Importance of accurate charges in molecular docking: quantum mechanical/molecular mechanical (QM/MM) approach

The extent to which accuracy of electric charges plays a role in protein-ligand docking is investigated through development of a docking algorithm, which incorporates quantum mechanical/molecular mechanical (QM/MM) calculations. In this algorithm, fixed charges of ligands obtained from force field parameterization are replaced by QM/MM calculations in the protein environment, treating only the ligands as the quantum region. The algorithm is tested on a set of 40 cocrystallized structures taken from the Protein Data Bank (PDB) and provides strong evidence that use of nonfixed charges is important. An algorithm, dubbed "Survival of the Fittest" (SOF) algorithm, is implemented to incorporate QM/MM charge calculations without any prior knowledge of native structures of the complexes. Using an iterative protocol, this algorithm is able in many cases to converge to a nativelike structure in systems where redocking of the ligand using a standard fixed charge force field exhibits nontrivial errors. The results demonstrate that polarization effects can play a significant role in determining the structures of protein-ligand complexes, and provide a promising start towards the development of more accurate docking methods for lead optimization applications.     

Simulations of liquid ammonia based on the combined quantum mechanical/molecular mechanical (QM/MM) approach

Two combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, namely, HF/MM and B3LYP/MM, have been performed to investigate the local structure and dynamics of liquid ammonia. The most interesting region, a sphere containing a central reference molecule and all its nearest surrounding molecules (first coordination shell), was treated by the Hartree-Fock (HF) and hybrid density functional B3LYP methods, whereas the rest of the system was described by the classical pair potentials. On the basis of both HF and B3LYP methods, it is observed that the hydrogen bonding in this peculiar liquid is weak. The structure and dynamics of this liquid are suggested to be determined by the steric packing effects, rather than by the directional hydrogen bonding interactions. Compared to previous empirical as well as Car-Parrinello (CP) molecular dynamics studies, our QM/MM simulations provide detailed information that is in better agreement with experimental data.     

The elusive oxidant species of cytochrome P450 enzymes: characterization by combined quantum mechanical/molecular mechanical (QM/MM) calculations

The primary oxidant of cytochrome P450 enzymes, Compound I, is hard to detect experimentally; in the case of cytochrome P450(cam), this intermediate does not accumulate in solution during the catalytic cycle even at temperatures as low as 200 K (ref 4). Theory can play an important role in characterizing such elusive species. We present here combined quantum mechanical/molecular mechanical (QM/MM) calculations of Compound I of cytochrome P450(cam) in the full enzyme environment as well as density functional studies of the isolated QM region. The calculations assign the ground state of the species, quantify the effect of polarization and hydrogen bonding on its properties, and show that the protein environment and its specific hydrogen bonding to the cysteinate ligand are crucial for sustaining the Fe-S bond and for preventing the full oxidation of the sulfur.     

Mixed quantum mechanical/molecular mechanical (QM/MM) study of the deacylation reaction in a penicillin binding protein (PBP) versus in a class C beta-lactamase

The origin of the substantial difference in deacylation rates for acyl-enzyme intermediates in penicillin-binding proteins (PBPs) and beta-lactamases has remained an unsolved puzzle whose solution is of great importance to understanding bacterial antibiotic resistance. In this work, accurate, large-scale mixed ab initio quantum mechanical/molecular mechanical (QM/MM) calculations have been used to study the hydrolysis of acyl-enzyme intermediates formed between cephalothin and the dd-peptidase of Streptomyces sp. R61, a PBP, and the Enterobacter cloacae P99 cephalosporinase, a class C beta-lactamase. Qualitative and, in the case of P99, quantitative agreement was achieved with experimental kinetics. The faster rate of deacylation in the beta-lactamase is attributed to a more favorable electrostatic environment around Tyr150 in P99 (as compared to that for Tyr159 in R61) which facilitates this residue's function as the general base. This is found to be in large part accomplished by the ability of P99 to covalently bind the ligand without concurrent elimination of hydrogen bonds to Tyr150, which proves not to be the case with Tyr159 in R61. This work provides an essential foundation for further work in this area, such as selecting mutations capable of converting the PBP into a beta-lactamase.     

Ab initio quantum mechanical charge field (QMCF) molecular dynamics: a QM/MM – MD procedure for accurate simulations of ions and complexes

A new formalism for quantum mechanical / molecular mechanical (QM/MM) dynamics of chemical species in solution has been developed, which does not require the construction of any other potential functions except those for solvent–solvent interactions, maintains all the advantages of large simulation boxes and ensures the accuracy of ab initio quantum mechanics for all forces acting in the chemically most relevant region. Interactions between solute and more distant solvent molecules are incorporated by a dynamically adjusted force field corresponding to the actual molecular configuration of the simulated system and charges derived from the electron distribution in the solvate. The new formalism has been tested with some examples of hydrated ions, for which accurate conventional ab initio QM/MM simulations have been previously performed, and the comparison shows equivalence and in some aspects superiority of the new method. As this simulation procedure does not require any tedious construction of two-and three-body interaction potentials inherent to conventional QM/MM approaches, it opens the straightforward access to ab initio molecular dynamics simulations of any kind of solutes, such as metal complexes and other composite species in solution.     

