QM/MM methods for biomolecular systems

Multilevel Fragment-Based Approach (MFBA): A Novel Hybrid Computational Method for the Study of Large Molecules

We present a novel method for the calculation of large molecules and systems, the multilevel fragment-based approach. It is based on dividing the system into small fragments followed by separate calculations of these fragments and the interactions between them. Unlike previous fragmentation-based methods, we use multiple computational methods for the individual calculations. Using an accurate method only to calculate local interactions and more approximate methods for interactions over larger distances, it is possible to achieve results very close to a more demanding fragmented calculation using the higher level method only. The number of calculations performed at the higher level scales linearly with the size of the system, which significantly improves the efficiency and allows this scheme to be used for very large systems. In this work, we have combined density functional theory with the more approximate density functional tight binding method and applied this method to the calculation of model peptides. Formulation of first derivatives of the total energy within this fragmentation scheme is also presented and tested.

Increasing the time step with mass scaling in Born-Oppenheimer ab initio QM/MM molecular dynamics simulations

Born-Oppenheimer ab initio QM/MM molecular dynamics simulation with umbrella sampling is a state-of-the-art approach to calculate free energy profiles of chemical reactions in complex systems. To further improve its computational efficiency, a mass-scaling method with the increased time step in MD simulations has been explored and tested. It is found that by increasing the hydrogen mass to 10 amu, a time step of 3 fs can be employed in ab initio QM/MM MD simulations. In all our three test cases, including two solution reactions and one enzyme reaction, the resulted reaction free energy profiles with 3 fs time step and mass scaling are found to be in excellent agreement with the corresponding simulation results using 1 fs time step and the normal mass. These results indicate that for Born-Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, the mass-scaling method can significantly reduce its computational cost while has little effect on the calculated free energy profiles.

Active site cysteine is protonated in the PAD4 Michaelis complex: evidence from Born-Oppenheimer ab initio QM/MM molecular dynamics simulations

The protein arginine deiminase 4 (PAD4) catalyzes the citrullination of the peptidylarginine and plays a critical role in rheumatoid arthritis (RA) and gene regulation. Understanding its catalytic mechanism is not only of fundamental importance but also of significant medical interest for the rational design of new inhibitors. By employing on-the-fly Born-Oppenheimer ab initio QM/MM molecular dynamics simulations, we have demonstrated that it is unlikely for the active site cysteine and histidine to exist as a thiolate-imidazolium ion pair in the PAD4 Michaelis reactant complex. Instead, a substrate-assisted proton transfer mechanism for the deimination reaction step has been characterized: both Cys645 and His471 in the PAD4 active site are neutral prior to the reaction; the deprotonation of Cys645 by the substrate arginine occurs in concert with the nucleophilic addition of the Cys thiolate to Czeta of the substrate, and leads to a covalent tetrahedral intermediate; then, the Czeta-Neta1 bond cleaves and the resulted ammonia is displaced by a solvent water molecule. The initial deprotonation and nucleophilic attack step is found to be rate-determining. The computed free energy barrier with B3LYP(6-31G*) QM/MM MD simulations and umbrella sampling is 20.9 kcal.mol(-1), consistent with the experimental kinetic data. During the deimination, His471 plays an important role in stabilizing the transition state through the formation of the hydrogen bond with the guanidinium group. Our current studies further demonstrated the viability and strength of the ab initio QM/MM molecular dynamics approach in simulating enzyme reactions.

Peptide conformer acidity analysis of protein flexibility monitored by hydrogen exchange

