A semiempirical method optimized for modeling proteins.

CONTEXT: In recent years, semiempirical methods such as PM6, PM6-D3H4, and PM7 have been increasingly used for modeling proteins, in particular enzymes. These methods were designed for more general use, and consequently were not optimized for studying proteins. Because of this, various specific errors have been found that could potentially cast doubt on the validity of these methods for modeling phenomena of biochemical interest such as enzyme catalytic mechanisms and protein-ligand interactions. To correct these and other errors, a new method specifically designed for use in organic and biochemical modeling has been developed. METHODS: Two alterations were made to the procedures used in developing the earlier PMx methods. A minor change was made to the theoretical framework, which affected only the non-quantum theory interatomic interaction function, while the major change involved changing the training set for optimizing parameters, moving the focus to systems of biochemical significance. This involved both the selection of reference data and the weighting factors, i.e., the relative importance that the various data were given. As a result of this change of focus, the accuracy in prediction of heats of formation, hydrogen bonding, and geometric quantities relating to non-covalent interactions in proteins was improved significantly.

Experimental and computational snapshots of C-C bond formation in a C-nucleoside synthase.

The biosynthetic enzyme, ForT, catalyses the formation of a C-C bond between 4-amino-1H-pyrazoledicarboxylic acid and MgPRPP to produce a C-nucleoside precursor of formycin A. The transformation catalysed by ForT is of chemical interest because it is one of only a few examples in which C-C bond formation takes place via an electrophilic substitution of a small, aromatic heterocycle. In addition, ForT is capable of discriminating between the aminopyrazoledicarboxylic acid and an analogue in which the amine is replaced by a hydroxyl group; a remarkable feat given the steric and electronic similarities of the two molecules. Here we report biophysical measurements, structural biology and quantum chemical calculations that provide a detailed molecular picture of ForT-catalysed C-C bond formation and the conformational changes that are coupled to catalysis. Our findings set the scene for employing engineered ForT variants in the biocatalytic production of novel, anti-viral C-nucleoside and C-nucleotide analogues.

AutoMeKin2021: An open-source program for automated reaction discovery.

AutoMeKin2021 is an updated version of tsscds2018, a program for the automated discovery of reaction mechanisms (J. Comput. Chem. 2018, 39, 1922). This release features a number of new capabilities: rare-event molecular dynamics simulations to enhance reaction discovery, extension of the original search algorithm to study van der Waals complexes, use of chemical knowledge, a new search algorithm based on bond-order time series analysis, statistics of the chemical reaction networks, a web application to submit jobs, and other features. The source code, manual, installation instructions and the website link are available at: https://rxnkin.usc.es/index.php/AutoMeKin.

An examination of the nature of localized molecular orbitals and their value in understanding various phenomena that occur in organic chemistry.

While canonical molecular orbitals have been used in computational chemistry for almost a century, the use of localized molecular orbitals is relatively new, and generating them has been difficult until recently. This has impeded their routine use in modeling chemical systems and reactions so that, even though localized molecular orbitals can now be generated easily, their usefulness in interpreting chemical phenomena has not been properly appreciated. Localized molecular orbitals can provide useful insights into chemical phenomena such as two-electron bonds, π delocalization, and lone pairs. A potentially important application would be interpreting the phenomena that occur in chemical reactions, in particular those reactions which can be described using the Lewis curly-arrow electron pushing convention. This paper considers how canonical and localized molecular orbitals are generated, their usefulness and limitations, and some issues that could be considered controversial regarding their nature, and it presents examples of the usefulness of LMOs in describing six chemical systems and one reaction.

An investigation into the applicability of the semiempirical method PM7 for modeling the catalytic mechanism in the enzyme chymotrypsin.

The catalytic cycle for the serine protease α-chymotrypsin was investigated in an attempt to determine the suitability of using the semiempirical method PM7 in the program MOPAC for investigating enzyme-catalyzed reactions. All six classical intermediates were modeled using standard methods, and were characterized as stable minima on the potential energy surface. Using a modified saddle point optimization method, five transition states were located and verified both by vibrational and by intrinsic reaction coordinate analysis. Some individual features, such as the hydrogen bonds in the oxyanion hole, the nature of various electrostatic interactions, and the role of Met192, were examined. This involved designing and running computational experiments to model mutations that would allow features of interest, in particular the energies involved, to be isolated. Three features within the enzyme were examined in detail: the reaction site itself, where covalent bonds were made and broken, the electrostatic effects of the buried aspartate anion, a passive but essential component of the catalytic triad, and the oxyanion hole, where hydrogen bonds help stabilize charged intermediates. With one minor exception, all phenomena investigated agreed with previously-reported descriptions. This result, along with the fact that all the techniques used were relatively straightforward, leads to the recommendation that PM7 and related methods, such as PM6-D3H4, are appropriate for modeling similar enzyme-catalyzed reactions. Graphical abstract Fifth of six transition states, showing water splitting into hydroxyl anion and a proton, to form the second tetrahedral intermediate and histidinium ion. Atoms of the water molecule involved in the hydrolysis are indicated by halos.

