Modeling zinc in biomolecules with the self consistent charge-density functional tight binding (SCC-DFTB) method: applications to structural and energetic analysis

Obtaining Robust Density Functional Tight-Binding Parameters for Solids across the Periodic Table

The density functional tight-binding (DFTB) approach allows electronic structure-based simulations at length and time scales far beyond what is possible with first-principles methods. This is achieved by using minimal basis sets and empirical approximations. Unfortunately, the sparse availability of parameters across the periodic table is a significant barrier to the use of DFTB in many cases. We therefore propose a workflow that allows the robust and consistent parametrization of DFTB across the periodic table. Importantly, our approach requires no element-pairwise parameters so that the parameters can be used for all element combinations and are readily extendable. This is achieved by parametrizing all elements on a consistent set of artificial homoelemental crystals, spanning a wide range of coordination environments. The transferability of the resulting periodic table baseline parameters to multielement systems and unknown structures is explored and the model is extensively benchmarked against previous specialized and general DFTB parametrizations.

Characterization of the Coordination and Solvation Dynamics of Solvated Systems─Implications for the Analysis of Molecular Interactions in Solutions and Pure H2O

The characterization of solvation shells of atoms, ions, and molecules in solution is essential to relate solvation properties to chemical phenomena such as complex formation and reactivity. Different definitions of the first-shell coordination sphere from simulation data can lead to potentially conflicting data on the structural properties and associated ligand exchange dynamics. The definition of a solvation shell is typically based on a given threshold distance determined from the respective solute-solvent pair distribution function g(r) (i.e., GC). Alternatively, a nearest neighbor (NN) assignment based on geometric properties of the coordination complex without the need for a predetermined cutoff criterion, such as the relative angular distance (RAD) or the modified Voronoi (MV) tessellation, can be applied. In this study, the effect of different NN algorithms on the coordination number and ligand exchange dynamics evaluated for a series of monatomic ions in aqueous solution, carbon dioxide in aqueous and dichloromethane solutions, and pure liquid water has been investigated. In the case of the monatomic ions, the RAD approach is superior in achieving a well separated definition of the first solvation layer. In contrast, the MV algorithm provides a better separation of the NNs from a molecular point of view, leading to better results in the case of solvated CO2. When analyzing the coordination environment in pure water, the cutoff-based GC framework was found to be the most reliable approach. By comparison of the number of ligand exchange reactions and the associated mean ligand residence times (MRTs) with the properties of the coordination number autocorrelation functions, it is shown that although the average coordination numbers are sensitive to the different definitions of the first solvation shell, highly consistent estimates for the associated MRT of the solvated system are obtained in the majority of cases.

Benchmarking quantum mechanical methods for calculating reaction energies of reactions catalyzed by enzymes

To assess the accuracy of different quantum mechanical methods for biochemical modeling, the reaction energies of 20 small model reactions (chosen to represent chemical steps catalyzed by commonly studied enzymes) were calculated. The methods tested included several popular Density Functional Theory (DFT) functionals, second-order Møller Plesset perturbation theory (MP2) and its spin-component scaled variant (SCS-MP2), and coupled cluster singles and doubles and perturbative triples (CCSD(T)). Different basis sets were tested. CCSD(T)/aug-cc-pVTZ results for all 20 reactions were used to benchmark the other methods. It was found that MP2 and SCS-MP2 reaction energy calculation results are similar in quality to CCSD(T) (mean absolute error (MAE) of 1.2 and 1.3 kcal mol−1, respectively). MP2 calculations gave a large error in one case, and are more subject to basis set effects, so in general SCS-MP2 calculations are a good choice when CCSD(T) calculations are not feasible. Results with different DFT functionals were of reasonably good quality (MAEs of 2.5–5.1 kcal mol−1), whereas popular semi-empirical methods (AM1, PM3, SCC-DFTB) gave much larger errors (MAEs of 11.6–14.6 kcal mol−1). These results should be useful in guiding methodological choices and assessing the accuracy of QM/MM calculations on enzyme-catalyzed reactions.

Quantum Chemical Calculation of Molecular and Periodic Peptide and Protein Structures

Special-purpose classical force fields (FFs) provide good accuracy at very low computational cost, but their application is limited to systems for which potential energy functions are available. This excludes most metal-containing proteins or those containing cofactors. In contrast, the GFN2-xTB semiempirical quantum chemical method is parametrized for almost the entire periodic table. The accuracy of GFN2-xTB is assessed for protein structures with respect to experimental X-ray data. Furthermore, the results are compared with those of two special-purpose FFs, HF-3c, PM6-D3H4X, and PM7. The test sets include proteins without any prosthetic groups as well as metalloproteins. Crystal packing effects are examined for a set of smaller proteins to validate the molecular approach. For the proteins without prosthetic groups, the special purpose FF OPLS-2005 yields the smallest overall RMSD to the X-ray data but GFN2-xTB provides similarly good structures with even better bond-length distributions. For the metalloproteins with up to 5000 atoms, a good overall structural agreement is obtained with GFN2-xTB. The full geometry optimizations of protein structures with on average 1000 atoms in wall-times below 1 day establishes the GFN2-xTB method as a versatile tool for the computational treatment of various biomolecules with a good accuracy/computational cost ratio.

