Development of the four-body corrected fragment molecular orbital (FMO4) method

Combining the Fragment Molecular Orbital and GRID Approaches for the Prediction of Ligand-Metalloenzyme Binding Affinity: The Case Study of hCA II Inhibitors

Polarization and charge-transfer interactions play an important role in ligand-receptor complexes containing metals, and only quantum mechanics methods can adequately describe their contribution to the binding energy. In this work, we selected a set of benzenesulfonamide ligands of human Carbonic Anhydrase II (hCA II)-an important druggable target containing a Zn2+ ion in the active site-as a case study to predict the binding free energy in metalloprotein-ligand complexes and designed specialized computational methods that combine the ab initio fragment molecular orbital (FMO) method and GRID approach. To reproduce the experimental binding free energy in these systems, we adopted a machine-learning approach, here named formula generator (FG), considering different FMO energy terms, the hydrophobic interaction energy (computed by GRID) and logP. The main advantage of the FG approach is that it can find nonlinear relations between the energy terms used to predict the binding free energy, explicitly showing their mathematical relation. This work showed the effectiveness of the FG approach, and therefore, it might represent an important tool for the development of new scoring functions. Indeed, our scoring function showed a high correlation with the experimental binding free energy (R2 = 0.76-0.95, RMSE = 0.34-0.18), revealing a nonlinear relation between energy terms and highlighting the relevant role played by hydrophobic contacts. These results, along with the FMO characterization of ligand-receptor interactions, represent important information to support the design of new and potent hCA II inhibitors.

How E-, L-, and P-Selectins Bind to sLex and PSGL-1: A Quantification of Critical Residue Interactions

Selectins and their ability to interact with specific ligands are a cornerstone in cell communication. Over the last three decades, a considerable wealth of experimental and molecular modeling insights into their structure and modus operandi were gathered. Nonetheless, explaining the role of individual selectin residues on a quantitative level remained elusive, despite its importance in understanding the structure-function relationship in these molecules and designing their inhibitors. This work explores essential interactions of selectin-ligand binding, employing a multiscale approach that combines molecular dynamics, quantum-chemical calculations, and residue interaction network models. Such an approach successfully reproduces most of the experimental findings. It proves to be helpful, with the potential for becoming an established tool for quantitative predictions of residue contribution to the binding of biomolecular complexes. The results empower us to quantify the importance of particular residues and functional groups in the protein-ligand interface and to pinpoint differences in molecular recognition by the three selectins. We show that mutations in the E-, L-, and P-selectins, e.g., different residues in positions 46, 85, 97, and 107, present a crucial difference in how the ligand is engaged. We assess the role of sulfation of tyrosine residues in PSGL-1 and suggest that TyrSO3- in position 51 interacting with Arg85 in P-selectin is a significant factor in the increased affinity of P-selectin to PSGL-1 compared to E- and L-selectins. We propose an original pharmacophore targeting five essential PSGL-binding sites based on the analysis of the selectin···PSGL-1 interactions.

Discovery of Novel Substrate-Competitive Lysine Methyltransferase G9a Inhibitors as Anticancer Agents

Identification of structurally novel inhibitors of lysine methyltransferase G9a has been a subject of intense research in cancer epigenetics. Starting with the high-throughput screening (HTS) hit rac-10a obtained from the chemical library of the University of Tokyo Drug Discovery Initiative, the structure-activity relationship of the unique substrate-competitive inhibitors was established with the help of X-ray crystallography and fragment molecular orbital (FMO) calculations for the ligand-protein interaction. Further optimization of the in vitro characteristics and drug metabolism and pharmacokinetics (DMPK) properties led to the identification of 26j (RK-701), which is a structurally distinct potent inhibitor of G9a/GLP (IC50 = 27/53 nM). Compound 26j exhibited remarkable selectivity against other related methyltransferases, dose-dependent attenuation of cellular H3K9me2 levels, and tumor growth inhibition in MOLT-4 cells in vitro. Moreover, compound 26j showed inhibition of tumor initiation and growth in a carcinogen-induced hepatocellular carcinoma (HCC) in vivo mouse model without overt acute toxicity.