A method for predicting individual residue contributions to enzyme specificity and binding-site energies, and its application to MTH1.

A new method for predicting the energy contributions to substrate binding and to specificity has been developed. Conventional global optimization methods do not permit the subtle effects responsible for these properties to be modeled with sufficient precision to allow confidence to be placed in the results, but by making simple alterations to the model, the precisions of the various energies involved can be improved from about ±2 kcal mol-1 to ±0.1 kcal mol-1. This technique was applied to the oxidized nucleotide pyrophosphohydrolase enzyme MTH1. MTH1 is unusual in that the binding and reaction sites are well separated-an advantage from a computational chemistry perspective, as it allows the energetics involved in docking to be modeled without the need to consider any issues relating to reaction mechanisms. In this study, two types of energy terms were investigated: the noncovalent interactions between the binding site and the substrate, and those responsible for discriminating between the oxidized nucleotide 8-oxo-dGTP and the normal dGTP. Both of these were investigated using the semiempirical method PM7 in the program MOPAC. The contributions of the individual residues to both the binding energy and the specificity of MTH1 were calculated by simulating the effect of mutations. Where comparisons were possible, all calculated results were in agreement with experimental observations. This technique provides fresh insight into the binding mechanism that enzymes use for discriminating between possible substrates.

A comparison of X-ray and calculated structures of the enzyme MTH1.

Modern computational chemistry methods provide a powerful tool for use in refining the geometry of proteins determined by X-ray crystallography. Specifically, computational methods can be used to correctly place hydrogen atoms unresolved by this experimental method and improve bond geometry accuracy. Using the semiempirical method PM7, the structure of the nucleotide-sanitizing enzyme MTH1, complete with hydrolyzed substrate 8-oxo-dGMP, was optimized and the resulting geometry compared with the original X-ray structure of MTH1. After determining hydrogen atom placement and the identification of ionized sites, the charge distribution in the binding site was explored. Where comparison was possible, all the theoretical predictions were in good agreement with experimental observations. However, when these were combined with additional predictions for which experimental observations were not available, the result was a new and alternative description of the substrate-binding site interaction. An estimate was made of the strengths and weaknesses of the PM7 method for modeling proteins on varying scales, ranging from overall structure to individual interatomic distances. An attempt to correct a known fault in PM7, the under-estimation of steric repulsion, is also described. This work sheds light on the specificity of the enzyme MTH1 toward the substrate 8-oxo-dGTP; information that would facilitate drug development involving MTH1. Graphical Abstract Overlay of the backbone traces of the two MTH1 protein chains (green and orange respectively) in PDB 3ZR0 and the equivalent PM7 structures (magenta and cyan respectively) each optimized separately.

Standards-based curation of a decade-old digital repository dataset of molecular information.

BACKGROUND: The desirable curation of 158,122 molecular geometries derived from the NCI set of reference molecules together with associated properties computed using the MOPAC semi-empirical quantum mechanical method and originally deposited in 2005 into the Cambridge DSpace repository as a data collection is reported. RESULTS: The procedures involved in the curation included annotation of the original data using new MOPAC methods, updating the syntax of the CML documents used to express the data to ensure schema conformance and adding new metadata describing the entries together with a XML schema transformation to map the metadata schema to that used by the DataCite organisation. We have adopted a granularity model in which a DataCite persistent identifier (DOI) is created for each individual molecule to enable data discovery and data metrics at this level using DataCite tools. CONCLUSIONS: We recommend that the future research data management (RDM) of the scientific and chemical data components associated with journal articles (the "supporting information") should be conducted in a manner that facilitates automatic periodic curation. Graphical abstractStandards and metadata-based curation of a decade-old digital repository dataset of molecular information.

Insights into colour-tuning of chlorophyll optical response in green plants.

