Equations are derived for potassium (K+) dynamics in simplified models of brain tissue. These describe K+ movement in extracellular space, transfer of K+ associated with current flow through cells (the so-called spatial buffer mechanism) and equilibration between extracellular space and cytoplasm. Numerical calculations show that the principal data on K+ dynamics from various laboratories can be accounted for with simple assumptions about spatial buffer action and uptake. Much of the data is inconsistent with extracellular diffusion being the main mechanism for K+ flux through brain tissue, including some that has earlier been cited in support of this hypothesis. The buffering actions of spatial buffer transfer of K+ and of cytoplasmic equilibration, in which these mechanisms reduce rises of [K+]o that would otherwise occur, are analysed quantitatively for specific K+ source distributions and for spatial and temporal frequency components of general disturbances. Spatial buffer action has most effect in reducing [K+]o rises with net release over extensive zones of tissue (greater than ca. 200 micron in diameter) for periods of the order of minutes. Reductions greater than 75% may be achieved. With localized but prolonged release, the maximum [K+]o rise is little affected but the volume of tissue affected by more moderate rises is substantially reduced. Cytoplasmic K+ uptake also has most effect with widespread release, but its effect diminishes with prolonged periods of release. The effects of the buffering mechanisms and of K+ re-uptake into active neurones in determining the decline of [K+]o after a period of stimulation are considered. Re-uptake is unlikely to be the major factor responsible for [K+]o decline when this has a time course of only a few seconds. The properties necessary for the cells mediating the spatial buffer mechanisms, possibly glial cells, are assessed.
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