An efficient linear scaling method for ab initio calculation of electron density of proteins

Quantum biochemistry description of PI3Kα enzyme bound to selective inhibitors

The PI3K class I is composed of four PI3K isoforms that serve as regulatory enzymes governing cellular metabolism, proliferation, and survival. The hyperactivation of PI3Kα is observed in various types of cancer and is linked to poor prognosis. Unfortunately, the development inhibitors selectively targeting one of the isoforms remains challenging, with only few agents in clinical use. The main difficulty arises from the high conservation among residues at the ATP-binding pocket across isoforms, which also serves as target pocket for inhibitors. In this work, molecular dynamics and quantum calculations were performed to investigate the molecular features guiding the binding of selective inhibitors, alpelisib and GDC-0326, into the ATP-binding pocket of PI3Kα. While molecular dynamics allowed crystallographic coordinates to relax, the interaction eergy between each amino acid residues and inhibitors was obtained by combining the Molecular Fractionation with Conjugated Caps scheme with Density Functional Theory calculations. In addition, the atomic charge of ligands in the bound and unbound (free) was calculated. Results indicated that the most relevant residues for the binding of alpelisib are Ile932, Glu859, Val851, Val850, Tyr836, Met922, Ile800, and Ile848, while the most important residues for the binding of GDC-0326 are Ile848, Ile800, Ile932, Gln859, Glu849, and Met922. In addition, residues Trp780, Ile800, Tyr836, Ile848, Gln859 Val850, Val851, Ile932 and Met922 are common hotspots for both inhibitors. Overall, the results from this work contribute to improving the understanding of the molecular mechanisms controlling selectivity and highlight important interactions to be considered during the rational design of new agents.Communicated by Ramaswamy H. Sarma.

Toward a general neural network force field for protein simulations: Refining the intramolecular interaction in protein

Molecular dynamics (MD) is an extremely powerful, highly effective, and widely used approach to understanding the nature of chemical processes in atomic details for proteins. The accuracy of results from MD simulations is highly dependent on force fields. Currently, molecular mechanical (MM) force fields are mainly utilized in MD simulations because of their low computational cost. Quantum mechanical (QM) calculation has high accuracy, but it is exceedingly time consuming for protein simulations. Machine learning (ML) provides the capability for generating accurate potential at the QM level without increasing much computational effort for specific systems that can be studied at the QM level. However, the construction of general machine learned force fields, needed for broad applications and large and complex systems, is still challenging. Here, general and transferable neural network (NN) force fields based on CHARMM force fields, named CHARMM-NN, are constructed for proteins by training NN models on 27 fragments partitioned from the residue-based systematic molecular fragmentation (rSMF) method. The NN for each fragment is based on atom types and uses new input features that are similar to MM inputs, including bonds, angles, dihedrals, and non-bonded terms, which enhance the compatibility of CHARMM-NN to MM MD and enable the implementation of CHARMM-NN force fields in different MD programs. While the main part of the energy of the protein is based on rSMF and NN, the nonbonded interactions between the fragments and with water are taken from the CHARMM force field through mechanical embedding. The validations of the method for dipeptides on geometric data, relative potential energies, and structural reorganization energies demonstrate that the CHARMM-NN local minima on the potential energy surface are very accurate approximations to QM, showing the success of CHARMM-NN for bonded interactions. However, the MD simulations on peptides and proteins indicate that more accurate methods to represent protein-water interactions in fragments and non-bonded interactions between fragments should be considered in the future improvement of CHARMM-NN, which can increase the accuracy of approximation beyond the current mechanical embedding QM/MM level.

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

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

Fragmentation and transferability in Hirshfeld atom refinement

Hirshfeld atom refinement (HAR) is one of the most effective methods for obtaining accurate structural parameters for hydrogen atoms from X-ray diffraction data. Unfortunately, it is also relatively computationally expensive, especially for larger molecules due to wavefunction calculations. Here, a fragmentation approach has been tested as a remedy for this problem. It gives an order of magnitude improvement in computation time for larger organic systems and is a few times faster for metal-organic systems at the cost of only minor differences in the calculated structural parameters when compared with the original HAR calculations. Fragmentation was also applied to polymeric and disordered systems where it provides a natural solution to problems that arise when HAR is applied. The concept of fragmentation is closely related to the transferable aspherical atom model (TAAM) and allows insight into possible ways to improve TAAM. Hybrid approaches combining fragmentation with the transfer of atomic densities between chemically similar atoms have been tested. An efficient handling of intermolecular interactions was also introduced for calculations involving fragmentation. When applied in fragHAR (a fragmentation approach for polypeptides) as a replacement for the original approach, it allowed for more efficient calculations. All of the calculations were performed with a locally modified version of Olex2 combined with a development version of discamb2tsc and ORCA. Care was taken to efficiently use the power of multicore processors by simple implementation of load-balancing, which was found to be very important for lowering computational time.

