*Math. Method. Appl. Sci.*, in press (2008)

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Identification of Cl(Ca) channel distributions in olfactory cilia.

#### Badamdorj, D^{1}, French, DA^{1}, Edwards, D^{2}, and Kleene, SJ^{3}

^{1}Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221;
^{2}Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716;
^{3}Department of Cell and Cancer Biology, University of Cincinnati, Cincinnati, Ohio 45267.

Identification of detailed features of neuronal systems is an important
challenge in the biosciences today.
Transduction
of an odor into an electrical signal occurs in the membranes of the cilia.
The Cl(Ca) channels which reside in the ciliary membrane are activated by
calcium, allow a depolarizing efflux of ClÂ¯ and are thought to amplify the
electrical signal to the brain.

In this paper, a mathematical model consisting of partial differential
equations is developed to study two different experiments; one involving
the interaction of the CNG and Cl(Ca) channels and the other, the diffusion
of Ca^{2+} into cilia.
This work builds on an earlier study which suggested that the CNG channels
are clustered at about 0.28 of the length of a cilium from its open
end.
Closed form solutions are derived after certain reductions in the model are
made.
These special solutions provide estimates of the channel
distributions.
Scientific computation is also used.
This preliminary study suggests that the Cl(Ca) ion channels are also
clustered at about 1/3 of the length of a cilium from its open end.

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