title: A master equation formalism for macroscopic modeling of asynchronous irregular activity states.
abstract: Many efforts have been devoted to modeling asynchronous irregular (AI) activity states, which resemble the complex activity states seen in the cerebral cortex of awake animals. Most of models have considered balanced networks of excitatory and inhibitory spiking neurons in which AI states are sustained through recurrent sparse connectivity, with or without external input. In this letter we propose a mesoscopic description of such AI states. Using master equation formalism, we derive a second-order mean-field set of ordinary differential equations describing the temporal evolution of randomly connected balanced networks. This formalism takes into account finite size effects and is applicable to any neuron model as long as its transfer function can be characterized. We compare the predictions of this approach with numerical simulations for different network configurations and parameter spaces. Considering the randomly connected network as a unit, this approach could be used to build large-scale networks of such connected units, with an aim to model activity states constrained by macroscopic measurements, such as voltage-sensitive dye imaging.
authors.affiliation: Unité de Neurosciences Intégratives et Computationnelles, CNRS, 91198 Gif-sur-Yvette, France. elbousta@unic.cnrs-gif.fr
authors.forename: Sami
authors.initials: S
authors.lastname: El Boustani
authors.forename: Alain
authors.initials: A
authors.lastname: Destexhe
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000818:Animals; D002540:Cerebral Cortex / Q000166:cytology* / Q000502:physiology; D003198:Computer Simulation; D016014:Linear Models; D008959:Models, Neurological; D009433:Neural Inhibition / Q000502:physiology; D016571:Neural Networks, Computer; D009474:Neurons / Q000145:classification / Q000502:physiology*; D013997:Time Factors; D014851:Wakefulness