Three-Layer Multiscale Approach Based on Extremely Localized Molecular Orbitals to Investigate Enzyme Reactions

Quantum mechanics/molecular mechanics (QM/MM) calculations are widely used embedding techniques to computationally investigate enzyme reactions. In most QM/MM computations, the quantum mechanical region is treated through density functional theory (DFT), which offers the best compromise between chemical accuracy and computational cost. Nevertheless, to obtain more accurate results, one should resort to wave function-based methods, which however lead to a much larger computational cost already for relatively small QM subsystems. To overcome this drawback, we propose the coupling of our QM/ELMO (quantum mechanics/extremely localized molecular orbital) approach with molecular mechanics, thus introducing the three-layer QM/ELMO/MM technique. The QM/ELMO strategy is an embedding method in which the chemically relevant part of the system is treated at the quantum mechanical level, while the rest is described through frozen ELMOs. Since the QM/ELMO method reproduces results of fully QM computations within chemical accuracy and with a much lower computational effort, it can be considered a suitable strategy to extend the range of applicability and accuracy of the QM/MM scheme. In this paper, other than briefly presenting the theoretical bases of the QM/ELMO/MM technique, we will also discuss its validation on the well-tested deprotonation of acetyl coenzyme A by aspartate in citrate synthase.

Docking Paradigm in Drug Design

Docking is in demand for the rational computer aided structure based drug design. A review of docking methods and programs is presented. Different types of docking programs are described. They include docking of non-covalent small ligands, protein-protein docking, supercomputer docking, quantum docking, the new generation of docking programs and the application of docking for covalent inhibitors discovery. Taking into account the threat of COVID-19, we present here a short review of docking applications to the discovery of inhibitors of SARS-CoV and SARS-CoV-2 target proteins, including our own result of the search for inhibitors of SARS-CoV-2 main protease using docking and quantum chemical post-processing. The conclusion is made that docking is extremely important in the fight against COVID-19 during the process of development of antivirus drugs having a direct action on SARS-CoV-2 target proteins.

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.

Polarizable Density Embedding for Large Biomolecular Systems

We present an efficient and robust fragment-based quantum-classical embedding model capable of accurately capturing effects from complex environments such as proteins and nucleic acids. This is realized by combining the molecular fractionation with conjugate caps (MFCC) procedure with the polarizable density embedding (PDE) model at the level of Fock matrix construction. The PDE contributions to the Fock matrix of the core region are constructed using the local molecular basis of the individual fragments rather than the supermolecular basis of the entire system. Thereby, we avoid complications associated with the application of the MFCC procedure on environment quantities such as electronic densities and molecular-orbital energies. Moreover, the computational cost associated with solving self-consistent field (SCF) equations of the core region remains unchanged from that of purely classical polarized embedding models. We analyze the performance of the resulting model in terms of the reproduction of the electrostatic potential of an insulin monomer protein and further in the context of solving problems related to electron spill-out. Finally, we showcase the model for the calculation of one- and two-photon properties of the Nile red molecule in a protein environment. Based on our analyses, we find that the combination of the MFCC approach with the PDE model is an efficient, yet accurate approach for calculating molecular properties of molecules embedded in structured biomolecular environments.

mTOR–mLST8 interaction: hot spot identification through quantum biochemistry calculations

Quantum calculation of mTOR–mLST8 interaction.

