Extending the Power of Quantum Chemistry to Large Systems with the Fragment Molecular Orbital Method

Molecular Tailoring Approach for the Direct Estimation of Individual Noncovalent Interaction Energies in Molecular Systems

The noncovalent interactions (NCIs) are omnipresent in chemistry, physics, and biology. The study of such interactions offers insights into various physicochemical phenomena. Some indirect approaches proposed in the literature for exploring the NCIs are briefly reviewed in Section 1 of this Perspective. These include: (i) Shift in the stretching frequency of an X-Y bond involved in X-Y···Z interaction. (ii) Topological analysis of molecular electron density. (iii) Empirical equations derived employing experimental and theoretical quantities. However, a direct method for estimating individual intramolecular/intermolecular interaction energies has been conspicuous by its absence from the literature. We have developed a molecular tailoring approach (MTA)-based method enabling a direct and reliable estimation of the energy of intra- as well as intermolecular interactions. This method offers a direct and reliable estimation of these interactions, in particular of the hydrogen bonds (HB) in molecules/weakly bound clusters along with the respective cooperativity contribution. In Section 2, the basis of our method is discussed, along with some illustrative examples. The application of this method to a variety of molecules and clusters, with a special emphasis on estimating the HB energy along with the energy of other NCIs is presented in Section 3. Section 4 discusses some computational strategies for applying our method to large molecular clusters. The last Section provides a summary and a discussion on future developments.

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.

The Peptide Bond: Resonance Increases Bond Order and Complicates Fragmentation

The enhancement of the peptide bond order by a resonance in the lone pair of N and the π-bond of CO is analyzed. A decomposition of the bond order in terms of localized molecular orbitals is developed and applied to the peptide bond. A combination of two rotations of hybrid orbitals is proposed to improve the boundary treatment in the fragment molecular orbital method. The developed approach is applied to peptide bonds, and it is found crucial to retain the π orbital in the variational space of both fragments across the boundary. The interaction energies between conventional amino acid residues in Trp-cage (1L2Y) are discussed.

A many-body energy decomposition analysis (MB-EDA) scheme based on a target state optimization self-consistent field (TSO-SCF) method

In this paper, we combine an energy decomposition analysis (EDA) scheme with many-body expansion (MBE) to develop a MB-EDA method to study the cooperative and anti-cooperative effects in molecular cluster systems. Based on the target state optimization self-consistent field (TSO-SCF) method, the intermolecular interaction energy can be decomposed into five chemically meaningful terms, i.e., electrostatic, exchange, polarization, charge transfer and dispersion interaction energies. MB-EDA can decompose each of these terms in MBE. This MB-EDA has been applied to 3 different cluster systems: water clusters, ionic liquid clusters, and acetonitrile-methane clusters. This reveals that electrostatic, exchange, and dispersion interactions are highly pairwise additive in all systems. In water and ionic liquid clusters, the many-body effects are significant in both polarization and charge transfer interactions, but are cooperative and anti-cooperative, respectively. For acetonitrile-methane clusters, which do not involve hydrogen bonds or charge-charge Coulombic interactions, the many-body effects are quite small. The chemical origins of different many-body effects are deeply analyzed. The MB-EDA method has been implemented in Qbics (https://qbics.info) and can be a useful tool for understanding the many-body behavior in molecular aggregates at the quantum chemical level of theory.

Quantum Chemistry-Based Protein-Protein Docking without Empirical Parameters

This study developed a novel protein-protein docking approach based on quantum chemistry. To judge the appropriateness of complex structures, we introduced two criterion values, EV1 and EV2, computed using the fragment molecular orbital method without any empirical parameters. These criterion values enable us to search complex structures in which patterns of the electrostatic potential of the two proteins are optimally aligned at their interface. The performance of our method was validated using 53 complexes in a benchmark set provided for protein-protein docking. When employing bound state structures, docking success rates reached 64% for EV1 and 76% for EV2. On the other hand, when employing unbound state structures, docking success rates reached 13% for EV1 and 17% for EV2.

Discovery of a novel SHP2 allosteric inhibitor using virtual screening, FMO calculation, and molecular dynamic simulation

CONTEXT

SHP2 is a non-receptor protein tyrosine phosphatase to remove tyrosine phosphorylation. Functionally, SHP2 is an essential bridge to connect numerous oncogenic cell-signaling cascades including RAS-ERK, PI3K-AKT, JAK-STAT, and PD-1/PD-L1 pathways. This study aims to discover novel and potent SHP2 inhibitors using a hierarchical structure-based virtual screening strategy that combines molecular docking and the fragment molecular orbital method (FMO) for calculating binding affinity (referred to as the Dock-FMO protocol). For the SHP2 target, the FMO method prediction has a high correlation between the binding affinity of the protein-ligand interaction and experimental values (R2 = 0.55), demonstrating a significant advantage over the MM/PBSA (R2 = 0.02) and MM/GBSA (R2 = 0.15) methods. Therefore, we employed Dock-FMO virtual screening of ChemDiv database of ∼2,990,000 compounds to identify a novel SHP2 allosteric inhibitor bearing hydroxyimino acetamide scaffold. Experimental validation demonstrated that the new compound (E)-2-(hydroxyimino)-2-phenyl-N-(piperidin-4-ylmethyl)acetamide (7188-0011) effectively inhibited SHP2 in a dose-dependent manner. Molecular dynamics (MD) simulation analysis revealed the binding stability of compound 7188-0011 and the SHP2 protein, along with the key interacting residues in the allosteric binding site. Overall, our work has identified a novel and promising allosteric inhibitor that targets SHP2, providing a new starting point for further optimization to develop more potent inhibitors.

