Fragmentation methods have been widely studied for computing quantum mechanical (QM) energy of medium-sized water clusters, but less attention has been paid to large-sized ion–water clusters, in which many-body QM interaction is more significant, because of the charge-transfer effect between ions and water molecules. In this study, we utilized electrostatically embedded generalized molecular fractionation (EE-GMF) method for full QM calculation of the large-sized ion–water clusters (up to 15 Na+ and 15 Cl– ions solvated with 119 water molecules). Through systematic validation using different fragment sizes, we show that, by using distance thresholds of 6 Å for both the two-body and three-body QM interactions, the EE-GMF method is capable of providing accurate ground-state energies of large-sized ion–water clusters at different ab initio levels (including HF, B3LYP, M06-2X, and MP2) with significantly reduced computational cost. The deviations of EE-GMF from full system calculations are within a few kcal/mol. The result clearly shows that the calculated energies of the ion–water clusters using EE-GMF are close to converge after the distance thresholds are larger than 6 Å for both the two-body and three-body QM interactions. This study underscores the importance of the three-body interactions in ion–water clusters. The EE-GMF method can also accurately reproduce the relative energy profiles of the ion–water clusters.

In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree–Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol.

The development of better approximations to the exact exchange-correlation functional is essential to the accuracy of density functionals. A recent study suggested that functionals with few parameters provide more accurate electron densities than recently developed many-parameter functionals for light closed-shell atomic systems. In this study, we calculated electron densities, their gradients, and Laplacians of Ne, Ne6+, and Ne8+ using 19 electronic structure methods, and we compared them to the CCSD reference results. Two basis sets, namely, aug-cc-pωCV5Z and aug-cc-pV5Z, are utilized in the calculations. We found that the choice of basis set has a significant impact on the errors and rankings of some of the selected methods. The errors of electron densities, their gradients, and Laplacians calculated with the aug-cc-pV5Z basis set are substantially reduced, especially for Minnesota density functionals, as compared to the results using the aug-cc-pωCV5Z basis set (a larger basis set utilized in earlier work (Medvedev et al. Science 2017, 355, 49–52)). The rankings of the M06 suite of functionals among the 19 methods are greatly improved with the aug-cc-pV5Z basis set. In addition, the performances of the HSE06, BMK, MN12-L, and MN12-SX functionals are also improved with the aug-cc-pV5Z basis set. The M06 suite of functionals is capable of providing accurate electron densities, gradients, and Laplacians using the aug-cc-pV5Z basis set, and thus it is suitable for a wide range of applications in chemistry and physics.

•Aflatoxin is one of the most toxic mycotoxins contaminating various food products. Our study provided one of the very first studies to try to find proteins that can bind strongly with the molecule using computational screening.•Our study combined target fishing, molecular docking, molecular dynamics simulation, MM/PBSA calculation, and the interaction entropy (IE) method in search for new aflatoxin B1 binding proteins. The IE method was utilized to efficiently compute entropic contribution to protein-ligand binding complexes.•Our study identified three proteins that can bind the toxin strongly. These predicted aflatoxin binding proteins can be further investigated for experimental verification with the potential to develop biosensor applications for detecting the toxin in food screening. Such detection is mandatory in government regulation.Aflatoxin is one of the mycotoxins that contaminate various food products. Among various aflatoxin types (B1, B2, G1, G2 and M1), aflatoxin B1 is the most important and the most toxic one. In this study, through computational screening, we found that several proteins may bind specifically with different type of aflatoxins. Combination of theoretical methods including target fishing, molecular docking, molecular dynamics (MD) simulation, MM/PBSA calculation were utilized to search for new aflatoxin B1 binding proteins. A recently developed method for calculating entropic contribution to binding free energy called interaction entropy (IE) was employed to compute the binding free energy between the protein and aflatoxin B1. Through comprehensive comparison, three proteins, namely, trihydroxynaphthalene reductase, GSK-3b, and Pim-1 were eventually selected as potent aflatoxin B1 binding proteins. GSK-3b and Pim-1 are drug targets of cancers or neurological diseases. GSK-3b is the strongest binder for aflatoxin B1.Download high-res image (36KB)Download full-size image

Accurate prediction of physicochemical properties of ionic liquids (ILs) is of great significance to understand and design novel ILs with unique properties. This study employed the electrostatically embedded generalized molecular fractionation (EE-GMF) method for accurate energy calculation of IL clusters. The accuracy and efficiency of the EE-GMF method are systematically assessed at different ab initio levels (including HF, DFT and MP2) with diverse basis sets. With the fixed charge model for the embedding field, the deviations of the EE-GMF approach from conventional full system calculations are within 2.58 kcal mol−1 for all IL clusters with up to 30 ion pairs (720 atoms), tested in this study. Moreover, this linear-scaling fragment quantum mechanical (QM) method can significantly reduce the total computational cost for post-HF methods. The EE-GMF approach is well-suited for studying the energetic, structural and dynamical properties of ILs using high-level ab initio theories.

