Modeling of Ion Channels

Modeling of biological ion channels has a long history, going back more then 100 yr (Hille 1984). In the old, premolecular biology era, interpretation of these simple models provided the primary source of information about channel structure. As molecular biology and, now, x-ray diffraction have provided direct information about structure, modeling has been reduced to playing more of a secondary role in channel biochemistry. The early channel models were always understood to be highly simplified approximations that, hopefully, captured the “essential” features of the channel. The combination of atomic resolution channel structures plus highly sophisticated computer routines raises the possibility of obtaining “exact” (molecular dynamic) solutions for channel flux—something that would have seemed a wild dream only a few years ago. Such solutions have the purpose of interpreting and relating the channel structure to its function. As will be discussed below, although this exact solution is still beyond our reach, a combination of currently available approaches now make it possible to obtain solutions that approach this ideal. In this review I will attempt to illustrate the various approaches and approximations that are currently being used to model ion channels by starting with this exact solution, and then describing the series of assumptions that are made as one progresses to simpler and simpler models. No attempt is made to provide a comprehensive review of each of the approximations and the few specific examples that are referred to were chosen simply to provide illustrations of the different approaches (see Jakobsson, 1998, for a recent review).