Network topology of neural systems supporting avalanche dynamics predicts stimulus propagation and recovery

Abstract

Many neural systems display avalanche behavior characterized by uninterrupted sequences of neuronal firing whose distributions of size and durations are heavy-tailed. Theoretical models of such systems suggest that these dynamics support optimal information transmission and storage. However, the unknown role of network structure precludes an understanding of how variations in network topology manifest in neural dynamics and either support or impinge upon information processing. Here, using a generalized spiking model, we develop a mechanistic understanding of how network topology supports information processing through network dynamics. First, we show how network topology determines network dynamics by analytically and numerically demonstrating that network topology can be designed to propagate stimulus patterns for long durations. We then identify strongly connected cycles as empirically observable network motifs that are prevalent in such networks. Next, we show that within a network, mathematical intuitions from network control theory are tightly linked with dynamics initiated by node-specific stimulation and can identify stimuli that promote long-lasting cascades. Finally, we use these network-based metrics and control-based stimuli to demonstrate that long-lasting cascade dynamics facilitate delayed recovery of stimulus patterns from network activity, as measured by mutual information. Collectively, our results provide evidence that cortical networks are structured with architectural motifs that support long-lasting propagation and recovery of a few crucial patterns of stimulation, especially those consisting of activity in highly controllable neurons. Broadly, our results imply that avalanching neural networks could contribute to cognitive faculties that require persistent activation of neuronal patterns, such as working memory or attention.keywords linear dynamical systems, network control, mutual information 2/25

The growing topology of theC. elegansconnectome

“…Indeed, the absence of connections between multiple neurons can be particularly important for many informational processes, such as isolating functions or providing parallel routing. A sparse area within a network might manifest within a pattern of neurons connected as a loop, which can induce periodic activity patters [8,9] and support memory [10,11,12]. Additionally, biological processes are inherently noisy but must overcome this randomness in healthy development.…”