| We have developed a continuum model of the cortex that incorporates both chemical and electrical (gap junction) synapses. We have identified two distinctive operational modes dependent on the strength and timeliness of the feedback between neuron soma and its dendrite: (i) If the soma response is slow relative to dendritic events, the model predicts ultra-slow spatiotemporal oscillations in cortical activity reminiscent of BOLD patterns seen in fMRI. This slow oscillation arises from nonlinear interactions between Turing (spatial) and Hopf (temporal) symmetry-breaking instabilities. Formation of the spatial patterns is sensitively dependent on the strength of the gap-junction diffusive coupling between interneurons, acting to stabilize the slow mode. (ii) If the soma response to dendritic input is prompt and immediate, a gamma-band (~40-Hz) standing-wave instability emerges, entraining the cortex into long-range synchronous oscillations. In this second limit, the generation of the wave instability requires an adequate level of subcortical stimulation. We comment on the role of gap junctions in seizure initiation and cessation. |
|