Random compositional networks of synfire chains dynamically self-tune to the critical state for ongoing percolation of activity

Abstract

Event Abstract Back to Event Random compositional networks of synfire chains dynamically self-tune to the critical state for ongoing percolation of activity Chris Trengove1*, Cees V. Leeuwen2 and Markus Diesmann3 1 RIKEN CSRP, Diesmann Research Unit, Brain and Neural Systems Team, Japan 2 RIKEN Brain Science Institute, Laboratory for Perceptual Dynamics, Japan 3 RIKEN Brain Science Institute, Diesmann Research Unit, Japan Synfire chains are spiking networks with a sequential pool structure that supports the robust propagation of a 'wave' of precisely timed spikes and have been proposed as a mechanism for cognition in which component chains represent features and feature composition (binding) is accomplished by links between chains (Abeles et al. 2004). Recent spiking network simulations (Trengove et al. 2010) show that a large number of synfire chains can be embedded in a network the size of a cortical column (~1000 chains of length ~100 in a network of ~100,000 neurons). Activity is stabilized by feedback in the form of balanced excitatory and inhibitory recurrent input ('noise') which limits the number of co-active waves. This set-up opens the door to simulating large-scale compositional systems of synfire chains in which many feature relationships can be represented. As a first step in exploring the dynamics of large compositional systems, we study a compositional network formed by random pair-wise composition of chains. We consider two types of pair-wise composition (as illustrated): Type 1: longitudinal (end-to-end) composition, which results in a feed-forward branching chain structure; and Type 2: lateral composition (with a longitudinal offset) using excitatory cross-links, which supports lateral ignition of waves leading to simultaneous activation of coupled chains by synchronised synfire waves. Both topologies in principle allow wave activity to multiply and spread through the network. However, due to the regulation by noise, we find that both types of network support a stable equilibrium state that is sustained without external input. When a distribution of chain strengths is used in the Type 1 model, the equilibrium level of synfire wave activity is tuned to a near-critical level in which the number of chains strong enough to propagate activity is just enough to support ongoing percolation of synfire wave activity through the system. This is because the amount of noise which a propagating wave can tolerate increases monotonically with the strength of the chain. The Type 2 model parameters can be set so that the noise limit for lateral ignition is lower than that for wave propagation, and hence the effectiveness of lateral ignition determines the spread of wave activity through the system. The model can therefore be understood as a random directed graph in which chains are nodes, cross-links are edges, and the effectiveness of an edge is conditional on the global mean activity level. Thus, with a distribution of cross-link strengths, the system equilibrates at the activity level where the effective connectivity is at the percolation threshold: the mean effective out-degree of each node is 1. This dynamic self-tuning to a critical level may relate to the criticality of spike-avalanche phenomena observed both in neural cultures and in vivo (Petermann et al 2009). The dynamics of the stable state in our models is consistent with observed electro-physiological data, both in terms of the low firing rate and the approximate statistics of membrane potential fluctuations. In simulated recordings replicating the under-sampling of present experimental techniques, the spiking appears irregular and asynchronous, and the precisely organised synfire chain structure and spike timing relationships are not detectable. Acknowledgements Partially supported by Next-Generation Supercomputer Project of MEXT, Japan, DIP F1.2, Helmholtz Alliance on Systems Biology, EU Grant 15879 (FACETS), and BMBF Grant 01GQ0420 to BCCN Freiburg. All network simulations were carried out with NEST (http://www.nest-initiative.org).