Ab initio quantum mechanical study of the binding energies of human estrogen receptor ? with its ligands: An application of fragment molecular orbital 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.

Prediction of Binding Pose and Affinity of Nelfinavir, a SARS-CoV-2 Main Protease Repositioned Drug, by Combining Docking, Molecular Dynamics, and Fragment Molecular Orbital Calculations

A novel in silico drug design procedure is described targeting the Main protease (Mpro) of the SARS-CoV-2 virus. The procedure combines molecular docking, molecular dynamics (MD), and fragment molecular orbital (FMO) calculations. The binding structure and properties of Mpro were predicted for Nelfinavir (NFV), which had been identified as a candidate compound through drug repositioning, targeting Mpro. Several poses of the Mpro and NFV complexes were generated by docking, from which four docking poses were selected by scoring with FMO energy. Then, each pose was subjected to MD simulation, 100 snapshot structures were sampled from each of the generated MD trajectories, and the structures were evaluated by FMO calculations to rank the pose based on binding energy. Several residues were found to be important in ligand recognition, including Glu47, Asp48, Glu166, Asp187, and Gln189, all of which interacted strongly with NFV. Asn142 is presumably regarded to form hydrogen bonds or CH/π interaction with NFV; however, in the present calculation, their interactions were transient. Moreover, the tert-butyl group of NFV had no interaction with Mpro. Identifying such strong and weak interactions provides candidates for maintaining and substituting ligand functional groups and important suggestions for drug discovery using drug repositioning. Besides the interaction between NFV and the amino acid residues of Mpro, the desolvation effect of the binding pocket also affected the ranking order. A similar procedure of drug design was applied to Lopinavir, and the calculated interaction energy and experimental inhibitory activity value trends were consistent. Our approach provides a new guideline for structure-based drug design starting from a candidate compound whose complex crystal structure has not been obtained.

Probing RNA-Small Molecule Interactions Using Biophysical and Computational Approaches

Interest in small molecules that target RNA is flourishing, and the expectation set on them to treat diseases with unmet medical needs is high. However, several challenges remain, including difficulties in selecting suitable tools and establishing workflows for their discovery. In this context, we optimized experimental and computational approaches that were previously employed for the protein targets. Here, we demonstrate that a fluorescence-based assay can be effectively used to screen small molecule libraries for their ability to bind and stabilize an RNA stem-loop. Our screen identified several fluoroquinolones that bind to the target stem-loop. We further probed their interactions with the target using biolayer interferometry, isothermal titration calorimetry (ITC), and nuclear magnetic resonance spectroscopy. The results of these biophysical assays suggest that the fluoroquinolones bind the target in a similar manner. Armed with this knowledge, we built models for the complexes of the fluoroquinolones and the RNA target. Then, we performed fragment molecular orbital (FMO) calculations to dissect the interactions between the fluoroquinolones and the RNA. We found that the binding free energies obtained from the ITC experiments correlated strongly with the interaction energies calculated by FMO. Finally, we designed fluoroquinolone analogues and performed FMO calculations to predict their binding free energies. Taken together, the results of this study support the importance of conducting orthogonal assays in binding confirmation and compound selection and demonstrate the usefulness of FMO calculations in the rational design of RNA-targeted small molecules.

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.

Evaluating the correlation of binding affinities between isothermal titration calorimetry and fragment molecular orbital method of estrogen receptor beta with diarylpropionitrile (DPN) or DPN derivatives