The nature of the dynamical hydrogen-bond network of liquid water under ambient conditions has challenged both experimental and theoretical researchers for decades and remains a topic of intense debate. In this work, we addressed the structural issue of the hydrogen-bond network of liquid water based on an accurate ab initio molecular dynamics simulation. The present work showed clearly that liquid water is neither accurately described by a static picture of mostly tetrahedral water molecules nor dominated by “ring-and-chain” like structures. Instead, the structure of water is a dynamical mixture of tetrahedral and ‘ring-and-chain’ like structures with a slight bias toward the former. On average, each water molecule forms about three hydrogen bonds with the surrounding water molecules. The present accurate ab initio molecular dynamics simulation of liquid water was made possible by using a fragment-based second-order Møller–Plesset perturbation theory (MP2) with a large basis set to treat a large body of water molecules. This level of ab initio theory is sufficiently accurate for describing water interactions, and the simulated structural and dynamical properties of liquid water, including radial distribution functions, diffusion coefficient, dipole moment, etc., are uniformly in excellent agreement with experimental observations.

Geometry optimization and vibrational spectra (infrared and Raman spectra) calculations of proteins are carried out by a quantum chemical approach using the EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) method (J. Phys. Chem. A, 2013, 117, 7149). The first and second derivatives of the EE-GMFCC energy are derived and employed in geometry optimization and vibrational frequency calculations for several test systems, including a polypeptide ((GLY)6), an α-helix (AKA), a β-sheet (Trpzip2) and ubiquitin (76 residues with 1231 atoms). Comparison of the present results with those obtained from full system QM (quantum mechanical) calculations shows that the EE-GMFCC approach can give accurate molecular geometries, vibrational frequencies and vibrational intensities. The EE-GMFCC method is also employed to simulate the amide I vibration of proteins, which has been widely used for the analysis of peptide and protein structures, and the results are in good agreement with the experimental observations.

Improving the accuracy of scoring functions for estimating protein–ligand binding affinity is of significant interest as well as practical utility in drug discovery. In this work, PBSA_E, a new free energy estimator based on the molecular mechanics/Poisson–Boltzmann surface area (MM/PBSA) descriptors, has been developed. This free energy estimator was optimized using high-quality experimental data from a training set consisting of 145 protein–ligand complexes. The method was validated on two separate test sets containing 121 and 130 complexes. Comparison of the binding affinities predicted using the present method with those obtained using three popular scoring functions, i.e., GlideXP, GlideSP, and SYBYL_F, demonstrated that the PBSA_E method is more accurate. This new energy estimator requires a MM/PBSA calculation of the protein–ligand binding energy for a single complex configuration, which is typically obtained by optimizing the crystal structure. The present study shows that PBSA_E has the potential to become a robust tool for more reliable estimation of protein–ligand binding affinity in structure-based drug design.

•Accurate description of the conformational energies of the amino acids is essential for molecular dynamics simulation of protein structures.•In this study, the computed relative energies of trialanine at various theoretical levels, including the semiempirical methods, HF, DFT, MP2 and CCSD(T), are compared with each other.•This work demonstrates that the inclusion of the empirical London dispersion energies in HF and DFT methods consistently improves their performance over those without dispersion corrections.•Correct description of electronic correlation and dispersion energies are both important for modeling of biological systems. Considering both the accuracy and computational efficiency, the Minnesota density functional M06L-D and M062X-D are efficient and accurate for modeling of trialanine structures.•This study provides a full landscape for the screening of modern QM methods, that may be used for protein structure modeling. The current result should be of interest to a broad range of audiences in theoretical chemistry and computational biology.Accurate description of the conformational energies of the amino acids is essential for molecular dynamics simulation of protein structures. In this study, we compute the relative energies at 51 conformations for a trialanine tetrapeptide at different levels of theory. The computed energies at various theoretical levels, including the semiempirical DFTB method, HF, DFT, MP2 and CCSD(T), are compared with each other. The calculated energies from density-fitting local CCSD(T)/CBS (complete basis set) calculations are taken as the benchmark. The accuracy of the theoretical methods is highly dependent on the electronic correlation and dispersion corrections as well as the size of the basis sets. The involvement of the empirical dispersion energies in HF and DFT methods consistently improves their performance. Considering both the accuracy and computational efficiency, the Minnesota density functional M06-L-D and M06-2X-D are efficient and accurate for modeling of trialanine structures.Relationship between (a) the linear correlation coefficients (R2); (b) root-mean-square deviation (RMSD) and the computational cost (CPU time) at different QM levels (with the ADZ basis set) for 51 trialanine conformations with reference to the DF-LCCSD(T)/CBS results.

