Kenneth M. Merz

Protein NMR Chemical Shift Calculations Based on the Automated Fragmentation QM/MM Approach

An automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach has been developed to routinely calculate ab initio protein NMR chemical shielding constants. The AF-QM/MM method is linear-scaling and trivially parallel. A general fragmentation scheme is employed to generate each residue-centric region which is treated by quantum mechanics, and the environmental electrostatic field is described with molecular mechanics. The AF-QM/MM method shows good agreement with standard self-consistent field (SCF) calculations of the NMR chemical shieldings for the mini-protein Trp cage. The root-mean-square errors (RMSEs) for 1H, 13C, and 15N NMR chemical shieldings are equal to or less than 0.09, 0.32, and 0.78 ppm, respectively, for all Hartree-Fock (HF) and density functional theory (DFT) calculations reported in this work. The environmental electrostatic potential is necessary to accurately reproduce the NMR chemical shieldings using the AF-QM/MM approach. The point-charge models provided by AMBER, AM1/CM2, PM3/CM1, and PM3/CM2 all effectively model the electrostatic field. The latter three point-charge models are generated via semiempirical linear-scaling SCF calculations of the entire protein system. The correlations between experimental 1H NMR chemical shifts and theoretical predictions are >0.95 for AF-QM/MM calculations using B3LYP with the 6-31G**, 6-311G**, and 6-311++G** basis sets. Our study, not unexpectedly, finds that conformational changes within a protein structure play an important role in the accurate prediction of experimental NMR chemical shifts from theory.

Explicitly representing the solvation shell in continuum solvent calculations.

A method is presented to explicitly represent the first solvation shell in continuum solvation calculations. Initial solvation shell geometries were generated with classical molecular dynamics simulations. Clusters consisting of solute and 5 solvent molecules were fully relaxed in quantum mechanical calculations. The free energy of solvation of the solute was calculated from the free energy of formation of the cluster, and the solvation free energy of the cluster was calculated with continuum solvation models. The method has been implemented with two continuum solvation models, a Poisson-Boltzmann model and the IEF-PCM model. Calculations were carried out for a set of 60 ionic species. Implemented with the Poisson-Boltzmann model the method gave an unsigned average error of 2.1 kcal/mol and a rmsd of 2.6 kcal/mol for anions; for cations the unsigned average error was 2.8 kcal/mol and the rmsd 3.9 kcal/mol. Similar results were obtained with the IEF-PCM model.

Importance of Dispersion and Electron Correlation in ab Initio Protein Folding

Dispersion is well-known to be important in biological systems, but the effect of electron correlation in such systems remains unclear. In order to assess the relationship between the structure of a protein and its electron correlation energy, we employed both full system Hartree-Fock (HF) and second-order Møller-Plesset perturbation (MP2) calculations in conjunction with the Polarizable Continuum Model (PCM) on the native structures of two proteins and their corresponding computer-generated decoy sets. Because of the expense of the MP2 calculation, we have utilized the fragment molecular orbital method (FMO) in this study. We show that the sum of the Hartree-Fock (HF) energy and force field (LJ6)-derived dispersion energy (HF + LJ6) is well correlated with the energies obtained using second-order Møller-Plesset perturbation (MP2) theory. In one of the two examples studied, the correlation energy as well as the empirical dispersive energy term was able to discriminate between native and decoy structures. On the other hand, for the second protein we studied, neither the correlation energy nor dispersion energy showed discrimination capabilities; however, the ab initio MP2 energy and the HF+LJ6 both ranked the native structure correctly. Furthermore, when we randomly scrambled the Lennard-Jones parameters, the correlation between the MP2 energy and the sum of the HF energy and dispersive energy (HF+LJ6) significantly drops, which indicates that the choice of Lennard-Jones parameters is important.