Estrogen receptors (ERs) are ligand-activated transcription factors, with two subtypes ERα and ERβ. The endogenous ligand of ERs is the common 17β-estradiol, and the ligand-binding pocket of ERα and ERβ is very similar. Nevertheless, some ERβ-selective agonist ligands have been reported. DPN (diarylpropionitrile) is a widely used ERβ-selective agonist; however, the structure of the ERβ-DPN complex has not been solved. Therefore, the bound-state conformation of DPN and its enantioselectivity remain unresolved. In this report, we present the structures of the complexes of ERβ with DPN or its derivatives that include a chlorine atom by the X-ray crystallography. Additionally, we measured the binding affinity between ERβ and DPN or derivatives by isothermal titration calorimetry (ITC) and estimated the binding affinity by fragment molecular orbital (FMO) calculations. We also examined the correlation between the ITC data and results from the FMO calculations. FMO calculations showed that S-DPN interacts strongly with three amino acids (Glu305, Phe356, and His475) of ERβ, and ITC measurements confirmed that the chlorine atom of the DPN derivatives enhances binding affinity. The enthalpy change by ITC correlated strongly with the interaction energy (total IFIEs; inter-fragment interaction energies) calculated by FMO (R = 0.870). We propose that FMO calculations are a valuable approach for enhancing enthalpy contributions in drug design, and its scope of applications includes halogen atoms such as chlorine. This study is the first quantitative comparison of thermodynamic parameters obtained from ITC measurements and FMO calculations, providing new insights for future precise drug design.

Protein-ligand binding affinity prediction of cyclin-dependent kinase-2 inhibitors by dynamically averaged fragment molecular orbital-based interaction energy

Fragment molecular orbital (FMO) method is a powerful computational tool for structure-based drug design, in which protein-ligand interactions can be described by the inter-fragment interaction energy (IFIE) and its pair interaction energy decomposition analysis (PIEDA). Here, we introduced a dynamically averaged (DA) FMO-based approach in which molecular dynamics simulations were used to generate multiple protein-ligand complex structures for FMO calculations. To assess this approach, we examined the correlation between the experimental binding free energies and DA-IFIEs of six CDK2 inhibitors whose net charges are zero. The correlation between the experimental binding free energies and snapshot IFIEs for X-ray crystal structures was R²  = 0.75. Using the DA-IFIEs, the correlation significantly improved to 0.99. When an additional CDK2 inhibitor with net charge of -1 was added, the DA FMO-based scheme with the dispersion energies still achieved R²  = 0.99, whereas R² decreased to 0.32 employing all the energy terms of PIEDA.

Computational prediction of heteromeric protein complex disassembly order using hybrid Monte Carlo/molecular dynamics simulation

The physicochemical entities comprising the biological phenomena in the cell form a network of biochemical reactions and the activity of such a network is regulated by multimeric protein complexes. Mass spectroscopy (MS) experiments and multimeric protein docking simulations based on structural bioinformatics techniques have revealed the molecular-level stoichiometry and static configuration of subcomplexes in their bound forms, thus revealing the subcomplex population and formation orders. Meanwhile, these methodologies are not designed to straightforwardly examine the temporal dynamics of multimeric protein assembly and disassembly, essential physicochemical properties to understand the functional expression mechanisms of proteins in the biological environment. To address this problem, we have developed an atomistic simulation in the framework of the hybrid Monte Carlo/molecular dynamics (hMC/MD) method and succeeded in observing the disassembly of a homomeric pentamer of the serum amyloid P component protein in an experimentally consistent order. In this study, we improved the hMC/MD method to examine the disassembly processes of the tryptophan synthase tetramer, a paradigmatic heteromeric protein complex in MS studies. We employed the likelihood-based selection scheme to determine a dissociation-prone subunit pair at every hMC/MD simulation cycle and achieved highly reliable predictions of the disassembly orders without a priori knowledge of the MS experiments and structural bioinformatics simulations. The success rate for the experimentally-observed disassembly order is over 0.9. We similarly succeeded in reliable predictions for three other tetrameric protein complexes. These achievements indicate the potential applicability of our hMC/MD approach as a general-purpose methodology to obtain microscopic and physicochemical insights into multimeric protein complex formation.

