Binding Energy and Free Energy of Calcium Ion to Calmodulin EF-Hands with the Drude Polarizable Force Field.

Abstract

Calcium ions are important messenger molecules in cells, which bind calcium-binding proteins to trigger many biochemical processes. We constructed four model systems, each containing one EF-hand loop of calmodulin with one calcium ion bound, and investigated the binding energy and free energy of Ca2+ by the quantum mechanics symmetry-adapted perturbation theory (SAPT) method and the molecular mechanics with the additive CHARMM36m (C36m) and the polarizable Drude force fields (FFs). Our results show that the explicit introduction of polarizability in the Drude not only yields considerably improved agreement with the binding energy calculated from the SAPT method but is also able to capture each component of the binding energies including electrostatic, induction, exchange, and dispersion terms. However, binding free energies computed with the Drude and the C36m FFs both deviated significantly from the experimental measurements. Detailed analysis indicated that one of main reasons might be that the strong interactions between Ca2+ and the side chain nitrogen of Asn/Gln in the Drude FF caused the distorted coordination geometries of calcium. Our work illustrated the importance of polarization in modeling ion-protein interactions and the difficulty in generating accurate and balanced FF models to represent the polarization effects.