In the introduction to the recent JGP series Perspectives on: Ion selectivity, Andersen (2011) notes that present theoretical models do not yet deal fully with the energetic consequences of the known flexibility of ion binding sites in proteins (how changes in flexibility alter the ion selectivity of a site). I therefore write to point out that this question was addressed long ago by Eisenman and Alvarez (1992), who proposed that analysis of the energetic changes that occur in valinomycin, a cyclic ion-binding depsipeptide that binds cations to its backbone carbonyls after folding around them, might be useful in extending the modeling of ion binding sites to the actual sites in deformable membrane proteins.

Valinomycin offers a model system to study the origin of ion binding selectivity in a small peptidelike molecule held together by the forces and bonds that exist in proteins. Eisenman and Alvarez (1992) used molecular dynamics and molecular mechanics simulations to first explore the experimentally defined ion selectivity using two different-sized standard oxygen molecules used in Groningen Molecular Simulation (GROMOS; van Gunsteren and Berendsen, 1987) and AMINO88 (Warshel and Creighton, 1989). They obtained excellent energetic and crystallographically correct agreement with experimental data by varying the values of oxygen partial charge (i.e., the field strength) for the GROMOS and AMINO88 oxygens. After organizing and analyzing the experimentally observed free energy differences among the group 1a cations, they characterized the different simulated energy differences as a function of varying the partial charge of the oxygen, finding values for the partial charge that worked best for GROMOS and AMINO88 carbonyls and observing inversions of the Na+/K+ selectivity and changes of sequence of the type expected from Eisenman’s primitive field strength theory (Eisenman, 1961). They then examined the role of field strength and steric fit for the total structural energy and its components (van der Waals, coulombs, bond stretch, bond angle bend, dihedral angle torsion, inversion, and constraint) for four separate situations: first, when K+ is isomorphously replaced by Li+, Na+, Rb+, or Cs+ in a rigid structure frozen at the coordinates of the crystallographic structure of the K+ form; second, when the ions are unconstrained but the molecule is frozen in the x-ray structure of the K+ form; third, when the ions are allowed to move freely and the constraints on the atoms in the protein model are partially constrained; and fourth, when the atoms in the valinomycin molecule are allowed to move freely under the molecular constraints usual for proteins.

In the first case (completely rigid system), the only factor determining selectivity is the steric fit describing the van der Waals repulsion between different-sized ions. This was true regardless of the partial charge of the carbonyl oxygens because the van der Waals force confines the ions to be near their original positions. Thus, in this case, selectivity is completely independent of field strength. In contrast, in the fourth case (when the protein atoms are allowed to move freely), the 12th power van der Waals term distributes itself by rearranging adjacent atoms that are less sharply spatially dependent on the van der Waals force field, such as bond angle bending, long-range coulomb effects, and inversions. In this realistic situation, there appeared to be a stress–strain compensation in which the conformational energy changes in the protein and the van der Waals terms tend to compensate each other, leaving the field strength as the major variable determining selectivity!

Acknowledgments

Olaf S. Andersen served as editor.

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