METHODS

All the molecular docking studies were employed to identify potential leads with Maestro v10.1. The protein-ligand binding affinities of potential leads were further predicted by FMO calculations at MP2/6-31G* level using GAMESS v2020 system. MD simulations were carried out with AmberTools18 by applying the FF14SB force field. MD trajectories were analyzed using VMD v1.9.3. MM/GB(PB)SA binding free energy analysis was carried out with the mmpbsa.py tool of AmberTools18. The docking and MD simulation results were visualized through PyMOL v2.5.0.

The Effective Fragment Molecular Orbital Method: Achieving High Scalability and Accuracy for Large Systems

The effective fragment molecular orbital (EFMO) method has been developed to predict the total energy of a very large molecular system accurately (with respect to the underlying quantum mechanical method) and efficiently by taking advantage of the locality of strong chemical interactions and employing a two-level hierarchical parallelism. The accuracy of the EFMO method is partly attributed to the accurate and robust intermolecular interaction prediction between distant fragments, in particular, the many-body polarization and dispersion effects, which require the generation of static and dynamic polarizability tensors by solving the coupled perturbed Hartree-Fock (CPHF) and time-dependent HF (TDHF) equations, respectively. Solving the CPHF and TDHF equations is the main EFMO computational bottleneck due to the inefficient (serial) and I/O-intensive implementation of the CPHF and TDHF solvers. In this work, the efficiency and scalability of the EFMO method are significantly improved with a new CPU memory-based implementation for solving the CPHF and TDHF equations that are parallelized by either message passing interface (MPI) or hybrid MPI/OpenMP. The accuracy of the EFMO method is demonstrated for both covalently bonded systems and noncovalently bound molecular clusters by systematically examining the effects of basis sets and a key distance-related cutoff parameter, Rcut. Rcut determines whether a fragment pair (dimer) is treated by the chosen ab initio method or calculated using the effective fragment potential (EFP) method (separated dimers). Decreasing the value of Rcut increases the number of separated (EFP) dimers, thereby decreasing the computational effort. It is demonstrated that excellent accuracy (<1 kcal/mol error per fragment) can be achieved when using a sufficiently large basis set with diffuse functions coupled with a small Rcut value. With the new parallel implementation, the total EFMO wall time is substantially reduced, especially with a high number of MPI ranks. Given a sufficient workload, nearly ideal strong scaling is achieved for the CPHF and TDHF parts of the calculation. For the first time, EFMO calculations with the inclusion of long-range polarization and dispersion interactions on a hydrated mesoporous silica nanoparticle with explicit water solvent molecules (more than 15k atoms) are achieved on a massively parallel supercomputer using nearly 1000 physical nodes. In addition, EFMO calculations on the carbinolamine formation step of an amine-catalyzed aldol reaction at the nanoscale with explicit solvent effects are presented.

Reformulation of All ONIOM-Type Molecular Fragmentation Approaches and Many-Body Theories Using Graph-Theory-Based Projection Operators: Applications to Dynamics, Molecular Potential Surfaces, Machine Learning, and Quantum Computing

We present a graph-theory-based reformulation of all ONIOM-based molecular fragmentation methods. We discuss applications to (a) accurate post-Hartree-Fock AIMD that can be conducted at DFT cost for medium-sized systems, (b) hybrid DFT condensed-phase studies at the cost of pure density functionals, (c) reduced cost on-the-fly large basis gas-phase AIMD and condensed-phase studies, (d) post-Hartree-Fock-level potential surfaces at DFT cost to obtain quantum nuclear effects, and (e) novel transfer machine learning protocols derived from these measures. Additionally, in previous work, the unifying strategy discussed here has been used to construct new quantum computing algorithms. Thus, we conclude that this reformulation is robust and accurate.

The Pivotal Distinction between Antagonists' and Agonists' Binding into Dopamine D4 Receptor-MD and FMO/PIEDA Studies

The dopamine D4 receptor (D4R) is a promising therapeutic target in widespread diseases, and the search for novel agonists and antagonists appears to be clinically relevant. The mechanism of binding to the receptor (R) for antagonists and agonists varies. In the present study, we conducted an in-depth computational study, teasing out key similarities and differences in binding modes, complex dynamics, and binding energies for D4R agonists and antagonists. The dynamic network method was applied to investigate the communication paths between the ligand (L) and G-protein binding site (GBS) of human D4R. Finally, the fragment molecular orbitals with pair interaction energy decomposition analysis (FMO/PIEDA) scheme was used to estimate the binding energies of L-R complexes. We found that a strong salt bridge with D3.32 initiates the inhibition of the dopamine D4 receptor. This interaction also occurs in the binding of agonists, but the change in the receptor conformation to the active state starts with interaction with cysteine C3.36. Such a mechanism may arise in the case of agonists unable to form a hydrogen bond with the serine S5.46, considered, so far, to be crucial in the activation of GPCRs. The energy calculations using the FMO/PIEDA method indicate that antagonists show higher residue occupancy of the receptor binding site than agonists, suggesting they could form relatively more stable complexes. Additionally, antagonists were characterized by repulsive interactions with S5.46 distinguishing them from agonists.

Structure-Based Optimization and Biological Evaluation of Potent and Selective MMP-7 Inhibitors for Kidney Fibrosis

Matrix metalloproteinase-7 (MMP-7) has been shown to play important roles in pathophysiological processes involved in the development/progression of diseases such as cancer and fibrosis. We discovered selective MMP-7 inhibitors composed of arylsulfonamide, carboxylate, and short peptides by a molecular hybridization approach. These compounds interacted with MMP-7 via multiple hydrogen bonds in the cocrystal structures. To obtain compounds for in vivo evaluation, we attempted structural optimization, particularly targeting Tyr167 at the S3 subsite through structure-based drug design, and identified compound 15 as showing improved MMP-7 potency and MMP subtype selectivity. A novel π-π stacking interaction with Tyr167 was achieved when 4-pyridylalanine was introduced as the P3 residue. Compound 15 suppressed the progression of kidney fibrosis in a dose-dependent manner in a mouse model of unilateral ureteral obstruction. Thus, we demonstrated, for the first time, that potent and selective MMP-7 inhibitors could prevent the progression of kidney fibrosis.

