DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB)

Anomalous stability of graphene containing defects covered by a water layer

Defects are inevitably present in graphene and can alter its properties and thus its applications. Interestingly, we find that commonly observed Stone-Wales and double vacancy defects do not affect graphene's hydrophilic and hydrophobic properties and that an adsorbed single water layer does not noticeably affect the defect-containing graphene's electronic properties. Our findings are based on calculations using a density functional tight-binding theory. Specifically, we observe negligible alteration in the interaction strength (less than 0.1 kcal mol(-1)) between a single water layer and graphene upon the incorporation of the various types of defects, which indicates that graphene has relatively stable hydrophilic and hydrophobic properties. The presence of a single water layer causes only negligible changes in the energy gap and a small charge transfer to the aqueous layer (less than 0.1 e). The results indicate that the electronic properties of graphene are determined mainly by its own structural characteristics and are not considerably affected by the adsorbed water layer. Further electronic structure analysis reveals that the two commonly observed defects do not change the sp(2) hybridization characteristics of the C atoms of graphene even in the water environment. Our results are significant for graphene studies and applications in areas such as life sciences and materials science where hydrophilic and hydrophobic properties and electronic properties are important.

A hybrid approach to simulation of electron transfer in complex molecular systems

Electron transfer (ET) reactions in biomolecular systems represent an important class of processes at the interface of physics, chemistry and biology. The theoretical description of these reactions constitutes a huge challenge because extensive systems require a quantum-mechanical treatment and a broad range of time scales are involved. Thus, only small model systems may be investigated with the modern density functional theory techniques combined with non-adiabatic dynamics algorithms. On the other hand, model calculations based on Marcus's seminal theory describe the ET involving several assumptions that may not always be met. We review a multi-scale method that combines a non-adiabatic propagation scheme and a linear scaling quantum-chemical method with a molecular mechanics force field in such a way that an unbiased description of the dynamics of excess electron is achieved and the number of degrees of freedom is reduced effectively at the same time. ET reactions taking nanoseconds in systems with hundreds of quantum atoms can be simulated, bridging the gap between non-adiabatic ab initio simulations and model approaches such as the Marcus theory. A major recent application is hole transfer in DNA, which represents an archetypal ET reaction in a polarizable medium. Ongoing work focuses on hole transfer in proteins, peptides and organic semi-conductors.

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.

A big data approach to the ultra-fast prediction of DFT-calculated bond energies

Background

The rapid access to intrinsic physicochemical properties of molecules is highly desired for large scale chemical data mining explorations such as mass spectrum prediction in metabolomics, toxicity risk assessment and drug discovery. Large volumes of data are being produced by quantum chemistry calculations, which provide increasing accurate estimations of several properties, e.g. by Density Functional Theory (DFT), but are still too computationally expensive for those large scale uses. This work explores the possibility of using large amounts of data generated by DFT methods for thousands of molecular structures, extracting relevant molecular properties and applying machine learning (ML) algorithms to learn from the data. Once trained, these ML models can be applied to new structures to produce ultra-fast predictions. An approach is presented for homolytic bond dissociation energy (BDE).

Results

Machine learning models were trained with a data set of >12,000 BDEs calculated by B3LYP/6-311++G(d,p)//DFTB. Descriptors were designed to encode atom types and connectivity in the 2D topological environment of the bonds. The best model, an Associative Neural Network (ASNN) based on 85 bond descriptors, was able to predict the BDE of 887 bonds in an independent test set (covering a range of 17.67–202.30 kcal/mol) with RMSD of 5.29 kcal/mol, mean absolute deviation of 3.35 kcal/mol, and R² = 0.953. The predictions were compared with semi-empirical PM6 calculations, and were found to be superior for all types of bonds in the data set, except for O-H, N-H, and N-N bonds. The B3LYP/6-311++G(d,p)//DFTB calculations can approach the higher-level calculations B3LYP/6-311++G(3df,2p)//B3LYP/6-31G(d,p) with an RMSD of 3.04 kcal/mol, which is less than the RMSD of ASNN (against both DFT methods). An experimental web service for on-line prediction of BDEs is available at http://joao.airesdesousa.com/bde.

