Parameters of Cable Theory Are Mostly Unaffected by the Geometry of Dendritic Spines

Dendritic spines are extremely small and experimentally difficult to access. Therefore, it is still uncertain whether all assumptions of basic neuroscientific theories, such as cable theory, are valid there. Previous theoretical work suggests that electroneutrality could be violated in dendritic spines. If this were true, new theories would be required. Unfortunately, these results were based on a greatly simplified model system with unrealistic ion concentrations. Inspired by these studies, we apply Poison-Nernst-Planck (PNP) equations to study the profiles of ion concentrations and the membrane potential in dendritic spines in a physiologically relevant regime. We find that, for realistic ion concentrations and in contrast to previous results, electroneutrality is a valid assumption for all tested geometries, irrespective of size and shape. However, the surface charge causes an accumulation of counter ions and a strong electric field near the surface of the membrane in the intra- and extracellular space. Still, a plate capacitor model accurately describes the capacitance of the membrane. Most importantly, the two cable parameters - the specific capacitance and the intracellular resistivity - are constants over a wide range of parameters. These results justify the application of models based on cable theory to dendritic spines.