Signal transfer in passive dendrites with nonuniform membrane conductance

In recent years it became clear that dendrites possess a host of ion channels that may be distributed nonuniformly over their membrane surface. In cortical pyramids, for example, it was demonstrated that the resting membrane conductance G(m)(x) is higher (the membrane is "leakier") at distal dendritic regions than at more proximal sites. How does this spatial nonuniformity in G(m)(x) affect the input-output function of the neuron? The present study aims at providing basic insights into this question. To this end, we have analytically studied the fundamental effects of membrane non-uniformity in passive cable structures. Keeping the total membrane conductance over a given modeled structure fixed (i.e., a constant number of passive ion channels), the classical case of cables with uniform membrane conductance is contrasted with various nonuniform cases with the following general conclusions. (1) For cylindrical cables with "sealed ends," monotonic increase in G(m)(x) improves voltage transfer from the input location to the soma. The steeper the G(m)(x), the larger the improvement. (2) This effect is further enhanced when the stimulation is distal and consists of a synaptic input rather than a current source. (3) Any nonuniformity in G(m)(x) decreases the electrotonic length, L, of the cylinder. (4) The system time constant tau(0) is larger in the nonuniform case than in the corresponding uniform case. (5) When voltage transients relax with tau(0), the dendritic tree is not isopotential in the nonuniform case, at variance with the uniform case. The effect of membrane nonuniformity on signal transfer in reconstructed dendritic trees and on the I/f relation of the neuron is also considered, and experimental methods for assessing membrane nonuniformity in dendrites are discussed.