Extracting functionally feedforward networks from a population of spiking neurons

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.

Maximum likelihood estimators for truncated and censored power-law distributions show how neuronal avalanches may be misevaluated

“…Another characteristic feature of multielectrode data is that estimates of power-law slopes are reported to be around 3/2 [1,23] (with pharmacological manipulation, we have obtained a range of slopes from 1.47 to 1.63 [29]). Around these values, numerical simulations show that the approach of Clauset leads to an overestimation of the slope, while the approach of Bauke leads to an underestimation [Figs.…”

“…These approaches improve upon previous work by taking into account key aspects of observed data, including their continuous, discrete, and bounded nature. These aspects reflect features of neuronal recordings obtained with multielectrodes [1,23,29,31], where the number of electrodes offers a natural upper bound on distributions derived from the data. Here, numerical simulations as well as analyses of in vitro cortical activity show that commonly employed approaches fail to take into account these aspects of the observed data and therefore lead to a sharp misestimation of the slope of power laws.…”

“…The distribution of neurons active during avalanches roughly followed a power law [ Fig. 3(b)] [1,29]. Increased noise near the tail of the distribution is in part attributed to the presence of fewer data points as values (i.e., number of active neurons) increase [30].…”

“…Multielectrode data recorded from cultured cortical neurons were obtained from previous work [29]. We identified neuronal avalanches with nonoverlapping time bins of fixed duration.…”

Altered Network Communication Following a Neuroprotective Drug Treatment

“…Multi-electrode arrays record neuronal activity at a spatial resolution that is a compromise between microscale (i.e., single synapses) and macroscale (on the order of millions of neurons, as in neuroimaging) approaches [6]. The spatiotemporal patterns of bursting activity revealed by multi-electrode arrays provide a glimpse of the underlying functional connectivity in the neuronal network [7], [8]. Highly non-random graph-theoretic properties have been characterized in functional networks of dissociated neurons, including a small-world organization [9], [10].…”