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      Analysis and Modeling of Subthreshold Neural Multi-Electrode Array Data by Statistical Field Theory

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          Abstract

          Multi-electrode arrays (MEA) are increasingly used to investigate spontaneous neuronal network activity. The recorded signals comprise several distinct components: Apart from artifacts without biological significance, one can distinguish between spikes (action potentials) and subthreshold fluctuations (local fields potentials). Here we aim to develop a theoretical model that allows for a compact and robust characterization of subthreshold fluctuations in terms of a Gaussian statistical field theory in two spatial and one temporal dimension. What is usually referred to as the driving noise in the context of statistical physics is here interpreted as a representation of the neural activity. Spatial and temporal correlations of this activity give valuable information about the connectivity in the neural tissue. We apply our methods on a dataset obtained from MEA-measurements in an acute hippocampal brain slice from a rat. Our main finding is that the empirical correlation functions indeed obey the logarithmic behavior that is a general feature of theoretical models of this kind. We also find a clear correlation between the activity and the occurrence of spikes. Another important insight is the importance of correctly separating out certain artifacts from the data before proceeding with the analysis.

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          Most cited references18

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          Intrinsic circuit organization and theta-gamma oscillation dynamics in the entorhinal cortex of the rat.

          A thorough knowledge of the intrinsic circuit properties of the entorhinal cortex (EC) and the temporal dynamics these circuits support is essential for understanding how information is exchanged between the hippocampus and neocortex. Using intracellular and extracellular recordings in the anesthetized rat and anatomical reconstruction of single cells, we found that EC5 and EC2 principal neurons form large axonal networks mainly within their layers, interconnected by the more vertically organized axon trees of EC3 pyramidal cells. Principal cells showed layer-specific unique membrane properties and contributed differentially to theta and gamma oscillations. EC2 principal cells were most strongly phase modulated by EC theta. The multiple gamma oscillators, present in the various EC layers, were temporally coordinated by the phase of theta waves. Putative interneurons in all EC layers fired relatively synchronously within the theta cycle, coinciding with the maximum power of gamma oscillation. The special wiring architecture and unique membrane properties of EC neurons may underlie their behaviorally distinct firing patterns in the waking animal.
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            Effect of stimulus intensity on the spike-local field potential relationship in the secondary somatosensory cortex.

            Neuronal oscillations in the gamma frequency range have been reported in many cortical areas, but the role they play in cortical processing remains unclear. We tested a recently proposed hypothesis that the intensity of sensory input is coded in the timing of action potentials relative to the phase of gamma oscillations, thus converting amplitude information to a temporal code. We recorded spikes and local field potential (LFP) from secondary somatosensory (SII) cortex in awake monkeys while presenting a vibratory stimulus at different amplitudes. We developed a novel technique based on matching pursuit to study the interaction between the highly transient gamma oscillations and spikes with high time-frequency resolution. We found that spikes were weakly coupled to LFP oscillations in the gamma frequency range (40-80 Hz), and strongly coupled to oscillations in higher gamma frequencies. However, the phase relationship of neither low-gamma nor high-gamma oscillations changed with stimulus intensity, even with a 10-fold increase. We conclude that, in SII, gamma oscillations are synchronized with spikes, but their phase does not vary with stimulus intensity. Furthermore, high-gamma oscillations (>60 Hz) appear to be closely linked to the occurrence of action potentials, suggesting that LFP high-gamma power could be a sensitive index of the population firing rate near the microelectrode.
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              Human embryonic stem cell-derived neuronal cells form spontaneously active neuronal networks in vitro.

              The production of functional human embryonic stem cell (hESC)-derived neuronal cells is critical for the application of hESCs in treating neurodegenerative disorders. To study the potential functionality of hESC-derived neurons, we cultured and monitored the development of hESC-derived neuronal networks on microelectrode arrays. Immunocytochemical studies revealed that these networks were positive for the neuronal marker proteins beta-tubulin(III) and microtubule-associated protein 2 (MAP-2). The hESC-derived neuronal networks were spontaneously active and exhibited a multitude of electrical impulse firing patterns. Synchronous bursts of electrical activity similar to those reported for hippocampal neurons and rodent embryonic stem cell-derived neuronal networks were recorded from the differentiated cultures until up to 4 months. The dependence of the observed neuronal network activity on sodium ion channels was examined using tetrodotoxin (TTX). Antagonists for the glutamate receptors NMDA [D(-)-2-amino-5-phosphonopentanoic acid] and AMPA/kainate [6-cyano-7-nitroquinoxaline-2,3-dione], and for GABAA receptors [(-)-bicuculline methiodide] modulated the spontaneous electrical activity, indicating that pharmacologically susceptible neuronal networks with functional synapses had been generated. The findings indicate that hESC-derived neuronal cells can generate spontaneously active networks with synchronous communication in vitro, and are therefore suitable for use in developmental and drug screening studies, as well as for regenerative medicine.
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                Author and article information

                Contributors
                Journal
                Front Comput Neurosci
                Front Comput Neurosci
                Front. Comput. Neurosci.
                Frontiers in Computational Neuroscience
                Frontiers Media S.A.
                1662-5188
                18 April 2017
                2017
                : 11
                : 26
                Affiliations
                [1] 1Division of Biological Physics, Department of Physics, Chalmers University of Technology Göteborg, Sweden
                [2] 2Department of Physiology, Institute of Neuroscience and Physiology, Sahgrenska Academy, University of Gothenburg Göteborg, Sweden
                Author notes

                Edited by: Markus Diesmann, Forschungszentrum Jülich, Germany

                Reviewed by: J. Michael Herrmann, University of Edinburgh, UK; Stephan Theiss, University of Düsseldorf, Germany; John A. Hertz, Niels Bohr Institute, Denmark

                *Correspondence: Måns Henningson mans@ 123456chalmers.se
                Article
                10.3389/fncom.2017.00026
                5394179
                be0b6c69-5380-416e-b4f0-f081ccff3d86
                Copyright © 2017 Henningson and Illes.

                This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

                History
                : 15 July 2016
                : 29 March 2017
                Page count
                Figures: 13, Tables: 0, Equations: 31, References: 22, Pages: 12, Words: 6861
                Categories
                Neuroscience
                Original Research

                Neurosciences
                multi-electrode-array,statistical field theory,subthreshold oscillations,hippocampus,slice preparation

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