A Fragment Quantum Mechanical Method for Metalloproteins

The density-based many-body expansion for poly-peptides and proteins

Fragmentation schemes enable the efficient quantum-chemical treatment of large biomolecular systems, and provide an ideal starting point for the development of accurate machine-learning potentials for proteins. Here, we present a fragment-based method that only uses calculations for single-amino acids and their dimers, and is able to reduce the fragmentation error in total energies to ca. 1 kJ mol-1 per amino acid for polypeptides and proteins across different structural motifs. This is achieved by combining a two-body extension of the molecular fractionation with conjugate caps (MFCC) scheme with the density-based many-body expansion (db-MBE), thus extending the applicability of the db-MBE from molecular clusters to polypeptides and proteins.

Convergent Protocols for Computing Protein-Ligand Interaction Energies Using Fragment-Based Quantum Chemistry

Fragment-based quantum chemistry methods offer a means to sidestep the steep nonlinear scaling of electronic structure calculations so that large molecular systems can be investigated using high-level methods. Here, we use fragmentation to compute protein-ligand interaction energies in systems with several thousand atoms, using a new software platform for managing fragment-based calculations that implements a screened many-body expansion. Convergence tests using a minimal-basis semiempirical method (HF-3c) indicate that two-body calculations, with single-residue fragments and simple hydrogen caps, are sufficient to reproduce interaction energies obtained using conventional supramolecular electronic structure calculations, to within 1 kcal/mol at about 1% of the computational cost. We also demonstrate that the HF-3c results are illustrative of trends obtained with density functional theory in basis sets up to augmented quadruple-ζ quality. Strategic deployment of fragmentation facilitates the use of converged biomolecular model systems alongside high-quality electronic structure methods and basis sets, bringing ab initio quantum chemistry to systems of hitherto unimaginable size. This will be useful for generation of high-quality training data for machine learning applications.

Delocalization error poisons the density-functional many-body expansion

The many-body expansion is a fragment-based approach to large-scale quantum chemistry that partitions a single monolithic calculation into manageable subsystems. This technique is increasingly being used as a basis for fitting classical force fields to electronic structure data, especially for water and aqueous ions, and for machine learning. Here, we show that the many-body expansion based on semilocal density functional theory affords wild oscillations and runaway error accumulation for ion-water interactions, typified by F-(H2O) N with N ≳ 15. We attribute these oscillations to self-interaction error in the density-functional approximation. The effect is minor or negligible in small water clusters, explaining why it has not been noticed previously, but grows to catastrophic proportion in clusters that are only moderately larger. This behavior can be counteracted with hybrid functionals but only if the fraction of exact exchange is ≳50%, whereas modern meta-generalized gradient approximations including ωB97X-V, SCAN, and SCAN0 are insufficient to eliminate divergent behavior. Other mitigation strategies including counterpoise correction, density correction (i.e., exchange-correlation functionals evaluated atop Hartree-Fock densities), and dielectric continuum boundary conditions do little to curtail the problematic oscillations. In contrast, energy-based screening to cull unimportant subsystems can successfully forestall divergent behavior. These results suggest that extreme caution is warranted when the many-body expansion is combined with density functional theory.

Protein-Ligand Interaction Energies from Quantum-Chemical Fragmentation Methods: Upgrading the MFCC-Scheme with Many-Body Contributions

Quantum-chemical fragmentation methods offer an attractive approach for the accurate calculation of protein-ligand interaction energies. While the molecular fractionation with conjugate caps (MFCC) scheme offers a rather straightforward approach for this purpose, its accuracy is often not sufficient. Here, we upgrade the MFCC scheme for the calculation of protein-ligand interactions by including many-body contributions. The resulting fragmentation scheme is an extension of our previously developed MFCC-MBE(2) scheme [J. Comput. Chem. 2023, 44, 1634-1644]. For a diverse test set of protein-ligand complexes, we demonstrate that by upgrading the MFCC scheme with many-body contributions, the error in protein-ligand interaction energies can be reduced significantly, and one generally achieves errors below 20 kJ/mol. Our scheme allows for systematically reducing these errors by including higher-order many-body contributions. As it combines the use of single amino acid fragments with high accuracy, our scheme provides an ideal starting point for the parametrization of accurate machine learning potentials for proteins and protein-ligand interactions.

