Extending integrate-and-fire model neurons to account for the effects of   weak electric fields and input filtering mediated by the dendrite
  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. 
Florian Aspart, Josef Ladenbauer, Klaus Obermayer
q-bio.NC