A modified cable model analysis of microscopic axonal and dendritic processes

The computational background for analysing the passive, subthreshold properties of fine-scale ramifications such as "en-passant" and "terminal ladder" type chains of boutons and spiny dendrites is presented. The segment-by-segment approximation of a cable composed of serial or parallel chains of identical units (modules) is based on the cable representations of boutons, axon, spines and dendrit. Pulse response in the time domain is evaluated from the narrow-bandwidth, recursive estimation of the input and transfer impedances by means of inverse Laplace transformation. The shape of the voltage transients in semi-infinite chain of cable units is found by the input impedance computed under the equilibrium condition. The model predicts differences of subthreshold responses in relation to a change in modular geometry or membrane electrical parameters. The results may help in finding the relationship between the physical and electrotonical geometries of nerve cells with non-smooth processes. The smoothing procedure gives a possibility for the functional unification and simplification of those fine-scale processes of nerve cells where the characteristic space constants are much greater than the intersynaptic distances.