Two-Dimensional Correlation of Quantum-Mechanical Infrared Spectra Reveals Order of Vibrational-Mode Positions and Predicts Classical RMSD Structural Descriptor

Abstract Quantum mechanics (QM) provides the fundamental basis for an in silico (computational) analogue to infrared (IR) spectroscopy. Quantum-chemical vibrational analysis, as used here with the normal-mode approximation, provides an approximate description of molecular vibrations and yields calculated vibrational transition wavenumbers and infrared intensities for the normal modes of a given molecular conformation. One challenge in quantum normal-mode analysis is identifying structural or functional group relationships between modes of two different molecular conformations. Phospholipids, which are of supreme biomedical importance because they form cell membranes, are ideal-sized targets for density functional theory (DFT) scaling in quantum vibrational analysis. Hundreds of QM spectra can be readily simulated by using DFT, enabling comparisons of modes across many lipid conformations. In addition, lipids are long enough in the Z-dimension (perpendicular to the membrane) that the ordering of molecular functional groups based on Z-coordinate centers can help describe the lipid conformation. Snapshots from triplicate bilayer systems in a vacuum were collected in a library of phospholipid quantum-mechanical models. The library illustrates how two-dimensional correlation spectroscopy (2D-COS) can be applied to assign normal modes to local regions and develop a particular order of functional group positions (order-of-positions) of a phospholipid structure. A k-nearest-neighbor (KNN) approach is applied to relate normal-mode wavenumbers and normal-mode Z-dimension positions to find the modes that are most similar in different lipid conformations. This mode-to-mode mapping enables predictions of the atomic position RMSD for pairs of lipids. A separate application of KNN allows for comparisons of many lipids against a fixed reference point. This enables fine-tuning of the reference-point wavenumber and Z-count values to correlate to a given functional group. The reference-point-based KNN reveals a second spectrum-to-structure relationship that shows that quantum normal modes correlate with the actual positions of the functional groups.