Parametrized quantum-mechanical approaches combined with the fragment molecular orbital method

Fast parameterized methods such as density-functional tight-binding (DFTB) facilitate realistic calculations of large molecular systems, which can be accelerated by the fragment molecular orbital (FMO) method. Fragmentation facilitates interaction analyses between functional parts of molecular systems. In addition to DFTB, other parameterized methods combined with FMO are also described. Applications of FMO methods to biochemical and inorganic systems are reviewed.

An Embedded Fragment Method for Molecules in Strong Magnetic Fields

An extension of the embedded fragment method for calculations on molecular clusters is presented, which includes strong external magnetic fields. The approach is flexible, allowing for calculations at the Hartree-Fock, current-density-functional theory, Møller-Plesset perturbation theory, and coupled-cluster levels using London atomic orbitals. For systems consisting of discrete molecular subunits, calculations using London atomic orbitals can be performed in a computationally tractable manner for systems beyond the reach of conventional calculations, even those accelerated by resolution-of-the-identity or Cholesky decomposition methods. To assess the applicability of the approach, applications to water clusters are presented, showing how strong magnetic fields enhance binding within the clusters. However, our calculations suggest that, contrary to previous suggestions in the literature, this enhanced binding may not be directly attributable to strengthening of hydrogen bonding. Instead, these results suggest that this arises for larger field strengths as a response of the system to the presence of the external field, which induces a charge density build up between the monomer units. The approach is embarrassingly parallel and its computational tractability is demonstrated for clusters of up to 103 water molecules in triple-ζ basis sets, which would correspond to conventional calculations with more than 12 000 basis functions.

The FMO2 analysis of the ligand-receptor binding energy: the Biscarbene-Gold(I)/DNA G-Quadruplex case study

In this work, the ab initio fragment molecular orbital (FMO) method was applied to calculate and analyze the binding energy of two biscarbene-Au(I) derivatives, [Au(9-methylcaffein-8-ylidene)₂]⁺ and [Au(1,3-dimethylbenzimidazol-2-ylidene)₂]⁺, to the DNA G-Quadruplex structure. The FMO2 binding energy considers the ligand-receptor complex as well as the isolated forms of energy-minimum state of ligand and receptor, providing a better description of ligand-receptor affinity compared with simple pair interaction energies (PIE). Our results highlight important features of the binding process of biscarbene-Au(I) derivatives to DNA G-Quadruplex, indicating that the total deformation-polarization energy and desolvation penalty of the ligands are the main terms destabilizing the binding. The pair interaction energy decomposition analysis (PIEDA) between ligand and nucleobases suggest that the main interaction terms are electrostatic and charge-transfer energies supporting the hypothesis that Au(I) ion can be involved in π-cation interactions further stabilizing the ligand-receptor complex. Moreover, the presence of polar groups on the carbene ring, as C = O, can improve the charge-transfer interaction with K⁺ ion. These findings can be employed to design new powerful biscarbene-Au(I) DNA-G quadruplex binders as promising anticancer drugs. The procedure described in this work can be applied to investigate any ligand-receptor system and is particularly useful when the binding process is strongly characterized by polarization, charge-transfer and dispersion interactions, properly evaluated by ab initio methods.

pyProGA-A PyMOL plugin for protein residue network analysis

The field of protein residue network (PRN) research has brought several useful methods and techniques for structural analysis of proteins and protein complexes. Many of these are ripe and ready to be used by the proteomics community outside of the PRN specialists. In this paper we present software which collects an ensemble of (network) methods tailored towards the analysis of protein-protein interactions (PPI) and/or interactions of proteins with ligands of other type, e.g. nucleic acids, oligosaccharides etc. In parallel, we propose the use of the network differential analysis as a method to identify residues mediating key interactions between proteins. We use a model system, to show that in combination with other, already published methods, also included in pyProGA, it can be used to make such predictions. Such extended repertoire of methods allows to cross-check predictions with other methods as well, as we show here. In addition, the possibility to construct PRN models from various kinds of input is so far a unique asset of our code. One can use structural data as defined in PDB files and/or from data on residue pair interaction energies, either from force-field parameters or fragment molecular orbital (FMO) calculations. pyProGA is a free open-source software available from https://gitlab.com/Vlado_S/pyproga.

