Why do sodium and potassium ions not diffuse in equal numbers through ligand-gated cation channels?

Sodium and potassium ions do not diffuse in equal numbers through ligand-gated cation channels primarily due to the electrical gradient established across the cell membrane. The inside of the sarcolemma (the plasma membrane of muscle cells) carries a negative charge relative to the outside. This negative charge creates an electrical potential that influences the movement of positively charged ions such as sodium and potassium.

When these cation channels open, the influx of sodium ions is favored not only because there is typically a higher concentration of sodium outside the cell (encouraging sodium to move in) but also because the negative internal environment attracts positively charged sodium ions, enhancing their diffusion into the cell. In contrast, potassium ions, which are more concentrated inside the cell, are repelled by the negative charge within the cell, reducing their tendency to leave despite their concentration gradient.

This combined effect of concentration gradients and electrical charge across the membrane leads to a preferential movement of sodium ions compared to potassium ions through these channels. Thus, the unique properties of the membrane's charge facilitate the unequal diffusion rates of these two critical ions.