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J Neurophysiol 99: 2320-2328, 2008. First published February 27, 2008; doi:10.1152/jn.00280.2007
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A Cost–Benefit Analysis of Neuronal Morphology

¹Cold Spring Harbor Laboratory, Cold Spring Harbor; and ²Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, New York

Submitted 12 March 2007; accepted in final form 24 February 2008

Over hundreds of millions of years, evolution has optimized brain design to maximize its functionality while minimizing costs associated with building and maintenance. This observation suggests that one can use optimization theory to rationalize various features of brain design. Here, we attempt to explain the dimensions and branching structure of dendritic arbors by minimizing dendritic cost for given potential synaptic connectivity. Assuming only that dendritic cost increases with total dendritic length and path length from synapses to soma, we find that branching, planar, and compact dendritic arbors, such as those belonging to Purkinje cells in the cerebellum, are optimal. The theory predicts that adjacent Purkinje dendritic arbors should spatially segregate. In addition, we propose two explicit cost function expressions, falsifiable by measuring dendritic caliber near bifurcations.

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