Energy-based automatic determination of buffer region in the divide-and-conquer second-order Møller-Plesset perturbation theory

In the linear‐scaling divide‐and‐conquer (DC) electronic structure method, each subsystem is calculated together with the neighboring buffer region, the size of which affects the energy error introduced by the fragmentation in the DC method. The DC self‐consistent field calculation utilizes a scheme to automatically determine the appropriate buffer region that is as compact as possible for reducing the computational time while maintaining acceptable accuracy (J. Comput. Chem. 2018, 39, 909). To extend the automatic determination scheme of the buffer region to the DC second‐order Møller–Plesset perturbation (MP2) calculation, a scheme for estimating the subsystem MP2 correlation energy contribution from each atom in the buffer region is proposed. The estimation is based on the atomic orbital Laplace MP2 formalism. Based on this, an automatic buffer determination scheme for the DC‐MP2 calculation is constructed and its performance for several types of systems is assessed.

Structural Basis of Activin Receptor-Like Kinase 2 (R206H) Inhibition by Bis-heteroaryl Pyrazole-Based Inhibitors for the Treatment of Fibrodysplasia Ossificans Progressiva Identified by the Integration of Ligand-Based and Structure-Based Drug Design Approaches

Fibrodysplasia ossificans progressiva (FOP) is a rare but severe genetic disorder in which acute inflammation elicits progressive heterotopic ossification in the muscles, tendons, and ligaments. Classic FOP is caused by the R206H mutation in ALK2/ACVR1. While several activin receptor-like kinase 2 (ALK2) inhibitors were found to be efficacious in animal models of FOP, most of the ALK2 (R206H) inhibitors lacked sufficient oral bioavailability for efficacy. Previously, the synthesis of a series of novel bis-heteroaryl pyrazole-based ALK2 (R206H) inhibitors that achieved both substantial potency and an improved ADMET profile was reported. In the present study, the detailed procedure of the in silico approach employed to identify the initial bis-heteroaryl pyrazole-based ALK2 (R206H) inhibitor RK-59638 and the analysis of the ALK2 (R206H) RK-59638 complex structure to guide the synthetic optimization of the chemical series, obtaining RK-71807 showing improved potency and metabolic stability, were described. According to the initial in silico screening, the screening efficiencies and chemical diversity of the hit compounds of both ligand-based and structure-based methods were evaluated. Then, X-ray structures of ALK2 (R206H) and the inhibitors were analyzed to assess the structure-activity relationships of the synthesized compounds. The 3D-RISM analysis indicated the existence of the additional hydrogen bond via water molecules restricting the attachment point in the pyrazole scaffold. The quantum mechanics calculation of the newly determined ALK2 (R206H) RK-71807 complex structure using a fragment molecular orbital method and pair interaction energy decomposition analysis was employed to evaluate the interaction energies between the inhibitor and each of the amino acid residues and decompose them to electrostatic, exchange-repulsion, and charge transfer energies. The pattern of decomposed interaction energies was then compared to that formed by RK-59638 and LDN-193189 to investigate the structural basis of ALK2 (R206H) inhibition.

Fragmentation at sp2 carbon atoms in fragment molecular orbital method

In the fragment molecular orbital (FMO) method, a given molecular system is usually fragmented at sp³ carbon atoms. However, fragmentation at different sites sometimes becomes necessary. Hence, we propose fragmentation at sp² carbon atoms in the FMO method. Projection operators are constructed using sp² local orbitals. To maintain practical accuracy, it is essential to consider the three-body effect. In order to suppress the corresponding increase of computational cost, we propose approximate models considering local trimers. Numerical verification shows that the present models are as accurate as or better than the standard FMO2 method in total energy with fragmentation at sp³ carbon atoms.