Conclusion

Knowledge could be automatically extracted by machine learning techniques from a data set of calculated BDEs, providing ultra-fast access to accurate estimations of DFT-calculated BDEs. This demonstrates how to extract value from large volumes of data currently being produced by quantum chemistry calculations at an increasing speed mostly without human intervention. In this way, high-level theoretical quantum calculations can be used in large-scale applications that otherwise would not afford the intrinsic computational cost.

A Caveat on SCC-DFTB and Noncovalent Interactions Involving Sulfur Atoms

Accurate modeling of noncovalent interactions involving sulfur today is ubiquitous, particularly with regard to the role played by sulfur-containing heterocycles in the field of organic electronics. The density functional tight binding (DFTB) method offers a good compromise between computational efficiency and accuracy, enabling the treatment of thousands of atoms at a fraction of the cost of density functional theory (DFT) evaluations. DFTB is an approximate quantum chemical approach that is based on the DFT total energy expression. Here, we address a critical issue inherent to the DFTB parametrization, which prevents the use of the DFTB framework for simulating noncovalent interactions involving sulfur atoms and precludes its combination with a dispersion correction. (1-5) Dramatic examples of structural patterns relevant to the field of organic electronics illustrate that DFTB delivers erroneous (i.e., qualitatively wrong) results involving spurious binding.

Parametrization of the SCC-DFTB Method for Halogens

Parametrization of the approximative DFT method SCC-DFTB for halogen elements is presented. The new parameter set is intended to describe halogenated organic as well as inorganic molecules, and it is compatible with the established parametrization of SCC-DFTB for carbon, hydrogen, oxygen, and nitrogen. The performance of the parameter set is tested on a representative set of molecules and discussed.

Solution NMR refinement of a metal ion bound protein using metal ion inclusive restrained molecular dynamics methods

Correctly calculating the structure of metal coordination sites in a protein during the process of nuclear magnetic resonance (NMR) structure determination and refinement continues to be a challenging task. In this study, we present an accurate and convenient means by which to include metal ions in the NMR structure determination process using molecular dynamics (MD) simulations constrained by NMR-derived data to obtain a realistic and physically viable description of the metal binding site(s). This method provides the framework to accurately portray the metal ions and its binding residues in a pseudo-bond or dummy-cation like approach, and is validated by quantum mechanical/molecular mechanical (QM/MM) MD calculations constrained by NMR-derived data. To illustrate this approach, we refine the zinc coordination complex structure of the zinc sensing transcriptional repressor protein Staphylococcus aureus CzrA, generating over 130 ns of MD and QM/MM MD NMR-data compliant sampling. In addition to refining the first coordination shell structure of the Zn(II) ion, this protocol benefits from being performed in a periodically replicated solvation environment including long-range electrostatics. We determine that unrestrained (not based on NMR data) MD simulations correlated to the NMR data in a time-averaged ensemble. The accurate solution structure ensemble of the metal-bound protein accurately describes the role of conformational sampling in allosteric regulation of DNA binding by zinc and serves to validate our previous unrestrained MD simulations of CzrA. This methodology has potentially broad applicability in the structure determination of metal ion bound proteins, protein folding and metal template protein-design studies.

Specific Reaction Path Hamiltonian for Proton Transfer in Water: Reparameterized Semiempirical Models

The semiempirical MNDO-based AM1 and PM3 methods and the orthogonalization-corrected OM1, OM2, and OM3 models were reparameterized to improve their description of bulk water and of proton transfer in water. Reference data included the gas-phase geometries and energies of the water molecule, small water clusters, the hydronium ion, and small hydronium ion-water clusters, as well as the gas-phase potential energy surface for proton transfer between the two water molecules in a Zundel ion, all calculated at the MP2/aug-cc-pVTZ level of theory. Combined QM/MM molecular dynamics simulations were carried out for bulk water and for a proton solvated in water using large cluster models. Both the authentic and reparameterized semiempirical models were employed in the simulations. The reparameterization led to significantly better results in all cases. The new set of OM3 parameters gave the best overall results for the structural and dynamic properties of water and the hydrated proton, with a small but finite barrier of 0.1-0.2 kcal/mol in the potential of mean force for proton transfer, in agreement with ab initio path-integral molecular dynamics simulations. The reparameterized OM3 model is expected to be useful for efficient modeling of proton transfer in aqueous solution.