Improved pseudobonds for combined ab initio quantum mechanical/molecular mechanical methods

The pseudobond approach offers a smooth connection at the quantum mechanical/molecular mechanical interface which passes through covalent bonds. It replaces the boundary atom of the environment part with a seven-valence-electron atom to form a pseudobond with the boundary atom of the active part [Y. Zhang, T. S. Lee, and W. Yang, J. Chem. Phys. 110, 46 (1999)]. In its original formulation, the seven-valence-electron boundary atom has the basis set of fluorine and a parametrized effective core potential. Up to now, only the Cps(sp3)-C(sp3) pseudobond has been successfully developed; thus in the case of proteins, it can only be used to cut the protein side chains. Here we employ a different formulation to construct this seven-valence-electron boundary atom, which has its own basis set as well as the effective core potential. We have not only further improved Cps(sp3)-C(sp3) pseudobond, but also developed Cps(sp3)-C(sp2,carbonyl) and Cps(sp3)-N(sp3) pseudobonds for the cutting of protein backbones and nucleic acid bases. The basis set and effective core potential for the seven-valence-electron boundary atom are independent of the molecular mechanical force field. Although the parametrization is performed with density functional calculations using hybrid B3LYP exchange-correlation functional, it is found that the same set of parameters is also applicable to Hartree-Fock and MP2 methods, as well as DFT calculations with other exchange-correlation functionals. Tests on a series of molecules yield very good structural, electronic, and energetic results in comparison with the corresponding full ab initio quantum mechanical calculations.     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999     

Prediction and rationalization of protein pKa values using QM and QM/MM methods

We describe the development and application of a computational method for the prediction and rationalization of pKa values of ionizable residues in proteins, based on ab initio quantum mechanics (QM) and the effective fragment potential (EFPs) method (a hybrid QM/MM method). The theoretical developments include (1) a covalent boundary method based on frozen localized orbitals, (2) divide-and-conquer methods for the ab initio computation of protein EFPs consisting of multipoles up to octupoles and dipole polarizability tensors, (3) a method for computing vibrational free energies for a localized molecular region, and (4) solutions of the polarized continuum model of bulk solvation equations for protein-sized systems. The QM-based pKa prediction method is one of the most accurate methods currently available and can be used in cases where other pKa prediction methods fail. Preliminary analysis of the computed results indicate that many pKa values (1) are primarily determined by hydrogen bonds rather than long-range charge-charge interactions and (2) are relatively insensitive to large-scale dynamical fluctuations of the protein structure.     

Comparative quantum mechanics/molecular mechanics (QM/MM) and density functional theory calculations on the oxo-iron species of taurine/alpha-ketoglutarate dioxygenase

We present here the first quantum mechanical/molecular mechanics (QM/MM) studies of taurine/alpha-ketoglutarate dioxygenase (TauD) enzymes. Our studies are focused on the chemical properties of the oxo-iron species and the effect of the protein environment on its structural and electronic behavior. Although the active site region of TauD is very polar with many key hydrogen bonding interactions and salt bridges, the actual effect of the protein environment on the ordering and relative energies of the possible spin state structures is found to be quite small. Optimized geometries are very close to ones observed with density functional theory models that did not take the protein environment into consideration. The calculations show that protonation of the histidine ligands of iron is essential to reproduce the correct electronic representations of the enzyme. Hydroxylation studies of taurine by the oxo-iron active species predict that it is a very efficient catalyst that reacts with substrates via low reaction barriers.     

An extensible interface for QM/MM molecular dynamics simulations with AMBER

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface. © 2013 Wiley Periodicals, Inc.     

Revealing the molecular mechanisms of proteolysis of SARS-CoV-2 Mpro by QM/MM computational methods

SARS-CoV-2 M^pro is one of the enzymes essential for the replication process of the virus responsible for the COVID-19 pandemic. This work is focused on exploring its proteolysis reaction by means of QM/MM methods. The resulting free energy landscape of the process provides valuable information on the species appearing along the reaction path and suggests that the mechanism of action of this enzyme, taking place in four steps, slightly differs from that of other cysteine proteases. Our predictions, which are in agreement with some recently published experimental data, can be used to guide the design of COVID-19 antiviral compounds with clinical potential.

The molecular mechanism of the proteolysis reaction catalyzed by SARS-CoV-2 M^pro, one of the enzymes essential for the replication process of the virus responsible for the COVID-19 pandemic, is described using computational QM/MM methods.     

Gold(I) in liquid ammonia: ab initio QM/MM molecular dynamics simulation

Structure and dynamics investigations of Au(I) ion in liquid ammonia have been performed by means of a molecular dynamics simulation based on ab initio quantum mechanical/molecular mechanical forces, where the first solvation shell was treated by quantum mechanics at Hartree-Fock level. The outer region of the system was described using a newly constructed classical three-body corrected potential. A rigid structure of the first solvation shell was observed with an average Au-N distance of 2.15 A and a coordination number of 2.0.     

QM/MM Methods for Biomolecular Systems

Two are better than one : Quantum mechanics/molecular mechanics (QM/MM) methods are the state‐of‐the‐art computational technique for treating reactive and other “electronic” processes in biomolecular systems. This Review presents the general methodological aspects of the QM/MM approach, its use within optimization and simulation techniques, and its areas of application, always with a biomolecular focus.