Optimal sizes of dendritic and axonal arbors in a topographic projection
Abstract
I consider a topographic projection between two neuronal layers with different densities of neurons. Given the number of output neurons connected to each input neuron (divergence) and the number of input neurons synapsing on each output neuron (convergence) I determine the widths of axonal and dendritic arbors which minimize the total volume of axons and dendrites. Analytical results for onedimensional and twodimensional projections can be summarized qualitatively in the following rule: neurons of the sparser layer should have arbors wider than those of the denser layer. This agrees with the anatomical data from retinal and cerebellar neurons whose morphology and connectivity are known. The rule may be used to infer connectivity of neurons from their morphology.
 Publication:

arXiv eprints
 Pub Date:
 June 1999
 DOI:
 10.48550/arXiv.condmat/9906207
 arXiv:
 arXiv:condmat/9906207
 Bibcode:
 1999cond.mat..6207C
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Soft Condensed Matter;
 Physics  Biological Physics;
 Quantitative Biology
 EPrint:
 8 pages, 7 figures, submitted to Nature Neuroscience