Quantum Mechanics/Extremely Localized Molecular Orbital Method: A Fully Quantum Mechanical Embedding Approach for Macromolecules

The development of methods for the quantum mechanical study of macromolecules has always been an important challenge in theoretical chemistry. Nowadays, the techniques proposed in this context can be used to investigate very large systems and can be subdivided into two main categories: fragmentation and embedding strategies. In this paper, by modifying and improving the local self-consistent field approach originally proposed for quantum mechanics/molecular mechanics techniques, we introduce the new multiscale embedding quantum mechanics/extremely localized molecular orbital (QM/ELMO) method. The new strategy enables treatment of chemically relevant regions of large biological molecules through usual methods of quantum chemistry while describing the remaining parts of the systems by means of frozen extremely localized molecular orbitals transferred from properly constructed libraries. Test calculations have shown the correct functioning and the high reliability of the new approach, thus anticipating its possible applications to different fields of physical chemistry, such as rational drug design and structural refinements of proteins.

Toward Building Protein Force Fields by Residue-Based Systematic Molecular Fragmentation and Neural Network

Accurate force fields are crucial for molecular dynamics investigation of complex biological systems. Building accurate protein force fields from quantum mechanical (QM) calculations is challenging due to the complexity of proteins and high computational costs of QM methods. In order to overcome these two difficulties, here we developed the residue-based systematic molecular fragmentation method to partition general proteins into only 20 types of amino acid dipeptides and one type of peptide bond at level 1. The total energy of proteins is the combination of the energies of these fragments. Each type of the fragments is then parametrized using neural network (NN) representation of the QM reference. Adopting NN representation can circumvent the limitation of the analytic form of classical molecular mechanics (MM) force fields. Using MM force fields as the baseline, our method adds NN representation of QM corrections at the length scale of amino acid dipeptides. We tested our force fields for both homogeneous and heterogeneous polypeptides. Energy and forces predicted by our force fields compare favorably with full QM calculations from tripeptides to decapeptides. Our development provides an efficient and accurate method of building protein force fields fully from ab initio QM calculations.

Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks

The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.

Charge-patching method for the calculation of electronic structure of polypeptides

Based on the CPM method, the charge densities of polypeptides can be generated and their electronic structure can be further calculated.

Outlining migrainous through dihydroergotamine–serotonin receptor interactions using quantum biochemistry

We present the electronic structure of the complex dihydroergotamine–serotonin receptor to unveil new medications to treat migraine and related diseases.

Quantum mechanical force fields for condensed phase molecular simulations

Molecular simulations are powerful tools for providing atomic-level details into complex chemical and physical processes that occur in the condensed phase. For strongly interacting systems where quantum many-body effects are known to play an important role, density-functional methods are often used to provide the model with the potential energy used to drive dynamics. These methods, however, suffer from two major drawbacks. First, they are often too computationally intensive to practically apply to large systems over long time scales, limiting their scope of application. Second, there remain challenges for these models to obtain the necessary level of accuracy for weak non-bonded interactions to obtain quantitative accuracy for a wide range of condensed phase properties. Quantum mechanical force fields (QMFFs) provide a potential solution to both of these limitations. In this review, we address recent advances in the development of QMFFs for condensed phase simulations. In particular, we examine the development of QMFF models using both approximate and ab initio density-functional models, the treatment of short-ranged non-bonded and long-ranged electrostatic interactions, and stability issues in molecular dynamics calculations. Example calculations are provided for crystalline systems, liquid water, and ionic liquids. We conclude with a perspective for emerging challenges and future research directions.

Full QM Calculation of RNA Energy Using Electrostatically Embedded Generalized Molecular Fractionation with Conjugate Caps Method

In this study, the electrostatically embedded generalized molecular fractionation with conjugate caps (concaps) method (EE-GMFCC) was employed for efficient linear-scaling quantum mechanical (QM) calculation of total energies of RNAs. In the EE-GMFCC approach, the total energy of RNA is calculated by taking a proper combination of the QM energy of each nucleotide-centric fragment with large caps or small caps (termed EE-GMFCC-LC and EE-GMFCC-SC, respectively) deducted by the energies of concaps. The two-body QM interaction energy between non-neighboring ribonucleotides which are spatially in close contact are also taken into account for the energy calculation. Numerical studies were carried out to calculate the total energies of a number of RNAs using the EE-GMFCC-LC and EE-GMFCC-SC methods at levels of the Hartree-Fock (HF) method, density functional theory (DFT), and second-order many-body perturbation theory (MP2), respectively. The results show that the efficiency of the EE-GMFCC-SC method is about 3 times faster than the EE-GMFCC-LC method with minimal accuracy sacrifice. The EE-GMFCC-SC method is also applied for relative energy calculations of 20 different conformers of two RNA systems using HF and DFT, respectively. Both single-point and relative energy calculations demonstrate that the EE-GMFCC method has deviations from the full system results of only a few kcal/mol.