QM/MM investigation of substrate binding of subclass B3 metallo-β-lactamase SMB-1 from Serratia marcescents: insights into catalytic mechanism

Metallo-β-lactamases (MβLs) can hydrolyze and deactivate lactam-containing antibiotics, which are the major mechanism to cause drug resistance in the treatment of bacterial infections. This has become a global concern due to the lack of clinically approved inhibitors so far. SMB-1 from Serratia marcescents is a novel B3 subclass MβL, which could inactivate nearly all β-lactam-containing antibiotics, e.g., cephalosporins and carbapenems. It represents a new round of worrisome bacterial resistance. In this work, the Michaelis model of SMB-1 in complex with ampicillin was simulated using combined quantum mechanical and molecular mechanical method. Similar with other dizinc MβLs, a Zn-bridged hydroxide ion was simulated as the nucleophile for the hydrolysis reaction assisted by D120. The protonation of D120 could lead to the loss of O_δ2-Zn2 coordination bond, whereas the C3 carboxylate group moves down to become a new ligand to Zn2. The initial β-lactam ring-opening reaction leads to a conserved nitrogen anionic intermediate, which forms a new ligation between the resulted nitrogen anion and Zn2. The corresponding reaction free energy barrier for the first step of lactam ring-opening reaction was calculated to be 19.2 kcal/mol. During the reaction, Q157 serves as the putative "oxyanion hole" rather than Zn1 in L1 enzyme, which was confirmed via the site-directed mutagenesis simulation of Q157A. Our theoretical studies showed some insights into the substrate binding and catalytic mechanism of the SMB-1 metallo-β-lactamase.

Crowder-Induced Conformational Ensemble Shift in Escherichia coli Prolyl-tRNA Synthetase

The effect of molecular crowding on the structure and function of Escherichia coli prolyl-transfer RNA synthetase (Ec ProRS), a member of the aminoacyl-transfer RNA synthetase family, has been investigated using a combined experimental and theoretical method. Ec ProRS is a multidomain enzyme; coupled-domain dynamics are essential for efficient catalysis. To gain insight into the mechanistic detail of the crowding effect, kinetic studies were conducted with varying concentrations and sizes of crowders. In parallel, spectroscopic and quantum chemical studies were employed to probe the "soft interactions" between crowders and protein side chains. Finally, the dynamics of the dimeric protein was examined in the presence of crowders using a long-duration (70 ns) classical molecular dynamic simulations. The results of the simulations revealed a shift in the conformational ensemble, which is consistent with the preferential exclusion of cosolutes. The "soft interactions" model of the crowding effect also explained the alteration in kinetic parameters. In summary, the study found that the effects of molecular crowding on both conformational dynamics and catalytic function are correlated in the multidomain Ec ProRS, an enzyme that is central to protein synthesis in all living cells. This study affirmed that large and small cosolutes have considerable impacts on the structure, dynamics, and function of modular proteins and therefore must be considered for stabilizing protein-based pharmaceuticals and industrial enzymes.

Spectral and Structural Variations of Biomimetic Light-Harvesting Nanotubes

Bioinspired, self-assembled nanotubes have been investigated by low-temperature, polarization-resolved single-tube spectroscopy. These assemblies are based on zinc chlorin monomers and are considered as model systems that resemble the secondary structural elements in the natural light-harvesting systems of green (non)sulfur bacteria. Compared to the natural systems, the spectral parameters extracted from the single-nanotube spectra feature distributions with significantly smaller widths, which is ascribed to a tremendous reduction of structural heterogeneity in the artificial systems. Employing quantum chemical molecular modeling the spectra of individual nanotubes can be explained consistently only for a molecular packing model that is fundamentally different from those considered so far for the natural systems. Subsequent theoretical simulations reveal that the remaining spectral variations between single nanotubes can be traced back to small variations of the mutual orientations of the monomer transition dipole moments that are far beyond the resolving power of high-resolution electron microscopy imaging techniques.

Development of Divide-and-Conquer Density-Functional Tight-Binding Method for Theoretical Research on Li-Ion Battery

The density-functional tight-binding (DFTB) method is one of the useful quantum chemical methods, which provides a good balance between accuracy and computational efficiency. In this account, we reviewed the basis of the DFTB method, the linear-scaling divide-and-conquer (DC) technique, as well as the parameterization process. We also provide some refinement, modifications, and extension of the existing parameters that can be applicable for lithium-ion battery systems. The diffusion constants of common electrolyte molecules and LiTFSA salt in solution have been estimated using DC-DFTB molecular dynamics simulation with our new parameters. The resulting diffusion constants have good agreement to the experimental diffusion constants.

Cyclic Changes in Active Site Polarization and Dynamics Drive the 'Ping-pong' Kinetics in NRH:Quinone Oxidoreductase 2: An Insight from QM/MM Simulations

Quinone reductases belong to the family of flavin-dependent oxidoreductases. With the redox active cofactor, flavin adenine dinucleotide, quinone reductases are known to utilize a 'ping-pong' kinetic mechanism during catalysis in which a hydride is bounced back and forth between flavin and its two substrates. However, the continuation of this catalytic cycle requires product displacement steps, where the product of one redox half-cycle is displaced by the substrate of the next half-cycle. Using improved hybrid quantum mechanical/molecular mechanical simulations, both the catalytic hydride transfer and the product displacement reactions were studied in NRH:quinone oxidoreductase 2. Initially, the self-consistent charge-density functional tight binding theory was used to describe flavin ring and the substrate atoms, while embedded in the molecular mechanically-treated solvated active site. Then, for each step of the catalytic cycle, a further improvement of energetics was made using density functional theory-based corrections. The present study showcases an integrated interplay of solvation, protonation, and protein matrix-induced polarization as the driving force behind the thermodynamic wheel of the 'ping-pong' kinetics. Reported here is the first-principles model of the 'ping-pong' kinetics that portrays how cyclic changes in the active site polarization and dynamics govern the oscillatory hydride transfer and product displacement in this enzyme.

