No abstract

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.

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 provided by a recently proposed pseudobond QM/MM approach [J. Chem. Phys. 110, 46 (1999)]. The methods have been demonstrated by studying the initial proton transfer step in the reaction catalyzed by the enzyme triosephosphate isomerase (TIM).

For a linear combination of electron densities of degenerate ground states, it is shown that the value of any energy functional is the ground state energy, if the energy functional is exact for ground state densities, size consistent, and translational invariant. The corresponding functional of kinetic and interaction energy is the linear combination of the functionals of the degenerate densities. Without invoking ensembles, it is shown that the energy functional of fractional number electrons is a series of straight lines interpolating its values at integers. These results underscore the importance of grand canonical ensemble formulation in density functional theory.

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.

We have carried out density functional theory QM/MM calculations on the catalytic subunit of cAMP-dependent protein kinase (PKA). The QM/MM calculations indicate that the phosphorylation reaction catalyzed by PKA is mainly dissociative, and Asp166 serves as the catalytic base to accept the proton delivered by the substrate peptide. Among the key interactions in the active site, the Mg(2+) ions, glycine rich loop, and Lys72 are found to stabilize the transition state through electrostatic interactions. On the other hand, Lys168, Asn171, Asp184, and the conserved waters bound to Mg(2+) ions do not directly contribute to lower the energy barrier of the phosphorylation reaction, and possible roles for these residues are proposed. The QM/MM calculations with different QM/MM partition schemes or different initial structures yield consistent results. In addition, we have carried out 12 ns molecular dynamics simulations on both wild type and K168A mutated PKA, respectively, to demonstrate that the catalytic role of Lys168 is to keep ATP and substrate peptide in the near-attack reactive conformation.

The initial step of the acylation reaction catalyzed by acetylcholinesterase (AChE) has been studied by a combined ab initio quantum mechanical/molecular mechanical (QM/MM) approach. The reaction proceeds through the nucleophilic addition of the Ser203 O to the carbonyl C of acetylcholine, and the reaction is facilitated by simultaneous proton transfer from Ser203 to His447. The calculated potential energy barrier at the MP2(6-31+G) QM/MM level is 10.5 kcal/mol, consistent with the experimental reaction rate. The third residue of the catalytic triad, Glu334, is found to be essential in stabilizing the transition state through electrostatic interactions. The oxyanion hole, formed by peptidic NH groups from Gly121, Gly122, and Ala204, is also found to play an important role in catalysis. Our calculations indicate that, in the AChE-ACh Michaelis complex, only two hydrogen bonds are formed between the carbonyl oxygen of ACh and the peptidic NH groups of Gly121 and Gly122. As the reaction proceeds, the distance between the carbonyl oxygen of ACh and NH group of Ala204 becomes smaller, and the third hydrogen bond is formed both in the transition state and in the tetrahedral intermediate.

The development of new protein-ligand scoring functions using machine learning algorithms, such as random forest, has been of significant interest. By efficiently utilizing expanded feature sets and a large set of experimental data, random forest based scoring functions (RFbScore) can achieve better correlations to experimental protein-ligand binding data with known crystal structures; however, more extensive tests indicate that such enhancement in scoring power comes with significant under-performance in docking and screening power tests compared to traditional scoring functions. In this work, in order to improve scoring-docking-screening powers of protein-ligand docking functions simultaneously, we have introduced a ΔvinaRF parameterization and feature selection framework based on random forest. Our developed scoring function ΔvinaRF20, which employs twenty descriptors in addition to the AutoDock Vina score, can achieve superior performance in all power tests of both CASF-2013 and CASF-2007 benchmarks compared to classical scoring functions. The ΔvinaRF20 scoring function and its code are freely available on the web at: https://www.nyu.edu/projects/yzhang/DeltaVina.