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We examined the effects of both intrinsic neuronal membrane properties and network parameters on oscillatory activity in a model of neocortex. A scalable network model with six different cell types was built with the pGENESIS neural simulator. The neocortical network consisted of two types of pyramidal cells and four types of inhibitory interneurons. All cell types contained both fast sodium and delayed rectifier potassium channels for generation of action potentials. A subset of the pyramidal neurons contained an additional slow inactivating (persistent) sodium current (NaP). The neurons with the NaP current showed spontaneous bursting activity in the absence of external stimulation. The model also included a routine to calculate a simulated electroencephalogram (EEG) trace from the population activity. This revealed emergent network behavior which ranged from desynchronized activity to different types of seizure-like bursting patterns. At settings with weaker excitatory network effects, the propensity to generate seizure-like behavior increased. Strong excitatory network connectivity destroyed oscillatory behavior, whereas weak connectivity enhanced the relative importance of the spontaneously bursting cells. Our findings are in contradiction with the general opinion that strong excitatory synaptic and/or insufficient inhibition effects are associated with seizure initiation, but are in agreement with previously reported behavior in neocortex.