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Mathematical Medicine and Biology Advance Access published online on March 10, 2006
Mathematical Medicine and Biology, doi:10.1093/imammb/dql004
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© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.
Received June 15, 2005
Revised September 12, 2005
Accepted January 28, 2006

Article

An adjoint method for channel localization

Steven J. Cox 1 *

1 Computational and Applied Mathematics, MS 134, Rice University, 6100 Main, Houston, TX 77006, USA

* To whom correspondence should be addressed.
Steven J. Cox, E-mail: cox{at}caam.rice.edu


  Abstract

Single cells learn by tuning their synaptic conductances and redistributing their excitable machinery. To reveal its learning rules, one must therefore know how the cell remaps its ion channels in response to physiological stimuli. We here develop an adjoint approach for discerning the non-uniform distribution of a given channel type from knowledge of the time course of membrane potential at two distinct locations following a prescribed injection of current.

Keywords: nonuniform cable; analytical gradient; lagrange multiplier.
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