A Statistical Mechanical Approach to Modeling the Connectivity and Criticality of Spiking and C. elegans Neural Networks

Abstract

Many of the highly researched cognitive functions of the brain arise due the collective activity of large groups of neurons. With new large-scale recordings of neural signals, we’d like to investigate the mechanisms behind this phenomenon, but the immense quantity of individual cells makes a standard, deterministic approach to the modeling of population neural dynamics challenging. Drawing from concepts and techniques in statistical mechanics, a field dedicated to the emergence of macroscopic properties from local interactions, this senior thesis involves a theoretical and computational exploration of the connectivity and criticality of both spiking networks and C. elegans neural activity using Ising and Potts maximum entropy models respectively. For the theoretical component, we discussed methods for inferring the parameters of these distributions, as well as how to identify a signature of criticality for these networks known as the divergence of heat capacity. From there, we apply these methods to datasets of neural activity, successfully recovering the average activities and correlations that constrained our model, predicting the probabilities of neural patterns and configurations not explicitly accounted for with our distributions, and demonstrating that these systems may plausibly exist near a self-organized criticality – a criticality that can be disrupted with network perturbations. Future work will involve more rigorous methods for determining criticality and extending the model to account for temporal correlations.