A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

IVSPlat 1.0: an integrated virtual screening platform with a molecular graphical interface

<p>Abstract</p> <p>Background</p> <p>The virtual screening (VS) of lead compounds using molecular docking and pharmacophore detection is now an important tool in drug discovery. VS tasks typically require a combination of several software tools and a molecular graphics system. Thus, the integration of all the requisite tools in a single operating environment could reduce the complexity of running VS experiments. However, only a few freely available integrated software platforms have been developed.</p> <p>Results</p> <p>A free open-source platform, IVSPlat 1.0, was developed in this study for the management and automation of VS tasks. We integrated several VS-related programs into a molecular graphics system to provide a comprehensive platform for the solution of VS tasks based on molecular docking, pharmacophore detection, and a combination of both methods. This tool can be used to visualize intermediate and final results of the VS execution, while also providing a clustering tool for the analysis of VS results. A case study was conducted to demonstrate the applicability of this platform.</p> <p>Conclusions</p> <p>IVSPlat 1.0 provides a plug-in-based solution for the management, automation, and visualization of VS tasks. IVSPlat 1.0 is an open framework that allows the integration of extra software to extend its functionality and modified versions can be freely distributed. The open source code and documentation are available at <url>http://kyc.nenu.edu.cn/IVSPlat/.</url></p

Binding Modes of Peptidomimetics Designed to Inhibit STAT3

STAT3 is a transcription factor that has been found to be constitutively activated in a number of human cancers. Dimerization of STAT3 via its SH2 domain and the subsequent translocation of the dimer to the nucleus leads to transcription of anti-apoptotic genes. Prevention of the dimerization is thus an attractive strategy for inhibiting the activity of STAT3. Phosphotyrosine-based peptidomimetic inhibitors, which mimic pTyr-Xaa-Yaa-Gln motif and have strong to weak binding affinities, have been previously investigated. It is well-known that structures of protein-inhibitor complexes are important for understanding the binding interactions and designing stronger inhibitors. Experimental structures of inhibitors bound to the SH2 domain of STAT3 are, however, unavailable. In this paper we describe a computational study that combined molecular docking and molecular dynamics to model structures of 12 peptidomimetic inhibitors bound to the SH2 domain of STAT3. A detailed analysis of the modeled structures was performed to evaluate the characteristics of the binding interactions. We also estimated the binding affinities of the inhibitors by combining MMPB/GBSA-based energies and entropic cost of binding. The estimated affinities correlate strongly with the experimentally obtained affinities. Modeling results show binding modes that are consistent with limited previous modeling studies on binding interactions involving the SH2 domain and phosphotyrosine(pTyr)-based inhibitors. We also discovered a stable novel binding mode that involves deformation of two loops of the SH2 domain that subsequently bury the C-terminal end of one of the stronger inhibitors. The novel binding mode could prove useful for developing more potent inhibitors aimed at preventing dimerization of cancer target protein STAT3

Antibody Recognition of Cancer-Related Gangliosides and Their Mimics Investigated Using in silico Site Mapping

Modified gangliosides may be overexpressed in certain types of cancer, thus, they are considered a valuable target in cancer immunotherapy. Structural knowledge of their interaction with antibodies is currently limited, due to the large size and high flexibility of these ligands. In this study, we apply our previously developed site mapping technique to investigate the recognition of cancer-related gangliosides by anti-ganglioside antibodies. The results reveal a potential ganglioside-binding motif in the four antibodies studied, suggesting the possibility of structural convergence in the anti-ganglioside immune response. The structural basis of the recognition of ganglioside-mimetic peptides is also investigated using site mapping and compared to ganglioside recognition. The peptides are shown to act as structural mimics of gangliosides by interacting with many of the same binding site residues as the cognate carbohydrate epitopes. These studies provide important clues as to the structural basis of immunological mimicry of carbohydrates

Application of the PM6 semi-empirical method to modeling proteins enhances docking accuracy of AutoDock

<p>Abstract</p> <p>Background</p> <p>Molecular docking methods are commonly used for predicting binding modes and energies of ligands to proteins. For accurate complex geometry and binding energy estimation, an appropriate method for calculating partial charges is essential. AutoDockTools software, the interface for preparing input files for one of the most widely used docking programs AutoDock 4, utilizes the Gasteiger partial charge calculation method for both protein and ligand charge calculation. However, it has already been shown that more accurate partial charge calculation - and as a consequence, more accurate docking- can be achieved by using quantum chemical methods. For docking calculations quantum chemical partial charge calculation as a routine was only used for ligands so far. The newly developed Mozyme function of MOPAC2009 allows fast partial charge calculation of proteins by quantum mechanical semi-empirical methods. Thus, in the current study, the effect of semi-empirical quantum-mechanical partial charge calculation on docking accuracy could be investigated.</p> <p>Results</p> <p>The docking accuracy of AutoDock 4 using the original AutoDock scoring function was investigated on a set of 53 protein ligand complexes using Gasteiger and PM6 partial charge calculation methods. This has enabled us to compare the effect of the partial charge calculation method on docking accuracy utilizing AutoDock 4 software. Our results showed that the docking accuracy in regard to complex geometry (docking result defined as accurate when the RMSD of the first rank docking result complex is within 2 Å of the experimentally determined X-ray structure) significantly increased when partial charges of the ligands and proteins were calculated with the semi-empirical PM6 method.</p> <p>Out of the 53 complexes analyzed in the course of our study, the geometry of 42 complexes were accurately calculated using PM6 partial charges, while the use of Gasteiger charges resulted in only 28 accurate geometries. The binding affinity estimation was not influenced by the partial charge calculation method - for more accurate binding affinity prediction development of a new scoring function for AutoDock is needed.</p> <p>Conclusion</p> <p>Our results demonstrate that the accuracy of determination of complex geometry using AutoDock 4 for docking calculation greatly increases with the use of quantum chemical partial charge calculation on both the ligands and proteins.</p