Exploring the applicability of density functional tight binding to transition metal ions. Parameterization for nickel with the spin-polarized DFTB3 model

In this work, we explore the applicability and limitations of the current third order density functional tight binding (DFTB3) formalism for treating transition metal ions using nickel as an example. To be consistent with recent parameterization of DFTB3 for copper, the parametrization for nickel is conducted in a spin-polarized formulation and with orbital-resolved Hubbard parameters and their charge derivatives. The performance of the current parameter set is evaluated based on structural and energetic properties of a set of nickel-containing compounds that involve biologically relevant ligands. Qualitatively similar to findings in previous studies of copper complexes, the DFTB3 results are more reliable for nickel complexes with neutral ligands than for charged ligands; nevertheless, encouraging agreement is noted in comparison to the reference method, B3LYP/aug-cc-pVTZ, especially for structural properties, including cases that exhibit Jahn-Teller distortions; the structures also compare favorably to available X-ray data in the Cambridge Crystallographic Database for a number of nickel-containing compounds. As to limitations, we find it is necessary to use different d shell Hubbard charge derivatives for Ni(I) and Ni(II), due to the distinct electronic configurations for the nickel ion in the respective complexes, and substantial errors are observed for ligand binding energies, especially for charged ligands, d orbital splitting energies and splitting between singlet and triplet spin states for Ni(II) compounds. These observations highlight that future improvement in intra-d correlation and ligand polarization is required to enable the application of the DFTB3 model to complex transition metal ions. © 2018 Wiley Periodicals, Inc.

Catalytic mechanism of type C sialidase from Streptococcus pneumoniae: from covalent intermediate to final product

Streptococcus pneumoniae is a Gram-positive human pathogenic bacterium, which is the main cause of pneumonia and meningitis in children and the elderly. Three sialidases (or neuraminidases) encoded from Streptococcus pneumoniae could catalyze the cleavage of sialic acid linkages. This mechanism is directly connected with infection, apoptosis, and signaling, and usually considered to be one of the critical virulence factors. Type C neuraminidase (NanC) is unique because its primary product of Neu5Ac2en is considered to be an inhibitor to the other two sialidases. Experimentally, there are two different pathways for the formation mechanism of Neu5Ac2en catalyzed by NanC. In this work, a combined quantum mechanical and molecular mechanical approach was employed in all calculations. Starting from the covalent sialylated intermediate, we first examined the reaction to Neu5Ac2en and found the reaction prefers a direct proton abstraction mechanism rather than the water mediated proton abstraction mechanism. Free energy profiles can confirm that Neu5Ac2en is the major product of NanC. Functional roles of some important residues were also investigated, e.g., D315 acts as the proton acceptor during the formation of Neu5Ac2en, while the general base for the hydrolytic reaction to Neu5Ac. This study can facilitate the understanding of the catalytic mechanism of NanC and has the potential to aid in future inhibitor design studies.

QM/MM Molecular Dynamics Investigations of the Substrate Binding of Leucotriene A4 Hydrolase: Implication for the Catalytic Mechanism

LTA4H is a monozinc bifunctional enzyme which exhibits both aminopeptidase and epoxide hydrolase activities. Its dual functions in anti- and pro-inflammatory roles have attracted wide attention to the inhibitor design. In this work, we tried to construct Michaelis complexes of LTA4H with both a native peptide substrate and LTA4 molecule using combined quantum mechanics and molecular mechanics molecular dynamics simulations. First of all, the zinc ion is coordinated by H295, H299, and E318. For its aminopeptidase activity, similar to conventional peptidases, the fourth ligand to the zinc ion is suggested to be an active site water, which is further hydrogen bonded with a downstream glutamic acid, E296. For the epoxide hydrolase activity, the fourth ligand to the zinc ion is found to be an epoxy oxygen atom. The potential of mean force calculation indicates about an 8.5 kcal/mol activation barrier height for the ring-opening reaction, which will generate a metastable carbenium intermediate. Subsequent frontier molecular orbital analyses suggest that the next step would be the nucleophilic attacking reaction at the C12 atom by a water molecule activated by D375. Our simulations also analyzed functions of several important residues like R563, K565, E271, Y383, and Y378 in the binding of peptide and LTA4.

Quantum Mechanics/Molecular Mechanics Simulations Identify the Ring-Opening Mechanism of Creatininase

Creatininase catalyzes the conversion of creatinine (a biosensor for kidney function) to creatine via a two-step mechanism: water addition followed by ring opening. Water addition is common to other known cyclic amidohydrolases, but the precise mechanism for ring opening is still under debate. The proton donor in this step is either His178 or a water molecule bound to one of the metal ions, and the roles of His178 and Glu122 are unclear. Here, the two possible reaction pathways have been fully examined by means of combined quantum mechanics/molecular mechanics simulations at the SCC-DFTB/CHARMM22 level of theory. The results indicate that His178 is the main catalytic residue for the whole reaction and explain its role as proton shuttle during the ring-opening step. In the first step, His178 provides electrostatic stabilization to the gem-diolate tetrahedral intermediate. In the second step, His178 abstracts the hydroxyl proton of the intermediate and delivers it to the cyclic amide nitrogen, leading to ring opening. The latter is the rate-limiting step with a free energy barrier of 18.5 kcal/mol, in agreement with the experiment. We find that Glu122 must be protonated during the enzyme reaction, so that it can form a stable hydrogen bond with its neighboring water molecule. Simulations of the E122Q mutant showed that this replacement disrupts the H-bond network formed by three conserved residues (Glu34, Ser78, and Glu122) and water, increasing the energy barrier. Our computational studies provide a comprehensive explanation for previous structural and kinetic observations, including why the H178A mutation causes a complete loss of activity but the E122Q mutation does not.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Geometries and Electronic States of Divacancy Defect in Finite-Size Hexagonal Graphene Flakes

