1. A model has been proposed of picrotoxin-induced hippocampal in vitro afterdischarges; it depends critically upon a-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid (AMPA) and N-methyl-D-aspartate (NMDA) receptors in the recurrent excitatory connections between pyramidal neurones, and upon the ability of pyramidal neurones to generate bursts at about 10 Hz when their dendrites are sufficiently depolarized. 2. We study here the question of whether this model can account for spatial - as well as temporal - aspects of after-discharges in guinea-pig hippocampal slices. For example, can the model explain the propagation along a transverse slice of the initial burst and the secondary bursts at about the same velocity, approximately 0.10-0.20 m s-1? Under what conditions might the secondary bursts exhibit a different spatial pattern to the initial burst, as we now show can occur in longitudinal slices? To examine these questions, we increased the number of cells in our model from 100 to 8000 (in a 20 x 400 array), arranging the excitatory synaptic connections in a spatially restricted fashion, with an average extent of 1.0 mm (as suggested experimentally). 3. Our model suggests that both AMPA and NMDA receptors contribute to the propagation pattern and velocity of the initial and the secondary bursts in an after-discharge. 4. When unitary AMPA and NMDA conductances are in the range where the primary burst lasts for 100-200 ms, and there are three or four secondary bursts, then both primary and secondary bursts propagate near to the experimentally observed velocity for transverse slices. ln the model, however. secondary bursts propagate at somewhat slower velocities than the initial burst. 5. The mechanisms of propagation are different for the initial and for the secondary bursts: propagation of the primary burst depends upon the initiation of electrogenesis in 'resting' dendrites by AMPA and NMDA inputs that are rapidly increasing in time. Propagation of secondary bursts depends upon the timing of calcium spikes in depolarized dendrites with slowly varying NMDA inputs; the timing of calcium spikes can be influenced by a 'wave' of AMPA input, but calcium spikes - we predict - should occur even without the AMPA input, once the after-discharge has been initiated. The blockade of firing in an intermediate region of the disinhibited slice is predicted to have different effects on the primary burst and on secondary bursts distal to the region of blockade. 6. In transverse slices, and in some longitudinal slices, there is a preferred direction of propagation for the secondary bursts, so that the initial burst propagates away from a stimulus, but later bursts propagate in a constant direction whichever end of the slice is stimulated. The model exhibits this same behaviour when there is a linear gradient of either (a) excitatory synaptic conductances (AMPA or NMDA), (b) excitatory connectivity, (c) slow calcium-dependent potassium conductance density, or (d) GABA(B) conductance. Secondary bursts are initiated respectively at sites of larger synaptic strength, higher connectivity, or smaller potassium conductance (either intrinsic or synaptic). 7. We have previously shown, using intracellular recording and network simulations, that both AMPA and NMDA receptors (along with intrinsic membrane properties) contribute to shaping the temporal pattern of the after-discharge in a local population of pyramidal neurones. The present results suggest that both types of receptors also shape the spatial pattern of the after-discharge in larger neuronal populations.