A Perspective on Sustainable Computational Chemistry Software Development and Integration

The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.

IRMPD spectroscopy and quantum-chemical simulations of the reaction products of cisplatin with the dipeptide CysGly

The inorganic antineoplastic drug cisplatin was made to react in solution with the dipeptide cysteinylglycine (CysGly), chosen as a functional model of glutathione, and the reaction products were analyzed using electrospray ionization mass spectrometry (ESI-MS). Selected complexes, i.e., the primary substitution product cis-[PtCl(NH3)2(CysGly)]+ and the chelate cis-[PtCl(NH3)(CysGly)]+, were submitted to IR multiple photon dissociation (IRMPD) spectroscopy obtaining their vibrational features. The experimental IR ion spectra were compared with the calculated IR absorptions of different plausible isomeric families, finding CysGly to bind preferentially platinum(II) via its deprotonated thiolic group in the monovalent complex, cis-[PtCl(NH3)2(CysGly)]+, and to evolve in the S,N-bound chelate structure cis-[PtCl(NH3)(CysGly)]+ through the SH and NH2 functionality of the cysteine residue. Moreover, our findings indicate that the platination reaction does not affect the CysGly peptide bond, which remains in its trans configuration. These results provide additional insights into the reactivity of Pt(II)-complexes with glutathione which is involved in cellular cisplatin resistance.

Structure-Guided Design and Synthesis of a Pyridazinone Series of Trypanosoma cruzi Proteasome Inhibitors

There is an urgent need for new treatments for Chagas disease, a parasitic infection which mostly impacts South and Central America. We previously reported on the discovery of GSK3494245/DDD01305143, a preclinical candidate for visceral leishmaniasis which acted through inhibition of the Leishmania proteasome. A related analogue, active against Trypanosoma cruzi, showed suboptimal efficacy in an animal model of Chagas disease, so alternative proteasome inhibitors were investigated. Screening a library of phenotypically active analogues against the T. cruzi proteasome identified an active, selective pyridazinone, the development of which is described herein. We obtained a cryo-EM co-structure of proteasome and a key inhibitor and used this to drive optimization of the compounds. Alongside this, optimization of the absorption, distribution, metabolism, and excretion (ADME) properties afforded a suitable compound for mouse efficacy studies. The outcome of these studies is discussed, alongside future plans to further understand the series and its potential to deliver a new treatment for Chagas disease.

SophosQM: Accurate Binding Affinity Prediction in Compound Optimization

The optimization of compounds' binding affinity for a biological target is a crucial aspect of the drug development process. Being able to accurately predict binding energies in advance of synthesizing compounds would have a massive impact on the speed of the drug discovery process. The ideal binding affinity prediction method should combine accuracy, reliability, and speed. In this paper, we present SophosQM, a quantum mechanics (QM)-based approach, which can accurately predict the binding affinities of compounds to proteins. The binding affinity predictive models generated by SophosQM are based on the fragment molecular orbital (FMO) method to estimate the enthalpic component of the binding free energy, and a macroscopic descriptor, clog P, is used as an approximation of the entropic component. The affinity prediction is performed using multilinear regression, fitting the experimental values against the FMO-computed enthalpic term and clog P. The quality of the prediction can be assessed in terms of the correlation coefficient between experimental and predicted values. In this work, the method's reliability and accuracy are exemplified by applying SophosQM to 70 compounds binding to six different targets of pharmaceutical relevance. Overall, the results show a very satisfactory performance with a global correlation coefficient in the order of 0.9. Our predictions also show a satisfactory performance compared to data based on free energy perturbation. Finally, SophosQM can also be applied in high-throughput mode by using semiempirical QM methods to evaluate large portions of chemical space, while retaining a good level of accuracy, but decreasing the computing time to just a few seconds per compound.

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.

Quantification and Neutralization of the Interfacial Electrostatic Potential and Visualization of the Dispersion Interaction in Visualization of the Interfacial Electrostatic Complementarity

Visualization of the interfacial electrostatic complementarity (VIINEC) is a quantum chemistry-based method to examine protein-protein interactions (PPI). In VIINEC, the electrostatic complementarity between proteins at the interface is visually and quantitatively evaluated using the partial electrostatic potential (pESP), which is defined based on the fragment molecular orbital method. In this work, new quantification and neutralization methods of the pESP were proposed together with a method to visualize the dispersion interaction. The reliability and efficiency of these methods were evaluated using 17 models of the complex. It was found that the quantification of the electrostatic complementarity with the pESP using the new neutralization method has a high correlation with the interaction energy, supporting the reliability of VIINEC. As an illustrative example, the PPI between a major histocompatibility complex class I molecule and a T-cell receptor was examined, which demonstrated the value of VIINEC in chemical and biological research.

Computational methods for calculation of protein-ligand binding affinities in structure-based drug design

Drug design is an expensive and time-consuming process. Any method that allows reducing the time the costs of the drug development project can have great practical value for the pharmaceutical industry. In structure-based drug design, affinity prediction methods are of great importance. The majority of methods used to predict binding free energy in protein-ligand complexes use molecular mechanics methods. However, many limitations of these methods in describing interactions exist. An attempt to go beyond these limits is the application of quantum-mechanical description for all or only part of the analyzed system. However, the extensive use of quantum mechanical (QM) approaches in drug discovery is still a demanding challenge. This chapter briefly reviews selected methods used to calculate protein-ligand binding affinity applied in virtual screening (VS), rescoring of docked poses, and lead optimization stage, including QM methods based on molecular simulations.

