Extracting functionally feedforward networks from a population of spiking neurons

Kathleen Vincent,Joseph S Tauskela,Jean-Philippe Thivierge

doi:10.3389/fncom.2012.00086

Abstract

Neuronal avalanches are a ubiquitous form of activity characterized by spontaneous bursts whose size distribution follows a power-law. Recent theoretical models have replicated power-law avalanches by assuming the presence of functionally feedforward connections (FFCs) in the underlying dynamics of the system. Accordingly, avalanches are generated by a feedforward chain of activation that persists despite being embedded in a larger, massively recurrent circuit. However, it is unclear to what extent networks of living neurons that exhibit power-law avalanches rely on FFCs. Here, we employed a computational approach to reconstruct the functional connectivity of cultured cortical neurons plated on multielectrode arrays (MEAs) and investigated whether pharmacologically induced alterations in avalanche dynamics are accompanied by changes in FFCs. This approach begins by extracting a functional network of directed links between pairs of neurons, and then evaluates the strength of FFCs using Schur decomposition. In a first step, we examined the ability of this approach to extract FFCs from simulated spiking neurons. The strength of FFCs obtained in strictly feedforward networks diminished monotonically as links were gradually rewired at random. Next, we estimated the FFCs of spontaneously active cortical neuron cultures in the presence of either a control medium, a GABAA receptor antagonist (PTX), or an AMPA receptor antagonist combined with an NMDA receptor antagonist (APV/DNQX). The distribution of avalanche sizes in these cultures was modulated by this pharmacology, with a shallower power-law under PTX (due to the prominence of larger avalanches) and a steeper power-law under APV/DNQX (due to avalanches recruiting fewer neurons) relative to control cultures. The strength of FFCs increased in networks after application of PTX, consistent with an amplification of feedforward activity during avalanches. Conversely, FFCs decreased after application of APV/DNQX, consistent with fading feedforward activation. The observed alterations in FFCs provide experimental support for recent theoretical work linking power-law avalanches to the feedforward organization of functional connections in local neuronal circuits.

Highlights

Spontaneous activity accounts for a significant proportion of the brain’s energy consumption (Raichle, 2006) and serves important roles both in the development of neural circuits (Blankenship and Feller, 2010) and in the modulation of neuronal responses to external stimuli (Arieli et al, 1996)
We computed a graph of directed functional connectivity based on transfer entropy (TE) (Equation 11), and performed a Schur decomposition to estimate the strength of feedforward connectivity (FFC) (Equations 14, 15)
We found a striking similarity between the P matrix and the matrix of functional connectivity obtained by TE (Figure 3B), showing that TE captured the statistics of interactions amongst pairs of neurons in the model

Summary

Introduction

Spontaneous activity accounts for a significant proportion of the brain’s energy consumption (Raichle, 2006) and serves important roles both in the development of neural circuits (Blankenship and Feller, 2010) and in the modulation of neuronal responses to external stimuli (Arieli et al, 1996). A hallmark of spontaneous activity is its high degree of spatial and temporal organization. In one regime of activity, these bursts follow a power-law distribution, in which bursts recruiting a small number of neurons occur markedly more often than larger bursts (Beggs and Plenz, 2003). This characteristic distribution of bursts, termed a neuronal avalanche, has been reported in several systems, including dissociated hippocampal cultures (Tang et al., 2008), somatosensory cortical slices (Gireesh and Plenz, 2008), and in vivo (Petermann et al, 2009). A power-law distribution of avalanches is indicative of neural dynamics with no characteristic scale and is conjectured to form an optimal state for information processing, computation, and learning (Shew et al, 2011)

Methods

Results

Conclusion