Mathematical Sciences: Stochastic Modeling of Ion Channels

离子通道是一种大的蛋白质，它允许离子形式的电流穿过细胞膜。各种离子通道之间的相互关系决定了神经肌肉系统的电信号。单通道膜片钳记录提供了有关这些通道的重要信息。记录到的电流的明显随机性导致了随机模型的广泛使用。我们建议对离子通道的随机行为建模和膜片钳记录分析中出现的一些问题进行研究。电荷的流动对神经系统的运作及其与肌肉系统的相互作用是基本的。在微观层面上，电荷通过细胞膜中的称为离子通道的通道传导。Sakmann和Neger获得诺贝尔奖的开创性工作允许直接测量通过单一离子通道的电流。由此产生的记录表明，频道以随机方式打开和关闭，因此概率和统计方法在记录分析中发挥了重要作用。我们建议调查在这类分析中出现的一些问题。

Ion channels are large proteins that allow current in the form of ions to pass across cell membranes. The inter- relationships of a large variety of ion channels shape the electrical signals of the neuro-muscular system. Single channels patch clamp recordings provide important information about these channels. The apparently random character of the recorded currents has led to the widespread use of stochastic models. We propose to investigate a number of problems that arise in modeling the stochastic behavior of ion channels and in the analysis of patch clamp recordings. The flow of electrical charge is fundamental to the operation of the nervous system and its interaction with the muscular system. At a microscopic level, charge is conducted through channels in the cell membrane called ion channels. The pioneering work of Sakmann and Neger, for which they received the Nobel Prize, allows direct measurement of the current flow through a single ion channel. The resulting recordings reveal that the channels open and close in a random fashion and consequently methods of probability and statistics have played an important role in the analysis of the recordings. We propose to investigate a number of problems that arise in such analyses.