Ab initio characterization of protein molecular dynamics with AI2BMD

Biomolecular dynamics simulation is a fundamental technology for life sciences research, and its usefulness depends on its accuracy and efficiency1-3. Classical molecular dynamics simulation is fast but lacks chemical accuracy4,5. Quantum chemistry methods such as density functional theory can reach chemical accuracy but cannot scale to support large biomolecules6. Here we introduce an artificial intelligence-based ab initio biomolecular dynamics system (AI2BMD) that can efficiently simulate full-atom large biomolecules with ab initio accuracy. AI2BMD uses a protein fragmentation scheme and a machine learning force field7 to achieve generalizable ab initio accuracy for energy and force calculations for various proteins comprising more than 10,000 atoms. Compared to density functional theory, it reduces the computational time by several orders of magnitude. With several hundred nanoseconds of dynamics simulations, AI2BMD demonstrated its ability to efficiently explore the conformational space of peptides and proteins, deriving accurate 3J couplings that match nuclear magnetic resonance experiments, and showing protein folding and unfolding processes. Furthermore, AI2BMD enables precise free-energy calculations for protein folding, and the estimated thermodynamic properties are well aligned with experiments. AI2BMD could potentially complement wet-lab experiments, detect the dynamic processes of bioactivities and enable biomedical research that is impossible to conduct at present.

FMOe: Preprocessing and Visualizing Package of the Fragment Molecular Orbital Method for Molecular Operating Environment and Its Applications in Covalent Ligand and Metalloprotein Analyses

The fragment molecular orbital (FMO) method is an efficient quantum chemical calculation technique for large biomolecules, dividing each into smaller fragments and providing interfragment interaction energies (IFIEs) that support our understanding of molecular recognition. The ab initio fragment MO method (ABINIT-MP), an FMO processing program, can automatically divide typical proteins and nucleic acids. In contrast, small molecules such as ligands and heterosystems must be manually divided. Thus, we developed a graphical user interface to easily handle such manual fragmentation as a library for the Molecular Operating Environment (MOE) that preprocesses and visualizes FMO calculations. We demonstrated fragmentation with IFIE analyses for the two following cases: (1) covalent cysteine-ligand bonding inside the SARS-CoV-2 main protease (Mpro) and nirmatrelvir (Paxlovid) complex and (2) the metal coordination inside a zinc-bound cyclic peptide. IFIE analysis successfully identified the key amino acid residues for the molecular recognition of nirmatrelvir with Mpro and the details of their interactions (e.g., hydrogen bonds and CH/π interactions) via ligand fragmentation of functional group units. In metalloproteins, we found an efficient and accurate scheme for the fragmentation of Zn2+ ions with four histidines coordinated to the ion. FMOe simplifies manual fragmentation, allowing users to experiment with various fragmentation patterns and perform in-depth IFIE analysis with high accuracy. In the future, our findings will provide valuable insight into complicated cases, such as ligand fragmentation in modality drug discovery, especially for medium-sized molecules and metalloprotein fragmentation around metals.

Many-Body Expansion-Based Quantum Mechanical Force Field for Cyclotrimethylene Trinitramine under High Pressure

RDX undergoes pressures of approximately 30-50 GPa during detonation, leading to significant changes in intermolecular interactions. Accurately describing these interactions is crucial for understanding the energy transfer in the detonation process. To address this, this work introduces a many-body expansion-based quantum mechanical force field (MB-QMFF) to accurately describe RDX's intermolecular interactions under high pressures. Using MB-QMFF, we evaluated various density functionals and found that the M062X functional with GD3 dispersion correction provided the highest accuracy. Regarding intermolecular forces, two-body interactions were the most significant, with three-body interactions being negligible. Additionally, we investigated intermolecular energy variations at different densities (or pressures). The results clearly demonstrate an accurate description of intermolecular interactions by the MB-QMFF scheme. Therefore, we believe that the MB-QMFF scheme can serve as a foundation for the development of RDX-specific force fields and pave the way for future studies on the detonation process of RDX.

