Spatial Buffering Mechanism: Mathematical Model and Computer Simulations
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-dimensionaldesc...
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| Language: | English |
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AIMS Press
2005-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.675 |
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| author | Benjamin Steinberg Yuqing Wang Huaxiong Huang Robert M. Miura |
| author_facet | Benjamin Steinberg Yuqing Wang Huaxiong Huang Robert M. Miura |
| author_sort | Benjamin Steinberg |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c7c5768800964e069746fcc5b83b5f2c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2005-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c7c5768800964e069746fcc5b83b5f2c2025-01-24T01:49:46ZengAIMS PressMathematical Biosciences and Engineering1551-00182005-09-012467570210.3934/mbe.2005.2.675Spatial Buffering Mechanism: Mathematical Model and Computer SimulationsBenjamin Steinberg0Yuqing Wang1Huaxiong Huang2Robert M. Miura3Institute of Medical Science, University of Toronto, Toronto, Ontario, M5S 1A8Pacific Institute for the Mathematical Sciences, Vancouver, BC, V6T 1Z2Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON M3J 1P3Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102It 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.https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.675brain-cell microenvironmentspatial bu®eringlattice cellular automata.glial cellsmathemat-ical model |
| spellingShingle | Benjamin Steinberg Yuqing Wang Huaxiong Huang Robert M. Miura Spatial Buffering Mechanism: Mathematical Model and Computer Simulations Mathematical Biosciences and Engineering brain-cell microenvironment spatial bu®ering lattice cellular automata. glial cells mathemat-ical model |
| title | Spatial Buffering Mechanism: Mathematical Model and Computer Simulations |
| title_full | Spatial Buffering Mechanism: Mathematical Model and Computer Simulations |
| title_fullStr | Spatial Buffering Mechanism: Mathematical Model and Computer Simulations |
| title_full_unstemmed | Spatial Buffering Mechanism: Mathematical Model and Computer Simulations |
| title_short | Spatial Buffering Mechanism: Mathematical Model and Computer Simulations |
| title_sort | spatial buffering mechanism mathematical model and computer simulations |
| topic | brain-cell microenvironment spatial bu®ering lattice cellular automata. glial cells mathemat-ical model |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2005.2.675 |
| work_keys_str_mv | AT benjaminsteinberg spatialbufferingmechanismmathematicalmodelandcomputersimulations AT yuqingwang spatialbufferingmechanismmathematicalmodelandcomputersimulations AT huaxionghuang spatialbufferingmechanismmathematicalmodelandcomputersimulations AT robertmmiura spatialbufferingmechanismmathematicalmodelandcomputersimulations |