Optimal sizes of dendritic and axonal arbors in a topographic projection

TL;DR

This paper derives optimal dendritic and axonal arbor sizes in topographic neural projections to minimize total volume, aligning with observed neuronal structures and aiding in inferring connectivity from morphology.

Contribution

It provides an analytical framework for determining optimal arbor sizes based on neuron density differences, a novel approach in neural morphology analysis.

Findings

Optimal arbor sizes depend on layer densities.

Neurons in sparser layers have wider arbors.

Results match anatomical data from retina and cerebellum.

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 one-dimensional and two-dimensional 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.