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Synaptic potential summation and repetitive firing mechanisms:

input-output theory for the recruitment of neurons into epileptic bursting firing patterns.WILLIAM H. CALVIN

Departments of Neurological Surgery and of Physiology and Biophysics,

University of Washington School of Medicine,

Seattle, Washington 98105

SUMMARYNeurons in human epileptic foci (and in the various animal models of epilepsy) tend to discharge in high-frequency bursts. If a normal neuron received enough inputs from such epileptic bursting neurons, the temporal and spatial summation of PSPs might elicit a high-frequency burst from the normal neuron itself. This paper considers quantitative models for PSP summation: The average depolarization is the product of mean PSP rates and the area beneath a single PSP, ignoring non-linearities. The size of PSPs, due to single inputs, in mammalian CNS neurons is reviewed and used to estimate the mean depolarization caused by nominal 20/sec firing rates in an input fiber; from this, it is estimated that 2 % of a normal neuron's inputs would be required to give enough spatial summation to start low frequency firing, 8% to cause highfrequency responses. Temporal and spatial summation were simulated on a computer using actual spike trains from epileptic neurons bursting at high frequency, thus giving an estimate of the depolarization sequence to be expected in a norma]cortical neuron which might receive synapses from an epileptic bursting neuron. Depolarization-to-firing-rate curves from normal cortical neurons were then used to illustrate the firing patterns to be expected from the normal neuron's response. It was concluded that a normal neuron could be recruited into a high-frequency bursting firing pattern if about 1% of its inputs possessed such firing.patterns. The input spikes need not be synchronous; only the bursts themselves need overlap in time (simultaneous recording from several epileptic neurons often exhibit such overlap of bursts). Bursts lasting longer than several postsynaptic time constants will nearly achieve their maximal mean depolarizations; bursts longer than that may not achieve significantly greater depolarization levels, but will increase the chances of overlap in bursts from different inputs.