Density Embedding Method for Nanoscale Molecule-Metal Interfaces

In this work, we extend the applicability of standard Kohn-Sham DFT (KS-DFT) to model realistically sized molecule-metal interfaces where the metal slabs venture into the tens of nanometers in size. Employing state-of-the-art noninteracting kinetic energy functionals, we describe metallic subsystems with orbital-free DFT and combine their electronic structure with molecular subsystems computed at the KS-DFT level resulting in a multiscale subsystem DFT method. The method reproduces within a few millielectronvolts the binding energy difference of water and carbon dioxide molecules adsorbed on the top and hollow sites of an Al(111) surface compared to KS-DFT of the combined supersystem. It is also robust for Born-Oppenheimer molecular dynamics simulations. Very large system sizes are approached with standard computing resources thanks to a parallelization scheme that avoids accumulation of memory at the gather-scatter stage. The results as presented are encouraging and open the door to ab initio simulations of realistically sized, mesoscopic molecule-metal interfaces.

Hotspot Identification and Drug Design of Protein-Protein Interaction Modulators Using the Fragment Molecular Orbital Method

Protein-protein interactions (PPIs) are essential for the function of many proteins. Aberrant PPIs have the potential to lead to disease, making PPIs promising targets for drug discovery. There are over 64,000 PPIs in the human interactome reference database; however, to date, very few PPI modulators have been approved for clinical use. Further development of PPI-specific therapeutics is highly dependent on the availability of structural data and the existence of reliable computational tools to explore the interface between two interacting proteins. The fragment molecular orbital (FMO) quantum mechanics method offers comprehensive and computationally inexpensive means of identifying the strength (in kcal/mol) and the chemical nature (electrostatic or hydrophobic) of the molecular interactions taking place at the protein-protein interface. We have integrated FMO and PPI exploration (FMO-PPI) to identify the residues that are critical for protein-protein binding (hotspots). To validate this approach, we have applied FMO-PPI to a dataset of protein-protein complexes representing several different protein subfamilies and obtained FMO-PPI results that are in agreement with published mutagenesis data. We observed that critical PPIs can be divided into three major categories: interactions between residues of two proteins (intermolecular), interactions between residues within the same protein (intramolecular), and interactions between residues of two proteins that are mediated by water molecules (water bridges). We extended our findings by demonstrating how this information obtained by FMO-PPI can be utilized to support the structure-based drug design of PPI modulators (SBDD-PPI).

Quantum computational study of chloride attack on chloromethane for chemical accuracy and quantum noise effects with UCCSD and k-UpCCGSD ansatzes

Quantum computing is expected to play an important role in solving the problem of huge computational costs in various applications by utilizing the collective properties of quantum states, including superposition, interference, and entanglement, to perform computations. Quantum mechanical (QM) methods are candidates for various applications and can provide accurate absolute energy calculations in structure-based methods. QM methods are powerful tools for describing reaction pathways and their potential energy surfaces (PES). In this study, we applied quantum computing to describe the PES of the bimolecular nucleophilic substitution (S_N2) reaction between chloromethane and chloride ions. We performed noiseless and noise simulations using quantum algorithms and compared the accuracy and noise effects of the ansatzes. In noiseless simulations, the results from UCCSD and k-UpCCGSD are similar to those of full configurational interaction (FCI) with the same active space, which indicates that quantum algorithms can describe the PES of the S_N2 reaction. In noise simulations, UCCSD is more susceptible to quantum noise than k-UpCCGSD. Therefore, k-UpCCGSD can serve as an alternative to UCCSD to reduce quantum noisy effects in the noisy intermediate-scale quantum era, and k-UpCCGSD is sufficient to describe the PES of the S_N2 reaction in this work. The results showed the applicability of quantum computing to the S_N2 reaction pathway and provided valuable information for structure-based molecular simulations with quantum computing.

Identification of Novel Natural Product Inhibitors against Matrix Metalloproteinase 9 Using Quantum Mechanical Fragment Molecular Orbital-Based Virtual Screening Methods

Matrix metalloproteinases (MMPs) are calcium-dependent zinc-containing endopeptidases involved in multiple cellular processes. Among the MMP isoforms, MMP-9 regulates cancer invasion, rheumatoid arthritis, and osteoarthritis by degrading extracellular matrix proteins present in the tumor microenvironment and cartilage and promoting angiogenesis. Here, we identified two potent natural product inhibitors of the non-catalytic hemopexin domain of MMP-9 using a novel quantum mechanical fragment molecular orbital (FMO)-based virtual screening workflow. The workflow integrates qualitative pharmacophore modeling, quantitative binding affinity prediction, and a raw material search of natural product inhibitors with the BMDMS-NP library. In binding affinity prediction, we made a scoring function with the FMO method and applied the function to two protein targets (acetylcholinesterase and fibroblast growth factor 1 receptor) from DUD-E benchmark sets. In the two targets, the FMO method outperformed the Glide docking score and MM/PBSA methods. By applying this workflow to MMP-9, we proposed two potent natural product inhibitors (laetanine 9 and genkwanin 10) that interact with hotspot residues of the hemopexin domain of MMP-9. Laetanine 9 and genkwanin 10 bind to MMP-9 with a dissociation constant (KD) of 21.6 and 0.614 μM, respectively. Overall, we present laetanine 9 and genkwanin 10 for MMP-9 and demonstrate that the novel FMO-based workflow with a quantum mechanical approach is promising to discover potent natural product inhibitors of MMP-9, satisfying the pharmacophore model and good binding affinity.