The geometries and electronic properties of divacancies with two kinds of structures were investigated by the first-principles (U) B3LYP/STO-3G and self-consistent-charge density-functional tight-binding (SCC-DFTB) method. Different from the reported understanding of these properties of divacancy in graphene and carbon nanotubes, it was found that the ground state of the divacancy with 585 configurations is closed shell singlet state and much more stable than the 555777 configurations in the smaller graphene flakes, which is preferred to triplet state. But when the sizes of the graphene become larger, the 555777 defects will be more stable. In addition, the spin density properties of the both configurations are studied in this paper.

Improved QM/MM Linear-Interaction Energy Model for Substrate Recognition in Zinc-Containing Metalloenzymes

One of the essential challenges in the description of receptor-drug interactions in the presence of various polyvalent cations (such as zinc, magnesium, or iron) is the accurate assessment of the electronic effects due to cofactor binding. The effects can range from partial electronic polarization of the proximal atoms in a receptor and bound substrate to long-range effects related to partial charge transfer and electronic delocalization effects between the cofactor and the drug. Here, we examine the role of the explicit account for electronic effects for a panel of small-molecule inhibitors binding to the zinc-aminopeptidase PfA-M1, an essential target for antimalarial drug development. Our study on PfA-M1:inhibitor interactions at the QM level reveals that the partial charge and proton transfer due to bound zinc ion are important mechanisms in the inhibitors' recognition and catalysis. The combination of classical MD simulations with a posteriori QM/MM corrections with novel DFTB parameters for the zinc cation and the linear-interaction energy (LIE) approach offers by far the most accurate estimates for the PfA-M1:inhibitor binding affinities, opening the door for future inhibitor design.

Insight into the kinetics and thermodynamics of the hydride transfer reactions between quinones and lumiflavin: a density functional theory study

The kinetics and equilibrium of the hydride transfer reaction between lumiflavin and a number of substituted quinones was studied using density functional theory. The impact of electron withdrawing/donating substituents on the redox potentials of quinones was studied. In addition, the role of these substituents on the kinetics of the hydride transfer reaction with lumiflavin was investigated in detail under the transition state (TS) theory assumption. The hydride transfer reactions were found to be more favorable for an electron-withdrawing substituent. The activation barrier exhibited a quadratic relationship with the driving force of these reactions as derived under the formalism of modified Marcus theory. The present study found a significant extent of electron delocalization in the TS that is stabilized by enhanced electrostatic, polarization, and exchange interactions. Analysis of geometry, bond-orders, and energetics revealed a predominant parallel (Leffler-Hammond) effect on the TS. Closer scrutiny reveals that electron-withdrawing substituents, although located on the acceptor ring, reduce the N-H bond order of the donor fragment in the precursor complex. Carried out in the gas-phase, this is the first ever report of a theoretical study of flavin's hydride transfer reactions with quinones, providing an unfiltered view of the electronic effect on the nuclear reorganization of donor-acceptor complexes.

QM/MM investigation of the catalytic mechanism of angiotensin-converting enzyme

Angiotensin-converting enzyme (ACE) converts angiotensin I to angiotensin II and degrades bradykinin and other vasoactive peptides. ACE inhibitors are used to treat diseases such as hypertension and heart failure. It is thus highly desirable to understand the catalytic mechanism of ACE, as this should facilitate the design of more powerful and selective ACE inhibitors. ACE exhibits two different active domains, the C-domain and the N-domain. In this work, we systematically investigated the inhibitor- and substrate-binding patterns in the N-domain of human ACE using a combined quantum mechanical and molecular mechanical approach. The hydrolysis of hippuryl-histidyl-leucine (HHL) as catalyzed by the N-domain of human somatic ACE was explored, and the effects of chloride ion on the overall reaction were also investigated. Two models, one with and one without a chloride ion at the first binding position, were then designed to examine the chloride dependence of inhibitor-substrate binding and the catalytic mechanism. Our calculations indicate that the hydrolysis reaction follows a stepwise general base/general acid catalysis path. The estimated mean free energy barrier height in the two models is about 15.6 kcal/mol, which agrees very well with the experimentally estimated value of 15.8 kcal/mol. Our simulations thus suggest that the N-domain is in a mixed form during ACE-catalyzed hydrolysis, with the single-chloride-ion and the double-chloride-ion forms existing simultaneously. Graphical Abstract Superposition of ACE C- and N- domains.

Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications

Semiempirical (SE) methods can be derived from either Hartree-Fock or density functional theory by applying systematic approximations, leading to efficient computational schemes that are several orders of magnitude faster than ab initio calculations. Such numerical efficiency, in combination with modern computational facilities and linear scaling algorithms, allows application of SE methods to very large molecular systems with extensive conformational sampling. To reliably model the structure, dynamics, and reactivity of biological and other soft matter systems, however, good accuracy for the description of noncovalent interactions is required. In this review, we analyze popular SE approaches in terms of their ability to model noncovalent interactions, especially in the context of describing biomolecules, water solution, and organic materials. We discuss the most significant errors and proposed correction schemes, and we review their performance using standard test sets of molecular systems for quantum chemical methods and several recent applications. The general goal is to highlight both the value and limitations of SE methods and stimulate further developments that allow them to effectively complement ab initio methods in the analysis of complex molecular systems.

Real-Time Quantum Dynamics Reveals Complex, Many-Body Interactions in Solvated Nanodroplets

Electronic excitations in the liquid phase are surprisingly rich and considerably more complex than either gas-phase or solid-state systems. While the majority of physical and biological processes take place in solvent, our understanding of nonequilibrium excited-state processes in these condensed phase environments remains far from complete. A central and long-standing issue in these solvated environments is the assessment of many-body interactions, particularly when the entire system is out of equilibrium and many quantum states participate in the overall process. Here we present a microscopic picture of solute-solvent electron dynamics and solvatochromic effects, which we uncover using a new real-time quantum dynamics approach for extremely large solvated nanodroplets. In particular, we find that a complex interplay of quantum interactions underlies our observations of solute-solvent effects, and simple macroscopic solvatochromic shifts can even be qualitatively different at the microscopic molecular level in these systems. By treating both the solvent and the solute on the same footing at a quantum-mechanical level, we demonstrate that the electron dynamics in these systems are surprisingly complex, and the emergence of many-body interactions underlies the dynamics in these solvated systems.

Zn Coordination Chemistry: Development of Benchmark Suites for Geometries, Dipole Moments, and Bond Dissociation Energies and Their Use To Test and Validate Density Functionals and Molecular Orbital Theory

We present nonrelativistic and relativistic benchmark databases (obtained by coupled cluster calculations) of 10 Zn-ligand bond distances, 8 dipole moments, and 12 bond dissociation energies in Zn coordination compounds with O, S, NH3, H2O, OH, SCH3, and H ligands. These are used to test the predictions of 39 density functionals, Hartree-Fock theory, and seven more approximate molecular orbital theories. In the nonrelativisitic case, the M05-2X, B97-2, and mPW1PW functionals emerge as the most accurate ones for this test data, with unitless balanced mean unsigned errors (BMUEs) of 0.33, 0.38, and 0.43, respectively. The best local functionals (i.e., functionals with no Hartree-Fock exchange) are M06-L and τ-HCTH with BMUEs of 0.54 and 0.60, respectively. The popular B3LYP functional has a BMUE of 0.51, only slightly better than the value of 0.54 for the best local functional, which is less expensive. Hartree-Fock theory itself has a BMUE of 1.22. The M05-2X functional has a mean unsigned error of 0.008 Å for bond lengths, 0.19 D for dipole moments, and 4.30 kcal/mol for bond energies. The X3LYP functional has a smaller mean unsigned error (0.007 Å) for bond lengths but has mean unsigned errors of 0.43 D for dipole moments and 5.6 kcal/mol for bond energies. The M06-2X functional has a smaller mean unsigned error (3.3 kcal/mol) for bond energies but has mean unsigned errors of 0.017 Å for bond lengths and 0.37 D for dipole moments. The best of the semiempirical molecular orbital theories are PM3 and PM6, with BMUEs of 1.96 and 2.02, respectively. The ten most accurate functionals from the nonrelativistic benchmark analysis are then tested in relativistic calculations against new benchmarks obtained with coupled-cluster calculations and a relativistic effective core potential, resulting in M05-2X (BMUE = 0.895), PW6B95 (BMUE = 0.90), and B97-2 (BMUE = 0.93) as the top three functionals. We find significant relativistic effects (∼0.01 Å in bond lengths, ∼0.2 D in dipole moments, and ∼4 kcal/mol in Zn-ligand bond energies) that cannot be neglected for accurate modeling, but the same density functionals that do well in all-electron nonrelativistic calculations do well with relativistic effective core potentials. Although most tests are carried out with augmented polarized triple-ζ basis sets, we also carried out some tests with an augmented polarized double-ζ basis set, and we found, on average, that with the smaller basis set DFT has no loss in accuracy for dipole moments and only ∼10% less accurate bond lengths.

Monoligand Zn(II) Complexes: Ab Initio Benchmark Calculations and Comparison with Density Functional Theory Methodologies

A systematic theoretical study on several models of Zn(II) complexes has been carried out employing both ab initio correlated wave function and density functional methods. The performance of five different functionals namely PW91, PBE, B3LYP, MPWLYP1M, and TPSS in the prediction of metal-ligand bond distances, binding energies, and proton affinities has been assessed comparing the results to those obtained with the MP2 and CCSD(T) wave function methodologies. Several basis sets ranging from double-ζ up to quintuple-ζ quality have been used, including the recently developed all-electron correlation consistent basis sets for zinc. It is shown that all the tested functionals overestimate both the metal-ligand bond distances and the binding energies, being that the B3LYP and TPSS functionals are the ones that perform the best. An analysis of the metal-ligand interaction energy shows that induction and charge-transfer effects play a prominent role in the bonding of these systems, even for those complexes with the less polarizable ligands. This finding highlights the importance of a correct description of the polarization of the monomers' charge densities by any theoretical method which aims to be applied to the study of Zn(II) complexes.