First-principles calculations within the framework of real-space time-dependent density functional theory have been performed for the complete chlorophyll (Chl) network of the light-harvesting complex from green plants, LHC-II. A local-dipole analysis method developed for this work has made possible the studies of the optical response of individual Chl molecules subjected to the influence of the remainder of the chromophore network. The spectra calculated using our real-space TDDFT method agree with previous suggestions that weak interaction with the protein microenvironment should produce only minor changes in the absorption spectrum of Chl chromophores in LHC-II. In addition, relative shifting of Chl absorption energies leads the stromal and lumenal sides of LHC-II to absorb in slightly different parts of the visible spectrum providing greater coverage of the available light frequencies. The site-specific alterations in Chl excitation energies support the existence of intrinsic energy transfer pathways within the LHC-II complex.

Accuracy issues involved in modeling in vivo protein structures using PM7.

Using the semiempirical method PM7, an attempt has been made to quantify the error in prediction of the in vivo structure of proteins relative to X-ray structures. Three important contributory factors are the experimental limitations of X-ray structures, the difference between the crystal and solution environments, and the errors due to PM7. The geometries of 19 proteins from the Protein Data Bank that had small R values, that is, high accuracy structures, were optimized and the resulting drop in heat of formation was calculated. Analysis of the changes showed that about 10% of this decrease in heat of formation was caused by faults in PM7, the balance being attributable to the X-ray structure and the difference between the crystal and solution environments. A previously unknown fault in PM7 was revealed during tests to validate the geometries generated using PM7. Clashscores generated by the Molprobity molecular mechanics structure validation program showed that PM7 was predicting unrealistically close contacts between nonbonding atoms in regions where the local geometry is dominated by very weak noncovalent interactions. The origin of this fault was traced to an underestimation of the core-core repulsion between atoms at distances smaller than the equilibrium distance.

An approach to creating a more realistic working model from a protein data bank entry.

An accurate model of three-dimensional protein structure is important in a variety of fields such as structure-based drug design and mechanistic studies of enzymatic reactions. While the entries in the Protein Data Bank ( http://www.pdb.org ) provide valuable information about protein structures, a small fraction of the PDB structures were found to contain anomalies not reported in the PDB file. The semiempirical PM7 method in MOPAC2012 was used for identifying anomalously short hydrogen bonds, C-H⋯O/C-H⋯N interactions, non-bonding close contacts, and unrealistic covalent bond lengths in recently published Protein Data Bank files. It was also used to generate new structures with these faults removed. When the semiempirical models were compared to those of PDB_REDO (http://www.cmbi.ru.nl/pdb_redo/), the clashscores, as defined by MolProbity ( http://molprobity.biochem.duke.edu/), were better in about 50% of the structures. The semiempirical models also had a lower root-mean-square-deviation value in nearly all cases than those from PDB_REDO, indicative of a better conservation of the tertiary structure. Finally, the semiempirical models were found to have lower clashscores than the initial PDB file in all but one case. Because this approach maintains as much of the original tertiary structure as possible while improving anomalous interactions, it should be useful to theoreticians, experimentalists, and crystallographers investigating the structure and function of proteins.

Self-consistent field convergence for proteins: a comparison of full and localized-molecular-orbital schemes.

Proteins in the gas phase present an extreme (and unrealistic) challenge for self-consistent-field iteration schemes because their ionized groups are very strong electron donors or acceptors, depending on their formal charge. This means that gas-phase proteins have a very small band gap but that their frontier orbitals are localized compared to "normal" conjugated semiconductors. The frontier orbitals are thus likely to be separated in space so that they are close to, but not quite, orthogonal during the SCF iterations. We report full SCF calculations using the massively parallel EMPIRE code and linear scaling localized-molecular-orbital (LMO) calculations using Mopac2009. The LMO procedure can lead to artificially over-polarized wavefunctions in gas-phase proteins. The full SCF iteration procedure can be very slow to converge because many cycles are needed to overcome the over-polarization by inductive charge shifts. Example molecules have been constructed to demonstrate this behavior. The two approaches give identical results if solvent effects are included.

Sparkle/PM7 Lanthanide Parameters for the Modeling of Complexes and Materials.

