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.
Highlights
Understanding how large groups of neurons process and represent information in neural systems is a fundamental problem of neuroscience
We found no significant differences between tissue types at individual time scales, though the time scale dependent behavior of the cortical networks tended to be more significant across different time scales in comparison to the hippocampal networks
Our analysis represents the first systematic examination of time scale dependent multiplex networks of individual neurons and it indicates that these time scale dependent networks potentially differ by function and brain region
Summary
Understanding how large groups of neurons process and represent information in neural systems is a fundamental problem of neuroscience. We are aware of only two other studies – both of which were conducted in vitro – that examined networks with time scale dependent connectivity at the cellular level [46,47,48] Though these works implicitly examined multiplex networks, both studies treated networks at different time scales as distinct with essentially independent nodes and only one type of connection. Cortical networks where shown to be significantly more assortative than hippocampal networks for short time scales, but the two tissue types were disassortative for longer time scales These results represent the first systematic examination of time scale dependent multiplex networks of individual neurons and they indicate that these time scale dependent networks potentially differ by function and brain region. The results in this paper were presented in earlier versions at two conferences [73, 74]
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