Self-organization and the selection of pinwheel density in visual cortical development

TL;DR

This paper provides a theoretical analysis of how self-organizing neural circuits in the visual cortex predict a specific pinwheel density, highlighting the role of long-range interactions in cortical development.

Contribution

It offers the first analytical calculation of pinwheel density in a cortical self-organization model, emphasizing the impact of non-local interactions.

Findings

Pinwheel density converges to π with infinite interaction range.

Robust pinwheel density near π is maintained at intermediate interaction ranges.

The model's predictions can be tested in future experiments.

Abstract

Self-organization of neural circuitry is an appealing framework for understanding cortical development, yet its applicability remains unconfirmed. Models for the self-organization of neural circuits have been proposed, but experimentally testable predictions of these models have been less clear. The visual cortex contains a large number of topological point defects, called pinwheels, which are detectable in experiments and therefore in principle well suited for testing predictions of self-organization empirically. Here, we analytically calculate the density of pinwheels predicted by a pattern formation model of visual cortical development. An important factor controlling the density of pinwheels in this model appears to be the presence of non-local long-range interactions, a property which distinguishes cortical circuits from many nonliving systems in which self-organization has been studied. We show that in the limit where the range of these interactions is infinite, the average pinwheel density converges to $\pi$. Moreover, an average pinwheel density close to this value is robustly selected even for intermediate interaction ranges, a regime arguably covering interaction-ranges in a wide range of different species. In conclusion, our paper provides the first direct theoretical demonstration and analysis of pinwheel density selection in models of cortical self-organization and suggests to quantitatively probe this type of prediction in future high-precision experiments.