Transient response in a tapering cable model with somatic shunt

TRANSIENT voltage responses (charging transients) to current stimulation are presented for a non-linearly tapering cable model of a neurone with a shunt at the soma. Exact expressions are given for the time constants of exponential decay expressed in terms of the passive membrane time constant and the taper rate constant. The effect of a somatic shunt on the membrane potential transients at the soma is shown to result in a more rapid final decay of the membrane potential than simple passive decay with membrane time constant. The theoretical analysis should be of use to electrophysiologists wishing to interpret their experimentally observed charging transients recorded at the soma in terms of cable properties of neurones in vivo.