Interaction Analysis of the Spike Protein of Delta and Omicron Variants of SARS-CoV-2 with hACE2 and Eight Monoclonal Antibodies Using the Fragment Molecular Orbital Method

In the past 2 years, since the emergence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), multiple SARS-CoV-2 variants have emerged. Whenever a new variant emerges, considerable time is required to analyze the binding affinity of the viral surface proteins to human angiotensin-converting enzyme 2 (hACE2) and monoclonal antibodies. To efficiently predict the binding affinities associated with hACE2 and monoclonal antibodies in a short time, herein, we propose a method applying statistical analysis to simulations performed using molecular and quantum mechanics. This method efficiently predicted the trend of binding affinity for the binding of the spike protein of each variant of SARS-CoV-2 to hACE2 and individually to eight commercial monoclonal antibodies. Additionally, this method accurately predicted interaction energy changes in the crystal structure for 10 of 13 mutated residues in the Omicron variant, showing a significant change in the interaction energy of hACE2. S375F was found to be a mutation that majorly changed the binding affinity of the spike protein to hACE2 and the eight monoclonal antibodies. Our proposed analysis method enables the prediction of the binding affinity of new variants to hACE2 or to monoclonal antibodies in a shorter time compared to that utilized by the experimental method.

A Study on the Effect of the Substituent against PAK4 Inhibition Using In Silico Methods

The intrinsic inductive properties of atoms or functional groups depend on the chemical properties of either electron-withdrawing groups (EWGs) or electron-donating groups (EDGs). This study aimed to evaluate in silico methods to determine whether changes in chemical properties of the compound by single atomic substitution affect the biological activity of target proteins and whether the results depend on the properties of the functional groups. We found an imidazo[4,5-b]pyridine-based PAK4 inhibitor, compound 1, as an initial hit compound with the well-defined binding mode for PAK4. In this study, we used both experimental and in silico methods to investigate the effect of atomic substitution on biological activity to optimize the initial hit compound. In biological assays, in the case of EWG, as the size of the halogen atom became smaller and the electronegativity increased, the biological activity IC₅₀ value ranged from 5150 nM to inactive; in the case of EDG, biological activity was inactive. Furthermore, we analyzed the interactions of PAK4 with compounds, focusing on the hinge region residues, L398 and E399, and gatekeeper residues, M395 and K350, of the PAK4 protein using molecular docking studies and fragment molecular orbital (FMO) methods to determine the differences between the effect of EWG and EDG on the activity of target proteins. These results of the docking score and binding energy did not explain the differences in biological activity. However, the pair-interaction energy obtained from the results of the FMO method indicated that there was a difference in the interaction energy between the EWG and EDG in the hinge region residues, L398 and E399, as well as in M395 and K350. The two groups with different properties exhibited opposite electrostatic energy and charge transfer energy between L398 and E399. Additionally, we investigated the electron distribution of the parts interacting with the hinge region by visualizing the molecular electrostatic potential (MEP) surface of the compounds. In conclusion, we described the properties of functional groups that affect biological activity using an in silico method, FMO.

Towards a quantitative description of excitonic couplings in photosynthetic pigment-protein complexes: quantum chemistry driven multiscale approaches

A structure-based quantitative calculation of excitonic couplings between photosynthetic pigments has to describe the dynamical polarization of the protein/solvent environment of the pigments, giving rise to reaction field and screening effects. Here, this challenging problem is approached by combining the fragment molecular orbital (FMO) method with the polarizable continuum model (PCM). The method is applied to compute excitonic couplings between chlorophyll a (Chl a) pigments of the water-soluble chlorophyll-binding protein (WSCP). By calibrating the vacuum dipole strength of the 0-0 transition of the Chl a chromophores according to experimental data, an excellent agreement between calculated and experimental linear absorption and circular dichroism spectra of WSCP is obtained. The effect of the mutual polarization of the pigment ground states is calculated to be very small. The simple Poisson-Transition-charge-from-Electrostatic-potential (Poisson-TrEsp) method is found to accurately describe the screening part of the excitonic coupling, obtained with FMO/PCM. Taking into account that the reaction field effects of the latter method can be described by a scalar constant leads to an improvement of Poisson-TrEsp that is expected to provide the basis for simple and realistic calculations of optical spectra and energy transfer in photosynthetic light-harvesting complexes. In addition, we present an expression for the estimation of Huang-Rhys factors of high-frequency pigment vibrations from experimental fluorescence line-narrowing spectra that takes into account the redistribution of oscillator strength by the interpigment excitonic coupling. Application to WSCP results in corrected Huang-Rhys factors that are less than one third of the original values obtained by the standard electronic two-state analysis that neglects the above redistribution. These factors are important for the estimation of the dipole strength of the 0-0 transition of the chromophores and for the development of calculation schemes for the spectral density of the exciton-vibrational coupling.

Local-Field Effects in Linear Response Properties within a Polarizable Frozen Density Embedding Method

In this work, we present a polarizable frozen density embedding (FDE) method for calculating polarizabilities of coupled subsystems. The method (FDE-pol) combines a FDE method with an explicit polarization model such that the expensive freeze/thaw cycles can be bypassed, and approximate nonadditive kinetic potentials are avoided by enforcing external orthogonality between the subsystems. To describe the polarization of the frozen environment, we introduce a Hirshfeld partition-based density-dependent method for calculating the atomic polarizabilities of atoms in molecules, which alleviates the need to fit the atomic parameters to a specific system of interest or to a larger general set of molecules. We show that the Hirshfeld partition-based method predicts molecular polarizabilities close to the basis set limit, and thus, a single basis set-dependent scaling parameter can be introduced to improve the agreement against the reference polarizability data. To test the model, we characterized the uncoupled and coupled response of small interacting molecular complexes. Here, the coupled response properties include the perturbation of the frozen system due to the external perturbation which is ignored in the uncoupled response. We show that FDE-pol can accurately reproduce both the exact uncoupled polarizability and the coupled polarizabilities of the supermolecular systems. Using damped response theory, we also demonstrate that the coupled frequency-dependent polarizability can be described by including local field effects. The results emphasize the necessity of including local-field effects for describing the response properties of coupled subsystems, as well as the importance of accurate atomic polarizability models.

