Computer simulation of voltage sensitive calcium ion channels in a dendritic spine

• The philosophy of the immersed boundary method is applied to electrodiffusion.
• We replace interface conditions by spatially continuous chemical potential barriers.
• We find that we can reproduce the Goldman–Hodgkin–Katz (GHK) current–voltage relationship.
• We find qualitatively reasonable behavior for a voltage-sensitive calcium channel.

Membrane current through voltage-sensitive calcium ion channels at the postsynaptic density of a dendritic spine is investigated. To simulate the ion channels that carry such current and the resulting temporal and spatial distribution of concentration, current, and voltage within the dendritic spine, the immersed boundary method with electrodiffusion is applied. In this simulation method a spatially continuous chemical potential barrier is used to simulate the influence of the membrane on each species of ion. The amplitudes of these barriers can be regulated to simulate channel gating. Here we introduce this methodology in a one-dimensional setting. First, we study the current–voltage relationship obtained with fixed chemical potential barriers. Next, we simulate stochastic ion-channel gating in a calcium channel with multiple subunits, and observe the diffusive wave of calcium entry within the dendritic spine that follows channel opening. This work lays the foundation for future three-dimensional studies of electrodiffusion and advection electrodiffusion in dendritic spines.