The amide hydrogens that are exposed to solvent in the high-resolution X-ray structures of ubiquitin, FK506-binding protein, chymotrypsin inhibitor 2, and rubredoxin span a billion-fold range in hydroxide-catalyzed exchange rates which are predictable by continuum dielectric methods. To facilitate analysis of transiently accessible amides, the hydroxide-catalyzed rate constants for every backbone amide of ubiquitin were determined under near physiological conditions. With the previously reported NMR-restrained molecular dynamics ensembles of ubiquitin (PDB codes 2NR2 and 2K39) used as representations of the Boltzmann-weighted conformational distribution, nearly all of the exchange rates for the highly exposed amides were more accurately predicted than by use of the high-resolution X-ray structure. More strikingly, predictions for the amide hydrogens of the NMR relaxation-restrained ensemble that become exposed to solvent in more than one but less than half of the 144 protein conformations in this ensemble were almost as accurate. In marked contrast, the exchange rates for many of the analogous amides in the residual dipolar coupling-restrained ubiquitin ensemble are substantially overestimated, as was particularly evident for the Ile 44 to Lys 48 segment which constitutes the primary interaction site for the proteasome targeting enzymes involved in polyubiquitylation. For both ensembles, “excited state” conformers in this active site region having markedly elevated peptide acidities are represented at a population level that is 10² to 10³ above what can exist in the Boltzmann distribution of protein conformations. These results indicate how a chemically consistent interpretation of amide hydrogen exchange can provide insight into both the population and the detailed structure of transient protein conformations.

Charge transfer equilibria of aqueous single stranded DNA

The charge transfer thermodynamics of a simple model of DNA, a single stranded 10-mer poly-adenine oligonucleotide, in water is investigated by means of a computational/theoretical procedure, in which all the relevant environmental effects are considered. Our data indicate that water and counterions ultimately dominate the DNA reduction and oxidation free energies, which are also strongly influenced by the base position along the strand. In fact, we estimated that reduction free energies are large and negative, particularly for the bases close to the 5' and 3' positions, whereas the electron detachment is thermodynamically unfavoured all along the strand, but with a higher free energy cost in the central region of the molecule. Further investigation on double charging, i.e. one nucleobase is oxidized and one is reduced within the strand, predicts that charge-separated states are possible and thermodynamically largely stable when the ionic forms are separated by several nucleobases.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Finite-temperature effects in enzymatic reactions — Insights from QM/MM free-energy simulations

We report potential-energy and free-energy data for three enzymatic reactions: carbon–halogen bond formation in fluorinase, hydrogen abstraction from camphor in cytochrome P450cam, and chorismate-to-prephenate Claisen rearrangement in chorismate mutase. The results were obtained by combined quantum mechanics/molecular mechanics (QM/MM) optimizations and two types of QM/MM free-energy simulations (free-energy perturbation and umbrella sampling) using semi-empirical or density-functional QM methods. Based on these results and our previously published free-energy data on electrophilic substitution in para-hydroxybenzoate hydroxylase, we discuss the importance of finite-temperature effects in the chemical step of enzyme reactions. We find that the entropic contribution to the activation barrier is generally rather small, usually of the order of 5 kJ mol–1 or less, consistent with the notion that enzymes bind and pre-organize the reactants in the active site. A somewhat larger entropic contribution is encountered in the case of chorismate mutase where the pericyclic transition state is intrinsically more rigid than the chorismate reactant (also in the enzyme). The present results suggest that barriers from QM/MM geometry optimization may often be close to free-energy barriers for the chemical step in enzymatic reactions.

Highly conserved histidine plays a dual catalytic role in protein splicing: a pKa shift mechanism

Protein splicing is a precise autocatalytic process in which an intein excises itself from a precursor with the concomitant ligation of the flanking sequences. Protein splicing occurs through acid-base catalysis in which the ionization states of active site residues are crucial to the reaction mechanism. In inteins, several conserved histidines have been shown to play important roles in protein splicing, including the most conserved "B-block" histidine. In this study, we have combined NMR pK(a) determination with quantum mechanics/molecular mechanics (QM/MM) modeling to study engineered inteins from Mycobacterium tuberculosis (Mtu) RecA intein. We demonstrate a dramatic pK(a) shift for the invariant B-block histidine, the most conserved residue among inteins. The B-block histidine has a pK(a) of 7.3 +/- 0.6 in a precursor and a pK(a) of <3.5 in a spliced intein. The pK(a) values and QM/MM data suggest that the B-block histidine has a dual role in the acid-base catalysis of protein splicing. This histidine likely acts as a general base to initiate splicing with an acyl shift and then as a general acid to cause the breakdown of the scissile bond at the N-terminal splicing junction. The proposed pK(a) shift mechanism accounts for the biochemical data supporting the essential role for the B-block histidine and for the near absolute sequence conservation of this residue.