Modeling Zinc Complexes Using Neural Networks

Understanding the energetic landscapes of large molecules is necessary for the study of chemical and biological systems. Recently, deep learning has greatly accelerated the development of models based on quantum chemistry, making it possible to build potential energy surfaces and explore chemical space. However, most of this work has focused on organic molecules due to the simplicity of their electronic structures as well as the availability of data sets. In this work, we build a deep learning architecture to model the energetics of zinc organometallic complexes. To achieve this, we have compiled a configurationally and conformationally diverse data set of zinc complexes using metadynamics to overcome the limitations of traditional sampling methods. In terms of the neural network potentials, our results indicate that for zinc complexes, partial charges play an important role in modeling the long-range interactions with a neural network. Our developed model outperforms semiempirical methods in predicting the relative energy of zinc conformers, yielding a mean absolute error (MAE) of 1.32 kcal/mol with reference to the double-hybrid PWPB95 method.

A simple and consistent quantum-chemical fragmentation scheme for proteins that includes two-body contributions

The Molecular Fractionation with Conjugate Caps (MFCC) method is a popular fragmentation method for the quantum-chemical treatment of proteins. However, it does not account for interactions between the amino acid fragments, such as intramolecular hydrogen bonding. Here, we present a combination of the MFCC fragmentation scheme with a second-order many-body expansion (MBE) that consistently accounts for all fragment-fragment, fragment-cap, and cap-cap interactions, while retaining the overall simplicity of the MFCC scheme with its chemically meaningful fragments. We show that with the resulting MFCC-MBE(2) scheme, the errors in the total energies of selected polypeptides and proteins can be reduced by up to one order of magnitude and relative energies of different protein conformers can be predicted accurately.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

Electronic structure calculations on enzymes require hundreds of atoms to obtain converged results, but fragment-based approximations offer a cost-effective solution. We present calculations on enzyme models containing 500-600 atoms using the many-body expansion, comparing to benchmarks in which the entire enzyme-substrate complex is described at the same level of density functional theory. When the amino acid fragments contain ionic side chains, the many-body expansion oscillates under vacuum boundary conditions but rapid convergence is restored using low-dielectric boundary conditions. This implies that full-system calculations in the gas phase are inappropriate benchmarks for assessing errors in fragment-based approximations. A three-body protocol retains sub-kilocalorie per mole fidelity with respect to a supersystem calculation, as does a two-body calculation combined with a full-system correction at a low-cost level of theory. These protocols pave the way for application of high-level quantum chemistry to large systems via rigorous, ab initio treatment of many-body polarization.

GPDOCK: highly accurate docking strategy for metalloproteins based on geometric probability

Accurately predicting the interaction modes for metalloproteins remains extremely challenging in structure-based drug design and mechanism analysis of enzymatic catalysis due to the complexity of metal coordination in metalloproteins. Here, we report a docking method for metalloproteins based on geometric probability (GPDOCK) with unprecedented accuracy. The docking tests of 10 common metal ions with 9360 metalloprotein-ligand complexes demonstrate that GPDOCK has an accuracy of 94.3% in predicting binding pose. What is more, it can accurately realize the docking of metalloproteins with ligand when one or two water molecules are engaged in the metal ion coordination. Since GPDOCK only depends on the three-dimensional structure of metalloprotein and ligand, structure-based machine learning model is employed for the scoring of binding poses, which significantly improves computational efficiency. The proposed docking strategy can be an effective and efficient tool for drug design and further study of binding mechanism of metalloproteins. The manual of GPDOCK and the code for the logistical regression model used to re-rank the docking results are available at https://github.com/wangkai-zhku/GPDOCK.git.

Fragmentation-Based Decomposition of a Metalloenzyme-Substrate Interaction: A Case Study for a Lytic Polysaccharide Monooxygenase

We present a novel decomposition scheme for electronic interaction energies based on the flexible formulation of fragmentation schemes through fragment combination ranges (FCRs; J. Chem. Phys., 2021, 155, 164105). We devise a clear additive decomposition with contribution of nondisjoint fragments and correction terms for overlapping fragments and apply this scheme to the metalloenzyme-substrate complex of a lytic polysaccharide monooxygenase (LPMO) with an oligosaccharide. By this, we further illustrate the straightforward adaptability of the FCR-based schemes to novel systems. Our calculations suggest that the description of the electronic structure is a larger error source than the fragmentation scheme. In particular, we find a large impact of the basis set size on the interaction energies. Still, the introduction of three-body interaction terms in the fragmentation setup improves the agreement to the supermolecular reference. Yet, the qualitative results for the decomposition scheme with two-body terms only largely agree within the investigated electronic-structure approaches and basis sets, which are B97-3c, DFT (TPSS and B3LYP), and MP2 methods. The overlap contributions are found to be small, allowing analysis of the interaction energy into individual amino acid residues: We find a particularly strong interaction between the substrate and the LPMO copper active site.