Quantum mechanical and molecular dynamics simulations of ureases and Zn β-lactamases

Herein we briefly review theoretical contributions that have increased our understanding of the structure and function of metallo‐β‐lactamases and ureases. Both are bimetallic metalloenzymes, with the former containing two zinc ions and the latter containing two nickel ions. We describe the use of several different methodologies, including quantum chemical calculations, molecular dynamic simulations, as well as mixed QM/MM approaches and how they have impacted our understanding of the structure and function of metallo‐β‐lactamases and ureases.

The energy computation paradox and ab initio protein folding.

The routine prediction of three-dimensional protein structure from sequence remains a challenge in computational biochemistry. It has been intuited that calculated energies from physics-based scoring functions are able to distinguish native from nonnative folds based on previous performance with small proteins and that conformational sampling is the fundamental bottleneck to successful folding. We demonstrate that as protein size increases, errors in the computed energies become a significant problem. We show, by using error probability density functions, that physics-based scores contain significant systematic and random errors relative to accurate reference energies. These errors propagate throughout an entire protein and distort its energy landscape to such an extent that modern scoring functions should have little chance of success in finding the free energy minima of large proteins. Nonetheless, by understanding errors in physics-based score functions, they can be reduced in a post-hoc manner, improving accuracy in energy computation and fold discrimination.

Parameterization of highly charged metal ions using the 12-6-4 LJ-type nonbonded model in explicit water.

Highly charged metal ions act as catalytic centers and structural elements in a broad range of chemical complexes. The nonbonded model for metal ions is extensively used in molecular simulations due to its simple form, computational speed, and transferability. We have proposed and parametrized a 12-6-4 LJ (Lennard-Jones)-type nonbonded model for divalent metal ions in previous work, which showed a marked improvement over the 12-6 LJ nonbonded model. In the present study, by treating the experimental hydration free energies and ion–oxygen distances of the first solvation shell as targets for our parametrization, we evaluated 12-6 LJ parameters for 18 M(III) and 6 M(IV) metal ions for three widely used water models (TIP3P, SPC/E, and TIP4PEW). As expected, the interaction energy underestimation of the 12-6 LJ nonbonded model increases dramatically for the highly charged metal ions. We then parametrized the 12-6-4 LJ-type nonbonded model for these metal ions with the three water models. The final parameters reproduced the target values with good accuracy, which is consistent with our previous experience using this potential. Finally, tests were performed on a protein system, and the obtained results validate the transferability of these nonbonded model parameters.

Systematic Parameterization of Monovalent Ions Employing the Nonbonded Model

Monovalent ions play fundamental roles in many biological processes in organisms. Modeling these ions in molecular simulations continues to be a challenging problem. The 12-6 Lennard-Jones (LJ) nonbonded model is widely used to model monovalent ions in classical molecular dynamics simulations. A lot of parameterization efforts have been reported for these ions with a number of experimental end points. However, some reported parameter sets do not have a good balance between the two Lennard-Jones parameters (the van der Waals (VDW) radius and potential well depth), which affects their transferability. In the present work, via the use of a noble gas curve we fitted in former work (J. Chem. Theory Comput. 2013, 9, 2733), we reoptimized the 12-6 LJ parameters for 15 monovalent ions (11 positive and 4 negative ions) for three extensively used water models (TIP3P, SPC/E, and TIP4P(EW)). Since the 12-6 LJ nonbonded model performs poorly in some instances for these ions, we have also parameterized the 12-6-4 LJ-type nonbonded model (J. Chem. Theory Comput. 2014, 10, 289) using the same three water models. The three derived parameter sets focused on reproducing the hydration free energies (the HFE set) and the ion-oxygen distance (the IOD set) using the 12-6 LJ nonbonded model and the 12-6-4 LJ-type nonbonded model (the 12-6-4 set) overall give improved results. In particular, the final parameter sets showed better agreement with quantum mechanically calculated VDW radii and improved transferability to ion-pair solutions when compared to previous parameter sets.

Insight into the cation-π interaction at the metal binding site of the copper metallochaperone CusF.

