Spatial buffering of potassium ions in brain extracellular space

It has long been assumed that one important mechanism for the dissipation of local potassium gradients in the brain extracellular space is the so-called spatial buffer, generally associated with glial cells. To date, however, there has been no analytical description of the characteristic patterns of K+ clearance mediated by such a mechanism. This study reanalyzed a mathematical model of Gardner-Medwin (1983, J. Physiol. (Lond.). 335:393-426) that had previously been solved numerically. Under suitable approximations, the transient solutions for the potassium concentrations and the corresponding membrane potentials of glial cells in a finite, parallel domain were derived. The analytic results were substantiated by numerical simulations of a detailed two-compartment model. This simulation explored the dependence of spatial buffer current and extracellular K+ on the distribution of inward rectifier K+ channels in the glial endfoot and nonendfoot membranes, the glial geometric length, and the effect of passive KCI uptake. Regarding the glial cells as an equivalent leaky cable, the analyses indicated that a maximum endfoot current occurs when the glial geometric length is equal to the corresponding electrotonic space constant. Consequently, a long glial process is unsuitable for spatial buffering, unless the axial space constant can match the length of the process. Finally, this study discussed whether the spatial buffer mechanism is able to efficiently transport K+ over distances of more than several glial space constants.