Large fast and slow pulses propagate in one-dimensional
networks composed of excitatory and inhibitory populations
David Golomb1, G. Bard Ermentrout2 and
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
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