Abstract: Herein we will focus on the use of quantum mechanics (QM) in drug design (DD) to solve disparate problems from scoring protein–ligand poses to building QM QSAR models. Through the variational principle of QM we know that we can obtain a more accurate representation of molecular systems than classical models, and while this is not a matter of debate, it still has not been shown that the expense of QM approaches is offset by improved accuracy in DD applications. Objectively validating the improved applicability and performance of QM over classical-based models in DD will be the focus of research in the coming years along with research on the conformational sampling problem as it relates to protein–ligand complexes.

Authors: Kaushik Raha, Martin B. Peters, Bing Wang, Ning Yu, Andrew M. Wollacott, Lance M. Westerhoff, and Kenneth M. Merz Jr.

Reference: Drug Discovery Today. 2007, 12:17-18, 725-731. (see link for full paper).

Abstract: Orf2, a recently identified prenyltransferase of aromatic natural products, displays relaxed substrate selectivity and interesting product regioselectivity. This gives rise to the opportunity to engineer the active site to tune the functionality of terpenoids for therapeutic applications. The structural basis of substrate binding has been determined, but the source of the observed substrate selectivity and product regioselectivity cannot be completely understood on the basis of the static picture that the crystal structures of Orf2 and its complexes afford. The electron density and B-factors of the substrates, particularly those of 1,6-dihydroxynaphthalene, suggest significant conformational fluctuation in the Orf2 binding site. We thoroughly explored the binding of 1,6-dihydroxynaphthalene and quantitatively evaluated the relative free energies of three binding states that we identified in terms of a two-dimensional potential of mean force. The available experimental orientation, which gives the major prenylated product of 1,6-dihydroxynaphthalene, corresponds to the global free energy minimum. Two alternative binding states were identified on the calculated free energy surface, and both are readily accessible at 300 K. The alternative binding conformations were extracted from the potential of mean force calculation and were subjected to further validation against the experimental X-ray diffraction data using a refinement protocol supplemented with a hybrid quantum mechanical and molecular mechanical energy function. The agreement was excellent as indicated by the R and Rfree factors that were comparable to that obtained for the published orientation using a similar protocol. These binding states are the origin of the selectivity and regioselectivity in Orf2-catalyzed aromatic prenylations. Our analyses also suggest that Ser214 and Tyr288, forming hydrogen bonds with the alternative binding states of 1,6-dihydroxynaphthalene and flaviolin, are good candidates for site-directed mutagenesis, and changing them to, for example, their hydrophobic counterparts would affect the substrate selectivity and product regioselectivity.

Authors: Guanglei Cui, Xue Li, and Kenneth M. Merz, Jr.

Reference: Biochemistry. 2007, 46(5), 1303-1311. (see link for full paper).

Abstract: β-Secretase, aka β-APP cleaving enzyme (BACE), is an aspartyl protease that has been implicated as a key target in the pathogenesis of Alzheimer's disease (AD). The identification of the protonation states of the key aspartates in -secretase is of great interest both in understanding the reaction mechanism and in guiding the design of drugs against AD. However, the resolutions of currently available crystal structures for BACE are not sufficient to determine the hydrogen atom locations. We have assigned the protonation states of the key aspartates using a novel method, QM/MM X-ray refinement. In our approach, an energy function is introduced to the refinement where the atoms in the active site are modeled by quantum mechanics (QM) and the other atoms are represented by molecular mechanics (MM). The gradients derived from the QM/MM energy function are combined with those from the X-ray target to refine the crystal structure of a complex containing BACE and an inhibitor. A total number of 8 protonation configurations of the aspartyl dyad were considered, and QM/MM X-ray refinements were performed for all of them. The relative stability of the refined structures was scored by constructing the thermodynamic cycle using the energetics calculated by fully quantum mechanical self-consistent reaction field (QM/SCRF) calculations. While all 8 refined structures fit the observed electron density about equally well, we find the monoprotonated configurations to be strongly favored energetically, especially the configuration with the inner oxygen of Asp32 protonated and the hydroxyl of the inhibitor pointing toward Asp228. It was also found that these results depend on the constraints imposed by the X-ray data. We suggest that one of the strengths of this approach is that the resulting structures are a consensus of theoretical and experimental data and remark on the significance of our results in structure based drug design and mechanistic studies.

Authors: Ning Yu, Seth A. Hayik, Bing Wang, Ning Liao, Charles H. Reynolds, and Kenneth M. Merz, Jr.

Reference: J. Chem. Theory Comput. 2006, 2(4), 1057-1069. (see link for full paper).

Abstract: A novel method is proposed in which combined energy restraints derived from linear-scaling semiempirical quantum mechanical (QM) calculations and X-ray diffraction data are combined to refine crystal structures of proteins. Its performance has been tested on a small protein molecule, bovine pancreatic trypsin inhibitor (BPTI). The refinement involves minimization of the sum of a geometric energy function and an X-ray target function based on either the least-square residual or the maximum-likelihood formalism. For comparison, similar refinement runs have also been performed using energy restraints derived from the force field available in the Crystallography & NMR System (CNS) program. The QM refinements were carried out with weights that were varied by several orders of magnitude and the optimal weights were identified by observing the trend in the final free R values, QM heats of formation and coordinate root-mean-square deviations (r.m.s.d.s) from the crystal structure. It is found that the QM weights are typically smaller but generally on the same scale as the molecular-mechanics (MM) weights for the respective X-ray target functions. The crystallographic R, free R, real-space R values and correlation coefficients based on the structures refined with the energy restraints derived from our QM calculations and Engh and Huber parameters are comparable, suggesting that the QM restraints are capable of maintaining reasonable stereochemistry to a similar degree as the force-field parameters. A detailed inspection of the structures refined with the QM and MM energy restraints reveals that one of the common differences between them and the crystal structure is that the strained bond angles in the crystal structure are corrected after energetically restrained refinements. Systematic differences in certain bond lengths between the QM-refined structures and the statistical averages of experimental structures have also been observed and discussed.

Authors: Ning Yu, Hemant P. Yennawar, and Kenneth M. Merz, Jr.

Reference: Acta Cryst. D. 2005, 61(3), 322-332. (see link for full paper).

Abstract: The electron density distributions of a small dipeptide molecule, glycyl-L-threonine dihydrate whose structure has recently been determined using accurate single-crystal X-ray diffraction to a resolution of 0.43A ˚ , have been studied theoretically at the semiempirical level and Hartree–Fock level employing varying sizes of basis sets up to the valence triple-zeta plus polarization level. Both theoretical structure factors and dynamic deformation maps are computed using the electronic wavefunctions derived in vacuo using MO methods. General agreement between theory and experiment is good and improves when larger basis sets are employed. The dynamic theoretical structure factors calculated at the HF/6-311G** level for all the experimentally observed reflection angles fit the experimental ones better with about a 0.01 decrease in the Rw value compared to the Independent Atom Model (IAM). The semiempirical MNDO density performs consistently better than the minimal basis Hartree–Fock density, but is shown to be slightly inferior to the Hartree–Fock density employing split-valence basis sets. The partial atomic charges are also computed and compared to experimental charges derived from the kappa refinement procedure.

Authors: Ning Yu and Kenneth M. Merz, Jr.

Reference: Mol. Phys. 2004, 102, 2545-2557. (see link for full paper).