Pii: S0025-5564(00)00032-8

We extend on the work developed by R.R. Poznanski and J. Bell from a linearized somatic persistent sodium current source to a non-linear representation of the dendritic Na‡P current source associated with a small number of persistent sodium channels. The main objective is to investigate the modulation in the ampli®cation of excitatory postsynaptic potentials (EPSPs) in dendrites studded with persistent sodium channels. The relation between membrane potential (V) and persistent sodium current density (INaP) is approximated heuristically with a sigmoidal function and the resultant cable equation is solved analytically using a regular perturbation expansion and GreenÕs function techniques. The transient simulated (nonevoked) response is found as a result of current injection in the form of synaptically induced voltage change located at a distance from the recording site in a cable with a uniform distribution of ion channel densities per unit length of cable (the so-called `hot-spots') and with the conductance of each hot-spot (i.e., number of channels per hot-spot) assumed to be a constant. The results show an ampli®cation in the observed EPSPs to be compatible with the experimentally derived estimates, and in addition a saturation in the ampli®cation is observed indicating an optimum number of ionic channels. Ó 2000 Elsevier Science Inc. All rights reserved.