The Effect of Interaction between Nanofillers and Epoxy on Mechanical and Thermal Properties of Nanocomposites: Theoretical Prediction and Experimental Analysis

Interfacial interaction between host matrix and nanofillers is a determinative parameter on the mechanical and thermal properties of nanocomposites. In this paper, we first investigated interaction between carbon nanotube (CNT) and montmorillonite clay (MMT) absorbing on epoxy surface in a theoretical study based on the density functional theory (DFT) calculations. Results showed the interaction energy of -1.93 and -0.11 eV for MMT/epoxy and CNT/epoxy, respectively. Therefore, the interaction between epoxy polymer and MMT is of the chemisorptions type, while epoxy physically interacts with CNT. In addition, thermal and mechanical analyses were conducted on nanocomposites. In DSC analysis the glass transition temperature which was 70°C in neat epoxy composite showed an improvement to about 90°C in MMT nanocomposites while it was about 70°C for CNT nanocomposites. Finally, mechanical properties were investigated and MMT nanocomposite showed a change in compressive strength which increased from 52.60 Mpa to 72.07 and 92.98 Mpa in CNT and MMT nanocomposites, respectively. Also tensile strength improved to the value of 1250.69 Mpa MMT nanocomposites while it was about 890 Mpa in both CNT nanocomposite and neat epoxy composite which corresponds to the calculation result prediction.

Fragment Molecular Orbital Calculations with Implicit Solvent Based on the Poisson-Boltzmann Equation: II. Protein and Its Ligand-Binding System Studies

In this study, the electronic properties of bioactive proteins were analyzed using an ab initio fragment molecular orbital (FMO) methodology in solution: coupling with an implicit solvent model based on the Poisson-Boltzmann surface area called as FMO-PBSA. We investigated the solvent effects on practical and heterogeneous targets with uneven exposure to solvents unlike deoxyribonucleic acid analyzed in our recent study. Interfragment interaction energy (IFIE) and its decomposition analyses by FMO-PBSA revealed solvent-screening mechanisms that affect local stability inside ubiquitin protein: the screening suppresses excessiveness in bare charge-charge interactions and enables an intuitive IFIE analysis. The electrostatic character and associated solvation free energy also give consistent results as a whole to previous studies on the explicit solvent model. Moreover, by using the estrogen receptor alpha (ERα) protein bound to ligands, we elucidated the importance of specific interactions that depend on the electric charge and activatability as agonism/antagonism of the ligand while estimating the influences of the implicit solvent on the ligand and helix-12 bindings. The predicted ligand-binding affinities of bioactive compounds to ERα also show a good correlation with their in vitro activities. The FMO-PBSA approach would thus be a promising tool both for biological and pharmaceutical research targeting proteins.

Towards good correlation between fragment molecular orbital interaction energies and experimental IC50 for ligand binding: A case study of p38 MAP kinase

We describe several procedures for the preprocessing of fragment molecular orbital (FMO) calculations on p38 mitogen-activated protein (MAP) kinase and discuss the influence of the procedures on the protein–ligand interaction energies represented by inter-fragment interaction energies (IFIEs). The correlation between the summation of IFIEs for a ligand and amino acid residues of protein (IFIE-sum) and experimental affinity values (IC₅₀) was poor when considered for the whole set of protein–ligand complexes. To improve the correlation for prediction of ligand binding affinity, we carefully classified data set by the ligand charge, the DFG-loop state (DFG-in/out loop), which is characteristic of kinase, and the scaffold of ligand. The correlation between IFIE-sums and the activity values was examined using the classified data set. As a result, it was confirmed that there was a selected data set that showed good correlation between IFIE-sum and activity value by appropriate classification. In addition, we found that the differences in protonation and hydrogen orientation caused by subtle differences in preprocessing led to a relatively large difference in IFIE values. Further, we also examined the effect of structure optimization with different force fields. It was confirmed that the difference in the force field had no significant effect on IFIE-sum. From the viewpoint of drug design using FMO calculations, various investigations on IFIE-sum in this research, such as those regarding several classifications of data set and the different procedures of structural preparation, would be expected to provide useful knowledge for improvement of prediction ability about the ligand binding affinity.

Fragment-based quantum mechanical calculation of protein-protein binding affinities

The electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method has been successfully utilized for efficient linear-scaling quantum mechanical (QM) calculation of protein energies. In this work, we applied the EE-GMFCC method for calculation of binding affinity of Endonuclease colicin-immunity protein complex. The binding free energy changes between the wild-type and mutants of the complex calculated by EE-GMFCC are in good agreement with experimental results. The correlation coefficient (R) between the predicted binding energy changes and experimental values is 0.906 at the B3LYP/6-31G*-D level, based on the snapshot whose binding affinity is closest to the average result from the molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) calculation. The inclusion of the QM effects is important for accurate prediction of protein-protein binding affinities. Moreover, the self-consistent calculation of PB solvation energy is required for accurate calculations of protein-protein binding free energies. This study demonstrates that the EE-GMFCC method is capable of providing reliable prediction of relative binding affinities for protein-protein complexes. © 2018 Wiley Periodicals, Inc.

