Nernst Equation and Membrane Potential

Question

I am a bit confused on how to use the Nernst equation to determine polarization. I saw in the textbook that if potassium channels were open in a neuron cell, there will be a net diffusion of $\ce{K+}$ out of the cell, making the membrane potential more negative.

However, if you use the Nernst equation $$V = \rm 62\;mV\times log\left(\frac{[ion]_{outside}}{[ion]_{inside}}\right),$$ it seems that the potential become less negative if there is a net diffusion of $\ce{K+}$ out of the cell.

For example, if we had 6 $\ce{K+}$ ions inside and 2 $\ce{K+}$ outside, and the channel opened, increasing the extracellular $\ce{K+}$ count to 3 and the intracellular to 5. Doesn't this lead to a less negative value?

I am having difficulty where I am going wrong with this. I saw other posts regarding this question, but I do not understand the explanation.

Is there an easier way to understand why this change doesn't correlate with a more negative potential?

Answer 1

Are you just counting up the potassium ions and subtracting them? Don't do that! That's not how it works. Potassium ions don't just exist by themselves, they come paired with negative ions of some sort which dissociate in water. There are lots of other ions of various charges too, we're just ignoring them all because the only ones that matter are the ones that can move.

In your story, a potassium ion has left the cell. A potassium ion has positive charge. When positive charge leaves the cell, what is left behind is more negative, not more positive.

Potassium ions will keep leaving down the potassium concentration gradient because all things tend to move down their concentration gradients. But as positive charge leaves the cell, potassium ions that leave are moving both down their concentration gradient (to lower concentration) and up their electrical gradient (toward positive charge). So, how do you know when those two forces will balance out?

That's what Nernst tells you: the voltage where a given concentration difference will be balanced so no more net flow of that ion occurs. That's what equilibrium means.

If you're thinking that after some ions move, you need to re-calculate the Nernst equation, that's not correct. For one thing, the ion concentrations don't actually change that much: very few ions have to actually move to change the voltage a lot and halt the flow of ions. For another, you can't ignore the ions that have already moved: the voltage they've created is already there and needs to be accounted for.