Evolving Networks and the Development of Neural Systems

TL;DR

This paper presents a general analytical framework for understanding how various topological features of evolving networks, including neural systems, can emerge from simple local rules, with applications to brain development in humans and C. elegans.

Contribution

It introduces a versatile method to analyze network evolution based on degree-dependent attachment and detachment functions, explaining complex neural topologies.

Findings

Good agreement with experimental data on brain development.

Nontrivial features of C. elegans neural network emerge at a critical point.

Simple assumptions can reproduce complex neural topologies.

Abstract

It is now generally assumed that the heterogeneity of most networks in nature probably arises via preferential attachment of some sort. However, the origin of various other topological features, such as degree-degree correlations and related characteristics, is often not clear and attributed to specific functional requirements. We show how it is possible to analyse a very general scenario in which nodes gain or lose edges according to any (e.g., nonlinear) functions of local and/or global degree information. Applying our method to two rather different examples of brain development -- synaptic pruning in humans and the neural network of the worm C. Elegans -- we find that simple biologically motivated assumptions lead to very good agreement with experimental data. In particular, many nontrivial topological features of the worm's brain arise naturally at a critical point.