Combined quantum mechanics/molecular mechanics (QM/MM) methods in computational enzymology

Computational enzymology is a rapidly maturing field that is increasingly integral to understanding mechanisms of enzyme-catalyzed reactions and their practical applications. Combined quantum mechanics/molecular mechanics (QM/MM) methods are important in this field. By treating the reacting species with a quantum mechanical method (i.e., a method that calculates the electronic structure of the active site) and including the enzyme environment with simpler molecular mechanical methods, enzyme reactions can be modeled. Here, we review QM/MM methods and their application to enzyme-catalyzed reactions to investigate fundamental and practical problems in enzymology. A range of QM/MM methods is available, from cheaper and more approximate methods, which can be used for molecular dynamics simulations, to highly accurate electronic structure methods. We discuss how modeling of reactions using such methods can provide detailed insight into enzyme mechanisms and illustrate this by reviewing some recent applications. We outline some practical considerations for such simulations. Further, we highlight applications that show how QM/MM methods can contribute to the practical development and application of enzymology, e.g., in the interpretation and prediction of the effects of mutagenesis and in drug and catalyst design.

A variational linear-scaling framework to build practical, efficient next-generation orbital-based quantum force fields

We introduce a new hybrid molecular orbital/density-functional modified divide-and-conquer (mDC) approach that allows the linear-scaling calculation of very large quantum systems. The method provides a powerful framework from which linear-scaling force fields for molecular simulations can be developed. The method is variational in the energy, and has simple, analytic gradients and essentially no break-even point with respect to the corresponding full electronic structure calculation. Furthermore, the new approach allows intermolecular forces to be properly balanced such that non-bonded interactions can be treated, in some cases, to much higher accuracy than the full calculation. The approach is illustrated using the second-order self-consistent charge density-functional tight-binding model (DFTB2). Using this model as a base Hamiltonian, the new mDC approach is applied to a series of water systems, where results show that geometries and interaction energies between water molecules are greatly improved relative to full DFTB2. In order to achieve substantial improvement in the accuracy of intermolecular binding energies and hydrogen bonded cluster geometries, it was necessary to extend the DFTB2 model to higher-order atom-centered multipoles for the second-order self-consistent intermolecular electrostatic term. Using generalized, linear-scaling electrostatic methods, timings demonstrate that the method is able to calculate a water system of 3000 atoms in less than half of a second, and systems of up to one million atoms in only a few minutes using a conventional desktop workstation.

A COMPARATIVE STUDY ON INTERMOLECULAR HYDROGEN BOND INTERACTIONS IN MOLECULAR DIMERS USING DIFFERENT LEVELS OF COMPUTATIONAL METHODS

Hydrogen bond interactions in biological systems are important scientific issues but are challenging for their theoretical determinations at quantum-mechanical level of theory. Due to the different approximations, the available theoretical approaches often predict diverse hydrogen bond lengths and strengths. In this work, we evaluated the reliabilities of a number of widely used theoretical approaches including HF, SVWN, BLYP, PW91, B3LYP, BH and HLYP, B97D, M06L, MP2, and DFTB-D in studying hydrogen bonding, by calculating the hydrogen bond lengths and binding energies of 23 dimers formed by HCOOH , NH3 and Glycine. We also compared the effects of STO-3G, 6-31+G**, 6-311++G** and 6-311++G(2df,2p) basis sets on the results. Our result shows that, M06L, B3LYP and BHandHLYP methods can predict accurate dimer structures with a moderate basis set. Moreover, DFTB-D also gives reasonably reliable results with high efficiency and satisfactory precision, being a good choice for studying complex structures which contain hydrogen bonds.

Energetics of zinc-mediated interactions in the allosteric pathways of metal sensor proteins

A metal-mediated interprotomer hydrogen bond has been implicated in the allosteric mechanism of DNA operator binding in several metal-sensing proteins. Using computational methods, we investigate the energetics of such zinc-mediated interactions in members of the ArsR/SmtB family of proteins (CzrA, SmtB, CadC, and NmtR) and the MarR family zinc-uptake repressor AdcR, which feature similar interactions, but in sites that differ widely in their allosteric responsiveness. We provide novel structural insight into previously uncharacterized allosteric forms of these proteins using computational methodologies. We find this metal-mediated interaction to be significantly stronger (∼8 kcal/mol) at functional allosteric metal binding sites compared to a nonresponsive site (CadC) and the apo-proteins. Simulations of the apo-proteins further reveal that the high interaction energy works to overcome the considerable disorder at these hydrogen-bonding sites and functions as a "switch" to lock in a weak DNA-binding conformation once metal is bound. These findings suggest a conserved functional role of metal-mediated second coordination shell hydrogen bonds at allosterically responsive sites in zinc-sensing transcription regulators.

