Help me understand my membrane potential assignment

Question

Epithelial with the ability to transport NaCl is bathed in an isotonic salt solution with these values (in mM): 136 Na, 6 K, 140 Cl. The intracellular concentrations are: 45 Na, 100 K, 13 Cl.

The cell's resting potential is -63 mV and the temperature is 37 Celcius.

Which ions will passively diffuse over the membrane?

My attempt: I calculate the nernst potential of each ion and taking the first ion (Na) as an example I get that it's equilibrium is at 29 mV. So as there are more of these cations outside the cell and the membrane potential is negative, the ions will want to "reach" 29 mV by flowing INSIDE the cell (to increase the membrane potential). I think they will do this by diffusing into the cell? I'm not sure if I am attacking the problem correctly or if it's rather lunging at my abilities in transporters. The NaK transporter is active transport so maybe the do not diffuse at all?? However there are Na channels that can open...Which is passive diffusion..

Calculate the cation permeability Pna/Pk

I have no idea how to do this. I still need more constants in the Goldman equation (Pcl for example) before I could isolate even one of these.

Thanks!

Answer 1

If there is passive transport for each ion, then every ion will diffuse over the membrane until the concentrations will be the same, and the membrane potential will be zero. So there is active transport in the cell, which maintains the resting potential which is -63mV.

So with the current concentrations the membrane potential will differ from this -63mV, and so the cell will change the ion levels to change the current potential to be equal to the resting potential.

I think you should try to simply summarize the Nernst potentials. It won't be so accurate as the Goldman equation, but you don't have the relative permeabilities of this cell type, so the questioner probably does not wait the Goldman equation from you.

I would solve it this way:

Em = RT/zF * ln(out/in)

R = 8,314 J/molK
T = 37 + 273 = 310K
F = 96485 J/molV

RT/F = 26,712mV

ENa = 26,712mV*ln(136/45) = +29,543mV
EK = 26,712mV*ln(6/100) = -75,152mV
ECl = -26,712mV*ln(140/13) = -63,486mV
Em = ENa + EK + ECl = -109,95mV

Emr = -63mV
Emr - Em = -63mV + 110mV = +47mV

So we have to increase the membrane potential. Decreasing intracellular K+, Cl- concentration and increasing intracellular Na+ concentration can do that.

Concentrations: extracellular 136 Na, 6 K, 140 Cl, intracellular 45 Na, 100 K, 13 Cl. So possible passive transports are increase Na+, decrease K+, increase Cl-.

Conclusion the passive transports will be increasing Na+, decreasing K+ the active transport will be decreasing Cl-.

Note that I haven't used these terms for 5 years, so if you can consult with somebody else about this, then ask him/her whether this is correct.