Yingkai Zhang

A PSEUDOBOND APPROACH TO COMBINING QUANTUM MECHANICAL AND MOLECULAR MECHANICAL METHODS

A major challenge for combined quantum mechanical and molecular mechanical methods (QM/MM) to study large molecules is how to treat the QM/MM boundary that bisects some covalent bonds. Here a pseudobond approach has been developed to solve this problem for ab initio QM/MM calculations: a one-free-valence atom with an effective core potential is constructed to replace the boundary atom of the environment part and to form a pseudobond with the boundary atom of the active part. This pseudobond, which is described only by the QM method, is designed to mimic the original bond with similar bond length and strength, and similar effects on the rest of the active part. With this pseudobond approach, some well-known deficiencies of the link atom approach have been circumvented and a well-defined potential energy surface of the whole QM/MM system has been provided. The construction of the effective core potential for the pseudobond is independent of the molecular mechanical force field and the same effective core potential is applicable to both Hartree–Fock and density functional methods. 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.

A challenge for density functionals: Self-interaction error increases for systems with a noninteger number of electrons

The difficulty of widely used density functionals in describing the dissociation behavior of some homonuclear and heteronuclear diatomic radicals is analyzed. It is shown that the self-interaction error of these functionals accounts for the problem—it is much larger for a system with a noninteger number of electrons than a system with an integer number of electrons. We find the condition for the erroneous dissociation behavior described by approximate density functionals: when the ionization energy of one dissociation partner differs from the electron affinity of the other partner by a small amount, the self-interaction error will lead to wrong dissociation limit. Systems with a noninteger number of electrons and hence the large amount of self-interaction error in approximate density functionals arise also in the transition states of some chemical reactions and in some charge-transfer complexes. In the course of analysis, we derive a scaling relation necessary for an exchange-correlation functional to be self-interaction free.

Free energy calculation on enzyme reactions with an efficient iterative procedure to determine minimum energy paths on a combined ab initio QM/MM potential energy surface

A new practical approach to studying enzyme reactions by combining ab initio QM/MM calculations with free energy perturbation is presented. An efficient iterative optimization procedure has been developed to determine optimized structures and minimum energy paths for a system with thousands of atoms on the ab initio QM/MM potential: the small QM sub-system is optimized using a quasi-Newton minimizer in redundant internal coordinates with ab initio QM/MM calculations, while the large MM sub-system is minimized by the truncated Newton method in Cartesian coordinates with only molecular mechanical calculations. The above two optimization procedures are performed iteratively until they converge. With the determined minimum energy paths, free energy perturbation calculations are carried out to determine the change in free energy along the reaction coordinate. Critical to the success of the iterative optimization procedure and the free energy calculations is the smooth connection between the QM and MM regions p...

DESCRIBING VAN DER WAALS INTERACTION IN DIATOMIC MOLECULES WITH GENERALIZED GRADIENT APPROXIMATIONS: THE ROLE OF THE EXCHANGE FUNCTIONAL

Generalized gradient approximations have been used to calculate the potential energy curves for six rare gas diatomic molecules. Several generalized gradient approximations are found to provide a good description of binding in these diatomic molecules and show a significant improvement over the local density approximation in the prediction of bond lengths and dissociation energies. It is shown here that the behavior of an exchange functional in the region of small density and large density gradient plays a very important role in the ability of the functional to describe this type of van der Waals attraction.

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.

A Proton-Shuttle Reaction Mechanism for Histone Deacetylase 8 and the Catalytic Role of Metal Ions

Zinc-dependent histone deacetylase 8 (HDAC8) catalyzes the removal of acetyl moieties from histone tails, and is critically involved in regulating chromatin structure and gene expression. The detailed knowledge of its catalytic process is of high importance since it has been established as a most promising target for the development of new antitumor drugs. By employing Born-Oppenheimer ab initio QM/MM molecular dynamics simulations and umbrella sampling, a state-of-the-art approach to simulate enzyme reactions, we have provided further evidence against the originally proposed general acid-base catalytic pair mechanism for Zinc-dependent histone deacetylases. Instead, our results indicated that HDAC8 employs a proton-shuttle catalytic mechanism, in which a neutral His143 first serves as the general base to accept a proton from the zinc-bound water molecule in the initial rate-determining nucleophilic attack step, and then shuttles it to the amide nitrogen atom to facilitate the cleavage of the amide bond. During the deacetylation process, the Zn(2+) ion changes its coordination mode and plays multiple catalytic roles. For the K(+) ion, which is located about 7 A from the catalytic Zn(2+) ion and conserved in class I and II HDACs, our simulations indicated that its removal would lead to the different transition state structure and a higher free energy reaction barrier for the rate-determining step. It is found that the existence of this conserved K(+) ion would enhance the substrate binding, increase the basicity of His143, strengthen the catalytic role of zinc ion, and improve the transition state stabilization by the enzyme environment.

