title: Invariant manifold reductions for Markovian ion channel dynamics.
abstract: We show that many Markov models of ion channel kinetics have globally attracting stable invariant manifolds, even when the Markov process is time dependent. The primary implication of this is that, since the dimension of the invariant manifold is often substantially smaller than the full master equation system, simulations of ion channel kinetics can be substantially simplified, with no approximation. We show that this applies to certain models of potassium channels, sodium channels, ryanodine receptors and IP(3) receptors. We also use this to show that the original Hodgkin-Huxley formulations of potassium channel conductance and sodium channel conductance are the exact solutions of full Markov models for these channels.
authors.affiliation: Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA. keener@math.utah.edu
authors.forename: James P
authors.initials: JP
authors.lastname: Keener
mesh_terms: D003198:Computer Simulation; D007473:Ion Channels / Q000378:metabolism*; D007700:Kinetics; D008390:Markov Chains; D008954:Models, Biological; D011487:Protein Conformation; D013269:Stochastic Processes
chemical_list: D007473:Ion Channels