Developing ab initio molecular dynamics (AIMD) methods for practical application in protein dynamics is of significant interest. Due to the large size of biomolecules, applying standard quantum chemical methods to compute energies for dynamic simulation is computationally prohibitive. In this work, a fragment based ab initio molecular dynamics approach is presented for practical application in protein dynamics study. In this approach, the energy and forces of the protein are calculated by a recently developed electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method. For simulation in explicit solvent, mechanical embedding is introduced to treat protein interaction with explicit water molecules. This AIMD approach has been applied to MD simulations of a small benchmark protein Trpcage (with 20 residues and 304 atoms) in both the gas phase and in solution. Comparison to the simulation result using the AMBER force field shows that the AIMD gives a more stable protein structure in the simulation, indicating that quantum chemical energy is more reliable. Importantly, the present fragment-based AIMD simulation captures quantum effects including electrostatic polarization and charge transfer that are missing in standard classical MD simulations. The current approach is linear-scaling, trivially parallel, and applicable to performing the AIMD simulation of proteins with a large size.

Correction for ‘Fragment density functional theory calculation of NMR chemical shifts for proteins with implicit solvation’ by Tong Zhu et al., Phys. Chem. Chem. Phys., 2012, 14, 7837–7845.

An electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method (J. Phys. Chem. A, 2013, 117, 7149) has been successfully used for efficient linear-scaling quantum mechanical (QM) calculations of protein energies. Furthermore, an efficient approach that combined the EE-GMFCC method with a conductor-like polarizable continuum model (CPCM), termed as EE-GMFCC-CPCM (J. Chem. Phys., 2013, 139, 214104), was developed for ab initio calculations of the electrostatic solvation energy of proteins. In this study, we applied the EE-GMFCC-CPCM method for the calculation of binding affinities of 14 avidin–biotin analogues. The calculation delineated the contributions of interaction energy and electrostatic solvation energy to the binding affinity. The binding affinity of each ligand bound to avidin was calculated at the HF/6-31G* and B3LYP/6-31G* levels with empirical dispersion corrections, respectively. The correlation coefficient (R) between the calculated binding energies and experimental values is 0.75 at the HF/6-31G*-D level based on single complex structure calculations, as compared to 0.73 of the force field result. On the other hand, the correlation coefficient between the calculated binding energies and the experimental values is 0.85 at the B3LYP/6-31G*-D level based on single complex structure calculations, and this correlation can be further improved to 0.88 when multiple snapshots are considered. Our study demonstrates that the EE-GMFCC-CPCM method is capable of providing reliable predictions of binding affinities for various ligands bound to the same target.

The desire to study molecular systems that are much larger than what the current state-of-the-art ab initio or density functional theory methods could handle has naturally led to the development of novel approximate methods, including semiempirical approaches, reduced-scaling methods, and fragmentation methods. The major computational limitation of ab initio methods is the scaling problem, because the cost of ab initio calculation scales nth power or worse with system size. In the past decade, the fragmentation approach based on chemical locality has opened a new door for developing linear-scaling quantum mechanical (QM) methods for large systems and for applications to large molecular systems such as biomolecules. The fragmentation approach is highly attractive from a computational standpoint. First, the ab initio calculation of individual fragments can be conducted almost independently, which makes it suitable for massively parallel computations. Second, the electron properties, such as density and energy, are typically combined in a linear fashion to reproduce those for the entire molecular system, which makes the overall computation scale linearly with the size of the system.In this Account, two fragmentation methods and their applications to macromolecules are described. They are the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method and the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. The EE-GMFCC method is developed from the MFCC approach, which was initially used to obtain accurate protein–ligand QM interaction energies. The main idea of the MFCC approach is that a pair of conjugate caps (concaps) is inserted at the location where the subsystem is divided by cutting the chemical bond. In addition, the pair of concaps is fused to form molecular species such that the overcounted effect from added concaps can be properly removed. By introducing the electrostatic embedding field in each fragment calculation and two-body interaction energy correction on top of the MFCC approach, the EE-GMFCC method is capable of accurately reproducing the QM molecular properties (such as the dipole moment, electron density, and electrostatic potential), the total energy, and the electrostatic solvation energy from full system calculations for proteins.On the other hand, the AF-QM/MM method was used for the efficient QM calculation of protein nuclear magnetic resonance (NMR) parameters, including the chemical shift, chemical shift anisotropy tensor, and spin–spin coupling constant. In the AF-QM/MM approach, each amino acid and all the residues in its vicinity are automatically assigned as the QM region through a distance cutoff for each residue-centric QM/MM calculation. Local chemical properties of the central residue can be obtained from individual QM/MM calculations. The AF-QM/MM approach precisely reproduces the NMR chemical shifts of proteins in the gas phase from full system QM calculations. Furthermore, via the incorporation of implicit and explicit solvent models, the protein NMR chemical shifts calculated by the AF-QM/MM method are in excellent agreement with experimental values. The applications of the AF-QM/MM method may also be extended to more general biological systems such as DNA/RNA and protein–ligand complexes.

