An important role for the functioning of a cell is the different chemical composition within and outside the cell in the vicinity of the cell membrane and the options available to the cell to regulate changes in the environment. The table below shows the concentrations (in mM) of major ion species outside (\([X]_\mathrm{e}\), with index 'e' for 'extracellular' or 'exterior'), and inside the cell (\([X]_\mathrm{i}\), with index 'i' for 'intracellular' or for 'interior'); remember that these numbers are realistic indications of size, but may vary depending on cell type. The anion \(A^{-}\) symbolizes phosphate and protein ions.

\[
\begin{array}{l|rrr}
\mathrm{ion\;} X & [X]_\mathrm{e} & [X]_\mathrm{i} & [X]_\mathrm{e}\mathrm{\;:\;}[X]_\mathrm{i} \\ \hline
\mathrm{K}^{+} & 5 & 100 & 1\mathrm{\;:\;}20 \\
\mathrm{Na}^{+} & 150 & 15 & 10\mathrm{\;:\;}\phantom{2}1\\
\mathrm{Ca}^{2+} & 2 & 0.0002 & 10000\mathrm{\;:\;}\phantom{2}1\\
\mathrm{Cl}^{-} & 150 & 13 & 11.5\mathrm{\;:\;}\phantom{2}1\\
\mathrm{A}^{-} & 0 & 170 & \\
\end{array}\]

In summary and to remember:

• \(\mathrm{K}^{+}\) more concentrated inside;
• \(\mathrm{Na}^{+}\) and \(\mathrm{Ca}^{2+}\) more concentrated outside;
• \(\mathrm{Cl}^{-}\) more concentrated outside.

For neurons, the ion compositions in the vicinity of the cell membrane are one of the most decisive factors for electrical phenomena; other main players are properties of the membrane and the proteins present (such as ion channels and ion pumps). This explains for instance the potential difference across the lipid bilayer of a cell 'at rest', and the fact that the cell membrane is a capacitor and can work as a battery in series with a resistor, and how the regulation of the membrane potential may result in the generation of action potentials in nerve cells. The previously discussed basics of electricity theory come in handy here.

First, we explain how the membrane potential can be explained and calculated through a mathematical-physical model. First we do this for a model in which only a single ion species plays a role and then we adapt it to cases involving two or more ion species.