Free Energy Perturbation Simulations of Cation Binding to Valinomycin

Abstract

Experimental values of the free energies of cation binding to the cyclic depsipeptide molecule, valinomycin, obtained from Pedersen-type salt extraction measurements, provide data against which it is possible to test the adequacy of the procedures and force fields of the molecular dynamics algorithms, MOLARIS and GROMOS. These data are then used to assess appropriate values for the partial charges of the ester carbonyl oxygen and carbon. Valinomycin was chosen because it has only one kind of ion-binding ligand and because the cation is sufficiently enfolded by the molecule in the ion-complexes that the overall size and shape of the complex is virtually the same regardless of the species of cation bound. For such an ‘isosteric complex’, the experimentally measured selectivities are sufficiently similar in a wide variety of solvent environments that the differences in free energies measured between the different ion-valinomycin complexes by two-phase salt extraction experiments into dichloromethane can be taken as equivalent to the differences in free energies in vacuo. These differences were therefore compared with those computed for ion-valinomycin complexation in vacuo by Free Energy Perturbation/ Molecular Dynamics (FEP/MD) simulations using the MOLARIS and GROMOS programs. Starting with a set of Lennard-Jones 6–12 parameters for the monovalent cations assessed for aqueous solution we explored the effect of varying the partial charges of the ester carbonyl ligands on binding free energy differences (i.e. the selectivity) among Na, K, Rb, and Cs. The computed selectivity was found to depend strongly on the value of partial charge, following a typical ‘Eisenman Selectivity Pattern’ in which the correct selectivity sequence and magnitude occurred only over a very narrow range of partial charge (around 0.33 and 0.6 for the standard carbonyls of MOLARIS and GROMOS, respectively). Using MOLARIS we explored the effect of varying the size of the ester carbonyl ligands by comparing the standard carbonyl of MOLARIS with the somewhat smaller carbonyls of GROMOS and found an equally satisfactory ability to reproduce the experimental data with a partial charge value of 0.41. These results validate the use of both the MOLARIS and GROMOS force fields as starting points for quantitative calculations of ion-binding in more complex molecules (e.g., ion-binding sites and channels in proteins).