An analytical method for investigating transient potentials in neurons with branching dendritic trees.

An analytical method is developed that allows one to explore the way in which the geometrical structure of a neuron's dendritic tree affects the time-course and amplitude of transient potentials generated at different locations on dendritic branches. The method requires that, for a given dendritic arborization, one associates a symmetric geometry for which exact mathematical expressions for time-varying dendritic potentials can be calculated. The value of the dendritic potential for the asymmetric geometry is evaluated by adding correction terms to the results for the symmetric geometry. Several model trees are examined, and in each case the analytical results are expressed in terms of two closely related families of functions. These functions provide a precise formulation for systematically analyzing the way in which the voltage transient at a given point depends upon the geometrical structure of the dentritic tree. Several numerical examples are presented. A discussion of how to generalize the method and of some potential applications are given.