Density-based energy decomposition analysis for intermolecular interactions with variationally determined intermediate state energies.

The first purely density-based energy decomposition analysis (EDA) for intermolecular binding is developed within the density functional theory. The most important feature of this scheme is to variationally determine the frozen density energy, based on a constrained search formalism and implemented with the Wu-Yang algorithm [Q. Wu and W. Yang, J. Chem. Phys. 118, 2498 (2003)]. This variational process dispenses with the Heitler-London antisymmetrization of wave functions used in most previous methods and calculates the electrostatic and Pauli repulsion energies together without any distortion of the frozen density, an important fact that enables a clean separation of these two terms from the relaxation (i.e., polarization and charge transfer) terms. The new EDA also employs the constrained density functional theory approach [Q. Wu and T. Van Voorhis, Phys. Rev. A 72, 24502 (2005)] to separate out charge transfer effects. Because the charge transfer energy is based on the density flow in real space, it has a small basis set dependence. Applications of this decomposition to hydrogen bonding in the water dimer and the formamide dimer show that the frozen density energy dominates the binding in these systems, consistent with the noncovalent nature of the interactions. A more detailed examination reveals how the interplay of electrostatics and the Pauli repulsion determines the distance and angular dependence of these hydrogen bonds.

An efficient approach for ab initio energy calculation of biopolymers

We present a new method for efficient total-energy calculation of biopolymers using the density-matrix (DM) scheme based on the molecular fractionation with conjugate caps (MFCC) approach. In this MFCC-DM method, a biopolymer such as a protein is partitioned into properly capped fragments whose density matrices are calculated by conventional ab initio methods which are then assembled to construct the full system density matrix. The assembled full density matrix is then employed to calculate the total energy and dipole moment of the protein using Hartree-Fock or density-functional theory methods. Using this MFCC-DM method, the self-consistent-field procedure for solving the full Hamiltonian problem is avoided and an efficient approach for ab initio energy calculation of biopolymers is achieved. Two implementations of the approach are presented in this paper. Systematic numerical studies are carried out on a series of extended polyglycines CH3CO-(GLY)n-NHCH3(n = 3-25) and excellent results are obtained.

Zinc Chelation with Hydroxamate in Histone Deacetylases Modulated by Water Access to the Linker Binding Channel

It is of significant biological interest and medical importance to develop class- and isoform-selective histone deacetylase (HDAC) modulators. The impact of the linker component on HDAC inhibition specificity has been revealed but is not understood. Using Born-Oppenheimer ab initio QM/MM MD simulations, a state-of-the-art approach to simulating metallo-enzymes, we have found that the hydroxamic acid remains to be protonated upon its binding to HDAC8, and thus disproved the mechanistic hypothesis that the distinct zinc-hydroxamate chelation modes between two HDAC subclasses come from different protonation states of the hydroxamic acid. Instead, our simulations suggest a novel mechanism in which the chelation mode of hydroxamate with the zinc ion in HDACs is modulated by water access to the linker binding channel. This new insight into the interplay between the linker binding and the zinc chelation emphasizes its importance and gives guidance regarding linker design for the development of new class-IIa-specific HDAC inhibitors.

Highly Dissociative and Concerted Mechanism for the Nicotinamide Cleavage Reaction in Sir2Tm Enzyme Suggested by Ab Initio QM/MM Molecular Dynamics Simulations

Sir2 enzymes catalyze the NAD+-dependent protein deacetylation and play critical roles in epigenetics, cell death, and lifespan regulation. In spite of a current flurry of experimental studies, the catalytic mechanism for this unique and important class of enzymes remains elusive. Employing on-the-fly Born-Oppenheimer molecular dynamics simulations with the B3LYP/6-31G(d) QM/MM potential and the umbrella sampling method, we have characterized the initial step of the Sir2Tm-catalyzed reaction, which is also the most controversial portion of its mechanism. Our results indicate that the nicotinamide cleavage reaction employs a highly dissociative and concerted displacement mechanism: the cleavage of the glycosidic bond is facilitated by the nucleophilic participation of the acetyl-lysine, and the dissociative transition state has a significant oxocarbenium ion character. During this step of the reaction, the Sir2Tm enzyme strongly stabilizes the covalent O-alkylamidate intermediate whereas its effect on the transition state is quite minimal. In addition, functional roles of key residues and motifs have been elucidated. This work further demonstrates the feasibility and applicability of the state-of-the-art ab initio QM/MM molecular dynamics approach in simulating enzyme reactions.