Synaptic Superstars

For a long time, neuroscientists have modeled brain activity as a predictable flow where the "average" connection dictates the outcome. However, recent biological evidence suggests that the brain is governed by "heavy-tailed" distributions, a mathematical structure where a few rare, incredibly strong synapses hold more power than thousands of weak ones combined. The Theory of Complex Systems and Neurophysics Group (Benjamin Lindner) investigated how the statistical shape of brain connections fundamentally changes how neurons fire. By comparing standard "light-tailed" models to "heavy-tailed" models, they discovered a phenomenon called directed percolation. In these heavy-tailed systems, activity acts like a spreading wildfire: if even a tiny number of neurons start spiking, the signal can "percolate" through the rare, powerful synapses to activate the entire network. Beyond the spread of activity, the study highlights a state of bistability, where a network can exist in two different modes: a low-activity "resting" state or a self-sustained "active" state. Learn more about heavy-tailed synaptic strength distributions in their article.

Abstract

We analyze states of stationary activity in randomly coupled quadratic integrate-and-fire neurons using stochastic mean-field theory. Specifically, we consider the two cases of Gaussian random coupling and Cauchy random coupling, which are representative of systems with light- or with heavy-tailed synaptic strength distributions. For both, Gaussian and Cauchy coupling, bistability between a low activity and a high activity state of self-sustained firing is possible in excitable neurons. In the system with Cauchy coupling we find analytically a directed percolation threshold, i.e., above a critical value of the synaptic strength, activity percolates through the whole network starting from a few spiking units only. The existence of the directed percolation threshold is in agreement with previous numerical results in the literature for integrate-and-fire neurons with heavy-tailed synaptic strength distribution. However, we have found that the transition can be continuous or discontinuous, depending on the excitatory-inhibitory imbalance in the network. Networks with Gaussian coupling and networks with Cauchy coupling and additional additive noise lack the percolation transition in the thermodynamic limit.