Large fast and slow pulses propagate in one-dimensional networks composed of excitatory and inhibitory populations

David Golomb1, G. Bard Ermentrout2 and Jian-Young Wu3

1Zlotowski Center for Neuroscience and Dept. of Physiology, Ben-Gurion University, Israel
2Dept. of Mathematics, University of Pittsburgh
3Dept. of Physiology and Biophysics, Georgetown Univ.

Evoked high-firing-rate discharges (Epileptiform) propagate over long distances in cortex when GABAA inhibition is blocked (by > 10 micromolar bicuculline), with velocity of about 6-15 cm/s. Without any GABAA blockade, evoked events with lower firing rate (``ensemble activities") propagate at much lower velocities, about 0.1 to 0.7 cm/s. In order to understand the reasons for the differences between fast and slow discharges, we have theoretically and computationally studied a one-dimensional network model of two-population (excitatory and inhibitory) networks, composed of integrate-and-fire neurons that are allowed to fire only one spike. Synaptic interactions between cells decay with distance. Increasing the inhibitory conductances gIE into excitatory cells gradually decreases the propagation velocity. Further increasing of gIE may cause these fast pulses to disappear via a saddle-node bifurcation (SNB). The slow pulse is generated in a second SNB, which occurs at lower gIE and much lower velocity. During the slow pulse, inhibitory cells fire well before their neighboring excitatory cells. There is a bistable regime in which both the fast and the slow pulses are stable. The fast pulse has a much larger basin of attraction. Enhancing slow NMDA excitation often increases the possibility that the slow pulse and the bistable regime exist, consistent with experimental observation. Simulations of conductance-based models are consistent with these results. Preliminary experimental observation show that a non-continuous transition in velocity occurs as the level of bicuculline concentration in the slice increases, as predicted by the theory.