Improved electronic properties from third-order SCC-DFTB with cost efficient post-SCF extensions

The present work outlines the implementation and performance of two cost efficient post-SCF extensions into the third-order SCC-DFTB code. The first one, the charge model 3 (CM3), corrects for errors in bond dipoles for an improved description of molecular charge distribution as compared to the standard Mulliken partitioning scheme. The second one focuses on the response of the charge density, that is, the electronic molecular polarizability, described inaccurately from SCC-DFTB due to the usage of a minimal atomic orbital basis. Here, a variational approach, based on scaled dipole integrals, was implemented, which clearly outperforms standard finite electric field approaches for polarizability calculations by approximately 1 order of magnitude. Both extensions in the present work rely on a set of empirical parameters, which were fitted against 112 organic molecules to match a reference data set from full density functional calculations with a large basis. As an achievement, notably improved electronic properties, that is, molecular dipole moments and polarizabilities, result from SCC-DFTB calculations at negligible additional computational cost. Furthermore, the accuracy of infrared and Raman intensities was tested as first-order derivatives of the new dipoles and polarizabilities as a function of normal mode vibrations. As a result, the current implementations cannot contribute to an improved prediction of relative intensity pattern from SCC-DFTB as compared to ab initio reference data.

A modified QM/MM Hamiltonian with the Self-Consistent-Charge Density-Functional-Tight-Binding Theory for highly charged QM regions

To improve the description of electrostatic interaction between QM and MM atoms when the QM is SCC-DFTB, we adopt a Klopman-Ohno (KO) functional form which considers the finite size of the QM and MM charge distributions. Compared to the original implementation that used a simple Coulombic interaction between QM Mulliken and MM point charges, the KO based QM/MM scheme takes charge penetration effect into consideration and therefore significantly improves the description of QM/MM interaction at short range, especially when the QM region is highly charged. To be consistent with the third-order formulation of SCC-DFTB, the Hubbard parameter in the KO functional is dependent on the QM charge. As a result, the effective size of the QM charge distribution naturally adjusts as the QM region undergoes chemical transformations, making the KO based QM/MM scheme particularly attractive for describing chemical reactions in the condensed phase. Together with the van der Waals parameters for the QM atom, the KO based QM/MM model introduces four parameters for each element type. They are fitted here based on microsolvation models of small solutes, focusing on negatively charged molecular ions, for elements O, C, H and P with a specific version of SCC-DFTB (SCC-DFTBPR). Test calculations confirm that the KO based QM/MM scheme significantly improves the interactions between QM and MM atoms over the original point charge based model and it is transferable due to the small number of parameters. The new form of QM/MM Hamiltonian will greatly improve the applicability of SCC-DFTB based QM/MM methods to problems that involve highly charged QM regions, such as enzyme catalyzed phosphoryl transfers.

Extended polarization in third-order SCC-DFTB from chemical-potential equalization

In this work, we augment the approximate density functional method SCC-DFTB (DFTB3) with the chemical-potential equalization (CPE) approach in order to improve the performance for molecular electronic polarizabilities. The CPE method, originally implemented for the NDDO type of methods by Giese and York, has been shown to significantly emend minimal basis methods with respect to the response properties and has been applied to SCC-DFTB recently. CPE allows this inherent limitation of minimal basis methods to be overcome by supplying an additional response density. The systematic underestimation is thereby corrected quantitatively without the need to extend the atomic orbital basis (i.e., without increasing the overall computational cost significantly). The dependency of polarizability as a function of the molecular charge state, especially, was significantly improved from the CPE extension of DFTB3. The empirical parameters introduced by the CPE approach were optimized for 172 organic molecules in order to match the results from density functional theory methods using large basis sets. However, the first-order derivatives of molecular polarizabilities (e.g., required to compute Raman activities) are not improved by the current CPE implementation (i.e., Raman spectra are not improved).

