Electrodiffusion model of synaptic potentials in dendritic spines

When modeling electric current flow in neurons and excitable cells, traditional cable theory ignores electrodiffusion (i.e. the interaction between electric fields and ionic diffusion) as it assumes that concentration changes associated with ionic currents are negligible. This assumption, while true for large neuronal compartments, fails when applied to femto-liter size compartments such as dendritic spines - small protrusions that form the main site of synaptic inputs in the brain. Here, we use the Poisson (P) and Nernst-Planck (NP) equations, which relate electric field to charge and couple Ficks law of diffusion to the electric field, to model ion concentration dynamics in dendritic spines. We use experimentally measured voltage transients from spines with nanoelectrodes to explore these dynamics with realistic parameters. We find that (i) passive diffusion and electrodiffusion jointly affect the kinetics of spine excitatory post-synaptic potentials (EPSPs); (ii) spine geometry plays a key role in shaping EPSPs; and, (iii) the spine-neck resistance dynamically decreases during EPSPs, leading to short-term synaptic facilitation. Our formulation can be easily adopted to model ionic biophysics in a variety of nanoscale bio-compartments.