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

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

Badamdorj, D¹, French, DA¹, Edwards, D², and Kleene, SJ³

¹Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221; ²Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716; ³Department 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 Cl¯ 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 Ca²⁺ 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.