Rate theoretical analysis of ion transport in membrane channels with elastically bound ligands

Abstract

This presentation consists of two parts. In the first one, a model Hamiltonian for a channel with elastically bound ligands is constructed. In the second one, escape rates are derived from the Hamiltonian and transport properties of the channel are discussed considering diffusion of ions as a random walk between binding sites. Rate theory as traditionally applied considers a potential energy profile as a sequence of rigid barriers. A realistic molecular channel, however, consists of elastically bound atomic groups (ligands) which are subject to temperature induced motion, and which can respond more or less to the presence of an ion. The elastic deformation of the channel gives rise to a correction of the interaction energy between the ion and the channel as a whole. The result is an effective potential for fixed position of the ion. Moreover, due to the finite masses of the ligands and their coupling to the ion in motion, the latter will experience inertia effects, which lead to an effective ion mass. It is shown that the introduction of an effective potential requires a canonical transformation of the generalized momenta. The corresponding Hamiltonian is directly used to calculate the jumping rates over a barrier, with the effective ion mass depending on all ligand masses and the geometry of the channel. In the present case, a model Hamiltonian for a helical arrangement of dipoles as hindered rotators is discussed, followed by an investigation of the diffusion constant for this system.