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Mathematical Medicine and Biology Advance Access originally published online on March 10, 2006
Mathematical Medicine and Biology 2006 23(2):139-152; 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.

An adjoint method for channel localization

Steven J. Cox**

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

** Email: cox{at}caam.rice.edu

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

Received on 15 June 2005. revised on 12 September 2005. accepted on 28 January 2006.


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