Computational biochemical investigation of the binding energy interactions between an estrogen receptor and its agonists

We present the energy profiles of estrogen receptor–agonist ligand interactions in atomic detail using a quantum biochemical approach.

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 BioFragment Database (BFDb): An open-data platform for computational chemistry analysis of noncovalent interactions

Accurate potential energy models are necessary for reliable atomistic simulations of chemical phenomena. In the realm of biomolecular modeling, large systems like proteins comprise very many noncovalent interactions (NCIs) that can contribute to the protein's stability and structure. This work presents two high-quality chemical databases of common fragment interactions in biomolecular systems as extracted from high-resolution Protein DataBank crystal structures: 3380 sidechain-sidechain interactions and 100 backbone-backbone interactions that inaugurate the BioFragment Database (BFDb). Absolute interaction energies are generated with a computationally tractable explicitly correlated coupled cluster with perturbative triples [CCSD(T)-F12] "silver standard" (0.05 kcal/mol average error) for NCI that demands only a fraction of the cost of the conventional "gold standard," CCSD(T) at the complete basis set limit. By sampling extensively from biological environments, BFDb spans the natural diversity of protein NCI motifs and orientations. In addition to supplying a thorough assessment for lower scaling force-field (2), semi-empirical (3), density functional (244), and wavefunction (45) methods (comprising >1M interaction energies), BFDb provides interactive tools for running and manipulating the resulting large datasets and offers a valuable resource for potential energy model development and validation.

Structural Basis and Mechanism of Chiral Benzedrine Molecules Interacting With Third Dopamine Receptor

In order to investigate the chiral benzedrine molecules corresponding to their different characteristics in biochemical systems, we studied their interaction with D3 R using the docking method, molecular dynamic simulation, and quantum chemistry. The obtained results indicate that the active residues for R-benzedrine (RAT) bound with D3 R are Ala132, Asp133, and Tyr55, while Asn57, Asp133, Asp168, Cys172, Gly54, Trp24, and Vall136 act as the active residues for S-benzedrine (SAT). The different active pockets are observed for ART or SAT because they possess different active residues. The binding energies between RAT and SAT with D3 R were determined to be -44.0 kJ.mol(-1) and -71.2 kJ.mol(-1) , respectively. These results demonstrate that SAT within the studied pocket of D3 R has a stronger capability of binding with D3 R, while it is more feasible for RAT to leave from the interior positions of D3 R. In addition, the results suggest that the D3 R protein can recognize chiral benzedrine molecules and influence their different addictive and pharmacological effects in biochemical systems. Chirality 28:674-685, 2016. © 2016 Wiley Periodicals, Inc.

Subsystem Analysis for the Fragment Molecular Orbital Method and Its Application to Protein-Ligand Binding in Solution

A subsystem analysis is derived incorporating interfragment interactions into the fragment properties, such as energies or charges. The relative stabilities of three alanine isomers, the α-helix, the β-turn, and the extended form are studied and the differences in fragment properties are elucidated. The analysis is further elaborated for studies of binding energies. The binding of the Trp-cage protein (PDB: 1L2Y ) to two ligands is studied in detail. Binding energies defined for each fragment can be used as a convenient descriptor for analyzing contributions to binding in solution.

