Subthreshold response to white-noise current input in a tapering cable model of a neuron

The expectation (mean) and variance of the depolarization in the absence of a threshold for action-potential generation is obtained in a neuron model represented by a tapering equivalent cable with a random (white noise) synaptic input current at a point along the dendrites. The results show that the introduction of a taper in the equivalent-cable representation of the neuron produces larger values for both the expectation and variance which are neither insensitive nor symmetrical with respect to the location of the input. It is also shown that taper extends the invariance of the variability in the steady-state somatic response to proximally located random inputs, implying that only small changes in the noisiness of the somatic response occur for a random input located in the dendrites.