  How extracellular electric fields, as generated endogenously or through
transcranial brain stimulation, affect the dynamics of large neuronal
populations is of great interest but not well understood. To study the
collective dynamics of large populations single-compartment (point) model
neurons have been proven very successful. These models, however, lack the
dendritic morphology to biophysically account for the effects of electric
fields, and for changes in synaptic integration due to morphology alone. Here
we (i) characterize the response of a canonical spatial (ball-and-stick) model
neuron to fluctuating synaptic input as well as an oscillatory, weak electric
field, and (ii) analytically derive an extension for popular integrate-and-fire
point neuron models to accurately reproduce these responses. We obtain distinct
filters mediated by the dendrite for inputs at the soma (high-pass filter) or
at the distal dendritic site (low-pass filter), and find that the electric
field induces spike rate resonance in the beta and gamma frequency bands or
even higher frequencies, depending on the location of synaptic background
input. Due to their computational efficiency the extended point models are well
suited for application in large populations of coupled neurons with different
morphology, exposed to extracellular electric fields.