Using DFT methodology for more reliable predictive models: Design of inhibitors of Golgi α-Mannosidase II

Human Golgi α-mannosidase II (GMII), a zinc ion co-factor dependent glycoside hydrolase (E.C.3.2.1.114), is a pharmaceutical target for the design of inhibitors with anti-cancer activity. The discovery of an effective inhibitor is complicated by the fact that all known potent inhibitors of GMII are involved in unwanted co-inhibition with lysosomal α-mannosidase (LMan, E.C.3.2.1.24), a relative to GMII. Routine empirical QSAR models for both GMII and LMan did not work with a required accuracy. Therefore, we have developed a fast computational protocol to build predictive models combining interaction energy descriptors from an empirical docking scoring function (Glide-Schrödinger), Linear Interaction Energy (LIE) method, and quantum mechanical density functional theory (QM-DFT) calculations. The QSAR models were built and validated with a library of structurally diverse GMII and LMan inhibitors and non-active compounds. A critical role of QM-DFT descriptors for the more accurate prediction abilities of the models is demonstrated. The predictive ability of the models was significantly improved when going from the empirical docking scoring function to mixed empirical-QM-DFT QSAR models (Q(2)=0.78-0.86 when cross-validation procedures were carried out; and R(2)=0.81-0.83 for a testing set). The average error for the predicted ΔGbind decreased to 0.8-1.1kcalmol(-1). Also, 76-80% of non-active compounds were successfully filtered out from GMII and LMan inhibitors. The QSAR models with the fragmented QM-DFT descriptors may find a useful application in structure-based drug design where pure empirical and force field methods reached their limits and where quantum mechanics effects are critical for ligand-receptor interactions. The optimized models will apply in lead optimization processes for GMII drug developments.

Synthesis of bio-based epoxy monomers from natural allyl- and vinyl phenols and the estimation of their affinity to the estrogen receptor α by molecular docking

Potential substitutes of diglycidyl ether of bisphenol A (DGEBA) were synthesized by the metathesis reaction of glycidylated biobased phenolic compounds.

Investigation of the molecular similarity in closely related protein systems: The PrP case study

The amyloid conversion is a massive detrimental modification affecting several proteins upon specific physical or chemical stimuli characterizing a plethora of diseases. In many cases, the amyloidogenic stimuli induce specific structural features to the protein conferring the propensity to misfold and form amyloid deposits. The investigation of mutants, structurally similar to their native isoform but inherently prone to amyloid conversion, may be a viable strategy to elucidate the structural features connected with amyloidogenesis. In this article, we present a computational protocol based on the combination of molecular dynamics (MD) and grid-based approaches suited for the pairwise comparison of closely related protein structures. This method was applied on the cellular prion protein (PrP(C)) as a case study and, in particular, addressed to the quali/quantification of the structural features conferred by either E200K mutations and treatment with CaCl(2), both able to induce the scrapie conversion of PrP. Several schemes of comparison were developed and applied to this case study, and made up suitable of application to other protein systems. At this purpose an in-house python codes has been implemented that, together with the parallelization of the GRID force fields program, will spread the applicability of the proposed computational procedure.

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.

Theoretical insight into the structural mechanism for the binding of vinblastine with tubulin

Vinblastine (VLB) is one of vinca alkaloids with high cytotoxicity toward cancer cells approved for clinical use. However, because of drug resistance, toxicity, and other side effects caused from the use of VLB, new vinca alkaloids with higher cytotoxicity toward cancer cells and other good qualities need to develop. One strategy is to further study and better understand the essence why VLB possesses the high cytotoxicity toward cancer cells. In present work, by using molecular simulation, molecular docking, density functional calculation, and the crystal structure of α,β-tubulin complex, we find two modes labeled in catharanthine moiety (CM) and vindoline moiety (VM) modes of VLB bound with the interface of α,β-tubulin to probe the essence why VLB has the high cytotoxicity toward cancer cells. In the CM mode, nine key residues B-Ser178, B-Asp179, B-Glu183, B-Tyr210, B-Asp226, C-Lys326, C-Asp327, C-Lys336, and C-Lys352 from the α,β-tubulin complex are determined as the active sites for the interaction of VLB with α,β-tubulin. Some of them such as B-Ser178, B-Glu183, B-Tyr210, B-Asp226, C-Lys326, C-Asp327, and C-Lys336 are newly identified as the active sites in present work. The affinity between VLB and the active pocket within the interface of α,β-tubulin is -60.8 kJ mol(-1) in the CM mode. In the VM mode, that is a new mode established in present paper, nine similar key residues B-Lys176, B-Ser178, B-Asp179, B-Glu183, B-Tyr210, B-Asp226, C-Lys326, C-Asp327, and C-Lys336 from the α,β-tubulin complex are found as the active sites for the interaction with VLB. The difference is from one key residue C-Lys352 in the CM mode changed to the key residue B-Lys176 in the VM mode. The affinity between VLB and the active pocket within the interface of α,β-tubulin is -96.3 kJ mol(-1) in the VM mode. Based on the results obtained in present work, and because VLB looks like two faces, composed of CM and VM both to have similar polar active groups, to interact with the active sites, we suggest double-faces sticking mechanism for the binding of VLB to the interface of α,β-tubulin. The double-faces sticking mechanism can be used to qualitatively explain high cytotoxicity toward cancer cells of vinca alkaloids including vinblastine, vincristine, vindestine, and vinorelbine approved for clinical use and vinflunine still in a phase III clinical trial. Furthermore, this mechanism will be applied to develop novel vinca alkaloids with much higher cytotoxicity toward cancer cells.