Two Binding Geometries for Risperidone in Dopamine D3 Receptors: Insights on the Fast-Off Mechanism through Docking, Quantum Biochemistry, and Molecular Dynamics Simulations

Risperidone is an atypical antipsychotic used in the treatment of schizophrenia and of symptoms of irritability associated with autism spectrum disorder (ASD). Its main action mechanism is the blockade of D2-like receptors acting over positive and negative symptoms of schizophrenia with small risk of extrapyramidal symptoms (EPS) at doses corresponding to low/moderate D2 occupancy. Such a decrease in the side effect incidence can be associated with its fast unbinding from D2 receptors in the nigrostriatal region allowing the recovery of dopamine signaling pathways. We performed docking essays using risperidone and the D3 receptor crystallographic data and results suggested two possible distinct orientations for risperidone at the binding pocket. Orientation 1 is more close to the opening of the binding site and has the 6-fluoro-1,2 benzoxazole fragment toward the bottom of the D3 receptor cleft, while orientation 2 is deeper inside the binding pocket with the same fragment toward to the receptor surface. In order to unveil the implications of these two binding orientations, classical molecular dynamics and quantum biochemistry computations within the density functional theory formalism and the molecular fractionation with conjugate caps framework were performed. Quantum mechanics/molecular mechanics suggests that orientation 2 (considering the contribution of Glu90) is slightly more energetically stable than orientation 1 with the main contribution coming from residue Asp110. The residue Glu90, positioned at the opening of the binding site, is closer to orientation 1 than 2, suggesting that it may have a key role in stability through attractive interaction with risperidone. Therefore, although orientations 1 and 2 are both likely to occur, we suggest that the occurrence of the first may contribute to the reduction of side effects in patients taking risperidone due to the reduction of dopamine receptor occupancy in the nigrostriatal region through a mechanism of fast dissociation. The atypical effect may be obtained simply by either delaying D3R full blockage by spatial hindrance of orientation 1 at the binding site or through an effective blockade followed by orientation 1 fast dissociation. While the molecular interpretation suggested in this work shed some light on the potential molecular mechanisms accounting for the reduced extrapyramidal symptoms observed during risperidone treatment, further studies are necessary in order to evaluate the implications of both orientations during the receptor activation/inhibition. Altogether these data highlight important hot spots in the dopamine receptor binding site bringing relevant information for the development of novel/derivative agents with atypical profile.

Analysis of Different Fragmentation Strategies on a Variety of Large Peptides: Implementation of a Low Level of Theory in Fragment-Based Methods Can Be a Crucial Factor

We have investigated the performance of two classes of fragmentation methods developed in our group (Molecules-in-Molecules (MIM) and Many-Overlapping-Body (MOB) expansion), to reproduce the unfragmented MP2 energies on a test set composed of 10 small to large biomolecules. They have also been assessed to recover the relative energies of different motifs of the acetyl(ala)18NH2 system. Performance of different bond-cutting environments and the use of Hartree-Fock and different density functionals (as a low level of theory) in conjunction with the fragmentation strategies have been analyzed. Our investigation shows that while a low level of theory (for recovering long-range interactions) may not be necessary for small peptides, it provides a very effective strategy to accurately reproduce the total and relative energies of larger peptides such as the different motifs of the acetyl(ala)18NH2 system. Employing M06-2X as the low level of theory, the calculated mean total energy deviation (maximum deviation) in the total MP2 energies for the 10 molecules in the test set at MIM(d=3.5Å), MIM(η=9), and MOB(d=5Å) are 1.16 (2.31), 0.72 (1.87), and 0.43 (2.02) kcal/mol, respectively. The excellent performance suggests that such fragment-based methods should be of general use for the computation of accurate energies of large biomolecular systems.