Interaction Analysis on the SARS-CoV-2 Spike Protein Receptor Binding Domain Using Visualization of the Interfacial Electrostatic Complementarity

Visualization of the interfacial electrostatic complementarity (VIINEC) is a recently developed method for analyzing protein-protein interactions using electrostatic potential (ESP) calculated via the ab initio fragment molecular orbital method. In this Letter, the molecular interactions of the receptor-binding domain (RBD) of the SARS-CoV-2 spike protein with human angiotensin-converting enzyme 2 (ACE2) and B38 neutralizing antibody were examined as an illustrative application of VIINEC. The results of VIINEC revealed that the E484 of RBD has a role in making a local electrostatic complementary with ACE2 at the protein-protein interface, while it causes a considerable repulsive electrostatic interaction. Furthermore, the calculated ESP map at the interface of the RBD/B38 complex was significantly different from that of the RBD/ACE2 complex, which is discussed herein in association with the mechanism of the specificity of the antibody binding to the target protein.

Subsystem Density Functional Theory Augmented by a Delta Learning Approach to Achieve Kohn-Sham Accuracy

Simulations based on electronic structure theory naturally include polarization and have no transferability problems. In particular, Kohn-Sham density functional theory (KS-DFT) has become the method of reference for ab initio molecular dynamics simulations of condensed matter systems. However, the high computational cost often poses strict limits on the affordable system size as well as on the extension of sampling (number of configurations). In this work, we propose an improvement to the subsystem density functional theory approach, known as the Kim-Gordon (KG) scheme, thus enabling the sampling of configurations for condensed molecular systems keeping the KS-DFT level accuracy at a fraction of computer time. Our scheme compensates the known KG shortcomings of the electronic kinetic energy term by adding a simple correction and can match KS-DFT accuracy in energies and forces. The computationally cheap correction is determined by means of a machine learning procedure. The proposed KG scheme is applied within a linear scaling self-consistent field formalism and is assessed by a series of molecular dynamics simulations of liquid water under different conditions. Although system-dependent, the correction is transferable between system sizes and temperatures.

Quantum-Mechanical Structure Optimization of Protein Crystals and Analysis of Interactions in Periodic Systems

A fast quantum-mechanical approach, density-functional tight-binding combined with the fragment molecular orbital method and periodic boundary conditions, is used to optimize atomic coordinates and cell parameters for a set of protein crystals: 1ETL, 5OQZ, 3Q8J, 1CBN, and 2VB1. Good agreement between experimental and calculated structures is obtained for both atomic coordinates and cell parameters. Sterical clashes present in the experimental structures are corrected by simulations. The partition analysis is extended to treat periodic boundary conditions and applied to analyze protein-solvent interactions in crystals.

Adaptive-Partitioning Multilayer Dynamics Simulations: 1. On-the-Fly Switch between Two Quantum Levels of Theory

We propose to generalize the previously developed two-layer permuted adaptive-partitioning quantum-mechanics/molecular-mechanics (QM/MM), which reclassifies atoms as QM or MM on-the-fly in dynamics simulations, to multilayer adaptive-partitioning algorithms that enable multiple levels of theory. In this work, we formulate two new algorithms that smoothly interpolate the energy between two QM (Q1 and Q2) levels of theory. The first "permuted adaptive-partitioning" scheme is based on the weighted many-body expansion of the potential, as in the adaptive-partitioning QM/MM. Unconventional and potentially more efficient, the second "interpolated adaptive-partitioning" method employs alchemical QM calculations with Q1/Q2-mixed basis sets, Fock matrices, and overlap matrices. To our knowledge, this is the first time that such alchemical calculations are performed in QM, although they are routinely done in MM. Test calculations on water-cluster models show that both new algorithms indeed yield smooth energy curves when water molecules shift between Q1 and Q2.

Visualization of the Interfacial Electrostatic Complementarity: A Method for Analysis of Protein-Protein Interaction Based on Ab Initio Quantum Chemical Calculations

In this study, we report a method for analyzing the protein-protein interaction based on ab initio quantum chemical calculations, which we refer to as "Visualization of the interfacial electrostatic complementarity (VIINEC)." This method visually provides the electrostatic complementarity at the protein-protein interface; in addition, the ratio of the attractive interaction is calculated. Illustrative calculations revealed that VIINEC could successfully quantify the electronic induced fit owing complex formation, which was responsible for 5%-10% of the total electrostatic complementarity. Furthermore, the contribution of each amino acid to the electrostatic complementarity was evaluated, providing useful information for various applications, including rational antibody designs. Interestingly, a part of the mechanism causing the specificity of the protein-protein bindings was also demonstrated using VIINEC. This is an important achievement of this study because the specificity of the biomolecular interactions is essential for biological functions.

