Accurate ab Initio Study on the Hydrogen-Bond Pairs in Protein Secondary Structures

Ab initio calculations up to the MP2/aug-cc-pVQZ//MP2/6-311+G** level have been carried out to characterize the four patterns of hydrogen-bond (H-bond) pairs in protein secondary structures. The unblocked and methyl-blocked glycine dipeptide dimers were arranged to model the H-bond pairs in α-helix (αHH) and antiparallel (Aββ-C₅ and Aββ-C₇) and parallel β-sheet (Pββ) secondary structures. The study uncovers that, in addition to the primary CO⋯NH H-bonds and the crossing secondary interactions, the CH⋯OC H-bonds and the tertiary effect (as we call it) also contribute substantially. The tertiary effect is due to the interpolarization between the donor and acceptor of a H-bond. This effect, which enhances the dipole-dipole interactions between two nearby H-bonds, stabilizes the β-sheet-like but destabilizes the helix-like H-bond pairs. The MP2 binding energies of the complexes were further refined by extrapolating to the complete basis set limit (CBS) according to Truhlar and co-workers and by a three-basis-set-based method. The best extrapolated CBS(aD-aT-aQ) binding energies of the unblocked dimers are -13.1 (αHH), -11.3 (Aββ-C₅), -19.2 (Aββ-C₇), and -14.8 kcal/mol (Pββ). For the methyl-blocked counterparts, the best extrapolated CBS(D-T-Q) binding energies are -14.8, -13.4, -20.8, and -16.7 kcal/mol, respectively. The interactions in the parallel β conformations are very close to the averages of the C₅ and C₇ antiparallel β conformations, and both are stronger than the helical dimers. Because the additive force fields are unable to account for the tertiary effect owing to the lack of polarization, all examined additive force fields significantly overestimate the interaction energies of the helix conformations relative to the β-sheet conformations. Notably, the agreement between molecular mechanical and quantum mechanical binding energies is improved after turning on the polarization. The study provides reference ab initio structures and binding energies for characterizing the backbone H-bonds of the protein secondary structures, which can be used for the parametrization of empirical molecular mechanics force fields.