Equivalence transformations for dendritic Y-junctions: a new definition ofdendritic sub-unit

A sequence of equivalence transformations is used to represent the mathemat ical model of a simply branched neuron with non-homogeneous membrane proper ties and non-uniform geometry by an entirely equivalent model of an unbranc hed structure. The analysis indicates how neuronal morphology, in combinati on with its biophysical properties, shapes neuronal output in response to c urrent input. The equivalence transformations described here reveal the typ es of operations that are likely to feature in the analysis of complex mult i-branched structures, neuronal or otherwise. These transformations provide a new definition of dendritic sub-unit and a basis of a mechanism for char acterising local and non-local signal processing within dendritic structure s. It is anticipated that the capacity to transform biological neurons into an equivalent unbranched structure will make an important contribution to the understanding of the functional role of neuron geometry as well as to t he construction of silicon neurons with realistic biological properties. (C ) 2001 Elsevier Science Inc. All rights reserved.