Energy decomposition analysis approaches and their evaluation on prototypical protein–drug interaction patterns

The partitioning of the interaction energy into chemical components such as electrostatics, polarization, and charge transfer is possible with energy decomposition analysis approaches. We review and evaluate these for biomolecular applications.

QM and QM/MM simulations of proteins

Molecular dynamics simulations of biomolecules have matured into powerful tools of structural biology. In addition to the commonly used empirical force field potentials, quantum mechanical descriptions are gaining popularity for structure optimization and dynamic simulations of peptides and proteins. In this chapter, we introduce methodological developments such as the QM/MM framework and linear-scaling QM that make efficient calculations on large biomolecules possible. We identify the most common scenarios in which quantum descriptions of peptides and proteins are employed, such as structural refinement, force field development, treatment of unusual residues, and predicting spectroscopic and exited state properties. The benefits and shortcomings of QM potentials, in comparison to classical force fields, are discussed, with special emphasis on the sampling problems of protein conformational space. Finally, recent examples of QM/MM calculations in light-sensitive membrane proteins illustrate typical applications of the reviewed methods.

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.

RANK-ORDERING THE BINDING AFFINITY FOR FKBP12 AND H1N1 NEURAMINIDASE INHIBITORS IN THE COMBINATION OF A PROTEIN MODEL WITH DENSITY FUNCTIONAL THEORY

The quantum mechanical interaction energies between FKBP12 as well as H1N1 neuraminidase and their inhibitors were directly calculated with an efficient density functional theory by mimicking the whole protein with a protein model composed of the amino acids surrounding the ligands. It was found that the calculated quantum mechanical interaction energies correlate well with the experimental binding free energies with the correlation coefficients of 0.88, 0.86, and the standard deviation of 0.93 and 1.00 kcal/mol, respectively. To compare with force field approach, the binding free energies with the correlation coefficient R = 0.80 and 0.47 were estimated by AutoDock 4.0 programs. It was indicated that the quantum interaction energy shows a better performance in rank-ordering the binding affinity between FKBP12 and H1N1 neuraminidase inhibitors than those of AutoDock 4.0 program. In combination protein model with density functional theory, the estimated quantum interaction energy could be a good predictor or scoring function in structure-based computer-aided drug design. Finally, five new FKBP12 inhibitors were designed based on calculated quantum mechanical interaction energy. In particular, the theoretical K i value of one compound is as low as 0.05 nM, nearly 8-fold more active than FK506.