A Benchmark Test Suite for Proton Transfer Energies and its Use to Test Electronic Structure Model Chemistries

We present benchmark calculations of nine selected points on potential energy surfaces describing proton transfer process in three model systems, H(5)O(2) (+), CH(3)OH…H(+)…OH(2), and CH(3)COOH…OH(2). The calculated relative energies of these geometries are compared to those calculated by various wave function and density functional methods, including the polarized molecular orbital (PMO) model recently developed in our research group and other semiempirical molecular orbital methods. We found that the SCC-DFTB and PMO methods (the latter available so far only for molecules consisting of only O and H and therefore only for the first of the three model systems) give results that are, on average, within 2 kcal/mol of the benchmark results. Other semiempirical molecular orbital methods have mean unsigned errors (MUEs) of 3 to 8 kcal/mol, local density functionals have MUEs in the range 0.7 to 3.7 kcal/mol, and hybrid density functionals have MUEs of only 0.3 to 1.0 kcal/mol, with the best density functional performance obtained by hybrid meta-GGAs, especially M06 and PW6B95.

Solution structure of Mycobacterium tuberculosis NmtR in the apo state: insights into Ni(II)-mediated allostery

Mycobacterium tuberculosis is an obligate human respiratory pathogen that encodes approximately 10 arsenic repressor (ArsR) family regulatory proteins that allow the organism to respond to a wide range of changes in its immediate microenvironment. How individual ArsR repressors have evolved to respond to selective stimuli is of intrinsic interest. The Ni(II)/Co(II)-specific repressor NmtR and related actinomycete nickel sensors harbor a conserved N-terminal α-NH(2)-Gly2-His3-Gly4 sequence. Here, we present the solution structure of homodimeric apo-NmtR and show that the core of the molecule adopts a typical winged-helix ArsR repressor (α1-α2-α3-αR-β1-β2-α5) "open conformation" that is similar to that of the related zinc sensor Staphylococcus aureus CzrA, but harboring long, flexible N-terminal (residues 2-16) and C-terminal (residues 109-120) extensions. Binding of Ni(II) to the regulatory sites induces strong paramagnetic broadening of the α5 helical region and the extreme N-terminal tail to residue 10. Ratiometric pulse chase amidination mass spectrometry reveals that the rate of amidination of the α-amino group of Gly2 is strongly attenuated in the Ni(II) complex relative to the apo state and noncognate Zn(II) complex. Ni(II) binding also induces dynamic disorder on the microsecond to millisecond time scale of key DNA interacting regions that likely contributes to the negative regulation of DNA binding by Ni(II). Molecular dynamics simulations and quantum chemical calculations reveal that NmtR readily accommodates a distal Ni(II) hexacoordination model involving the α-amine and His3 of the N-terminal region and α5 residues Asp91', His93', His104, and His107, which collectively define a new metal sensing site configuration in ArsR family regulators.

Density-functional expansion methods: Grand challenges

We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian.

Simulations of allosteric motions in the zinc sensor CzrA

The zinc sensing transcriptional repressor Staphylococcus aureus CzrA represents an excellent model system to understand how metal sensor proteins maintain cellular metal homeostasis. Zn(II) binding induces a quaternary structural switch from a "closed" conformation to a more "open" conformation, reducing the DNA binding affinity by 4 orders of magnitude. In this study, we use classical molecular dynamics and quantum mechanical/molecular mechanical molecular dynamics simulations to investigate the molecular basis for the large conformational motions and allosteric coupling free energy (~6 kcal/mol) associated with Zn(II) binding. Our simulations successfully capture the closed to open allosteric switching in DNA bound CzrA on Zn(II) binding. They reveal that zinc binding quenches global conformational sampling by CzrA, whereas DNA binding enhances the mobility of residues in the allosteric metal binding sites. These findings are in close agreement with experiments. We also identify networks of residues involved in correlated and anticorrelated motions that connect the metal binding and DNA binding sites. Our analysis of the essential dynamics shows metal ion binding to be the primary driving force for the quaternary structural change in CzrA. We also show that Zn(II) binding limits the conformational space sampled by CzrA and causes the electrostatic surface potential at the DNA binding interface to become less favorable toward DNA binding. Finally, our simulations provide strong support for a proposed hydrogen-bonding pathway that physically connects the metal binding residue, His97, to the DNA binding interface through the αR helix that is present only in the Zn(II)-bound state. Overall, our simulations provide molecular-level insights into the mechanism of allosteric regulation by CzrA and demonstrate the importance of protein motion in its biological activity.

