Close agreement between the orientation dependence of hydrogen bonds observed in protein structures and quantum mechanical calculations

Abstract

Hydrogen bonding is a key contributor to the exquisite specificity of the interactions within and between biological macromolecules, and hence accurate modeling of such interactions requires an accurate description of hydrogen bonding energetics. Here we investigate the orientation and distance dependence of hydrogen bonding energetics by combining two quite disparate but complementary approaches: quantum mechanical electronic structure calculations and protein structural analysis. We find a remarkable agreement between the energy landscapes obtained from the electronic structure calculations and the distributions of hydrogen bond geometries observed in protein structures. In contrast, molecular mechanics force fields commonly used for biomolecular simulations do not consistently exhibit close correspondence to either quantum mechanical calculations or experimentally observed hydrogen bonding geometries. These results suggest a route to improved energy functions for biological macromolecules that combines the generality of quantum mechanical electronic structure calculations with the accurate context dependence implicit in protein structural analysis. Hydrogen bonds are partially covalent interactions between a hydrogen atom covalently bound to an electronegative atom and an electronegative acceptor atom (1). They play an important role in defining the structure and function of biological macromolecular systems and contribute to the specificity of molecular recognition (2), the formation of secondary structures (3), and the energetics of protein folding (4). Numerous studies of experimentally available protein and small molecule structures have revealed the directional character of hydrogen bonds and in particular the nonlinear geometry at the acceptor atom (5-8). Computational modeling of hydrogen bonding energy landscapes is a challenging problem; current approaches include quantum mechanical calculations on model systems (usually small molecules analogous to either a main-chain peptide unit or an amino acid side chain) (9, 10), molecular mechanics (force field) approaches (11-13), and knowledge-based potentials derived from small molecule structure databases (14) or the Protein Data Bank (PDB) (15,16).For application to macromolecular systems, different approaches have complementary strengths and weaknesses. Quantum mechanical electronic structure calculations are clearly the most fundamental and general but can be carried out at a rigorous level of theory only for systems much smaller than biological macromolecules, and the results are not necessarily transferable to the complex macromolecular environment. Empirical molecular mechanics force fields are constructed to apply generally to macromolecules and so are not subject to the size limitations of electronic structure calculations, but their accuracy may be limited by the (necessary) simplification of the quantum mechanical system and the large number of parameters that need to be obtained by fitting against experimental data. Inference of interaction ener...

Generalized ensemble methods for de novo structure prediction

“…This energy is a linear combination of four terms that are parameterized by using a set of high-resolution protein crystal structures: (i) distancedependent energy term derived from the distribution of distances between the hydrogen and acceptor atoms (distances range from 1.4 to 2.6 Å), (ii) angular energy measuring angle at Native-like average Z score (top portion of the table), Pearson's correlation coefficient between rmsd and energy score (bottom portion of the table), for low-rmsdnat vs. low-score4ext and low-rmsdext vs. low-score4ext the hydrogen atom, (iii) angular energy measuring angle at the acceptor atom, and (iv) dihedral angle term corresponding to rotation around the acceptor-acceptor base bond in the case of an sp 2 hybridized acceptor (21). It has also been shown that this knowledge-based hydrogen-bonding potential in Rosetta is consistent with the quantum mechanical calculations unlike molecular mechanics force fields, including CHARM27, OPLS-AA, and MM3-2000 (22). Recently a modified version of Rosetta's hydrogen bonding potential was successfully used for protein structure refinement of homology models (23).…”

Hydrogen bond rotations as a uniform structural tool for analyzing protein architecture

“…Hydrogen bond free energy 5,24 relying on the distribution of hydrogen bond rotations within each cluster could be readily implemented as Boltzmann statistics based on HQ60 for example. Coupled to chord diagrams with chords labelled by cluster and the backbone labelled by amino acids, this could provide a new tool for ab initio protein folding.…”

“…As the geometric phase space of hydrogen bonds has large dimension a priori, 3D and 4D simplifications have captured only part of their geometry 5,6 . Here, we introduce a systematic 3D descriptor of main chain hydrogen bond geometry by assigning to each hydrogen bond between backbone C ¼ O and N-H atoms a spatial rotation, which is evidently independent of the overall spatial orientation of the protein just as for dihedral angles.…”

Binding energies of tyrosine kinase inhibitors: Error assessment of computational methods for imatinib and nilotinib binding

“…Baker & Hubbard (1984) [18,19] found that 90% of analysed NH --O hydrogen bonds in the PDB structure data bank have bond angles about 158 o , and most analysed C=O -H hydrogen bonds have angles about 129 o . Morozov (2004) [20] in a later examination of the high resolution X-ray PDB data bank found the average bond angle for single hydrogen bonds was around 110-120 o . The extent of these errors in the X-ray structures and their effect on calculated binding energies is unknown, and may be large if configurational or molecular geometry distortions are also present.…”