The transmission of an odor stimulus to the brain begins in cilia, which are long thin processes that extend from the olfactory receptor neurons. These neurons are the first cells in the olfactory system that extend from the nose to the brain. The conversion of a chemical signal, the odor, into an electrical signal, appropriate for processing in the brain, is carried out by two sets of ion channels embedded in the membrane (surface layer) of the cilia. An interdisciplinary research group involving professors and graduate students in Mathematics and Experimental Neuroscience will develop procedures to determine the distributions of these channels through experimentation and the computer solution of a mathematical model. In a typical experiment, ligands for a specific channel type will be allowed to diffuse into a cilium, leading to a current after the molecules bind. The recorded current is the input data for the mathematical model. To determine the ion channel distribution at this stage requires the solution of an inverse or distributed parameter identification problem (DPIP) which is a nontrivial extension of more standard such problems. The main objectives of the work are the development of appropriate experimental procedures, mathematical models, and the solution of the resulting DPIPs. Both computational and analytical or perturbation approaches will be considered as will generalizations to other related situations.
Identification of detailed features in neuronal systems, such as the distributions of ion channels in cilia, forms an important challenge in the biosciences today. Although the properties of the olfactory channels have been determined, the distributions of the channels along the cilia are unknown. These distributions are crucial in determining the time course of the neuronal response. This work will have applications outside of olfaction in other areas in the brain such as the photoreceptor cells in the retina or the dendrites in the neocortex. It is also expected that this research will advance our understanding of the mathematics of inverse problems. Further, models of olfactory transduction are relevant to efforts to create mechanical-chemical "noses" for the detection of hazardous biological and chemical agents. The interdisciplinary nature of the research is also critical. It will enhance the infrastructure at the University of Cincinnati while providing interdisciplinary training to the students.
