Invariant manifold reductions for Markovian ion channel dynamics

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 IP₃ 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.