Synchronized burst discharge in disinhibited hippocampal slice. II. Model of cellular mechanism

Abstract

We have modeled the CA2-CA3 hippocampal region with 100 simplified pyramidal neurons, each capable of intrinsic bursting and each possessing a slow calcium-mediated K+ conductance. The neurons have sparse random excitatory interconnections and are also interconnected via inhibitory interneurons. Each pyramidal neuron has excitatory inputs from five other pyramidal neurons on the average. These 'chemical' excitatory synapses have the property that a single action potential in one cell induces an excitatory postsynaptic potential (EPSP) in a connected cell having an amplitude about one-seventh bursting threshold. When the strength of the inhibitory synapses is reduced below a critical level (as would happen with penicillin present in the medium), a synchronous population bursting discharge is produced when a stimulus is delivered to four neighboring cells; the latency to peak number of cells bursting is about 80 ms. This latency results because of the time required to bring these cells to threshold, the time required for them to recruit a follower subpopulation, and so on. A multipeaked field potential strongly resembling experimental records is produced in this simulation. Some of the field-potential peaks correspond to action potentials in various individual model neurons. Factors required for synchronous bursting include (but are not limited to) the following: the strength of inhibitory connections must be below a critical level, and excitatory connections cannot be too sparse or too weak. For example, if the probability of excitatory interconnection is reduced from 5 to 2.5% in an array of 100 cells and other parameters are unchanged, no population discharge will occur. In an array of 400 cells, however, a 2.5% or even 1.25% interconnection probability does allow synchronous bursting. When a tonic drive to four cells is maintained, periodic population discharges occur, with periods of about 2 s. The 'pacemaker cells' themselves burst approximately every second. Thus, we have reproduced the experimental observation that the synchronous discharge period can be longer than the intrinsic bursting period of the individual cells. This phenomenon occurs in the model because the follower subpopulation may still be relatively refractory (because of some persisting slow K+ conductance) 1 s after a synchronized population discharge. Increasing extracellular K+ has the expected effect of increasing the frequency of synchronized population discharges. At a time when the population is relatively refractory (e.g., 1 s after a spontaneous synchronized discharge), a second synchronized population discharge can only be evoked by stimulating more than four cells in the model; as many as nine may be required. This evoked discharge then resets the rhythm of spontaneous synchronized bursting, as observed by Lebovitz in the in vivo penicillin-treated hippocampus and by us in the slice preparation. Even while intrinsically bursting during a population discharge, a pyramidal neuron will be receiving a large excitatory synaptic input from those cells connected to it, for they also will be bursting during the population discharge and, hence, sending out trains of action potentials. Thus, the synchronized population event spike begins as an intrinsic bursting phenomenon in a few cells. EPSPs are then responsible for recruiting cells into the population discharge. Cells bursting during synchronized discharge will have a paroxysmal depolarizing shift or PDS consisting of both intrinsic regenerative depolarization and an underlying excitatory synaptic potential. This model, which is consistent with much of the known data on single hippocampal neurons and their interconnections, reproduces many of the observed properties of interictal spikes in the penicillin-treated in vivo hippocampus and in vitro hippocampal slice. It contains, however, simplifications required to reduce computation: we do not explicitly simulate inward currents or dendritic events, all synapses have the same strength, there is no modulation of synaptic efficacy, etc. These latter properties may be necessary for reproducing subtle aspects of the field potential and for understanding afterdischarges and 'full-blown' seizures.