In this work, protein side chain 1H chemical shifts are used as probes to detect and correct side-chain packing errors in protein's NMR structures through structural refinement. By applying the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method for ab initio calculation of chemical shifts, incorrect side chain packing was detected in the NMR structures of the Pin1 WW domain. The NMR structure is then refined by using molecular dynamics simulation and the polarized protein-specific charge (PPC) model. The computationally refined structure of the Pin1 WW domain is in excellent agreement with the corresponding X-ray structure. In particular, the use of the PPC model yields a more accurate structure than that using the standard (nonpolarizable) force field. For comparison, some of the widely used empirical models for chemical shift calculations are unable to correctly describe the relationship between the particular proton chemical shift and protein structures. The AF-QM/MM method can be used as a powerful tool for protein NMR structure validation and structural flaw detection.

A series of molecular dynamics (MD) simulations up to 1 μs for bovine insulin monomer in different external electric fields were carried out to study the effect of external electric field on conformational integrity of insulin. Our results show that the secondary structure of insulin is kept intact under the external electric field strength below 0.15 V/nm, but disruption of secondary structure is observed at 0.25 V/nm or higher electric field strength. Although the starting time of secondary structure disruption of insulin is not clearly correlated with the strength of the external electric field ranging between 0.15 and 0.60 V/nm, long time MD simulations demonstrate that the cumulative effect of exposure time under the electric field is a major cause for the damage of insulin’s secondary structure. In addition, the strength of the external electric field has a significant impact on the lifetime of hydrogen bonds when it is higher than 0.60 V/nm. The fast evolution of some hydrogen bonds of bovine insulin in the presence of the 1.0 V/nm electric field shows that different microwaves could either speed up protein folding or destroy the secondary structure of globular proteins deponding on the intensity of the external electric field.

We have performed densisty functional theory (DFT) calculations of vicinal J coupling constants involving the backbone torsional angle for the protein GB3 using our recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach (Xiao He et al. J. Phys. Chem. B 2009, 113, 10380–10388). Interestingly, the calculated values based on an NMR structure are more accurate than those based on a high-resolution X-ray strucure because the NMR structure was refined using a large number of residual dipolar couplings (RDCs) whereas the hydrogen atoms were added into the X-ray structure in idealized positions, confirming that the postioning of the hydrogen atoms relative to the backbone atoms is important to the accuracy of J coupling constant prediction. By comparing three Karplus equations, our results have demonstrated that hydrogen bonding, substituent and electrostatic effects could have significant impacts on vicinal J couplings even though they depend mostly on the intervening dihedral angles. The root-mean-square deviations (RMSDs) of the calculated 3J(HN,Hα), 3J(HN,Cβ), 3J(HN,C′) values based on the NMR structure are 0.52, 0.25, and 0.35 Hz, respectively, after taking the dynamic effect into consideration. The excellent accuracy demonstrates that our AF-QM/MM approach is a useful tool to study the relationship between J coupling constants and the structure and dynamics of proteins.

