Mathematical Sciences: Stochastic Modeling of Ion Channels

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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.