QM/MM analysis suggests that Alkaline Phosphatase (AP) and nucleotide pyrophosphatase/phosphodiesterase slightly tighten the transition state for phosphate diester hydrolysis relative to solution: implication for catalytic promiscuity in the AP superfamily

Several members of the Alkaline Phosphatase (AP) superfamily exhibit a high level of catalytic proffciency and promiscuity in structurally similar active sites. A thorough characterization of the nature of transition state for different substrates in these enzymes is crucial for understanding the molecular mechanisms that govern those remarkable catalytic properties. In this work, we study the hydrolysis of a phosphate diester, MpNPP(-), in solution, two experimentally well-characterized variants of AP (R166S AP, R166S/E322Y AP) and wild type Nucleotide pyrophosphatase/phosphodiesterase (NPP) by QM/MM calculations in which the QM method is an approximate density functional theory previously parametrized for phosphate hydrolysis (SCC-DFTBPR). The general agreements found between these calculations and available experimental data for both solution and enzymes support the use of SCC-DFTBPR/MM for a semiquantitative analysis of the catalytic mechanism and nature of transition state in AP and NPP. Although phosphate diesters are cognate substrates for NPP but promiscuous substrates for AP, the calculations suggest that their hydrolysis reactions catalyzed by AP and NPP feature similar synchronous transition states that are slightly tighter in nature compared to that in solution, due in part to the geometry of the bimetallic zinc motif. Therefore, this study provides the first direct computational support to the hypothesis that enzymes in the AP superfamily catalyze cognate and promiscuous substrates via similar transition states to those in solution. Our calculations do not support the finding of recent QM/MM studies by López-Canut and co-workers, who suggested that the same diester substrate goes through a much looser transition state in NPP/AP than in solution, a result likely biased by the large structural distortion of the bimetallic zinc site in their simulations. Finally, our calculations for different phosphate diester orientations and phosphorothioate diesters highlight that the interpretation of thio-substitution experiments is not always straightforward.

Insights into the mechanistic dichotomy of the protein farnesyltransferase peptide substrates CVIM and CVLS

Protein farnesyltransferase (FTase) catalyzes farnesylation of a variety of peptide substrates. (3)H α-secondary kinetic isotope effect (α-SKIE) measurements of two peptide substrates, CVIM and CVLS, are significantly different and have been proposed to reflect a rate-limiting S(N)2-like transition state with dissociative characteristics for CVIM, while, due to the absence of an isotope effect, CVLS was proposed to have a rate-limiting peptide conformational change. Potential of mean force quantum mechanical/molecular mechanical studies coupled with umbrella sampling techniques were performed to further probe this mechanistic dichotomy. We observe the experimentally proposed transition state (TS) for CVIM but find that CVLS has a symmetric S(N)2 TS, which is also consistent with the absence of a (3)H α-SKIE. These calculations demonstrate facile substrate-dependent alterations in the transition state structure catalyzed by FTase.

Glu-286 rotation and water wire reorientation are unlikely the gating elements for proton pumping in cytochrome C oxidase

One of the key unresolved issues regarding proton pumping in cytochrome c oxidase (CcO) is the identity of the gating element that prevents the backflow of protons. In this study, we analyze two popular proposals for this element: isomerization of the key branching residue (Glu-286) and (re)orientation of water molecules in the hydrophobic cavity. Using a multifaceted set of computational analyses that involve CcO embedded in either an implicit or explicit treatment of lipid membrane, we show that neither Glu-286 nor active-site water likely constitutes the gating element. Detailed energetic and structural analyses of the simulation results indicate that the gating-relevant properties of these structural motifs observed in previous work are likely a result of the simplified computational models employed in those studies.

Proton storage site in bacteriorhodopsin: new insights from quantum mechanics/molecular mechanics simulations of microscopic pK(a) and infrared spectra