The MOD-QM/MM Method: Applications to Studies of Photosystem II and DNA G-Quadruplexes

Quantum mechanics/molecular mechanics (QM/MM) hybrid methods are currently the most powerful computational tools for studies of structure/function relations and catalytic sites embedded in macrobiomolecules (eg, proteins and nucleic acids). QM/MM methodologies are highly efficient since they implement quantum chemistry methods for modeling only the portion of the system involving bond-breaking/forming processes (QM layer), as influenced by the surrounding molecular environment described in terms of molecular mechanics force fields (MM layer). Some of the limitations of QM/MM methods when polarization effects are not explicitly considered include the approximate treatment of electrostatic interactions between QM and MM layers. Here, we review recent advances in the development of computational protocols that allow for rigorous modeling of electrostatic interactions in biomacromolecules and structural refinement, beyond the common limitations of QM/MM hybrid methods. We focus on photosystem II (PSII) with emphasis on the description of the oxygen-evolving complex (OEC) and its high-resolution extended X-ray absorption fine structure spectra (EXAFS) in conjunction with Monte Carlo structural refinement. Furthermore, we review QM/MM structural refinement studies of DNA G4 quadruplexes with embedded monovalent cations and direct comparisons to NMR data.

Libraries of Extremely Localized Molecular Orbitals. 1. Model Molecules Approximation and Molecular Orbitals Transferability

Despite more and more remarkable computational ab initio results are nowadays continuously obtained for large macromolecular systems, the development of new linear-scaling techniques is still an open and stimulating field of research in theoretical chemistry. In this family of methods, an important role is occupied by those strategies based on the observation that molecules are generally constituted by recurrent functional units with well-defined intrinsic features. In this context, we propose to exploit the notion of extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, or functional groups), are in principle transferable from one molecule to another. Accordingly, the construction of orbital libraries to almost instantaneously build up approximate wave functions and electron densities of very large systems becomes conceivable. In this work, the ELMOs transferability is further investigated in detail and, furthermore, suitable rules to construct model molecules for the computation of ELMOs to be stored in future databanks are also defined. The obtained results confirm the reliable transferability of the ELMOs and show that electron densities obtained from the transfer of extremely localized molecular orbitals are very close to the corresponding Hartree-Fock ones. These observations prompt us to construct new ELMOs databases that could represent an alternative/complement to the already popular pseudoatoms databanks both for determining electron densities and for refining crystallographic structures of very large molecules.

A quantum chemistry investigation of a potential inhibitory drug against the dengue virus

The total interaction energy of the inhibitor Bz-nKRR-H bound to a serine protease of the dengue virus is mainly due to the action of Asn152, Met49, Tyr161, Asp129 and Gly151 (Met84, Met75, Asp81, Asp79 and Asp80) residues at the NS3 (NS2B) subunit.

Understanding the basis of I50V-induced affinity decrease in HIV-1 protease via molecular dynamics simulations using polarized force field

Human immunodeficiency virus (HIV)-1 protease is one of the most promising drug target commonly utilized to combat Acquired Immune Deficiency Syndrome (AIDS). However, with the emergence of drug resistance arising from mutations, the efficiency of protease inhibitors (PIs) as a viable treatment for AIDS has been greatly reduced. I50V mutation as one of the most significant mutations occurring in HIV-1 protease will be investigated in this study. Molecular dynamics (MD) simulation was utilized to examine the effect of I50V mutation on the binding of two PIs namely indinavir and amprenavir to HIV-1 protease. Prior to the simulations conducted, the electron density distributions of the PI and each residue in HIV-1 protease are derived by combining quantum fragmentation approach molecular fractionation with conjugate caps and Poisson-Boltzmann solvation model based on polarized protein-specific charge scheme. The atomic charges of the binding complex are subsequently fitted using delta restrained electrostatic potential (delta-RESP) method to overcome the poor charge determination of buried atom. This way, both intraprotease polarization and the polarization between protease and the PI are incorporated into partial atomic charges. Through this study, the mutation-induced affinity variations were calculated and significant agreement between experiments and MD simulations conducted was observed for both HIV-1 protease-drug complexes. In addition, the mechanism governing the decrease in the binding affinity of PI in the presence of I50V mutation was also explored to provide insights pertaining to the design of the next generation of anti-HIV drugs.

Calculation of protein–ligand binding affinities based on a fragment quantum mechanical method

An efficient fragment-based quantum mechanical method has been successfully applied for reliable prediction of protein–ligand binding affinities.

