Percolation Approach to Study Connectivity in Living Neural Networks

TL;DR

This paper investigates neural network connectivity in rat hippocampal cultures using percolation theory, revealing a phase transition and local connectivity properties through experiments and simulations.

Contribution

It introduces a percolation-based theoretical framework to analyze neural network disintegration and characterizes the connectivity as locally Gaussian, not scale-free.

Findings

Identified a percolation transition with critical exponent ~0.65

Demonstrated local Gaussian degree distribution in neural networks

Validated theoretical predictions with numerical simulations

Abstract

We study neural connectivity in cultures of rat hippocampal neurons. We measure the neurons' response to an electric stimulation for gradual lower connectivity, and characterize the size of the giant cluster in the network. The connectivity undergoes a percolation transition described by the critical exponent $\beta \simeq 0.65$. We use a theoretic approach based on bond.percolation on a graph to describe the process of disintegration of the network and extract its statistical properties. Together with numerical simulations we show that the connectivity in the neural culture is local, characterized by a gaussian degree distribution and not a power law on