Simulated seizures and spreading depression in a neuron model incorporating interstitial space and ion concentrations

Abstract

Sustained inward currents in neuronal membranes underlie tonic-clonic seizure discharges and spreading depression (SD). It is not known whether these currents flow through abnormally operating physiological ion channels or through pathological pathways that are not normally present. We have now used the NEURON simulating environment of Hines, Moore, and Carnevale to model seizure discharges and SD. The geometry and electrotonic properties of the model neuron conformed to a hippocampal pyramidal cell. Voltage-controlled transient and persistent sodium currents (I(Na,T) and I(Na,P)), potassium currents (I(K,DR) and I(K,A)), and N-methyl-D-aspartate (NMDA) receptor-controlled currents (I(NMDA)), were inserted in the appropriate regions of the model cell. The neuron was surrounded by an interstitial space where extracellular potassium and sodium concentration ([K(+)](o) and [Na(+)](o)) could rise or fall. Changes in intra- and extracellular ion concentrations and the resulting shifts in the driving force for ionic currents were continuously computed based on the amount of current flowing through the membrane. A Na-K exchange pump operated to restore ion balances. In addition, extracellular potassium concentration, [K(+)](o), was also controlled by a "glial" uptake function. Parameters were chosen to resemble experimental data. As long as [K(+)](o) was kept within limits by the activity of the Na-K pump and the "glial" uptake, a depolarizing current pulse applied to the cell soma evoked repetitive firing that ceased when the stimulating current stopped. If, however, [K(+)](o) was allowed to rise, then a brief pulse provoked firing that outlasted the stimulus. At the termination of such a burst, the cell hyperpolarized and then slowly depolarized and another burst erupted without outside intervention. Such "clonic" bursting could continue indefinitely maintained by an interplay of the rise and fall of potassium and sodium concentrations with membrane currents and threshold levels. SD-like depolarization could be produced in two ways, 1) by a dendritic NMDA-controlled current. Glutamate was assumed to be released in response to rising [K(+)](o). And 2) by the persistent (i.e., slowly inactivating) Na-current, I(Na,P). When both I(NMDA) and I(Na,P) were present, the two acted synergistically. We conclude that epileptiform neuronal behavior and SD-like depolarization can be generated by the feedback of ion currents that change ion concentrations, which, in turn, influence ion currents and membrane potentials. The normal stability of brain function must depend on the efficient control of ion activities, especially that of [K(+)](o).