Application of Consensus Scoring and Principal Component Analysis for Virtual Screening against β-Secretase (BACE-1)

BACKGROUND: In order to identify novel chemical classes of β-secretase (BACE-1) inhibitors, an alternative scoring protocol, Principal Component Analysis (PCA), was proposed to summarize most of the information from the original scoring functions and re-rank the results from the virtual screening against BACE-1. METHOD: Given a training set (50 BACE-1 inhibitors and 9950 inactive diverse compounds), three rank-based virtual screening methods, individual scoring, conventional consensus scoring and PCA, were judged by the hit number in the top 1% of the ranked list. The docking poses were generated by Surflex, five scoring functions (Surflex_Score, D_Score, G_Score, ChemScore, and PMF_Score) were used for pose extraction. For each pose group, twelve scoring functions (Surflex_Score, D_Score, G_Score, ChemScore, PMF_Score, LigScore1, LigScore2, PLP1, PLP2, jain, Ludi_1, and Ludi_2) were used for the pose rank. For a test set, 113,228 chemical compounds (Sigma-Aldrich® corporate chemical directory) were docked by Surflex, then ranked by the same three ranking methods motioned above to select the potential active compounds for experimental test. RESULTS: For the training set, the PCA approach yielded consistently superior rankings compared to conventional consensus scoring and single scoring. For the test set, the top 20 compounds according to conventional consensus scoring were experimentally tested, no inhibitor was found. Then, we relied on PCA scoring protocol to test another different top 20 compounds and two low micromolar inhibitors (S450588 and 276065) were emerged through the BACE-1 fluorescence resonance energy transfer (FRET) assay. CONCLUSION: The PCA method extends the conventional consensus scoring in a quantitative statistical manner and would appear to have considerable potential for chemical screening applications

Novel Allosteric Sites on Ras for Lead Generation

Aberrant Ras activity is a hallmark of diverse cancers and developmental diseases. Unfortunately, conventional efforts to develop effective small molecule Ras inhibitors have met with limited success. We have developed a novel multi-level computational approach to discover potential inhibitors of previously uncharacterized allosteric sites. Our approach couples bioinformatics analysis, advanced molecular simulations, ensemble docking and initial experimental testing of potential inhibitors. Molecular dynamics simulation highlighted conserved allosteric coupling of the nucleotide-binding switch region with distal regions, including loop 7 and helix 5. Bioinformatics methods identified novel transient small molecule binding pockets close to these regions and in the vicinity of the conformationally responsive switch region. Candidate binders for these pockets were selected through ensemble docking of ZINC and NCI compound libraries. Finally, cell-based assays confirmed our hypothesis that the chosen binders can inhibit the downstream signaling activity of Ras. We thus propose that the predicted allosteric sites are viable targets for the development and optimization of new drugs

Structure-Based Virtual Screening for Drug Discovery: a Problem-Centric Review

Structure-based virtual screening (SBVS) has been widely applied in early-stage drug discovery. From a problem-centric perspective, we reviewed the recent advances and applications in SBVS with a special focus on docking-based virtual screening. We emphasized the researchers’ practical efforts in real projects by understanding the ligand-target binding interactions as a premise. We also highlighted the recent progress in developing target-biased scoring functions by optimizing current generic scoring functions toward certain target classes, as well as in developing novel ones by means of machine learning techniques

Computational Methods Used in Hit-to-Lead and Lead Optimization Stages of Structure-Based Drug Discovery

GPCR modeling approaches are widely used in the hit-to-lead (H2L) and lead optimization (LO) stages of drug discovery. The aims of these modeling approaches are to predict the 3D structures of the receptor-ligand complexes, to explore the key interactions between the receptor and the ligand and to utilize these insights in the design of new molecules with improved binding, selectivity or other pharmacological properties. In this book chapter, we present a brief survey of key computational approaches integrated with hierarchical GPCR modeling protocol (HGMP) used in hit-to-lead (H2L) and in lead optimization (LO) stages of structure-based drug discovery (SBDD). We outline the differences in modeling strategies used in H2L and LO of SBDD and illustrate how these tools have been applied in three drug discovery projects