A quantum biochemistry investigation of willardiine partial agonism in AMPA receptors

We employ quantum biochemistry methods based on the Density Functional Theory (DFT) approach to unveil detailed binding energy features of willardiines co-crystallized with the AMPA receptor.

Antipsychotic haloperidol binding to the human dopamine D3 receptor: beyond docking through QM/MM refinement toward the design of improved schizophrenia medicines

As the dopamine D3R receptor is a promising target for schizophrenia treatment, an improved understanding of the binding of existing antipsychotics to this receptor is crucial for the development of new potent and more selective therapeutic agents. In this work, we have used X-ray cocrystallization data of the antagonist eticlopride bound to D3R as a template to predict, through docking essays, the placement of the typical antipsychotic drug haloperidol at the D3R receptor binding site. Afterward, classical and quantum mechanics/molecular mechanics (QM/MM) computations were employed to improve the quality of the docking calculations, with the QM part of the simulations being accomplished by using the density functional theory (DFT) formalism. After docking, the calculated QM improved total interaction energy EQMDI = -170.1 kcal/mol was larger (in absolute value) than that obtained with classical molecular mechanics improved (ECLDI = -156.3 kcal/mol) and crude docking (ECRDI = -137.6 kcal/mol) procedures. The QM/MM computations reveal the pivotal role of the Asp110 amino acid residue in the D3R haloperidol binding, followed by Tyr365, Phe345, Ile183, Phe346, Tyr373, and Cys114. Besides, it highlights the relevance of the haloperidol hydroxyl group axial orientation, which interacts with the Tyr365 and Thr369 residues, enhancing its binding to dopamine receptors. Finally, our computations indicate that functional substitutions in the 4-clorophenyl and in the 4-hydroxypiperidin-1-yl fragments (such as C3H and C12H hydrogen replacement by OH or COOH) can lead to haloperidol derivatives with distinct dopamine antagonism profiles. The results of our work are a first step using in silico quantum biochemical design as means to impact the discovery of new medicines to treat schizophrenia.

Fragment quantum mechanical calculation of proteins and its applications

Conspectus The desire to study molecular systems that are much larger than what the current state-of-the-art ab initio or density functional theory methods could handle has naturally led to the development of novel approximate methods, including semiempirical approaches, reduced-scaling methods, and fragmentation methods. The major computational limitation of ab initio methods is the scaling problem, because the cost of ab initio calculation scales nth power or worse with system size. In the past decade, the fragmentation approach based on chemical locality has opened a new door for developing linear-scaling quantum mechanical (QM) methods for large systems and for applications to large molecular systems such as biomolecules. The fragmentation approach is highly attractive from a computational standpoint. First, the ab initio calculation of individual fragments can be conducted almost independently, which makes it suitable for massively parallel computations. Second, the electron properties, such as density and energy, are typically combined in a linear fashion to reproduce those for the entire molecular system, which makes the overall computation scale linearly with the size of the system. In this Account, two fragmentation methods and their applications to macromolecules are described. They are the electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method and the automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) approach. The EE-GMFCC method is developed from the MFCC approach, which was initially used to obtain accurate protein-ligand QM interaction energies. The main idea of the MFCC approach is that a pair of conjugate caps (concaps) is inserted at the location where the subsystem is divided by cutting the chemical bond. In addition, the pair of concaps is fused to form molecular species such that the overcounted effect from added concaps can be properly removed. By introducing the electrostatic embedding field in each fragment calculation and two-body interaction energy correction on top of the MFCC approach, the EE-GMFCC method is capable of accurately reproducing the QM molecular properties (such as the dipole moment, electron density, and electrostatic potential), the total energy, and the electrostatic solvation energy from full system calculations for proteins. On the other hand, the AF-QM/MM method was used for the efficient QM calculation of protein nuclear magnetic resonance (NMR) parameters, including the chemical shift, chemical shift anisotropy tensor, and spin-spin coupling constant. In the AF-QM/MM approach, each amino acid and all the residues in its vicinity are automatically assigned as the QM region through a distance cutoff for each residue-centric QM/MM calculation. Local chemical properties of the central residue can be obtained from individual QM/MM calculations. The AF-QM/MM approach precisely reproduces the NMR chemical shifts of proteins in the gas phase from full system QM calculations. Furthermore, via the incorporation of implicit and explicit solvent models, the protein NMR chemical shifts calculated by the AF-QM/MM method are in excellent agreement with experimental values. The applications of the AF-QM/MM method may also be extended to more general biological systems such as DNA/RNA and protein-ligand complexes.