Polarization effects in molecular mechanical force fields

The focus here is on incorporating electronic polarization into classical molecular mechanical force fields used for macromolecular simulations. First, we briefly examine currently used molecular mechanical force fields and the current status of intermolecular forces as viewed by quantum mechanical approaches. Next, we demonstrate how some components of quantum mechanical energy are effectively incorporated into classical molecular mechanical force fields. Finally, we assess the modeling methods of one such energy component-polarization energy-and present an overview of polarizable force fields and their current applications. Incorporating polarization effects into current force fields paves the way to developing potentially more accurate, though more complex, parameterizations that can be used for more realistic molecular simulations.

Computational study on the conformation and vibration frequencies of β-sheet of ε-polylysine in vacuum

Two oligomers, each containing 3 l-lysine residues, were used as model molecules for the simulation of the β-sheet conformation of ɛ-polylysine (ɛ-PLL) chains. Their C terminals were capped with ethylamine and N terminals were capped with α-l-aminobutanoic acid, respectively. The calculations were carried out with the hybrid two-level ONOIM (B3LYP/6-31G:PM3) computational chemistry method. The optimized conformation was obtained and IR frequencies were compared with experimental data. The result indicated that the two chains were winded around each other to form a distinct cyclohepta structure through bifurcated hydrogen bonds. The groups of amide and α-amidocyanogen coming from one chain and the carbonyl group from the other chain were involved in the cyclohepta structure. The bond angle of the bifurcated hydrogen bonds was 66.6°. The frequency analysis at ONIOM [B3LYP/6-31G (d):PM3] level showed the IR absorbances of the main groups, such as the amide and amidocyanogen groups, were in accordance with the experimental data.

Polymerase-tailored variations in the water-mediated and substrate-assisted mechanism for nucleotidyl transfer: insights from a study of T7 DNA polymerase

The nucleotidyl transfer reaction catalyzed by DNA polymerases is the critical step governing the accurate transfer of genetic information during DNA replication, and its malfunctioning can cause mutations leading to human diseases, including cancer. Here, utilizing ab initio quantum mechanical/molecular mechanical calculations with free-energy perturbation, we carried out an extensive investigation of the nucleotidyl transfer reaction mechanism in the well-characterized high-fidelity replicative DNA polymerase from phage T7. Our defined mechanism entails an initial concerted deprotonation of a conserved crystal water molecule with protonation of the gamma-phosphate of the deoxynucleotide triphosphate(dNTP) via a solvent water molecule, and then the proton on the primer 3'-terminus is transferred to the resulting hydroxide ion. Subsequently, the nucleophilic attack takes place, with the formation of a metastable pentacovalent phosphorane intermediate. Finally, the pyrophosphate leaves, facilitated by the relay of the proton on the gamma-phosphate to the alpha-beta bridging oxygen via solvent water. The computed activation free-energy barrier is consistent with kinetic data for the chemistry step with correct nucleotide incorporation in T7 DNA polymerase. This variant of the water-mediated and substrate-assisted mechanism has features tailored to the structure of the T7 DNA polymerase. However, a unifying theme in the water-mediated and substrate-assisted mechanism is the cycling through crystal and solvent water molecules of the proton originating from the primer 3'-terminus to the alpha-beta bridging oxygen of the deoxynucleotide triphosphate; this neutralizes the evolving negative charge as pyrophosphate leaves and restores the polymerase to its pre-chemistry state. These unifying features are likely requisite elements for nucleotidyl transfer reactions.

Computational molecular biology approaches to ligand-target interactions

Binding of small molecules to their targets triggers complex pathways. Computational approaches are keys for predictions of the molecular events involved in such cascades. Here we review current efforts at characterizing the molecular determinants in the largest membrane-bound receptor family, the G-protein-coupled receptors (GPCRs). We focus on odorant receptors, which constitute more than half GPCRs. The work presented in this review uncovers structural and energetic aspects of components of the cellular cascade. Finally, a computational approach in the context of radioactive boron-based antitumoral therapies is briefly described.