Accurate theoretical prediction of vibrational frequencies in an inhomogeneous dynamic environment: a case study of a glutamate molecule in water solution and in a protein-bound form.

We propose a hierarchical approach to model vibrational frequencies of a ligand in a strongly fluctuating inhomogeneous environment such as a liquid solution or when bound to a macromolecule, e.g., a protein. Vibrational frequencies typically measured experimentally are ensemble averaged quantities which result (in part) from the influence of the strongly fluctuating solvent. Solvent fluctuations can be sampled effectively by a classical molecular simulation, which in our model serves as the first, low level of the hierarchy. At the second high level of the hierarchy a small subset of system coordinates is used to construct a patch of the potential surface (ab initio) relevant to the vibration in question. This subset of coordinates is under the influence of an instantaneous external force exerted by the environment. The force is calculated at the lower level of the hierarchy. The proposed methodology is applied to model vibrational frequencies of a glutamate in water and when bound to the Glutamate receptor protein and its mutant. Our results are in close agreement with the experimental values and frequency shifts measured by the Jayaraman group by the Fourier transform infrared spectroscopy [Q. Cheng et al., Biochem. 41, 1602 (2002)]. Our methodology proved useful in successfully reproducing vibrational frequencies of a ligand in such a soft, flexible, and strongly inhomogeneous protein as the Glutamate receptor.