Importance of polarization effect in the study of metalloproteins: application of polarized protein specific charge scheme in predicting the reduction potential of azurin

Molecular dynamics (MD) simulation is commonly used in the study of protein dynamics, and in recent years, the extension of MD simulation to the study of metalloproteins is gaining much interest. Choice of force field is crucial in MD studies, and the inclusion of metal centers complicates the process of accurately describing the electrostatic environment that surrounds the redox centre. Herein, we would like to explore the importance of including electrostatic contribution from both protein and solvent in the study of metalloproteins. MD simulations with the implementation of thermodynamic integration will be conducted to model the reduction process of azurin from Pseudomonas aeruginosa. Three charge schemes will be used to derive the partial charges of azurin. These charge schemes differ in terms of the amount of immediate environment, respective to copper, considered during charge fitting, which ranges from the inclusion of copper and residues in the first coordination sphere during density functional theory charge fitting to the comprehensive inclusion of protein and solvent effect surrounding the metal centre using polarized protein-specific charge scheme. From the simulations conducted, the relative reduction potential of the mutated azurins respective to that of wild-type azurin (ΔEcal) were calculated and compared with experimental values. The ΔEcal approached experimental value with increasing consideration of environmental effect hence substantiating the importance of polarization effect in the study of metalloproteins. This study also attests the practicality of polarized protein-specific charge as a computational tool capable of incorporating both protein environment and solvent effect into MD simulations.

Ab initio folding of extended α-helix: a theoretical study about the role of electrostatic polarization in the folding of helical structures

In this work, we report the ab initio folding of three different extended helical peptides namely 2khk, N36, and C34 through conventional molecular dynamics simulation at room temperature using implicit solvation model. Employing adaptive hydrogen bond specific charge (AHBC) scheme to account for the polarization effect of hydrogen bonds established during the simulation, the effective folding of the three extended helices were observed with best backbone RMSDs in comparison to the experimental structures over the helical region determined to be 1.30 Å for 2khk, 0.73 Å for N36 and 0.72 Å for C34. In this study, 2khk will be used as a benchmark case serving as a means to compare the ability of polarized (AHBC) and nonpolarized force field in the folding of an extended helix. Analyses conducted revealed the ability of the AHBC scheme in effectively folding the extended helix by promoting helix growth through the stabilization of backbone hydrogen bonds upon formation during the folding process. Similar observations were also noted when AHBC scheme was employed during the folding of C34 and N36. However, under Amber03 force field, helical structures formed during the folding of 2khk was not accompanied by stabilization thus highlighting the importance of electrostatic polarization in the folding of helical structures.

Improving the scoring of protein-ligand binding affinity by including the effects of structural water and electronic polarization

Docking programs that use scoring functions to estimate binding affinities of small molecules to biological targets are widely applied in drug design and drug screening with partial success. But accurate and efficient scoring functions for protein-ligand binding affinity still present a grand challenge to computational chemists. In this study, the polarized protein-specific charge model (PPC) is incorporated into the molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) method to rescore the binding poses of some protein-ligand complexes, for which docking programs, such as Autodock, could not predict their binding modes correctly. Different sampling techniques (single minimized conformation and multiple molecular dynamics (MD) snapshots) are used to test the performance of MM/PBSA combined with the PPC model. Our results show the availability and effectiveness of this approach in correctly ranking the binding poses. More importantly, the bridging water molecules are found to play an important role in correctly determining the protein-ligand binding modes. Explicitly including these bridging water molecules in MM/PBSA calculations improves the prediction accuracy significantly. Our study sheds light on the importance of both bridging water molecules and the electronic polarization in the development of more reliable scoring functions for predicting molecular docking and protein-ligand binding affinity.