Conformational studies of dammarane-type triterpenoids using computational and NMR spectroscopic methods

Natural triterpenoids are of great interest to researchers of various fields as they possess diverse physicochemical and biological properties. In medicinal chemistry, detailed information about the chemical structures of bioactive triterpenoids often helps find new lead compounds. Herein, the low-energy structures of (20S)-protopanaxadiol and (20S)-protopanaxatriol, the aglycones of various triterpenoid saponins found in Panax ginseng, and their (20R)-epimers have been predicted by the geometry optimization of the conformers extracted from molecular dynamics simulations with the self-consistent-charge density functional tight-binding method. By performing quantum mechanical calculations on the low-energy conformers, we have estimated the NMR chemical shifts of the compounds, which display good agreement with the most recently reported experimental values within an expected range of errors. Our results indicate that theoretical estimation of the NMR parameters of a relatively large molecule with a molecular mass of 500 is feasible.

DFTB3 Parametrization for Copper: The Importance of Orbital Angular Momentum Dependence of Hubbard Parameters

We report the parametrization of a density functional tight binding method (DFTB3) for copper in a spin-polarized formulation. The parametrization is consistent with the framework of 3OB for main group elements (ONCHPS) and can be readily used for biological applications that involve copper proteins/peptides. The key to our parametrization is to introduce orbital angular momentum dependence of the Hubbard parameter and its charge derivative, thus allowing the 3d and 4s orbitals to adopt different sizes and responses to the change of charge state. The parametrization has been tested by applying to a fairly broad set of molecules of biological relevance, and the properties of interest include optimized geometries, ligand binding energies, and ligand proton affinities. Compared to the reference QM level (B3LYP/aug-cc-pVTZ, which is shown here to be similar to the B97-1 and CCSD(T) results, in terms of many properties of interest for a set of small copper containing molecules), our parametrization generally gives reliable structural properties for both Cu(I) and Cu(II) compounds, although several exceptions are also noted. For energetics, the results are more accurate for neutral ligands than for charged ligands, likely reflecting the minimal basis limitation of DFTB3; the results generally outperform NDDO based methods such as PM6 and even PBE with the 6-31+G(d,p) basis. For all ligand types, single-point B3LYP calculations at DFTB3 geometries give results very close (∼1-2 kcal/mol) to the reference B3LYP values, highlighting the consistency between DFTB3 and B3LYP structures. Possible further developments of the DFTB3 model for a better treatment of transition-metal ions are also discussed. In the current form, our first generation of DFTB3 copper model is expected to be particularly valuable as a method that drives sampling in systems that feature a dynamical copper binding site.

QM/MM simulations of amyloid-β 42 degradation by IDE in the presence and absence of ATP

The ability of the insulin-degrading enzyme (IDE) to degrade amyloid-β 42 (Aβ42), a process regulated by ATP, has been studied as an alternative path in the development of drugs against Alzheimer's disease. In this study, we calculated the potential of mean force for the degradation of Aβ42 by IDE in the presence and absence of ATP by umbrella sampling with hybrid quantum mechanics and molecular mechanics (QM/MM) calculations, using the SCC-DFTB QM Hamiltonian and Amber ff99SB force field. Results indicate that the reaction occurs in two steps: The first step is characterized by the formation of the intermediate. The second step is characterized by breaking the peptide bond of the substrate, the latter being the rate-determining step. In our simulations, the activation energy barrier in the absence of ATP is 15 ± 2 kcal mol(-1), which is 7 kcal mol(-1) lower than in the presence of ATP, indicating that the presence of the nucleotide decreases the reaction rate by about 10(5) times.

Removal of dioxane pollutants from water by using Al-doped single walled carbon nanotubes

The detection and fast enrichment of toxic organic pollutants are challenging issues in the field of environmental science.

Effect of stacking interactions on the thermodynamics and kinetics of lumiflavin: a study with improved density functionals and density functional tight-binding protocol

The π-π stacking interaction between lumiflavin and a number of π-electron-rich molecules has been studied by density functional theory using several new-generation density functionals. Six known lumiflavin-aromatic adducts were used and the models were evaluated by comparing the geometry and energetics with experimental results. The study found that dispersion-corrected and hybrid functionals with larger (>50%) Hartree-Fock exchanges produced superior results in modeling thermodynamic characteristics of these complexes. The functional producing the best energetics for these model systems was used to study the stacking interactions of lumiflavin with biologically relevant aromatic groups. Additionally, the reduction of flavin-in the presence of both a hydride donor and a nondonor π-electronic system was also studied. Weak interactions were observed in the stacked lumiflavin complexes of benzene, phenol, and indole, mimicking phenyl alanine, tryptophan, and tyrosine side chains, respectively, of an enzyme. The stacked complex of naphthalene and flavin showed little change in flavin's redox potential indicating insignificant effect on the thermodynamics of the hydride transfer reaction. In contrast, the hydride transfer reaction with the hydride donor N-methyl nicotinamide tells a different story, as the transition state was found to be strongly impacted by the stacking interactions. A comparison of performance between the density functional theory (DFT) and the computationally less expensive dispersion-corrected self-consistent density functional tight-binding (SCC-DFTB-D) theory revealed that the latter produces consistent energetics for this hydride transfer reaction and additional DFT-computed perturbative corrections could significantly improve these results.