Review on the QM/MM Methodologies and Their Application to Metalloproteins

The multiscaling quantum mechanics/molecular mechanics (QM/MM) approach was introduced in 1976, while the extensive acceptance of this methodology started in the 1990s. The combination of QM/MM approach with molecular dynamics (MD) simulation, otherwise known as the QM/MM/MD approach, is a powerful and promising tool for the investigation of chemical reactions’ mechanism of complex molecular systems, drug delivery, properties of molecular devices, organic electronics, etc. In the present review, the main methodologies in the multiscaling approaches, i.e., density functional theory (DFT), semiempirical methodologies (SE), MD simulations, MM, and their new advances are discussed in short. Then, a review on calculations and reactions on metalloproteins is presented, where particular attention is given to nitrogenase that catalyzes the conversion of atmospheric nitrogen molecules N₂ into NH₃ through the process known as nitrogen fixation and the FeMo-cofactor.

Quantum Biochemical Investigation of Lys49-PLA2 from Bothrops moojeni

Envenomation via snakebites occurs largely in areas where it is harder to access the hospital. Its mortality rate and sequelae acquired by the survivors symbolize a big challenge for antivenom therapy. In particular, the homologous phospholipase A₂ (Lys49-PLA₂) proteins can induce myonecrosis and are not effectively neutralized by current treatments. Thus, by taking advantage of crystallographic structures of Bothrops moojeni Lys49-PLA₂ complexed with VRD (varespladib) and AIN (aspirin), a quantum biochemistry study based on the molecular fractionation with conjugate cap scheme within the density functional theory formalism is performed to unveil these complexes' detailed interaction energies. The calculations revealed that important interactions between ligands and the Lys49-PLA₂ pocket could occur up to a pocket radius of r = 6.5 (5.0 Å) for VRD (AIN), with the total interaction energy of the VRD ligand being higher than that of the AIN ligand, which is well-correlated with the experimental binding affinity. Furthermore, we have identified the role played by the amino acids LYS0069, LYS0049, LEU0005, ILE0009, CYS0029, GLY0030, HIS0048, PRO0018, ALA0019, CYS0045, TYR0052, TYR0022, PRO0125*, and PHE0126* (LYS0069, LYS0049, GLY0032, LEU0002, and LEU0005) in the VRD↔Lys49-PLA₂ (AIN↔Lys49-PLA₂) complex. Our simulations are a valuable tool to support the big challenge for neutralizing the damages in victims of snakebites.

Multiscale Workflow for Modeling Ligand Complexes of Zinc Metalloproteins

Zinc metalloproteins are ubiquitous, with protein zinc centers of structural and functional importance, involved in interactions with ligands and substrates and often of pharmacological interest. Biomolecular simulations are increasingly prominent in investigations of protein structure, dynamics, ligand interactions, and catalysis, but zinc poses a particular challenge, in part because of its versatile, flexible coordination. A computational workflow generating reliable models of ligand complexes of biological zinc centers would find broad application. Here, we evaluate the ability of alternative treatments, using (nonbonded) molecular mechanics (MM) and quantum mechanics/molecular mechanics (QM/MM) at semiempirical (DFTB3) and density functional theory (DFT) levels of theory, to describe the zinc centers of ligand complexes of six metalloenzyme systems differing in coordination geometries, zinc stoichiometries (mono- and dinuclear), and the nature of interacting groups (specifically the presence of zinc-sulfur interactions). MM molecular dynamics (MD) simulations can overfavor octahedral geometries, introducing additional water molecules to the zinc coordination shell, but this can be rectified by subsequent semiempirical (DFTB3) QM/MM MD simulations. B3LYP/MM geometry optimization further improved the accuracy of the description of coordination distances, with the overall effectiveness of the approach depending upon factors, including the presence of zinc-sulfur interactions that are less well described by semiempirical methods. We describe a workflow comprising QM/MM MD using DFTB3 followed by QM/MM geometry optimization using DFT (e.g., B3LYP) that well describes our set of zinc metalloenzyme complexes and is likely to be suitable for creating accurate models of zinc protein complexes when structural information is more limited.

