Solutions for transients in arbitrarily branching cables: IV. Nonuniform electrical parameters.

Solutions for transients in arbitrarily branching passive cable neurone models with a soma are extended to models with nonuniform electrical parameters and multiple dendritic shunts. The response to an injected current can again be represented as an infinite series of exponentially decaying components with system time constants obtained from the roots of a recursive transcendental equation. The reciprocity relations and global parameter dependencies are the same as for uniform models. Infinitely many "raw" electro-morphological models map onto a given "core" electrotonic model; local as well as global raw parameter trade-offs are now possible. The solutions are illustrated by means of biologically relevant examples: (i) the effects of nonuniform electrical parameters in a two-cylinder + soma cortical pyramidal cell model, (ii) the errors that can occur when uniformity is incorrectly assumed in a single cylinder model, (iii) nonsumming interactions between cells and electrodes that can dramatically increase the duration of the effective capacitative electrode artefact, and (iv) shunting inhibition and double impalements in a hippocampal CA1 pyramidal cell "cartoon" representation. These solutions should complement compartmental modelling techniques.