On the Accuracy of QM/MM Models: A Systematic Study of Intramolecular Proton Transfer Reactions of Amino Acids in Water

This work presents a systematic assessment of QM/QM' and QM/MM models with respect to direct QM calculations for the tautomerization (neutral to zwitterion) reactions of amino acids (glycine, alanine, valine, aspartate, and neutral and protonated histidine) solvated in a 160 water cluster. The effect of varying QM region size and choice of embedding potentials, including fixed-charge and polarizable molecular mechanics force fields (TIP3P and EFP) and various semiempirical QM methods (PM7, GFN2-xTB, DFTBA, DFTB3, HF-3c, and PBEh-3c), on the accuracy of the models was examined. A surprising finding was that molecular mechanics force fields outperformed many of the semiempirical methods. Generally, the errors in the QM/QM' and QM/MM models converge slowly with respect to the QM region size, requiring 50 or more waters to be included in the QM region before the error in the model falls below 1 kcal mol^-1 of its pure QM result. Different QM region selection schemes were also compared, and it was found that selection based on Natural Population Analysis (NPA) atomic charges significantly reduced the error in the QM/QM' and QM/MM models particularly if a low-quality embedding potential was used. It is envisaged that these results will be useful for the development of future hybrid QM models.

Identification of key stabilizing interactions of amyloid-β oligomers based on fragment molecular orbital calculations on macrocyclic β-hairpin peptides

Analyzing the electronic states and inter-/intra-molecular interactions of amyloid oligomers expand our understanding of the molecular basis of Alzheimer's disease and other amyloid diseases. In the current study, several high-resolution crystal structures of oligomeric assemblies of Aβ-derived peptides have been studied by the ab initio fragment molecular orbital (FMO) method. The FMO method provides comprehensive details of the molecular interactions between the residues of the amyloid oligomers at the quantum mechanical level. Based on the calculations, two sequential aromatic residues (F19 and F20) and negatively charged E22 on the central region of Aβ have been identified as key residues in oligomer stabilization and potential interesting pharmacophores for preventing oligomer formation.

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.

Machine learning builds full-QM precision protein force fields in seconds

Full-quantum mechanics (QM) calculations are extraordinarily precise but difficult to apply to large systems, such as biomolecules. Motivated by the massive demand for efficient calculations for large systems at the full-QM level and by the significant advances in machine learning, we have designed a neural network-based two-body molecular fractionation with conjugate caps (NN-TMFCC) approach to accelerate the energy and atomic force calculations of proteins. The results show very high precision for the proposed NN potential energy surface models of residue-based fragments, with energy root-mean-squared errors (RMSEs) less than 1.0 kcal/mol and force RMSEs less than 1.3 kcal/mol/Å for both training and testing sets. The proposed NN-TMFCC method calculates the energies and atomic forces of 15 representative proteins with full-QM precision in 10-100 s, which is thousands of times faster than the full-QM calculations. The computational complexity of the NN-TMFCC method is independent of the protein size and only depends on the number of residue species, which makes this method particularly suitable for rapid prediction of large systems with tens of thousands or even hundreds of thousands of times acceleration. This highly precise and efficient NN-TMFCC approach exhibits considerable potential for performing energy and force calculations, structure predictions and molecular dynamics simulations of proteins with full-QM precision.

Accurate Electronic Excitation Energies in Full-Valence Active Space via Bootstrap Embedding

Fragment embedding has been widely used to circumvent the high computational scaling of using accurate electron correlation methods to describe the electronic ground states of molecules and materials. However, similar applications that utilize fragment embedding to treat electronic excited states are comparably less reported in the literature. The challenge here is twofold. First, most fragment embedding methods are most effective when the property of interest is local, but the change of the wave function upon excitation is nonlocal in general. Second, even for local excitations, an accurate estimate of, for example, the excitation energy can still be challenging owing to the need for a balanced treatment of both the ground and the excited states. In this work, we show that bootstrap embedding (BE), a fragment embedding method developed recently by our group, is promising toward describing general electronic excitations. Numerical simulations show that the excitation energies in full-valence active space (FVAS) can be well-estimated by BE to an error of ∼0.05 eV using relatively small fragments, for both local excitations and the excitations of some large dye molecules that exhibit strong charge-transfer characters. We hence anticipate BE to be a promising solution to accurately describing the excited states of large chemical systems.

From NWChem to NWChemEx: Evolving with the Computational Chemistry Landscape

Since the advent of the first computers, chemists have been at the forefront of using computers to understand and solve complex chemical problems. As the hardware and software have evolved, so have the theoretical and computational chemistry methods and algorithms. Parallel computers clearly changed the common computing paradigm in the late 1970s and 80s, and the field has again seen a paradigm shift with the advent of graphical processing units. This review explores the challenges and some of the solutions in transforming software from the terascale to the petascale and now to the upcoming exascale computers. While discussing the field in general, NWChem and its redesign, NWChemEx, will be highlighted as one of the early codesign projects to take advantage of massively parallel computers and emerging software standards to enable large scientific challenges to be tackled.

The fragment molecular orbital method combined with density-functional tight-binding and periodic boundary conditions

The density-functional tight-binding (DFTB) formulation of the fragment molecular orbital method is combined with periodic boundary conditions. Long-range electrostatics and dispersion are evaluated with the Ewald summation technique. The first analytic derivatives of the energy with respect to atomic coordinates and lattice parameters are formulated. The accuracy of the method is established in comparison to numerical gradients and DFTB without fragmentation. The largest elementary cell in this work has 1631 atoms. The method is applied to elucidate the polarization, charge transfer, and interactions in the solution.

