Energy landscapes and dynamics of ion translocation through membrane transporters: a meeting ground for physics, chemistry, and biology

Abstract

The dynamics of ion translocation through membrane transporters is visualized from a comprehensive point of view by a Gibbs energy landscape approach. The ΔG calculations have been performed with the Kirkwood–Tanford–Warshel (KTW) electrostatic theory that properly takes into account the self-energies of the ions. The Gibbs energy landscapes for translocation of a single charge and an ion pair are calculated, compared, and contrasted as a function of the order parameter, and the characteristics of the frustrated system with bistability for the ion pair are described and quantified in considerable detail. These calculations have been compared with experimental data on the ΔG of ion pairs in proteins. It is shown that, under suitable conditions, the adverse Gibbs energy barrier can be almost completely compensated by the sum of the electrostatic energy of the charge–charge interactions and the solvation energy of the ion pair. The maxima in ΔG_KTW with interionic distance in the bound H⁺ – A⁻ charge pair on the enzyme is interpreted in thermodynamic and molecular mechanistic terms, and biological implications for molecular mechanisms of ATP synthesis are discussed. The timescale at which the order parameter moves between two stable states has been estimated by solving the dynamical equations of motion, and a wealth of novel insights into energy transduction during ATP synthesis by the membrane-bound F_OF₁-ATP synthase transporter is offered. In summary, a unifying analytical framework that integrates physics, chemistry, and biology has been developed for ion translocation by membrane transporters for the first time by means of a Gibbs energy landscape approach.

Graphical abstract