Why does K+ going out of the cell cause hyperpolarization?

I'm really confused by how the terms Hyperpolarization and Depolarization are used in Cell biology and hope somebody can enlighten me hopefully. Here's what they mean for me so far:

Depolarization means the inner and outer side of the cell membrane become less polarized (so the Nernst potential tends to 0 due to log(1) being 0)

Hyperpolarization that the inner and outer side become more polarized (so the Nernst potential increases).

Assuming I'm not completely wrong until here. Let me give some examples, so maybe you can see better where the problem lies:

• We have a model cell so (K+ internal is 140 mmol/l, K+ external is 4.5 mmol/l) and the external side is increased to 8 mmol/l , then a DEPOLARIZATION occurs because

roughly : $$-60 \cdot \log(140/4.5) = -90 mV < -60 \cdot \log(140/8) = -74 mV$$ ; or in other words, "energy" was used so a depolarization occurred (so far this seems correct with the solutions I can find to this example)

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• Now comes the second example (famous depolarization of a cell with the graph and the peak and repolarization): 1. Na+ enters the cell : the concentrations im gonna use for this example are inside:$$12 mmol/l$$ and outside $$140 mmol/l$$

so before the Na enters we have: $$-60 \log(12/140)= 60 mV$$

if Na+ enters the Cell, a depolarization should occur (because the difference inside and outside is decreased)

this seems fine with the graph...

• the part of the graph which goes over 0 (also called "overshoot"), is it not technically a hyperpolarisation+depolarization?

• repolarization: this occurs by K+ ions leaving the cell, but that doesn't make sense according to the Nernst equation?

The concentration inside before the cells leaving is 140, outside 4.5 ; if K+ leave the cell, its simply going to depolarize more... So why does repolarization occur and not depolarization?

1. It's commonly stated that Hyperpolarization is caused by K+ LEAVING the cell (for example with ion channels) , how does this make sense if the inner concentration is higher than the outer? If anything, this again should lead to depolarization

2. Same thing with K+ entering the cell, isn't that supposed to cause a hyperpolarization as well?

I appreciate any kind of insight into this matter, since it seems that I'm completely wrong.

• Why do you think that K+ leaving the cell is going to depolarise more? When Na+ enters the cell, it affects the total ionic concentration inside the cell, so that Na+ entering the cell (depolarisation) is “balanced” by K+ leaving the cell (repolarization). You also have to consider that a lot of channels are voltage-gated, so they regulate ionic transport based on a change in total membrane potential, regardless of which ion concentrations caused the change in potential. – P. SN Jun 8 at 11:25
• considering the Na+ entering is probably smart BUT for example; if you have a cell why is it said that K+ leaving the cell will cause hyperpolarization? if it is not true due to the Nernst equation ? Same with K+ entering the cell ; regardless of whether Na enters or not ; if K+ leaves the cell potential from nernst will go towards 0 ; yet it is still claimed that this will cause a hyperpolarization? Is my understanding of depolarization and hyperpolarization incorrect? – schokakola Jun 8 at 11:39
• since cell membranes are normally polarised at a resting potential of -70 mV, hyperpolarisation refers to any event that polarises the membrane even more, making the cell interior more negative beyond -70 mV (so the opposite of depolarisation). Hyperpolarisation is not specific to K+, and K+ leaving the cell doesn’t necessarily cause hyperpolarisation: it only does so when potassium channels stay open for a longer duration, allowing more K+ to leave the cell than needed to repolarise the cell back to -70mV. – P. SN Jun 8 at 12:19
• The extra efflux of K+ and hyperpolarisation are important concepts in neurons, because nerve cells can only be excited (depolarised) from their resting potential. Going from a hyperpolarised state to the resting potential of -70mV allows a gap in time between excitation events. Because you wouldn’t want neurons firing constantly! :) – P. SN Jun 8 at 12:22
• How does that relate to the simplified Nernst equation? I don't really see how your comment answers my question: $\frac{-60}{k} \log (C_{in}/C_{out})$. If you go from 140 inner and increase the concentration outside, then according to the equation it's going to go towards 0 ; this by definition is a depolarization ?????? – schokakola Jun 8 at 12:34