Criticality in neural networks: a study of the interplay between experimental tools and theoretical models

In the human brain trillions of neurons transmit information “firing” electrical pulses called action potentials or spikes. Neurons are connected to each other and form highly complex networks in which a single neuron may be connected to thousands of other neurons. The activity of single neurons and, more recently, the activity of groups of neurons have been monitored extensively using intracellular and extracellular recordings. One of the most striking observations arisen from such recordings is the fact that neuronal activity seems to be characterized by “avalanches” whose size and lifetime distributions obey a power law, which is typical of self-organized critical systems. Such critical behavior has been confirmed also by theoretical models, but the way avalanches are defined and detected in the experimental analysis is very different from the way they are defined and detected in theoretical simulations. In this work, after a brief review of the concept of Self-Organized Criticality, we describe the experiment that led to the observation of neuronal avalanches. Then, we describe the Millman model, a neuronal network model that reproduces the critical behavior observed in real networks. Finally, we investigate the differences between theoretical and experimental avalanches. In particular, we analyze the data from numerical simulations with the methods used to detect avalanches in real networks. We show that if the methods of analysis change, the critical behavior is no longer observed.