Doubling the concentration of extracellular calcium hyperpolarizes a neuron. Why?

I was doing some back of the envelope calculations to try to answer this question in more mathematical terms. Essentially the question states: Why does increasing the extracellular potassium concentration depolarize a neuron, while increasing the extracellular calcium concentration hyperpolarize the neuron?

My initial thought was that there is a change in the equilibrium potential for each ion. Working this out however I realized I was wrong in my reasoning; my math proved me wrong.

Doubling the concentration of extracellular potassium makes the equilibrium potential of potassium 17.8 mV more positive. For calcium, it increases the driving force by 8.9 mV (based on room 300 K temperature). What this means to me is that both will cause the resting potential of the neuron to become slightly more positive, though calcium less so.

This is indeed obvious: adding more positive ions to the outside of the cell increases the driving force for that ion, and assuming there is any conductance (albeit small) then there will be some depolarization of the neuron.

This makes me think that this is not a phenomena explained by a neuron at rest. Some other mechanism is responsible for increased extracellular calcium causing the neuron to hyperpolarize.

My possible guesses:

• If the calcium concentration is doubled, then the driving force for calcium increases, so there is more influx of calcium and thus the internal calcium concentration will increase. Because the concentration of calcium ions on the inside was previously near zero, now that internal concentration will rise to be some significant number, thereby hyperpolarizing the neuron.

• The internal concentration of calcium rises slightly, but instead of (or perhaps in conjunction with) lowering the resting potential directly, there is more activation of calcium-activated potassium channels, thus raising the conductance of potassium ions, and thus ultimately hyperpolarizing the neuron.

Am I on the right track or am I missing something?

• I edited this to clean up some of the misuses of terminology. One quick suggestion: the names of these ions are not capitalized ("Potassium", etc.). In fact, more often you will just see K+, Ca++, Na+, and Cl-, which is more convenient to write. Also, there is no such thing as the resting potential for an ion, just for the whole neuron; for the ion, it is the equilibrium potential or reversal potential. Etc. Sep 6 '15 at 15:55
• "This makes me think that this is not a phenomena explained by a neuron at rest." Why not? If the neuron is not spiking--which it is not in your example--it is at rest. Sep 6 '15 at 15:57