SUPPLEMENTING THE PBSA APPROACH WITH QUANTUM MECHANICS TO STUDY THE BINDING BETWEEN CDK2 AND N2-SUBSTITUTED O6-CYCLOHEXYLMETHOXYGUANINE INHIBITORS

Because classical Poisson–Boltzman Surface Area (PBSA) model does not allow re-polarization of charges and does not account for charge transfer when a ligand binds to a protein, we have examined a hybrid approach in which we describe the protein–ligand interface by quantum mechanics and the rest of the system with the classical PBSA model. We found this approach to rank order the binding of five N2 -substituted O6 -cyclohexylmethoxyguanine inhibitors to CDK2 (cyclin-dependent kinase 2) properly. The calculated binding free energy correlated well with experimental Log(IC50) with a correlation coefficient of 0.94. A regression fit between experimental Log(IC50) and calculated binding free energy yielded a root-mean-square error of 0.48 when Log(IC50) spanned a range over three units. In addition, we observed charge transfer between the ligand and the protein at the interface — an effect not accounted for by the classical PBSA model. We also found that the direct interactions between the protein and the ligands provided the dominant factor to distinguish the binding affinity of the five ligands studied here. This hybrid approach can better prioritize derivatives of lead compounds for synthesis and biological evaluation.

Model for the fast estimation of basis set superposition error in biomolecular systems

Basis set superposition error (BSSE) is a significant contributor to errors in quantum-based energy functions, especially for large chemical systems with many molecular contacts such as folded proteins and protein-ligand complexes. While the counterpoise method has become a standard procedure for correcting intermolecular BSSE, most current approaches to correcting intramolecular BSSE are simply fragment-based analogues of the counterpoise method which require many (two times the number of fragments) additional quantum calculations in their application. We propose that magnitudes of both forms of BSSE can be quickly estimated by dividing a system into interacting fragments, estimating each fragment's contribution to the overall BSSE with a simple statistical model, and then propagating these errors throughout the entire system. Such a method requires no additional quantum calculations, but rather only an analysis of the system's interacting fragments. The method is described herein and is applied to a protein-ligand system, a small helical protein, and a set of native and decoy protein folds.

Molecular dynamics simulation and density functional theory studies on the active pocket for the binding of paclitaxel to tubulin

Paclitaxel (PTX) is used to treat various cancers, but it also causes serious side effects and resistance. To better design similar compounds with less toxicity and more activity against drug-resistant tumors, it is important to clearly understand the PTX-binding pocket formed by the key residues of active sites on β-tubulin. Using a docking method, molecular dynamics (MD) simulation and density functional theory (DFT), we identified some residues (such as Arg278, Asp26, Asp226, Glu22, Glu27, His229, Arg369, Lys218, Ser277 and Thr276) on β-tubulin that are the active sites responsible for interaction with PTX. Another two residues, Leu371 and Gly279, also likely serve as active sites. Most of these sites contact with the "southern hemisphere" of PTX; only one key residue interacts with the "northern hemisphere" of PTX. These key residues can be divided into four groups, which serve as active compositions in the formation of an active pocket for PTX binding to β-tubulin. This active binding pocket enables a very strong interaction (the strength is predicted to be in the range of -327.8 to -365.7 kJ mol(-1)) between β-tubulin and PTX, with various orientated conformations. This strong interaction means that PTX possesses a high level of activity against cancer cells, a result that is in good agreement with the clinical mechanism of PTX. The described PTX pocket and key active residues will be applied to probe the mechanism of tumor cells resistant to PTX, and to design novel analogs with superior properties.

Formal Estimation of Errors in Computed Absolute Interaction Energies of Protein-ligand Complexes

A largely unsolved problem in computational biochemistry is the accurate prediction of binding affinities of small ligands to protein receptors. We present a detailed analysis of the systematic and random errors present in computational methods through the use of error probability density functions, specifically for computed interaction energies between chemical fragments comprising a protein-ligand complex. An HIV-II protease crystal structure with a bound ligand (indinavir) was chosen as a model protein-ligand complex. The complex was decomposed into twenty-one (21) interacting fragment pairs, which were studied using a number of computational methods. The chemically accurate complete basis set coupled cluster theory (CCSD(T)/CBS) interaction energies were used as reference values to generate our error estimates. In our analysis we observed significant systematic and random errors in most methods, which was surprising especially for parameterized classical and semiempirical quantum mechanical calculations. After propagating these fragment-based error estimates over the entire protein-ligand complex, our total error estimates for many methods are large compared to the experimentally determined free energy of binding. Thus, we conclude that statistical error analysis is a necessary addition to any scoring function attempting to produce reliable binding affinity predictions.