Why does hypercalcemia cause muscle weakness, yet hyperkalemia causes muscle excitation?

Question

The reasoning I've been given is that high extracellular $[K^+]$ increases the $E_v$ of potassium; therefore, membrane potential increases and the threshold for action potentials is more easily reached. Conversely, high extracellular $[Ca^{2+}]$ increases the accumulated positive charge outside the cell membrane and therefore increases the membrane potential.

However, like with $K^+$, wouldn't high ECF $[Ca^{2+}]$ also increase its $E_v$ and therefore membrane potential of the cell? Vice versa, high ECF $[K^+]$ should also increase membrane potential by accumulating charge.

Why are the effects different? A guess I had is that the relatively higher permeability of $K^+$ makes the effect on equilibrium potential larger than the effect of accumulating positive charge.

Answer 1

You're correct about your reasoning for potassium; high extracellular potassium concentration reduces the concentration gradient of potassium across the membrane, pushing the reversal potential for potassium towards neutral and therefore depolarizing cells due to resting potassium conductances.

For calcium it's quite different. Neurons and muscle cells are mostly impermeable to calcium at rest, and calcium is already high outside of cells relative to inside, so changing calcium concentration doesn't have any appreciable impact on resting potentials. From a pure ion-flow perspective, the primary change you'd expect in neurons is an increased action potential amplitude at the very peak: calcium reversal tends to be more positive than sodium reversal, so the very peak of the action potential is the part most influenced by calcium concentrations. This peak amplitude doesn't have much impact on all-or-nothing signaling, though.

You might also expect calcium concentrations to affect release probability of vesicles - that could increase neurotransmission.

However, that's not what's going on with muscle weakness. Instead, this is something special about calcium (well, divalent cations more generally) interacting with voltage gated sodium channels:

High Ca2+ levels (hypercalcemia) can block sodium movement through voltage-gated sodium channels, causing reduced depolarization and impaired action potential generation.

There's no way you can predict this from the principles of ion flow given by concentration gradients and voltages, and these sorts of things are why you have to do biological experiments with biology and not just computers: sometimes it doesn't work how you expect. The mechanism here is physical: calcium ions are big relative to sodium ions, but they have the same sign charge, so if possible, both would flow through a channel from the outside to the relatively negative inside. There's a place in the outer pore of voltage-gated sodium channels where calcium ions get stuck and just physically plug the hole. When a calcium ion is in the way, sodium can't flow (see Yamamoto et al 1984 and Santarelli et al 2007; the former looks at mechanism by altering voltage, the latter looks for specific residues on the channel that mediate calcium binding in the pore).

At typical low extracellular calcium levels, there aren't as many calcium ions around to block channels.

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Santarelli, V. P., Eastwood, A. L., Dougherty, D. A., Ahern, C. A., & Horn, R. (2007). Calcium block of single sodium channels: role of a pore-lining aromatic residue. Biophysical journal, 93(7), 2341-2349.

Yamamoto, D., Yeh, J. Z., & Narahashi, T. (1984). Voltage-dependent calcium block of normal and tetramethrin-modified single sodium channels. Biophysical Journal, 45(1), 337-345.