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Front Comput Neurosci. 2013 Mar 26;7:20. doi: 10.3389/fncom.2013.00020. eCollection 2013.

Inferring network properties of cortical neurons with synaptic coupling and parameter dispersion.

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Theoretical Neuroscience Group, Faculté de Médecine, Institut de Neurosciences des Systèmes, Inserm UMR1106, Aix-Marseille Université Marseille, France ; Bernstein Center for Computational Neuroscience Berlin, Germany ; Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin Berlin, Germany.


Computational models at different space-time scales allow us to understand the fundamental mechanisms that govern neural processes and relate uniquely these processes to neuroscience data. In this work, we propose a novel neurocomputational unit (a mesoscopic model which tell us about the interaction between local cortical nodes in a large scale neural mass model) of bursters that qualitatively captures the complex dynamics exhibited by a full network of parabolic bursting neurons. We observe that the temporal dynamics and fluctuation of mean synaptic action term exhibits a high degree of correlation with the spike/burst activity of our population. With heterogeneity in the applied drive and mean synaptic coupling derived from fast excitatory synapse approximations we observe long term behavior in our population dynamics such as partial oscillations, incoherence, and synchrony. In order to understand the origin of multistability at the population level as a function of mean synaptic coupling and heterogeneity in the firing rate threshold we employ a simple generative model for parabolic bursting recently proposed by Ghosh et al. (2009). Further, we use here a mean coupling formulated for fast spiking neurons for our analysis of generic model. Stability analysis of this mean field network allow us to identify all the relevant network states found in the detailed biophysical model. We derive here analytically several boundary solutions, a result which holds for any number of spikes per burst. These findings illustrate the role of oscillations occurring at slow time scales (bursts) on the global behavior of the network.


firing rate; generative model; multispikes; network synchrony; oscillations; parabolic burst; self-organization; transients

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