Integral equation models for the inverse problem of biological ion channel distributions

Olfactory cilia are thin hair-like filaments that extend from olfactory receptor neurons into the nasal mucus. Transduction of an odor into an electrical signal is accomplished by a depolarizing influx of ions through cyclic-nucleotide-gated channels in the membrane that forms the lateral surface of...

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Bibliographic Details
Published in:Journal of physics. Conference series 2007-06, Vol.73 (1), p.012006, Article 012006
Main Authors: French, D A, Groetsch, C W
Format: Article
Language:English
Subjects:
Depolarization
Filaments
Fredholm equations
Integral equations
Inverse problems
Ion channels
Mathematical models
Nucleotides
Physics
Spatial distribution
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Summary:Olfactory cilia are thin hair-like filaments that extend from olfactory receptor neurons into the nasal mucus. Transduction of an odor into an electrical signal is accomplished by a depolarizing influx of ions through cyclic-nucleotide-gated channels in the membrane that forms the lateral surface of the cilium. In an experimental procedure developed by S. Kleene, a cilium is detached at its base and drawn into a recording pipette. The cilium base is then immersed in a bath of a channel activating agent (cAMP) which is allowed to diffuse into the cilium interior, opening channels as it goes and initiating a transmembrane current. The total current is recorded as a function of time and serves as data for a nonlinear integral equation of the first kind modeling the spatial distribution of ion channels along the length of the cilium. We discuss some linear Fredholm integral equations that result from simplifications of this model. A numerical procedure is proposed for a class of integral equations suggested by this simplified model and numerical results using simulated and laboratory data are presented.
ISSN:1742-6596
1742-6588
1742-6596
DOI:10.1088/1742-6596/73/1/012006