Markov Models of Potassium Channel Gating

Modification of the magnitude and kinetics of K+ currents has been shown to be proarrhythmic, in response to both genetic abnormalities as well as pharmacologic intervention. The relationship between channel defects and altered repolarization or arrhythmogenesis is a complex problem which cannot be addressed intuitively. Describing the kinetic consequences of a point mutation requires the development of detailed mathematical models of ion channels. However, the tools for relating mutations to kinetic behavior have been limited. The most advanced models of structure have not yet been put into kinetic equations that are useful to investigators working at higher levels of integration in the heart. The broad goal of this proposal is to develop a systematic mathematical approach to developing structurally-based Markov models of channel kinetic behavior from mutational data. A new analysis approach will be developed to use non-linear parameter estimation to quantify the impact of a mutation or other manipulation (e.g., changes in pH, [K+]o) on kinetic behavior. The effects of altered kinetic behavior will be examined in conjunction with other mutations using mathematical adaptations of Hammond energy shifts and mutant cycle analysis. We will produce a generalization of these approaches to complex multi-step gating processes which can be applied to non-equilibrium situations. We will use this approach to develop Markov models of channel kinetics with high predictive values through three Specific Aims: (1) Develop base Markov models of Kv1.4, Kv4.3, KvLQT1 and HERG gating based on known and hypothesized structure-function relationships and voltage clamp data. (2) Map base Markov models to structures using site directed mutagenesis analyzed with parameter sensitivity analysis, optimization, Hammond energy shifts and kinetically-based mutant cycle analysis. (3) Incorporate modulation by pH and [K+]o into these Markov models. (4) To translate the structurally based Markov models of gating from Aims 1-3 into models of native myocyte currents This study will develop Markov models of channels and repolarization which will be unique in the degree to which the major gating states have been identified with mutagenesis and mapped to specific rigid domains of each respective K+ channel. The long term goal is to predict clinical phenotype directly from channel defect.