A computer simulation developed to examine activity-dependent, transient variations of local extracellular potassium ion concentration in the central nervous system is extended to a consideration of depolarizing interactions between an active (primary) neuronal membrane and adjacent quiescent neuronal membranes. A class of potassium-mediated depolarizing interactions is described and quantified in relation to the local histologic fine structure. With a relatively open and rapidly equilibrating extracellular environment, the interactions are in the millivolt range and thus are largely subthreshold. However, with a sufficiently restricted extracellular microenvironment and without additional dynamic mechanisms for enhanced potassium clearance, a single action potential is shown to be capable of producing secondary suprathreshold depolarization of the primary membrane. Such potassium-mediated self-excitation evolves to "autogenic" paroxysmal discharge, that is, a burst of activity terminating in sustained depolarization block. Similar suprathreshold ionic coupling between the primary membrane and its adjacent neuronal membranes can likewise yield "cooperative" paroxysmal discharge, wherein the burst of action potentials from the referential primary membrane interdigitates with homologous bursts in adjacent neuronal elements. The partitioning of the local extracellular space by fine cellular processes, fundamental to determining the magnitude of single-spike local extracellular potassium transients, is a basic determining factor for such putative potassium-mediated suprathreshold events. Of more general relevance is the existence of a class of robust but highly localized, subthreshold potassium-mediated ionic interactions that can support non-synaptic dynamic modulation of neuronal activity. Thus, in addition to providing a quantitative theory for the initiation and propagation of non-synaptic epileptiform events, the model suggests a mechanism for potassium-mediated and activity-dependent proximity modulation of neuronal network throughout that can be significant at normal levels of neuronal activity and normal histologic fine structure.