Multiplex Networks of Cortical and Hippocampal Neurons Revealed at Different Timescales

Abstract

Recent studies have emphasized the importance of multiplex networks – interdependent networks with shared nodes and different types of connections – in systems primarily outside of neuroscience. Though the multiplex properties of networks are frequently not considered, most networks are actually multiplex networks and the multiplex specific features of networks can greatly affect network behavior (e.g. fault tolerance). Thus, the study of networks of neurons could potentially be greatly enhanced using a multiplex perspective. Given the wide range of temporally dependent rhythms and phenomena present in neural systems, we chose to examine multiplex networks of individual neurons with time scale dependent connections. To study these networks, we used transfer entropy – an information theoretic quantity that can be used to measure linear and nonlinear interactions – to systematically measure the connectivity between individual neurons at different time scales in cortical and hippocampal slice cultures. We recorded the spiking activity of almost 12,000 neurons across 60 tissue samples using a 512-electrode array with 60 micrometer inter-electrode spacing and 50 microsecond temporal resolution. To the best of our knowledge, this preparation and recording method represents a superior combination of number of recorded neurons and temporal and spatial recording resolutions to any currently available in vivo system. We found that highly connected neurons (“hubs”) were localized to certain time scales, which, we hypothesize, increases the fault tolerance of the network. Conversely, a large proportion of non-hub neurons were not localized to certain time scales. In addition, we found that long and short time scale connectivity was uncorrelated. Finally, we found that long time scale networks were significantly less modular and more disassortative than short time scale networks in both tissue types. As far as we are aware, this analysis represents the first systematic study of temporally dependent multiplex networks among individual neurons.

Quantifying Information Modification in Developing Neural Networks via Partial Information Decomposition

“…This approach to cover a longer history at a low dimensionality amounts to a compressing of the information in the history of the process, aiming to retain what we perceive to be the most relevant information. This approach is similar to the one used by Timme et al [27], except for the use of nonuniform binwidths in our case. Alternative approaches to large bin widths exist that are either based (i) on nonuniform embedding, picking the most informative past samples (or bins with a small width on the order of the inverse sampling rate) from a collection of candidates (e.g., [28][29][30]), and the IDT xl toolbox [22]; or (ii) on varying the lag between an a vector of evenly spaced past bins and the current sample [4,31,32], but both of these approaches might be less suitable for relatively sparse binary data, such as spike trains.…”

Transfer entropy in continuous time, with applications to jump and neural spiking processes

“…How should one rigorously compute the transfer entropy for such data sets? Previous approaches have attempted to apply the discrete time formalism to such systems in a number of ways, for example, in examining the information between most recent events in an economic setting [22], or in discretizing time (i.e., time binning) for spiking neural processes [23][24][25][26][27]. Such approaches necessarily recast the dynamics in order to make empirical approxima-tions, which may ignore key mechanisms relevant to the source-target relationship.…”

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). These methods allow for the exploration of interactions over certain time scales, the search for interactions with set delays (e.g., synaptic connectivity), or interactions involving patterns of activity.…”

“…Surrogate data testing or Monte Carlo analysis is frequently the solution to significance testing in information theory analyses (Lindner et al, 2011; Timme et al, 2014b; Wibral et al, 2014a; Asaad et al, 2017). This type of analysis is performed by generating surrogate null model data that preserve certain aspects of the data while randomizing other aspects.…”

“…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).…”