A unified and flexible formulation of molecular fragmentation schemes

We present a flexible formulation for energy-based molecular fragmentation schemes. This framework does not only incorporate the majority of existing fragmentation expansions but also allows for flexible formulation of novel schemes. We further illustrate its application in multi-level approaches and for electronic interaction energies. For the examples of small water clusters, a small protein, and protein-protein interaction energies, we show how this flexible setup can be exploited to generate a well-suited multi-level fragmentation expansion for the given case. With such a setup, we reproduce the electronic protein-protein interaction energy of ten different structures of a neurotensin and an extracellular loop of its receptor with a mean absolute deviation to the respective super-system calculations below 1 kJ/mol.

iOI: An Iterative Orbital Interaction Approach for Solving the Self-Consistent Field Problem

An iterative orbital interaction (iOI) approach is proposed to solve, in a bottom-up fashion, the self-consistent field problem in quantum chemistry. While it belongs grossly to the family of fragment-based quantum chemical methods, iOI is distinctive in that (1) it divides and conquers not only the energy but also the wave function and that (2) the subsystem sizes are automatically determined by successively merging neighboring small subsystems until they are just enough for converging the wave function to a given accuracy. Orthonormal occupied and virtual localized molecular orbitals are obtained in a natural manner, which can be used for all post-SCF purposes.

Fragment-Based Ab Initio Molecular Dynamics Simulation for Combustion

We develop a fragment-based ab initio molecular dynamics (FB-AIMD) method for efficient dynamics simulation of the combustion process. In this method, the intermolecular interactions are treated by a fragment-based many-body expansion in which three- or higher body interactions are neglected, while two-body interactions are computed if the distance between the two fragments is smaller than a cutoff value. The accuracy of the method was verified by comparing FB-AIMD calculated energies and atomic forces of several different systems with those obtained by standard full system quantum calculations. The computational cost of the FB-AIMD method scales linearly with the size of the system, and the calculation is easily parallelizable. The method is applied to methane combustion as a benchmark. Detailed reaction network of methane reaction is analyzed, and important reaction species are tracked in real time. The current result of methane simulation is in excellent agreement with known experimental findings and with prior theoretical studies.

Exploring human porphobilinogen synthase metalloprotein by quantum biochemistry and evolutionary methods

Previous studies have shown the porphobilinogen synthase (PBGS) zinc-binding mechanism and its conservation among the living cells. However, the precise molecular interaction of zinc with the active center of the enzyme is unknown. In particular, quantum chemistry techniques within the density functional theory (DFT) framework have been the key methodology to describe metalloproteins, when one is looking for a compromise between accuracy and computational feasibility. Considering this, we used DFT-based models within the molecular fractionation with conjugate caps scheme to evaluate the binding energy features of zinc interacting with the human PBGS. Besides, phylogenetic and clustering analyses were successfully employed in extracting useful information from protein sequences to identify groups of conserved residues that build the ions-binding site. Our results also report a conservative assessment of the relevant amino acids, as well as the benchmark analysis of the calculation models used. The most relevant intermolecular interactions in Zn2+-PBGS are due to the amino acids CYS0122, CYS0124, CYS0132, ASP0169, SER0168, ARG0221, HIS0131, ASP0120, GLY0133, VAL0121, ARG0209, and ARG0174. Among these residues, we highlighted ASP0120, GLY0133, HIS0131, SER0168, and ARG0209 by co-occurring in all clusters generated by unsupervised clustering analysis. On the other hand, the triple cysteines at 2.5 Å from zinc (CYS0122, CYS0124, and CYS0132) have the highest energy attraction and are absent in the taxa Viridiplantae, Sar, Rhodophyta, and some Bacteria. Additionally, the performance of the DFT-based models shows that the processing time-dependence is more associated with the choice of the basis set than the exchange-correlation functional.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Solvent Screening in Zwitterions Analyzed with the Fragment Molecular Orbital Method

Based on induced solvent charges, a new model of solvent screening is developed in the framework of the fragment molecular orbital combined with the polarizable continuum model. The developed model is applied to analyze interactions in a prototypical zwitterionic system, sodium chloride in water, and it is shown that the large underestimation of the interaction in the original solvent screening based on local charges is successfully corrected. The model is also applied to a complex of the Trp-cage (PDB: 1L2Y ) miniprotein with an anionic ligand, and the physical factors determined protein-ligand binding in solution are unraveled.