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Dendritic Subunits Determined by Dendritic Morphology

Department of Mathematics, University of Glasgow, Glasgow G12 8QQ, Scotland

J. M. Ogden

Department of Mathematics, University of Glasgow, Glasgow G12 8QQ, Scotland

J. R. Rosenberg

Division of Neuroscience and Biomedical Systems, University of Glasgow, Glasgow G12 8QQ, Scotland

A theoretical framework is presented in which arbitrarily branched dendritic structures with nonhomogeneous membrane properties and non-uniform geometry can be transformed into an equivalent unbranched structure (equivalent cable). Rall's equivalent cylinder is seen to be one part of the equivalent cable in the special case of dendrites satisfying the Rall criteria. The relation between the branched dendrite and its equivalent unbranched representation is uniquely defined by an invertible mapping that connects configurations of inputs on the branched structure with those on the unbranched structure, and conversely. This mapping provides a new definition of dendritic subunit and provides a mechanism for characterizing local and nonlocal signal processing within dendritic structures.