Trajectory Surface Hopping Approach to Condensed-Phase Nonradiative Relaxation Dynamics Using Divide-and-Conquer Spin-Flip Time-Dependent Density-Functional Tight Binding

Nonradiative relaxation of excited molecules is central to many crucial issues in photochemistry. Condensed phases are typical contexts in which such problems are considered, and the nonradiative relaxation dynamics are expected to be significantly affected by interactions with the environment, for example, a solvent. We developed a nonadiabatic molecular dynamics simulation technique that can treat the nonradiative relaxation and explicitly include the environment in the calculations without a heavy computational burden. Specifically, we combined trajectory surface hopping with Tully's fewest-switches algorithm, a tight-binding approximated version of spin-flip time-dependent density-functional theory, and divide-and-conquer (DC) spatial fragmentation scheme. Numerical results showed that this method can treat systems with thousands of atoms within reasonable computational resources, and the error arising from DC fragmentation is negligibly small. Using this method, we obtained molecular insights into the solvent dependence of the photoexcited-state dynamics of trans-azobenzene, which demonstrate the importance of the environment for condensed-phase nonradiative relaxation.

Systematic Partitioning of Proteins for Quantum-Chemical Fragmentation Methods Using Graph Algorithms

Quantum-chemical fragmentation methods offer an efficient approach for the treatment of large proteins, in particular if local target quantities such as protein-ligand interaction energies, enzymatic reaction energies, or spectroscopic properties of embedded chromophores are sought. However, the accuracy that is achievable for such local target quantities intricately depends on how the protein is partitioned into smaller fragments. While the commonly employed naı̈ve approach of using fragments with a fixed size is widely used, it can result in large and unpredictable errors when varying the fragment size. Here, we present a systematic partitioning scheme that aims at minimizing the fragmentation error of a local target quantity for a given maximum fragment size. To this end, we construct a weighted graph representation of the protein, in which the amino acids constitute the nodes. These nodes are connected by edges weighted with an estimate for the fragmentation error that is expected when cutting this edge. This allows us to employ graph partitioning algorithms provided by computer science to determine near-optimal partitions of the protein. We apply this scheme to a test set of six proteins representing various prototypical applications of quantum-chemical fragmentation methods using a simplified molecular fractionation with conjugate caps (MFCC) approach with hydrogen caps. We show that our graph-based scheme consistently improves upon the naı̈ve approach.

Prediction of lattice energy of benzene crystals: A robust theoretical approach

We present an inexpensive and robust theoretical approach based on the fragment molecular orbital methodology and the spin-ratio scaled second-order Møller-Plesset perturbation theory to predict the lattice energy of benzene crystals within 2 kJ⋅mol^-1 . Inspired by the Harrison method to estimate the Madelung constant, the proposed approach calculates the lattice energy as a sum of two- and three-body interaction energies between a reference molecule and the surrounding molecules arranged in a sphere. The lattice energy converges rapidly at a radius of 13 Å. Adding the corrections to account for a higher correlated level of theory and basis set superposition for the Hartree Fock (HF) level produced a lattice energy of -57.5 kJ⋅mol^-1 for the benzene crystal structure at 138 K. This estimate is within 1.6 kJ⋅mol^-1 off the best theoretical prediction of -55.9 kJ⋅mol^-1 . We applied this approach to calculate lattice energies of the crystal structures of phase I and phase II-polymorphs of benzene-observed at a higher temperature of 295 K. The stability of these polymorphs was correctly predicted, with phase II being energetically preferred by 3.7 kJ⋅mol^-1 over phase I. The proposed approach gives a tremendous potential to predict stability of other molecular crystal polymorphs.

Computational Methods for Biochemical Simulations Implemented in GAMESS

Computational methods for modeling biochemical processes implemented in GAMESS package are reviewed; in particular, quantum mechanics combined with molecular mechanics (QM/MM), semi-empirical, and fragmentation approaches. A detailed summary of capabilities is provided for the QM/MM implementation in QuanPol program and the fragment molecular orbital (FMO) method. Molecular modeling and visualization packages useful for biochemical simulations with GAMESS are described. GAMESS capabilities with corresponding references are tabulated for reader's convenience.

Guiding Medicinal Chemistry with Fragment Molecular Orbital (FMO) Method

The understanding of binding interactions between a protein and a small molecule plays a key role in the rationalization of potency and selectivity and in design of new ideas. However, even when a target of interest is structurally enabled, visual inspection and force field-based molecular mechanics calculations cannot always explain the full complexity of the molecular interactions that are critical in drug design. Quantum mechanical methods have the potential to address this shortcoming, but traditionally, computational expense has made the application of these calculations impractical. The fragment molecular orbital (FMO) method offers a solution that combines accuracy, speed, and the ability to characterize important interactions (i.e. its strength in kcal/mol and chemical nature: hydrophobic, electrostatic, etc) that would otherwise be hard to detect. In this chapter, we describe the FMO method and illustrate its application in the discovery of the benzothiazole (BZT) series as novel tyrosine kinase ITK inhibitors for treatment of allergic asthma.

Analyzing GPCR-Ligand Interactions with the Fragment Molecular Orbital (FMO) Method

G-protein-coupled receptors (GPCRs) have enormous physiological and biomedical importance, and therefore it is not surprising that they are the targets of many prescribed drugs. Further progress in GPCR drug discovery is highly dependent on the availability of protein structural information. However, the ability of X-ray crystallography to guide the drug discovery process for GPCR targets is limited by the availability of accurate tools to explore receptor-ligand interactions. Visual inspection and molecular mechanics approaches cannot explain the full complexity of molecular interactions. Quantum mechanics (QM) approaches are often too computationally expensive to be of practical use in time-sensitive situations, but the fragment molecular orbital (FMO) method offers an excellent solution that combines accuracy, speed, and the ability to reveal key interactions that would otherwise be hard to detect. Integration of GPCR crystallography or homology modelling with FMO reveals atomistic details of the individual contributions of each residue and water molecule toward ligand binding, including an analysis of their chemical nature. Such information is essential for an efficient structure-based drug design (SBDD) process. In this chapter, we describe how to use FMO in the characterization of GPCR-ligand interactions.