Predicting mutation-induced Stark shifts in the active site of a protein with a polarized force field

The electric field inside a protein has a significant effect on the protein structure, function, and dynamics. Recent experimental developments have offered a direct approach to measure the electric field by utilizing a nitrile-containing inhibitor as a probe that can deliver a unique vibration to the specific site of interest in the protein. The observed frequency shift of the nitrile stretching vibration exhibits a linear dependence on the electric field at the nitrile site, thus providing a direct measurement of the relative electric field. In the present work, molecular dynamics simulations were carried out to compute the electric field shift in human aldose reductase (hALR2) using a polarized protein-specific charge (PPC) model derived from fragment-based quantum-chemistry calculations in implicit solvent. Calculated changes of electric field in the active site of hALR2 between the wild type and mutants were directly compared with measured vibrational frequency shifts (Stark shifts). Our study demonstrates that the Stark shifts calculated using the PPC model are in much better agreement with the experimental data than widely used nonpolarizable force fields, indicating that the electronic polarization effect is important for the accurate prediction of changes in the electric field inside proteins.

Electrostatically embedded generalized molecular fractionation with conjugate caps method for full quantum mechanical calculation of protein energy

An electrostatically embedded generalized molecular fractionation with conjugate caps (EE-GMFCC) method is developed for efficient linear-scaling quantum mechanical (QM) calculation of protein energy. This approach is based on our previously proposed GMFCC/MM method (He; et al. J. Chem. Phys. 2006, 124, 184703), In this EE-GMFCC scheme, the total energy of protein is calculated by taking a linear combination of the QM energy of the neighboring residues and the two-body QM interaction energy between non-neighboring residues that are spatially in close contact. All the fragment calculations are embedded in a field of point charges representing the remaining protein environment, which is the major improvement over our previous GMFCC/MM approach. Numerical studies are carried out to calculate the total energies of 18 real three-dimensional proteins of up to 1142 atoms using the EE-GMFCC approach at the HF/6-31G* level. The overall mean unsigned error of EE-GMFCC for the 18 proteins is 2.39 kcal/mol with reference to the full system HF/6-31G* energies. The EE-GMFCC approach is also applied for proteins at the levels of the density functional theory (DFT) and second-order many-body perturbation theory (MP2), also showing only a few kcal/mol deviation from the corresponding full system result. The EE-GMFCC method is linear-scaling with a low prefactor, trivially parallel, and can be readily applied to routinely perform structural optimization of proteins and molecular dynamics simulation with high level ab initio electronic structure theories.

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.

Solvent effect on the folding dynamics and structure of E6-associated protein characterized from ab initio protein folding simulations

Solvent effect on protein conformation and folding mechanism of E6-associated protein (E6ap) peptide are investigated using a recently developed charge update scheme termed as adaptive hydrogen bond-specific charge (AHBC). On the basis of the close agreement between the calculated helix contents from AHBC simulations and experimental results, we observed based on the presented simulations that the two ends of the peptide may simultaneously take part in the formation of the helical structure at the early stage of folding and finally merge to form a helix with lowest backbone RMSD of about 0.9 Å in 40% 2,2,2-trifluoroethanol solution. However, in pure water, the folding may start at the center of the peptide sequence instead of at the two opposite ends. The analysis of the free energy landscape indicates that the solvent may determine the folding clusters of E6ap, which subsequently leads to the different final folded structure. The current study demonstrates new insight to the role of solvent in the determination of protein structure and folding dynamics.

QM/MM Prediction of the Stark Shift in the Active Site of a Protein

Recent developments in the biophysical characterization of proteins have provided a means of directly measuring electrostatic fields by introducing a probe molecule to the system of interest and interpreting photon absorption in the context of the Stark effect. To fully account for this effect, the development of accurate atomistic models is of paramount importance. However, suitable computational protocols for evaluating Stark shifts in proteins are yet to be established. In this work, we present a comprehensive computational method to predict the change in absorption frequency of a probe functional group as a direct result of a perturbation in its surrounding electrostatic field created by a protein environment, i.e., the Stark shift. We apply the method to human aldose reductase, a key protein enzyme that catalyzes the reduction of monosaccharides. We develop a protocol based on a combination of molecular dynamics and moving-domain QM/MM methods, which achieves quantitative agreement with experiment. We outline the difficulties in predicting localized electrostatic field changes within a protein environment, and by extension the Stark shift, due to a protein site mutation. Furthermore, the combined use of Stark effect spectroscopy and computational modeling is used to predict the protonation state of ionizable residues in the vicinity of the electrostatic probe.