Exact reductions of Markovian dynamics for ion channels with a single permissive state

We show that the cooperative model for the kinetics of a tetrameric potassium ion channel derived in Nekouzadeh et al. (Biophys J 95(7):3510–3520, 2008) is an invariant manifold reduction of the full master equation for the channel kinetics. We further establish the validity of this reduction for ion channel models consisting of multiple independent subunits with cooperative transitions from a single permissive state to a conducting state. Finally, we conclude that solutions of the reduced model are globally asymptotically stable solutions of the full master equation system.