We have performed a density functional theory (DFT) calculation of the amide proton NMR chemical shift in proteins using a recently developed automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. Systematic investigation was carried out to examine the influence of explicit solvent molecules, cooperative hydrogen bonding effects, density functionals, size of the basis sets, and the local geometry of proteins on calculated chemical shifts. Our result demonstrates that the predicted amide proton (1HN) NMR chemical shift in explicit solvent shows remarkable improvement over that calculated with the implicit solvation model. The cooperative hydrogen bonding effect is also shown to improve the accuracy of 1HN chemical shifts. Furthermore, we found that the OPBE exchange-correlation functional is the best density functional for the prediction of protein 1HN chemical shifts among a selective set of DFT methods (namely, B3LYP, B3PW91, M062X, M06L, mPW1PW91, OB98, OPBE), and the locally dense basis set of 6-311++G**/4-31G* is shown to be sufficient for 1HN chemical shift calculation. By taking ensemble averaging into account, 1HN chemical shifts calculated by the AF-QM/MM approach can be used to validate the performance of various force fields. Our study underscores that the electronic polarization of protein is of critical importance to stabilizing hydrogen bonding, and the AF-QM/MM method is able to describe the local chemical environment in proteins more accurately than most widely used empirical models.

Docking programs that use scoring functions to estimate binding affinities of small molecules to biological targets are widely applied in drug design and drug screening with partial success. But accurate and efficient scoring functions for protein–ligand binding affinity still present a grand challenge to computational chemists. In this study, the polarized protein-specific charge model (PPC) is incorporated into the molecular mechanics/Poisson–Boltzmann surface area (MM/PBSA) method to rescore the binding poses of some protein–ligand complexes, for which docking programs, such as Autodock, could not predict their binding modes correctly. Different sampling techniques (single minimized conformation and multiple molecular dynamics (MD) snapshots) are used to test the performance of MM/PBSA combined with the PPC model. Our results show the availability and effectiveness of this approach in correctly ranking the binding poses. More importantly, the bridging water molecules are found to play an important role in correctly determining the protein–ligand binding modes. Explicitly including these bridging water molecules in MM/PBSA calculations improves the prediction accuracy significantly. Our study sheds light on the importance of both bridging water molecules and the electronic polarization in the development of more reliable scoring functions for predicting molecular docking and protein–ligand binding affinity.

The electric field inside a protein has a significant effect on the protein structure, function, and dynamics. Recent experimental developments have offered a direct approach to measure the electric field by utilizing a nitrile-containing inhibitor as a probe that can deliver a unique vibration to the specific site of interest in the protein. The observed frequency shift of the nitrile stretching vibration exhibits a linear dependence on the electric field at the nitrile site, thus providing a direct measurement of the relative electric field. In the present work, molecular dynamics simulations were carried out to compute the electric field shift in human aldose reductase (hALR2) using a polarized protein-specific charge (PPC) model derived from fragment-based quantum-chemistry calculations in implicit solvent. Calculated changes of electric field in the active site of hALR2 between the wild type and mutants were directly compared with measured vibrational frequency shifts (Stark shifts). Our study demonstrates that the Stark shifts calculated using the PPC model are in much better agreement with the experimental data than widely used nonpolarizable force fields, indicating that the electronic polarization effect is important for the accurate prediction of changes in the electric field inside proteins.

An electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method is developed for efficient linear-scaling quantum mechanical (QM) calculation of protein energy. This approach is based on our previously proposed GMFCC/MM method (He; et al. J. Chem. Phys. 2006, 124, 184703), In this EE-GMFCC scheme, the total energy of protein is calculated by taking a linear combination of the QM energy of the neighboring residues and the two-body QM interaction energy between non-neighboring residues that are spatially in close contact. All the fragment calculations are embedded in a field of point charges representing the remaining protein environment, which is the major improvement over our previous GMFCC/MM approach. Numerical studies are carried out to calculate the total energies of 18 real three-dimensional proteins of up to 1142 atoms using the EE-GMFCC approach at the HF/6-31G* level. The overall mean unsigned error of EE-GMFCC for the 18 proteins is 2.39 kcal/mol with reference to the full system HF/6-31G* energies. The EE-GMFCC approach is also applied for proteins at the levels of the density functional theory (DFT) and second-order many-body perturbation theory (MP2), also showing only a few kcal/mol deviation from the corresponding full system result. The EE-GMFCC method is linear-scaling with a low prefactor, trivially parallel, and can be readily applied to routinely perform structural optimization of proteins and molecular dynamics simulation with high level ab initio electronic structure theories.