The recently published Parametric Method number 7, PM7, is the first semiempirical method to be successfully tested by modeling crystal structures and heats of formation of solids. PM7 is thus also capable of producing results of useful accuracy for materials science, and constitutes a great improvement over its predecessor, PM6. In this article, we present Sparkle Model parameters to be used with PM7 that allow the prediction of geometries of metal complexes and materials which contain lanthanide trications. Accordingly, we considered the geometries of 224 high-quality crystallographic structures of complexes for the parameterization set and 395 more for the validation of the parameterization for the whole lanthanide series, from La(III) to Lu(III). The average unsigned error for Sparkle/PM7 for the distances between the metal ion and its coordinating atoms is 0.063Å for all lanthanides, ranging from a minimum of 0.052Å for Tb(III) to 0.088Å for Ce(III), comparable to the equivalent errors in the distances predicted by PM7 for other metals. These distance deviations follow a gamma distribution within a 95% level of confidence, signifying that they appear to be random around a mean, confirming that Sparkle/PM7 is a well-tempered method. We conclude by carrying out a Sparkle/PM7 full geometry optimization of two spatial groups of the same thulium-containing metal organic framework, with unit cells accommodating 376 atoms, of which 16 are Tm(III) cations; the optimized geometries were in good agreement with the crystallographic ones. These results emphasize the capability of the use of the Sparkle Model for the prediction of geometries of compounds containing lanthanide trications within the PM7 semiempirical model, as well as the usefulness of such semiempirical calculations for materials modeling. Sparkle/PM7 is available in the software package MOPAC2012, at no cost for academics and can be obtained from http://openmopac.net.

Optimization of parameters for semiempirical methods VI: more modifications to the NDDO approximations and re-optimization of parameters.

Modern semiempirical methods are of sufficient accuracy when used in the modeling of molecules of the same type as used as reference data in the parameterization. Outside that subset, however, there is an abundance of evidence that these methods are of very limited utility. In an attempt to expand the range of applicability, a new method called PM7 has been developed. PM7 was parameterized using experimental and high-level ab initio reference data, augmented by a new type of reference data intended to better define the structure of parameter space. The resulting method was tested by modeling crystal structures and heats of formation of solids. Two changes were made to the set of approximations: a modification was made to improve the description of noncovalent interactions, and two minor errors in the NDDO formalism were rectified. Average unsigned errors (AUEs) in geometry and ΔHf for PM7 were reduced relative to PM6; for simple gas-phase organic systems, the AUE in bond lengths decreased by about 5% and the AUE in ΔHf decreased by about 10%; for organic solids, the AUE in ΔHf dropped by 60% and the reduction was 33.3% for geometries. A two-step process (PM7-TS) for calculating the heights of activation barriers has been developed. Using PM7-TS, the AUE in the barrier heights for simple organic reactions was decreased from values of 12.6 kcal/mol(-1) in PM6 and 10.8 kcal/mol(-1) in PM7 to 3.8 kcal/mol(-1). The origins of the errors in NDDO methods have been examined, and were found to be attributable to inadequate and inaccurate reference data. This conclusion provides insight into how these methods can be improved.

Application of the PM6 method to modeling proteins.

The applicability of the newly developed PM6 method for modeling proteins is investigated. In order to allow the geometries of such large systems to be optimized rapidly, three modifications were made to the conventional semiempirical procedure: the matrix algebra method for solving the self-consistent field (SCF) equations was replaced with a localized molecular orbital method (MOZYME), Baker's Eigenfollowing technique for geometry optimization was replaced with the L-BFGS function minimizer, and some of the integrals used in the NDDO set of approximations were replaced with point-charge and polarization functions. The resulting method was used in the unconstrained geometry optimization of 45 proteins ranging in size from a simple nonapeptide of 244 atoms to an importin consisting of 14,566 atoms. For most systems, PM6 gave structures in good agreement with the reported X-ray structures. Some derived properties, such as pKa and bulk elastic modulus, were also calculated. The applicability of PM6 to model transition states was investigated by simulating a hypothetical reaction step in the chymotrypsin-catalyzed hydrolysis of a peptide bond. A proposed technique for generating accurate protein geometries, starting with X-ray structures, was examined.

Application of the PM6 method to modeling the solid state.

The applicability of the recently developed PM6 method for modeling various properties of a wide range of organic and inorganic crystalline solids has been investigated. Although the geometries of most systems examined were reproduced with good accuracy, severe errors were found in the predicted structures of a small number of solids. The origin of these errors was investigated, and a strategy for improving the method proposed.

Optimization of parameters for semiempirical methods V: modification of NDDO approximations and application to 70 elements.

