Ion-Concentration Gradients During Synaptic Input Increase the Voltage Depolarization in Dendritic Spines

The cable equation is key for understanding the electrical potential along dendrites or axons, but its application to dendritic spines remains limited. Their volume is extremely small so that moderate ionic currents suffice to alter ionic concentrations. The resulting chemical-potential gradients between dendrite and spine head lead to measurable electrical currents. The cable equation, however, considers electrical currents only as result of gradients in the electrical potential. The Poisson-Nernst-Planck (PNP) equations allow a more accurate description, as they include both types of currents. Previous PNP simulations predict a considerable change of ionic concentrations in spines during an excitatory postsynaptic potential (EPSP). However, solving PNP-equations is computationally expensive, limiting their applicability for complex structures. Here, we present a system of equations that generalizes the cable equation and considers both, electrical potentials and time-dependent concentrations of ion species with individual diffusion constants. Still, basic numerical algorithms can be employed to solve such systems. Based on simulations, we confirm that ion concentrations in dendritic spines are changing significantly during current injections that are comparable to synaptic events. Electrical currents reflecting ion diffusion through the spine neck increase voltage depolarizations in the spine head. Based on this effect, we identify a mechanism that affects the influx of Ca2+ in sequences of pre- and postsynaptic action potentials. Taken together, the diffusion of individual ion species need to be taken into account to accurately model electrical currents in dendritic spines. In the future the presented equations can be used to accurately integrate dendritic spines into multicompartment models to study synatptic integration.