Electro-geometrical coupling in non-uniform branching dendrites. Consequences for relative synaptic reflectiveness

The relationships between somatofugal electronic voltage spread, somatopetal charge transfer and non-uniform geometry of the neuronal dendrites were studied on the basis of the linear cable theory. It is demonstrated that for the dendritic arborization of arbitrary geometry, the path distribution of the relative effectiveness of somatopetal synaptic charge transfer defined as in Barrett and Crill (1974) is identical to that of the somatofugal steady electronic voltage normalized to the voltage at the soma. The features of both distributions are determined by breaks in the voltage gradient (the slope of monotonic voltage decay) at the sites of local non-uniformity of the dendritic geometry, such as abrupt change in diameter and asymmetric branching. If the membrane- and cytoplasm-specific electrical parameters are assumed as uniform and the branch diameter as piece-wise uniform, then at any site of step change the square reciprocal ratio of the pre- and poststep diameters determines the ratio of the pre- and poststep electronic gradients. At branching points this ratio is modulated by partition of the core current between the daughter branches in proportion to their input conductances depending on global geometries of the daughter subtrees originating there. Thus, simply computed steady somatofugal voltages provide a physiologically meaningful estimation of the relative influence of synaptic inputs in different parts of the dendritic arborization on the output of the neuron.