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Kernel representations for flux and concentration in ion channel models with time-varying concentrations

J. Chem. Phys. 125, 164703 (2006); doi:10.1063/1.2363187

Published 24 October 2006

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Juan Alvarez
Department of Mathematics and Statistics, University of Saskatchewan, 142 McLean Hall, 106 Wiggins Road, Saskatoon, Saskatchewan, S7N 5E6, Canada

Bruce Hajek
Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 and the Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
This paper explores stochastic models for the study of ion transport in biological cells. It considers one-dimensional models with time-varying concentrations at the boundaries. The average concentration and flux in the channel are obtained as kernel representations, where the kernel functions have a probabilistic interpretation which contributes to a better understanding of the models. In particular, the kernel representation is given for the flux at a boundary point, providing a correct version of a representation found in the literature. This requires special attention because one of the kernel functions exhibits a singularity. This kernel representation is feasible due to the linearity of the system that arises from the assumed independence between ions. ©2006 American Institute of Physics
History: Received 11 January 2006; accepted 19 September 2006; published 24 October 2006
Permalink: http://link.aip.org/link/?JCPSA6/125/164703/1
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KEYWORDS and PACS

Keywords
PACS
  • 87.16.Uv
    Biological active transport processes; ion channels
  • 87.16.Dg
    Biomembranes, bilayers, and vesicles
  • 87.16.Ac
    Theory and modeling of subcellular structure and processes; computer simulation
  • 05.40.-a
    Fluctuation phenomena, random processes, noise, and Brownian motion
  • YEAR: 2006

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PUBLICATION DATA

ISSN:
0021-9606 (print)   1089-7690 (online)
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