Spatial Buffering Mechanism: Mathematical Model and Computer Simulations - Benjamin Steinberg; Yuqing Wang; Huaxiong Huang; Robert M. Miura (Mathematical Biosciences and Engineering)
It is generally accepted that the spatial buffering mechanism isimportant to buffer extracellular-space potassium in thebrain-cell microenvironment. In the past, this phenomenon,generally associated with glial cells, has been treatedanalytically and numerically using a simplified one-dimensionaldescription. The present study extends the previous research byusing a novel numerical scheme for the analysis of potassiumbuffering mechanisms in the extracellular brain-cellmicroenvironment. In particular, a lattice-cellular automaton wasemployed to simulate a detailed two-compartment model of atwo-dimensional brain-cell system. With this numerical approach,the present study elaborates upon previous theoretical work onspatial buffering (SB) by incorporating a more realistic structureof the brain-cell microenvironment, which was not feasibleearlier. We use the experimental paradigm consisting ofiontophoretic injection of KCl to study the SB mechanism. Oursimulations confirmed the results reported in the literatureobtained by an averaged model. The results also show that theadditional effects captured by a simplified two-dimensionalgeometry do not alter significantly the conclusions obtained fromthe averaged model. The details of applying such a numericalmethod to the study of ion movements in cellular environments, aswell as its potential for future study, are discussed.