Several modifications that have been made to the NDDO core-core interaction term and to the method of parameter optimization are described. These changes have resulted in a more complete parameter optimization, called PM6, which has, in turn, allowed 70 elements to be parameterized. The average unsigned error (AUE) between calculated and reference heats of formation for 4,492 species was 8.0 kcal mol(-1). For the subset of 1,373 compounds involving only the elements H, C, N, O, F, P, S, Cl, and Br, the PM6 AUE was 4.4 kcal mol(-1). The equivalent AUE for other methods were: RM1: 5.0, B3LYP 6-31G*: 5.2, PM5: 5.7, PM3: 6.3, HF 6-31G*: 7.4, and AM1: 10.0 kcal mol(-1). Several long-standing faults in AM1 and PM3 have been corrected and significant improvements have been made in the prediction of geometries.

RM1: a reparameterization of AM1 for H, C, N, O, P, S, F, Cl, Br, and I.

Twenty years ago, the landmark AM1 was introduced, and has since had an increasingly wide following among chemists due to its consistently good results and time-tested reliability--being presently available in countless computational quantum chemistry programs. However, semiempirical molecular orbital models still are of limited accuracy and need to be improved if the full potential of new linear scaling techniques, such as MOZYME and LocalSCF, is to be realized. Accordingly, in this article we present RM1 (Recife Model 1): a reparameterization of AM1. As before, the properties used in the parameterization procedure were: heats of formation, dipole moments, ionization potentials and geometric variables (bond lengths and angles). Considering that the vast majority of molecules of importance to life can be assembled by using only six elements: C, H, N, O, P, and S, and that by adding the halogens we can now build most molecules of importance to pharmaceutical research, our training set consisted of 1736 molecules, representative of organic and biochemistry, containing C, H, N, O, P, S, F, Cl, Br, and I atoms. Unlike AM1, and similar to PM3, all RM1 parameters have been optimized. For enthalpies of formation, dipole moments, ionization potentials, and interatomic distances, the average errors in RM1, for the 1736 molecules, are less than those for AM1, PM3, and PM5. Indeed, the average errors in kcal x mol(-1) of the enthalpies of formation for AM1, PM3, and PM5 are 11.15, 7.98, and 6.03, whereas for RM1 this value is 5.77. The errors, in Debye, of the dipole moments for AM1, PM3, PM5, and RM1 are, respectively, 0.37, 0.38, 0.50, and 0.34. Likewise, the respective errors for the ionization potentials, in eV, are 0.60, 0.55, 0.48, and 0.45, and the respective errors, in angstroms, for the interatomic distances are 0.036, 0.029, 0.037, and 0.027. The RM1 average error in bond angles of 6.82 degrees is only slightly higher than the AM1 figure of 5.88 degrees, and both are much smaller than the PM3 and PM5 figures of 6.98 degrees and 9.83 degrees, respectively. Moreover, a known error in PM3 nitrogen charges is corrected in RM1. Therefore, RM1 represents an improvement over AM1 and its similar successor PM3, and is probably very competitive with PM5, which is a somewhat different model, and not fully disclosed. RM1 possesses the same analytical construct and the same number of parameters for each atom as AM1, and, therefore, can be easily implemented in any software that already has AM1, not requiring any change in any line of code, with the sole exception of the values of the parameters themselves.

A global resource for computational chemistry.

A modular distributable system has been built for high-throughput computation of molecular structures and properties. It has been used to process 250,000 compounds from the NCI database and to make the results searchable by structures and properties. The IUPAC/NIST InChI specification and algorithm has been used to index the structures and enforce integrity during computation. A number of novel features of the PM5 Hamiltonian were identified as a result of the high-throughput approach. The system and the data can be redistributed and reused and promote the value of computed data as a primary chemical resource.

Optimization of parameters for semiempirical methods IV: extension of MNDO, AM1, and PM3 to more main group elements.

The NDDO semiempirical methods MNDO, AM1, and PM3 have been extended to all the remaining non-radioactive elements of the main group, excluding the noble gases. Most of the new elements are of Groups I and II. 44 sets of parameters are presented for the following methods and elements. MNDO: Na, Mg, K, Ca, Ga, As, Se, Rb, Sr, In, Sb, Te, Cs, Ba, Tl, and Bi; AM1: Li, Be, Na, Mg, K, Ca, Ga, As, Se, Rb, Sr, In, Sn, Sb, Te, Cs, Ba, Tl, Pb, and Bi; PM3: B, Na, K, Ca, Rb, Sr, Cs, and Ba. Average errors are presented for heats of formation, molecular geometries, etc.