuned to function together to maintain conditions as we see them in 
the ‘standard cell’ or ‘typical cell’ (i.e., pumps, exchangers, 
permeability of ions at rest, and leak currents). There is a situation 
that is commonly refereed to in neuro text books with the inner ear in 
which the endolymph is higher in K+  and low in Na+ and Ca++  then most 
other extracellular fluids. I am not aware if the pumps and exchangers are 
altered in their function or properties in these cells surrounded by 
endolymph. Maybe another neurobiologist working in this area could be of 
assistance. Possibly poring over some of the primary literature would be 
of interest with this "strange" condition.

Refs:Sauer, Richter, Klinke. Sodium, potassium, chloride and calcium 
concentrations measured in pigeon perilymph and endolymph.
Hear Res. 1999 Mar;129(1-2):1-6.

All the best,
Robin