Identification of Ion Channel Distributions in Olfactory Cilia by Mathematical Modeling

气味刺激向大脑的传递始于纤毛，纤毛是从嗅觉受体神经元延伸出来的细长突起。 这些神经元是嗅觉系统中从鼻子延伸到大脑的第一批细胞。 将化学信号（气味）转化为适合大脑处理的电信号，是通过两组嵌入纤毛膜（表层）的离子通道进行的。 一个由数学和实验神经科学教授和研究生组成的跨学科研究小组将开发程序，通过实验和数学模型的计算机求解来确定这些通道的分布。 在典型的实验中，特定通道类型的配体将被允许扩散到纤毛中，从而在分子结合后产生电流。 记录的电流是数学模型的输入数据。 为了确定在这个阶段的离子通道分布需要解决的逆或分布参数识别问题（DPIP），这是一个非平凡的扩展更标准的这样的问题。 这项工作的主要目标是开发适当的实验程序，数学模型，并解决由此产生的DPIPs。 无论是计算和分析或扰动的方法将被认为是将概括到其他相关situations.Identification神经系统的详细功能，如纤毛中的离子通道的分布，形成了一个重要的挑战，在今天的生物科学。 虽然嗅觉通道的性质已经确定，通道的分布沿着纤毛是未知的。 这些分布在确定神经元反应的时间过程中是至关重要的。这项工作将在嗅觉之外的大脑其他区域，如视网膜中的感光细胞或新皮层中的树突中得到应用。 我们也期望这项研究将促进我们对反问题数学的理解。 此外，嗅觉传导模型与创造机械化学“鼻子”以检测有害生物和化学制剂的努力有关。 研究的跨学科性质也至关重要。 它将加强辛辛那提大学的基础设施，同时为学生提供跨学科的培训。

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.