Identification of detailed features of neuronal systems is an important challenge in the biosciences today. Cilia are long thin processes that extend from the olfactory receptor neurons. The first step in the transduction of an odor into an electrical signal occurs in the membranes of the cilia and is controlled primarily by ion channels.
A mathematical model consisting of two nonlinear differential equations and a constrained Fredholm integral equation of the first kind is developed to model experiments aimed at identifying gross features of the distribution of these ion channels. A simple numerical method is derived that can be used to obtain estimates of the spatial distribution of the ion channels along the length of a cilium. Simulations using experimental data indicate these channels have a non-uniform distribution.
Other approaches and related issues will also be discussed.