Fragment density functional theory (DFT) calculation of NMR chemical shifts for several proteins (Trp-cage, Pin1 WW domain, the third IgG-binding domain of Protein G (GB3) and human ubiquitin) has been carried out. The present study is based on a recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach but the solvent effects are included by using the PB (Poisson–Boltzmann) model. Our calculated chemical shifts of 1H and 13C for these four proteins are in excellent agreement with experimentally measured values and represent clear improvement over that from the gas phase calculation. However, although the inclusion of the solvent effect also improves the computed chemical shifts of 15N, the results do not agree with experimental values as well as 1H and 13C. Our study also demonstrates that AF-QM/MM calculated results accurately reproduce the separation of α-helical and β-sheet chemical shifts for 13Cα atoms in proteins, and using the 1H chemical shift to discriminate the native structure of proteins from decoys is quite remarkable.

Fragment density functional theory (DFT) calculation of NMR chemical shifts for several proteins (Trp-cage, Pin1 WW domain, the third IgG-binding domain of Protein G (GB3) and human ubiquitin) has been carried out. The present study is based on a recently developed automatic fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach but the solvent effects are included by using the PB (Poisson–Boltzmann) model. Our calculated chemical shifts of 1H and 13C for these four proteins are in excellent agreement with experimentally measured values and represent clear improvement over that from the gas phase calculation. However, although the inclusion of the solvent effect also improves the computed chemical shifts of 15N, the results do not agree with experimental values as well as 1H and 13C. Our study also demonstrates that AF-QM/MM calculated results accurately reproduce the separation of α-helical and β-sheet chemical shifts for 13Cα atoms in proteins, and using the 1H chemical shift to discriminate the native structure of proteins from decoys is quite remarkable.

In this work, protein side chain 1H chemical shifts are used as probes to detect and correct side-chain packing errors in protein's NMR structures through structural refinement. By applying the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) method for ab initio calculation of chemical shifts, incorrect side chain packing was detected in the NMR structures of the Pin1 WW domain. The NMR structure is then refined by using molecular dynamics simulation and the polarized protein-specific charge (PPC) model. The computationally refined structure of the Pin1 WW domain is in excellent agreement with the corresponding X-ray structure. In particular, the use of the PPC model yields a more accurate structure than that using the standard (nonpolarizable) force field. For comparison, some of the widely used empirical models for chemical shift calculations are unable to correctly describe the relationship between the particular proton chemical shift and protein structures. The AF-QM/MM method can be used as a powerful tool for protein NMR structure validation and structural flaw detection.

Correction for ‘Fragment density functional theory calculation of NMR chemical shifts for proteins with implicit solvation’ by Tong Zhu et al., Phys. Chem. Chem. Phys., 2012, 14, 7837–7845.

Geometry optimization and vibrational spectra (infrared and Raman spectra) calculations of proteins are carried out by a quantum chemical approach using the EE-GMFCC (electrostatically embedded generalized molecular fractionation with conjugate caps) method (J. Phys. Chem. A, 2013, 117, 7149). The first and second derivatives of the EE-GMFCC energy are derived and employed in geometry optimization and vibrational frequency calculations for several test systems, including a polypeptide ((GLY)6), an α-helix (AKA), a β-sheet (Trpzip2) and ubiquitin (76 residues with 1231 atoms). Comparison of the present results with those obtained from full system QM (quantum mechanical) calculations shows that the EE-GMFCC approach can give accurate molecular geometries, vibrational frequencies and vibrational intensities. The EE-GMFCC method is also employed to simulate the amide I vibration of proteins, which has been widely used for the analysis of peptide and protein structures, and the results are in good agreement with the experimental observations.

The nature of the dynamical hydrogen-bond network of liquid water under ambient conditions has challenged both experimental and theoretical researchers for decades and remains a topic of intense debate. In this work, we addressed the structural issue of the hydrogen-bond network of liquid water based on an accurate ab initio molecular dynamics simulation. The present work showed clearly that liquid water is neither accurately described by a static picture of mostly tetrahedral water molecules nor dominated by “ring-and-chain” like structures. Instead, the structure of water is a dynamical mixture of tetrahedral and ‘ring-and-chain’ like structures with a slight bias toward the former. On average, each water molecule forms about three hydrogen bonds with the surrounding water molecules. The present accurate ab initio molecular dynamics simulation of liquid water was made possible by using a fragment-based second-order Møller–Plesset perturbation theory (MP2) with a large basis set to treat a large body of water molecules. This level of ab initio theory is sufficiently accurate for describing water interactions, and the simulated structural and dynamical properties of liquid water, including radial distribution functions, diffusion coefficient, dipole moment, etc., are uniformly in excellent agreement with experimental observations.