Quorum Percolation in Living Neural Networks

TL;DR

This paper introduces quorum percolation as a model for neural network activation, demonstrating a phase transition in connectivity and matching experimental data to quantify neural connectivity properties.

Contribution

It presents a novel percolation model incorporating a threshold for neuron firing, aligning simulations with experiments to quantify neural network connectivity.

Findings

Identifies a phase transition in neural connectivity as the threshold increases.

The model accurately reproduces experimental neural activation patterns.

Provides estimates for average connectivity and connection distribution in neural networks.

Abstract

Cooperative effects in neural networks appear because a neuron fires only if a minimal number $m$ of its inputs are excited. The multiple inputs requirement leads to a percolation model termed {\it quorum percolation}. The connectivity undergoes a phase transition as $m$ grows, from a network--spanning cluster at low $m$ to a set of disconnected clusters above a critical $m$. Both numerical simulations and the model reproduce the experimental results well. This allows a robust quantification of biologically relevant quantities such as the average connectivity $\kbar$ and the distribution of connections $p_k$