Rich-Club Organization in Effective Connectivity among Cortical Neurons

Abstract

The performance of complex networks, like the brain, depends on how effectively their elements communicate. Despite the importance of communication, it is virtually unknown how information is transferred in local cortical networks, consisting of hundreds of closely spaced neurons. To address this, it is important to record simultaneously from hundreds of neurons at a spacing that matches typical axonal connection distances, and at a temporal resolution that matches synaptic delays. We used a 512-electrode array (60 m spacing) to record spontaneous activity at 20 kHz from up to 500 neurons simultaneously in slice cultures of mouse somatosensory cortex for 1 h at a time. We applied a previously validated version of transfer entropy to quantify information transfer. Similar to in vivo reports, we found an approximately lognormal distribution of firing rates. Pairwise information transfer strengths also were nearly lognormally distributed, similar to reports of synaptic strengths. Some neurons transferred and received much more information than others, which is consistent with previous predictions. Neurons with the highest outgoing and incoming information transfer were more strongly connected to each other than chance, thus forming a "rich club." We found similar results in networks recorded in vivo from rodent cortex, suggesting the generality of these findings. A rich-club structure has been found previously in large-scale human brain networks and is thought to facilitate communication between cortical regions. The discovery of a small, but information-rich, subset of neurons within cortical regions suggests that this population will play a vital role in communication, learning, and memory. Key words: effective connectivity; information transfer; microcircuits; rich club; transfer entropy Significance StatementMany studies have focused on communication networks between cortical brain regions. In contrast, very few studies have examined communication networks within a cortical region. This is the first study to combine such a large number of neurons (several hundred at a time) with such high temporal resolution (so we can know the direction of communication between neurons) for mapping networks within cortex. We found that information was not transferred equally through all neurons. Instead, ϳ70% of the information passed through only 20% of the neurons. Network models suggest that this highly concentrated pattern of information transfer would be both efficient and robust to damage. Therefore, this work may help in understanding how the cortex processes information and responds to neurodegenerative diseases.

Cancer as a disorder of patterning information: computational and biophysical perspectives on the cancer problem

“…In neuroscience, transfer entropy is used to uncover effective connectivity [423,424]. It has been used to evaluate information transfer between auditory cortical neurons [42], and on simulated data for cortical interactions [425], electroencephalogram (EEG) data [426], and fMRI data [427].…”

A Tutorial for Information Theory in Neuroscience

“…Due to the widespread interest in neural connectivity (Bullmore and Sporns, 2009; Friston, 2011), transfer entropy has been widely used in the literature (for example, Honey et al, 2007; Lizier et al, 2008; Ito et al, 2011; Vicente et al, 2011; Timme et al, 2014b, 2016; Wibral et al, 2014b; Nigam et al, 2016; Bossomaier et al, 2016). Numerous methods have been employed to define past and future state (Staniek and Lehnertz, 2008; Ito et al, 2011; Wibral et al, 2013; Timme et al, 2014b).…”

“…For instance, research has focused on analyses of electroencephalography (EEG), magnetoencephalography (MEG), and functional MRI (fMRI) data (Jeong et al, 2001; Lizier et al, 2011; Vicente et al, 2011). Research has also focused on trial-based data (Wollstadt et al, 2014; Gomez-Herraro et al, 2015; Asaad et al, 2017) and single-trial time-averaged analyses (Wibral et al, 2013; Timme et al, 2014b, 2016; Nigam et al, 2016). Two particular areas of interest include studies of connectivity (Honey et al, 2007; Ito et al, 2011; Timme et al, 2014b, 2016; Nigam et al, 2016; Wollstadt et al, 2017) and sensory encoding (Bialek et al, 1991; DeWeese and Meister, 1999; Brenner et al, 2000; Panzeri et al, 2001; Butts, 2003; Butts et al, 2007).…”

Communicability systematically explains transmission speed in a cortical macro-connectome

“…For instance, the comprehensive network (connectomics) approach is essential for studying brain wiring 13 , and graphtheoretic analyses have been used to study a range of relevant topics, such as the Small-World property, which can explain why spatially distant brain regions are able to communicate easily 7 , hubs and rich club organization, which can be used to extract a collection of highly-connected nodes 79 , and community architecture, which can characterize global groups of nodes 73 . The basic concepts of these approaches to network analysis have been previously summarized in textbooks on graph theory 51,5 .…”

“…This issue is also essential for studying microscopic neuronal networks 1,68,51,40 . Recently, connectomics studies have been made possible due to the massive efforts of collaborating teams, and the quality and resolution of data have gradually improved 29,51,55 . The main focus of these studies is often structural networks or spatial patterns of relatively stable neuronal activities 26 .…”