NMR studies of active-site properties of human carbonic anhydrase II by using (15) N-labeled 4-methylimidazole as a local probe and histidine hydrogen-bond correlations

By using a combination of liquid and solid-state NMR spectroscopy, (15) N-labeled 4-methylimidazole (4-MI) as a local probe of the environment has been studied: 1) in the polar, wet Freon CDF3 /CDF2 Cl down to 130 K, 2) in water at pH 12, and 3) in solid samples of the mutant H64A of human carbonic anhydrase II (HCA II). In the latter, the active-site His64 residue is replaced by alanine; the catalytic activity is, however, rescued by the presence of 4-MI. For the Freon solution, it is demonstrated that addition of water molecules not only catalyzes proton tautomerism but also lifts its quasidegeneracy. The possible hydrogen-bond clusters formed and the mechanism of the tautomerism are discussed. Information about the imidazole hydrogen-bond geometries is obtained by establishing a correlation between published (1) H and (15) N chemical shifts of the imidazole rings of histidines in proteins. This correlation is useful to distinguish histidines embedded in the interior of proteins and those at the surface, embedded in water. Moreover, evidence is obtained that the hydrogen-bond geometries of His64 in the active site of HCA II and of 4-MI in H64A HCA II are similar. Finally, the degeneracy of the rapid tautomerism of the neutral imidazole ring His64 reported by Shimahara et al. (J. Biol. Chem.- 2007, 282, 9646) can be explained with a wet, polar, nonaqueous active-site conformation in the inward conformation, similar to the properties of 4-MI in the Freon solution. The biological implications for the enzyme mechanism are discussed.

Parametrization of DFTB3/3OB for magnesium and zinc for chemical and biological applications

We report the parametrization of the approximate density functional theory, DFTB3, for magnesium and zinc for chemical and biological applications. The parametrization strategy follows that established in previous work that parametrized several key main group elements (O, N, C, H, P, and S). This 3OB set of parameters can thus be used to study many chemical and biochemical systems. The parameters are benchmarked using both gas-phase and condensed-phase systems. The gas-phase results are compared to DFT (mostly B3LYP), ab initio (MP2 and G3B3), and PM6, as well as to a previous DFTB parametrization (MIO). The results indicate that DFTB3/3OB is particularly successful at predicting structures, including rather complex dinuclear metalloenzyme active sites, while being semiquantitative (with a typical mean absolute deviation (MAD) of ∼3–5 kcal/mol) for energetics. Single-point calculations with high-level quantum mechanics (QM) methods generally lead to very satisfying (a typical MAD of ∼1 kcal/mol) energetic properties. DFTB3/MM simulations for solution and two enzyme systems also lead to encouraging structural and energetic properties in comparison to available experimental data. The remaining limitations of DFTB3, such as the treatment of interaction between metal ions and highly charged/polarizable ligands, are also discussed.

S/G-1: an ab initio force-field blending frozen Hermite Gaussian densities and distributed multipoles. Proof of concept and first applications to metal cations

We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar response level. This opens up the possibility of embodying explicit scalar relativistic effects in molecular mechanics thanks to the direct transferability of ab initio pseudopotentials. Therefore, incorporating GEM-like electron density for a metal cation enable the introduction of nonambiguous short-range quantum effects within any point-dipole based polarizable force field without the need of an extensive parametrization.

Parameterization of DFTB3/3OB for Sulfur and Phosphorus for Chemical and Biological Applications

We report the parametrization of the approximate density functional tight binding method, DFTB3, for sulfur and phosphorus. The parametrization is done in a framework consistent with our previous 3OB set established for O, N, C, and H, thus the resulting parameters can be used to describe a broad set of organic and biologically relevant molecules. The 3d orbitals are included in the parametrization, and the electronic parameters are chosen to minimize errors in the atomization energies. The parameters are tested using a fairly diverse set of molecules of biological relevance, focusing on the geometries, reaction energies, proton affinities, and hydrogen bonding interactions of these molecules; vibrational frequencies are also examined, although less systematically. The results of DFTB3/3OB are compared to those from DFT (B3LYP and PBE), ab initio (MP2, G3B3), and several popular semiempirical methods (PM6 and PDDG), as well as predictions of DFTB3 with the older parametrization (the MIO set). In general, DFTB3/3OB is a major improvement over the previous parametrization (DFTB3/MIO), and for the majority cases tested here, it also outperforms PM6 and PDDG, especially for structural properties, vibrational frequencies, hydrogen bonding interactions, and proton affinities. For reaction energies, DFTB3/3OB exhibits major improvement over DFTB3/MIO, due mainly to significant reduction of errors in atomization energies; compared to PM6 and PDDG, DFTB3/3OB also generally performs better, although the magnitude of improvement is more modest. Compared to high-level calculations, DFTB3/3OB is most successful at predicting geometries; larger errors are found in the energies, although the results can be greatly improved by computing single point energies at a high level with DFTB3 geometries. There are several remaining issues with the DFTB3/3OB approach, most notably its difficulty in describing phosphate hydrolysis reactions involving a change in the coordination number of the phosphorus, for which a specific parametrization (3OB/OPhyd) is developed as a temporary solution; this suggests that the current DFTB3 methodology has limited transferability for complex phosphorus chemistry at the level of accuracy required for detailed mechanistic investigations. Therefore, fundamental improvements in the DFTB3 methodology are needed for a reliable method that describes phosphorus chemistry without ad hoc parameters. Nevertheless, DFTB3/3OB is expected to be a competitive QM method in QM/MM calculations for studying phosphorus/sulfur chemistry in condensed phase systems, especially as a low-level method that drives the sampling in a dual-level QM/MM framework.