Identifying the group that acts as the proton storage/loading site is a challenging but important problem for understanding the mechanism of proton pumping in biomolecular proton pumps, such as bacteriorhodopsin (bR) and cytochrome c oxidase. Recent experimental studies of bR propelled the idea that the proton storage/release group (PRG) in bR is not an amino acid but a water cluster embedded in the protein. We argue that this idea is at odds with our knowledge of protein electrostatics, since invoking the water cluster as the PRG would require the protein to raise the pK(a) of a hydronium by almost 11 pK(a) units, which is difficult considering known cases of pK(a) shifts in proteins. Our recent quantum mechanics/molecular mechanics (QM/MM) simulations suggested an alternative "intermolecular proton bond" model in which the stored proton is shared between two conserved Glu residues (194 and 204). Here we show that this model leads to microscopic pK(a) values consistent with available experimental data and the functional requirement of a PRG. Extensive QM/MM simulations also show that, independent of a number of technical issues, such as the influence of QM region size, starting X-ray structure, and nuclear quantum effects, the "intermolecular proton bond" model is qualitatively consistent with available spectroscopic data. Potential of mean force calculations show explicitly that the stored proton strongly prefers the pair of Glu residues over the water cluster. The results and analyses help highlight the importance of considering protein electrostatics and provide arguments for why the "intermolecular proton bond" model is likely applicable to the PRG in biomolecular proton pumps in general.

Lagrangian formulation with dissipation of Born-Oppenheimer molecular dynamics using the density-functional tight-binding method

An important element determining the time requirements of Born-Oppenheimer molecular dynamics (BOMD) is the convergence rate of the self-consistent solution of Roothaan equations (SCF). We show here that improved convergence and dynamics stability can be achieved by use of a Lagrangian formalism of BOMD with dissipation (DXL-BOMD). In the DXL-BOMD algorithm, an auxiliary electronic variable (e.g., the electron density or Fock matrix) is propagated and a dissipative force is added in the propagation to maintain the stability of the dynamics. Implementation of the approach in the self-consistent charge density functional tight-binding method makes possible simulations that are several hundred picoseconds in lengths, in contrast to earlier DFT-based BOMD calculations, which have been limited to tens of picoseconds or less. The increase in the simulation time results in a more meaningful evaluation of the DXL-BOMD method. A comparison is made of the number of iterations (and time) required for convergence of the SCF with DXL-BOMD and a standard method (starting with a zero charge guess for all atoms at each step), which gives accurate propagation with reasonable SCF convergence criteria. From tests using NVE simulations of C(2)F(4) and 20 neutral amino acid molecules in the gas phase, it is found that DXL-BOMD can improve SCF convergence by up to a factor of two over the standard method. Corresponding results are obtained in simulations of 32 water molecules in a periodic box. Linear response theory is used to analyze the relationship between the energy drift and the correlation of geometry propagation errors.

Density-functional expansion methods: generalization of the auxiliary basis

The formulation of density-functional expansion methods is extended to treat the second and higher-order terms involving the response density and spin densities with an arbitrary single-center auxiliary basis. The two-center atomic orbital products are represented by the auxiliary functions centered about those two atoms, and the mapping coefficients are determined from a local constrained variational procedure. This two-center variational procedure allows the mapping coefficients to be pretabulated and splined as a function of internuclear separation for efficient look up. The splines of mapping coefficients have a range no longer than that of the overlap integrals, and the auxiliary density appears as a single point-multipole expansion to all nonoverlapping atoms, thus allowing for the trivial implementation of a linear-scaling algorithm. The method is tested using Gaussian multipole expansions, and the effect of angular and radial completeness is explored. Several auxiliary basis sets are parametrized and compared to an auxiliary basis analogous to that used in the self-consistent-charge density-functional tight-binding model, and the method is demonstrated to greatly improve the representation of the density response with respect to a reference expansion model that does not use an auxiliary basis.

Application of the SCC-DFTB method to neutral and protonated water clusters and bulk water

The self-consistent charge density functional tight-binding (SCC-DFTB) method has been actively employed to study proton-transfer processes in biological systems. Recent studies in the literature employing SCC-DFTB reported that the method favors the Zundel form of the hydrated proton over the Eigen form, both in gas-phase water clusters and in bulk water, in disagreement with both higher-level calculations and experimental data. In this work, we explore the performance of SCC-DFTB for protonated gas-phase water clusters and bulk water (the latter both with and without an excess proton) with a modified O-H repulsive potential reported in our earlier work and with on-site third-order expansion of the DFT energy. Our results show that, with the proper set of published parameters, SCC-DFTB does correctly favor the Eigen form of the hydrated proton as compared to the Zundel form, both in gas-phase clusters and in the bulk; the amphiphilic character of the hydrated proton discussed in the literature has also been observed. The analyses do, however, bring forth remaining limitations in terms of the solvation structure around the hydrated proton as well as the structure of bulk water, which can guide future improvements of the method.