2005, 2(4): 675-702. doi: 10.3934/mbe.2005.2.675

Spatial Buffering Mechanism: Mathematical Model and Computer Simulations

1. 

Institute of Medical Science, University of Toronto, Toronto, Ontario, M5S 1A8, Canada

2. 

Pacific Institute for the Mathematical Sciences, Vancouver, BC, V6T 1Z2, Canada

3. 

Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada

4. 

Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, United States

Received  December 2004 Revised  September 2005 Published  October 2005

It is generally accepted that the spatial buffering mechanism is important to buffer extracellular-space potassium in the brain-cell microenvironment. In the past, this phenomenon, generally associated with glial cells, has been treated analytically and numerically using a simplified one-dimensional description. The present study extends the previous research by using a novel numerical scheme for the analysis of potassium buffering mechanisms in the extracellular brain-cell microenvironment. In particular, a lattice-cellular automaton was employed to simulate a detailed two-compartment model of a two-dimensional brain-cell system. With this numerical approach, the present study elaborates upon previous theoretical work on spatial buffering (SB) by incorporating a more realistic structure of the brain-cell microenvironment, which was not feasible earlier. We use the experimental paradigm consisting of iontophoretic injection of KCl to study the SB mechanism. Our simulations confirmed the results reported in the literature obtained by an averaged model. The results also show that the additional effects captured by a simplified two-dimensional geometry do not alter significantly the conclusions obtained from the averaged model. The details of applying such a numerical method to the study of ion movements in cellular environments, as well as its potential for future study, are discussed.
Citation: Benjamin Steinberg, Yuqing Wang, Huaxiong Huang, Robert M. Miura. Spatial Buffering Mechanism: Mathematical Model and Computer Simulations. Mathematical Biosciences & Engineering, 2005, 2 (4) : 675-702. doi: 10.3934/mbe.2005.2.675
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