On the Distribution of Firing Rates in Networks of Cortical Neurons

Abstract

The distribution of in vivo average firing rates within local cortical networks has been reported to be highly skewed and long tailed. The distribution of average single-cell inputs, conversely, is expected to be Gaussian by the central limit theorem. This raises the issue of how a skewed distribution of firing rates might result from a symmetric distribution of inputs. We argue that skewed rate distributions are a signature of the nonlinearity of the in vivo f-I curve. During in vivo conditions, ongoing synaptic activity produces significant fluctuations in the membrane potential of neurons, resulting in an expansive nonlinearity of the f-I curve for low and moderate inputs. Here, we investigate the effects of single-cell and network parameters on the shape of the f-I curve and, by extension, on the distribution of firing rates in randomly connected networks.

A Canonical Neural Mechanism for Behavioral Variability

“…Highly irregular patterns of activity, which are ubiquitous in the brain 3 , are thought to underlie variable motor behaviors [4][5] . Specifically in songbirds, a neural circuit necessary for song learning in juveniles [6][7] has been recently shown to be responsible for vocal variability both in adults 8 and throughout development 7,[9][10] . This circuit includes two cortical-like areas: a premotor nucleus, the lateral magnocellular nucleus of the anterior nidopallium (LMAN), and its efferent motor nucleus, the robust nucleus of the arcopalium (RA).…”

“…This circuit includes two cortical-like areas: a premotor nucleus, the lateral magnocellular nucleus of the anterior nidopallium (LMAN), and its efferent motor nucleus, the robust nucleus of the arcopalium (RA). While RA is essential in driving the effectors (muscles or muscle synergies) producing the song 11 , LMAN is not necessary for song production in adults [6][7] , but has a key role throughout development and in adults in driving variability in the song [9][10] and in the activity of RA neurons 12 .…”

Extraction of Synaptic Input Properties in Vivo

“…This means that the probability for large events is larger than for a Gaussian with same mean and variance. Such heavy-tailed distributions have been observed in a number of systems (Sayer, Friedlander, and Redman, 1990;Song et al, 2005;Barbour et al, 2007;Ikegaya et al, 2013) and are believed to be an important characteristic of neural processing (Koulakov, Hromádka, and Zador, 2009;Roxin et al, 2011;Teramae, Tsubo, and Fukai, 2012). While any distribution can be tested (although for efficiency reasons the moments should ideally be available analytically), a future goal is to reconstruct the amplitude distribution directly, for instance by reconstructing it from it moments.…”

Estimating individual firing frequencies in a multiple spike train record

“…Despite some discussions about the way in which the firing frequency is understood in the context of neural network activity (Nawrot et al, 1999;Brunel, 2000;Lansky et al, 2004;Cherif et al, 2008;Ermentrout et al, 2010;Roxin et al, 2011), it is commonly related to the mean of the interspike intervals (ISIs). This is due to the fact that experimental results are mostly represented by recording the ISIs whereas real neuronal systems work on parallel processing and counting the spikes.…”