Analyzing Interactions with the Fragment Molecular Orbital Method

Basic concepts in the analysis of binding using the fragment molecular orbital method are discussed at length: polarization, desolvation, and interaction. The components in the pair interaction energy decomposition analysis are introduced, and the analysis is illustrated for a water dimer and a protein-ligand complex.

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.

Variational Formulation of the Generalized Many-Body Expansion with Self-Consistent Charge Embedding: Simple and Correct Analytic Energy Gradient for Fragment-Based ab Initio Molecular Dynamics

The many-body expansion (MBE) and its extension to overlapping fragments, the generalized (G)MBE, constitute the theoretical basis for most fragment-based approaches for large-scale quantum chemistry. We reformulate the GMBE for use with embedding charges determined self-consistently from the fragment wave functions, in a manner that preserves the variational nature of the underlying self-consistent field method. As a result, the analytic gradient retains the simple "sum of fragment gradients" form that is often assumed in practice, sometimes incorrectly. This obviates (without approximation) the need to solve coupled-perturbed equations, and we demonstrate stable, fragment-based ab initio molecular dynamics simulations using this technique. Energy conservation fails when charge-response contributions to the Fock matrix are neglected, even while geometry optimizations and vibrational frequency calculations may yet be accurate. Stable simulations can be recovered by means of straightforward modifications introduced here, providing a general paradigm for fragment-based ab initio molecular dynamics.

Theoretical Analysis of Activity Cliffs among Benzofuranone-Class Pim1 Inhibitors Using the Fragment Molecular Orbital Method with Molecular Mechanics Poisson-Boltzmann Surface Area (FMO+MM-PBSA) Approach

Significant activity changes due to small structural changes (i.e., activity cliffs) of serine/threonine kinase Pim1 inhibitors were studied theoretically using the fragment molecular orbital method with molecular mechanics Poisson-Boltzmann surface area (FMO+MM-PBSA) approach. This methodology enables quantum-chemical calculations for large biomolecules with solvation. In the course of drug discovery targeting Pim1, six benzofuranone-class inhibitors were found to differ only in the position of the indole-ring nitrogen atom. By comparing the various qualities of complex structures based on X-ray, classical molecular mechanics (MM)-optimized, and quantum/molecular mechanics (QM/MM)-optimized structures, we found that the QM/MM-optimized structures provided the best correlation (R² = 0.85) between pIC₅₀ and the calculated FMO+MM-PBSA binding energy. Combining the classical solvation energy with the QM binding energy was important to increase the correlation. In addition, decomposition of the interaction energy into various physicochemical components by pair interaction energy decomposition analysis suggested that CH-π and electrostatic interactions mainly caused the activity differences.

The role of CH/π interactions in the high affinity binding of streptavidin and biotin

The streptavidin-biotin complex has an extraordinarily high affinity (Ka: 10¹⁵mol^-1) and contains one of the strongest non-covalent interactions known. This strong interaction is widely used in biological tools, including for affinity tags, detection, and immobilization of proteins. Although hydrogen bond networks and hydrophobic interactions have been proposed to explain this high affinity, the reasons for it remain poorly understood. Inspired by the deceased affinity of biotin observed for point mutations of streptavidin at tryptophan residues, we hypothesized that a CH/π interaction may also contribute to the strong interaction between streptavidin and biotin. CH/π interactions were explored and analyzed at the biotin-binding site and at the interface of the subunits by the fragment molecular orbital method (FMO) and extended applications: PIEDA and FMO4. The results show that CH/π interactions are involved in the high affinity for biotin at the binding site of streptavidin. We further suggest that the involvement of CH/π interactions at the subunit interfaces and an extended CH/π network play more critical roles in determining the high affinity, rather than involvement at the binding site.

Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems

Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein-ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.

CH-π hydrogen bonds in biological macromolecules

This is a sequel to the previous Perspective "The CH-π hydrogen bond in chemistry. Conformation, supramolecules, optical resolution and interactions involving carbohydrates", which featured in a PCCP themed issue on "Weak Hydrogen Bonds - Strong Effects?": Phys. Chem. Chem. Phys., 2011, 13, 13873-13900. Evidence that weak hydrogen bonds play an enormously important role in chemistry and biochemistry has now accumulated to an extent that the rigid classical concept of hydrogen bonds formulated by Pauling needs to be seriously revised and extended. The concept of a more generalized hydrogen bond definition is indispensable for understanding the folding mechanisms of proteins. The CH-π hydrogen bond, a weak molecular force occurring between a soft acid CH and a soft base π-electron system, among all is one of the most important and plays a functional role in defining the conformation and stability of 3D structures as well as in many molecular recognition events. This concept is also valuable in structure-based drug design efforts. Despite their frequent occurrence in organic molecules and bio-molecules, the importance of CH-π hydrogen bonds is still largely unknown to many chemists and biochemists. Here we present a review that deals with the evidence, nature, characteristics and consequences of the CH-π hydrogen bond in biological macromolecules (proteins, nucleic acids, lipids and polysaccharides). It is hoped that the present Perspective will show the importance of CH-π hydrogen bonds and stimulate interest in the interactions of biological macromolecules, one of the most fascinating fields in bioorganic chemistry. Implication of this concept is enormous and valuable in the scientific community.

The use of many-body expansions and geometry optimizations in fragment-based methods

Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a many-body expansion in a formally two-body series, as exemplified in the development of the fragment molecular orbital (FMO) method. Fragment-based methods have been very successful in delivering the properties of fragments, as well as the fragment interactions, providing insights into complex chemical processes in large molecular systems. We briefly review geometry optimizations performed with fragment-based methods and present an efficient geometry optimization method based on the combination of FMO with molecular mechanics (MM), applied to the complex of a subunit of protein kinase 2 (CK2) with a ligand. FMO results are discussed in comparison with experimental and MM-optimized structures.

Three- and four-body corrected fragment molecular orbital calculations with a novel subdividing fragmentation method applicable to structure-based drug design

We develop an inter-fragment interaction energy (IFIE) analysis based on the three- and four-body corrected fragment molecular orbital (FMO3 and FMO4) method to evaluate the interactions of functional group units in structure-based drug design context. The novel subdividing fragmentation method for a ligand (in units of their functional groups) and amino acid residues (in units of their main and side chains) enables us to understand the ligand-binding mechanism in more detail without sacrificing chemical accuracy of the total energy and IFIEs by using the FMO4 method. We perform FMO4 calculations with the second order Møller-Plesset perturbation theory for an estrogen receptor (ER) and the 17β-estradiol (EST) complex using the proposed fragmentation method and assess the interaction for each ligand-binding site by the FMO4-IFIE analysis. When the steroidal EST is divided into two functional units including "A ring" and "D ring", respectively, the FMO4-IFIE analysis reveals their binding affinity with surrounding fragments of the amino acid residues; the "A ring" of EST has polarization interaction with the main chain of Thr347 and two hydrogen bonds with the side chains of Glu353 and Arg394; the "D ring" of EST has a hydrogen bond with the side chain of His524. In particular, the CH/π interactions of the "A ring" of EST with the side chains of Leu387 and Phe404 are easily identified in cooperation with the CHPI program. The FMO4-IFIE analysis using our novel subdividing fragmentation method, which provides higher resolution than the conventional IFIE analysis in units of ligand and each amino acid reside in the framework of two-body approximation, is a useful tool for revealing ligand-binding mechanism and would be applicable to rational drug design such as structure-based drug design and fragment-based drug design.