The periplasmic Cu(+)/Ag(+) chaperone CusF features a novel cation-π interaction between a Cu(+)/Ag(+) ion and Trp44 at the metal binding site. The nature and strength of the Cu(+)/Ag(+)-Trp44 interactions were investigated using computational methodologies. Quantum-mechanical (QM) calculations showed that the Cu(+) and Ag(+) interactions with Trp44 are of similar strength (~14 kcal/mol) and bond order. Quantum-mechanical/molecular-mechanical (QM/MM) calculations showed that Cu(+) binds in a distorted tetrahedral coordination environment in the Trp44Met mutant, which lacks the cation-π interaction. Molecular dynamics (MD) simulations of CusF in the apo and Cu(+)-bound states emphasized the importance of the Cu(+)-Trp44 interaction in protecting Cu(+) from water oxidation. The protein structure does not change over the time scale of hundreds of nanoseconds in the metal-bound state. The metal recognition site exhibits small motions in the apo state but remains largely preorganized toward metal binding. Trp44 remains oriented to form the cation-π interaction in the apo state and faces an energetic penalty to move away from the metal ion. Cu(+) binding quenches the proteins internal motions in regions linked to binding CusB, suggesting that protein motions play an essential role in Cu(+) transfer to CusB.

Drug design : structure- and ligand-based approaches

Preface 1. Progress and issues for computationally guided lead discovery and optimization William L. Jorgensen Part I. Structural biology: 2. X-ray crystallography in the service of structure-based drug design Gregory A. Petsko and Dagmar Ringe 3. Fragment-based structure-guided drug discovery: strategy, process, and lessons from human protein kinases Stephen K. Burley, Gavin Hirst, Paul Sprengeler and Siegfried Reich 4. NMR in fragment-based drug discovery Christopher A. Lepre, Peter J. Connolly and Jonathan M. Moore Part II. Computational Chemistry Methodology: 5. Free-energy calculations in structure-based drug design Michael R. Shirts, David L. Mobley and Scott P. Brown 6. Studies of drug resistance and the dynamic behavior of HIV-1 protease through molecular dynamics simulations Fangyu Ding and Carlos Simmerling 7. Docking: a domesday report Martha S. Head 8. The role of quantum mechanics in structure-based drug design Kenneth M. Merz 9. Pharmacophore methods Steven L. Dixon 10. QSAR in drug discovery Alexander Tropsha 11. Predicting ADME properties in drug discovery William J. Egan Part III. Applications to drug discovery: 12. Computer-aided drug design: a practical guide to protein-structure-based modeling Charles H. Reynolds 13. Structure-based drug design case study: p38 Arthur M. Doweyko 14. Structure-based design of novel P2-P4 macrocyclic inhibitors of hepatitis C NS3/4A protease M. Katharine Holloway and Nigel J. Liverton 15. Purine nucleoside phosphorylases as targets for transition-state analog design Andrew S. Murkin and Vern L. Schramm 16. GPCR 3D modeling Frank U. Axe 17. Structure-based design of potent glycogen phosphorylase inhibitors Qiaolin Deng.

QM/MM X-ray refinement of zinc metalloenzymes.

Zinc metalloenzymes play an important role in biology. However, due to the limitation of molecular force field energy restraints used in X-ray refinement at medium or low resolutions, the precise geometry of the zinc coordination environment can be difficult to distinguish from ambiguous electron density maps. Due to the difficulties involved in defining accurate force fields for metal ions, the QM/MM (quantum-mechanical/molecular-mechanical) method provides an attractive and more general alternative for the study and refinement of metalloprotein active sites. Herein we present three examples that indicate that QM/MM based refinement yields a superior description of the crystal structure based on R and R(free) values and on the inspection of the zinc coordination environment. It is concluded that QM/MM refinement is an useful general tool for the improvement of the metal coordination sphere in metalloenzyme active sites.