Density functional tight binding

This paper reviews the basic principles of the density-functional tight-binding (DFTB) method, which is based on density-functional theory as formulated by Hohenberg, Kohn and Sham (KS-DFT). DFTB consists of a series of models that are derived from a Taylor series expansion of the KS-DFT total energy. In the lowest order (DFTB1), densities and potentials are written as superpositions of atomic densities and potentials. The Kohn-Sham orbitals are then expanded to a set of localized atom-centred functions, which are obtained for spherical symmetric spin-unpolarized neutral atoms self-consistently. The whole Hamilton and overlap matrices contain one- and two-centre contributions only. Therefore, they can be calculated and tabulated in advance as functions of the distance between atomic pairs. The second contributions to DFTB1, the DFT double counting terms, are summarized together with nuclear repulsion energy terms and can be rewritten as the sum of pairwise repulsive terms. The second-order (DFTB2) and third-order (DFTB3) terms in the energy expansion correspond to a self-consistent representation, where the deviation of the ground-state density from the reference density is represented by charge monopoles only. This leads to a computationally efficient representation in terms of atomic charges (Mulliken), chemical hardness (Hubbard) parameters and scaled Coulomb laws. Therefore, no additional adjustable parameters enter the DFTB2 and DFTB3 formalism. The handling of parameters, the efficiency, the performance and extensions of DFTB are briefly discussed.

Insights from QM/MM Modeling the 3D Structure of the 2009 H1N1 Influenza A Virus Neuraminidase and Its Binding Interactions with Antiviral Drugs

Control of drug release through the inhibition of neuraminidase-1 has been identified as a potential target for the treatment of H1N1 influenza; however, the drug binding mode of neuraminidase is not yet completely understood. In this work, we propose a model for a neuraminidase-1 complex based on four known X-ray structures of drug/neuraminidase-1 complexes. Specifically, H1N1 neuraminidase-1 complexed with 4 drugs (zanamivir, laninamivir, laninamivir octanoate and oseltamivir) was first investigated using a combined quantum mechanical and molecular mechanical (QM/MM) approach. Based on these structures, a model for the H1N1 neuraminidase-1 complex was proposed and simulated using the same computational protocol. Implications to drug/H1N1 neuraminidase-1 binding modes are discussed. From our simulations, the predicted binding free energies of the four drugs are in good agreement with the experimental results, with the correlation coefficient being 0.84.

Strictly conserved lysine of prolyl-tRNA Synthetase editing domain facilitates binding and positioning of misacylated tRNA(Pro.)

To ensure high fidelity in translation, many aminoacyl-tRNA synthetases, enzymes responsible for attaching specific amino acids to cognate tRNAs, require proof-reading mechanisms. Most bacterial prolyl-tRNA synthetases (ProRSs) misactivate alanine and employ a post-transfer editing mechanism to hydrolyze Ala-tRNA(Pro). This reaction occurs in a second catalytic site (INS) that is distinct from the synthetic active site. The 2'-OH of misacylated tRNA(Pro) and several conserved residues in the Escherichia coli ProRS INS domain are directly involved in Ala-tRNA(Pro) deacylation. Although mutation of the strictly conserved lysine 279 (K279) results in nearly complete loss of post-transfer editing activity, this residue does not directly participate in Ala-tRNA(Pro) hydrolysis. We hypothesized that the role of K279 is to bind the phosphate backbone of the acceptor stem of misacylated tRNA(Pro) and position it in the editing active site. To test this hypothesis, we carried out pKa, charge neutralization, and free-energy of binding calculations. Site-directed mutagenesis and kinetic studies were performed to verify the computational results. The calculations revealed a considerably higher pKa of K279 compared to an isolated lysine and showed that the protonated state of K279 is stabilized by the neighboring acidic residue. However, substitution of this acidic residue with a positively charged residue leads to a significant increase in Ala-tRNA(Pro) hydrolysis, suggesting that enhancement in positive charge density in the vicinity of K279 favors tRNA binding. A charge-swapping experiment and free energy of binding calculations support the conclusion that the positive charge at position 279 is absolutely necessary for tRNA binding in the editing active site.

Stabilization of different types of transition states in a single enzyme active site: QM/MM analysis of enzymes in the alkaline phosphatase superfamily

The first step for the hydrolysis of a phosphate monoester (pNPP(2-)) in enzymes of the alkaline phosphatase (AP) superfamily, R166S AP and wild-type NPP, is studied using QM/MM simulations based on an approximate density functional theory (SCC-DFTBPR) and a recently introduced QM/MM interaction Hamiltonian. The calculations suggest that similar loose transition states are involved in both enzymes, despite the fact that phosphate monoesters are the cognate substrates for AP but promiscuous substrates for NPP. The computed loose transition states are clearly different from the more synchronous ones previously calculated for diester reactions in the same AP enzymes. Therefore, our results explicitly support the proposal that AP enzymes are able to recognize and stabilize different types of transition states in a single active site. Analysis of the structural features of computed transition states indicates that the plastic nature of the bimetallic site plays a minor role in accommodating multiple types of transition states and that the high degree of solvent accessibility of the AP active site also contributes to its ability to stabilize diverse transition-state structures without the need of causing large structural distortions of the bimetallic motif. The binding mode of the leaving group in the transition state highlights that vanadate may not always be an ideal transition state analog for loose phosphoryl transfer transition states.