Conformer Generation Research Articles

From polarized gravitational waves to analytically solvable electromagnetic beams

Using the correspondence between solutions of gravitational and gauge theories (the so-called classical double copy conjecture) some electromagnetic fields with vortices are constructed, for which the Lorentz force equations are analytically solvable. The starting point is a certain class of plane gravitational waves exhibiting the conformal symmetry. The notion of the Niederer transformation, crucial for the solvability, is analyzed in the case of the Lorentz force equation on the curved spacetimes as well as its derivation by means of integrals of motion (associated with conformal generators preserving these vortices) is presented. Furthermore, some models discussed recently in the context of the intense laser beams are constructed from their gravitational counterparts, with the special emphasis put on the focusing property, and new solvable examples are presented.

Computational basis for the design of PLK-2 inhibitors

PLK-2 is a serine/threonine protein kinase and plays a crucial role in cell cycle regulation; due to its pivotal function, this enzyme is approved as cancer drug target. We used BI-2536 a PLK-1/PLK-2 inhibitor to build a pharmacophore model and applied in the virtual screening of ZINC database to retrieve new molecules that bind the active site of PLK-2 environment with a high fit value. The molecules that do not fit the enzyme active site environment were subjected to conformation enrichment by generation of conformations in the active site environment by molecular docking, and the molecules with new scaffold that did not pass into the active site from molecular docking were subjected to molecular pruning to delete bulky substituents that prevent the molecules from binding. Molecular docking was used to find the binding pose of the selected molecules into active site of PLK-2; all screened-in hit molecules make favorable non-bonding interactions with PLK-2 active site similar to the reference inhibitor. Molecular dynamics simulations, the binding free energy calculations of the complexes, and the stability of hydrogen bonding interactions further revealed the usefulness of these screened compounds as suitable hit molecules for inhibition of PLK-2.

Niederer’s transformation, time-dependent oscillators and polarized gravitational waves

It is noted that the Niederer transformation can be used to find the explicit relation between time-dependent linear oscillators, including the most interesting case when one of them is harmonic. A geometric interpretation of this correspondence is provided by certain subclasses of pp-waves; in particular the ones strictly related to the proper conformal transformations. This observation allows us to show that the pulses of plane gravitational wave exhibiting the maximal conformal symmetry are analytically solvable. Particularly interesting is the circularly polarized family for which some aspects (such as the classical cross section, velocity memory effect and impulsive limit) are discussed in more detail. The role of the additional integrals of motion, associated with the conformal generators, is clarified by means of Ermakov–Lewis invariants. Possible applications to the description of interaction of electromagnetic beams with matter are also indicated.

A Practical Perspective: The Effect of Ligand Conformers on the Negative Image-Based Screening.

Negative image-based (NIB) screening is a rigid molecular docking methodology that can also be employed in docking rescoring. During the NIB screening, a negative image is generated based on the target protein’s ligand-binding cavity by inverting its shape and electrostatics. The resulting NIB model is a drug-like entity or pseudo-ligand that is compared directly against ligand 3D conformers, as is done with a template compound in the ligand-based screening. This cavity-based rigid docking has been demonstrated to work with genuine drug targets in both benchmark testing and drug candidate/lead discovery. Firstly, the study explores in-depth the applicability of different ligand 3D conformer generation software for acquiring the best NIB screening results using cyclooxygenase-2 (COX-2) as the example system. Secondly, the entire NIB workflow from the protein structure preparation, model build-up, and ligand conformer generation to the similarity comparison is performed for COX-2. Accordingly, hands-on instructions are provided on how to employ the NIB methodology from start to finish, both with the rigid docking and docking rescoring using noncommercial software. The practical aspects of the NIB methodology, especially the effect of ligand conformers, are discussed thoroughly, thus, making the methodology accessible for new users.

Bayesian optimization for conformer generation

Generating low-energy molecular conformers is a key task for many areas of computational chemistry, molecular modeling and cheminformatics. Most current conformer generation methods primarily focus on generating geometrically diverse conformers rather than finding the most probable or energetically lowest minima. Here, we present a new stochastic search method called the Bayesian optimization algorithm (BOA) for finding the lowest energy conformation of a given molecule. We compare BOA with uniform random search, and systematic search as implemented in Confab, to determine which method finds the lowest energy. Energetic difference, root-mean-square deviation, and torsion fingerprint deviation are used to quantify the performance of the conformer search algorithms. In general, we find BOA requires far fewer evaluations than systematic or uniform random search to find low-energy minima. For molecules with four or more rotatable bonds, Confab typically evaluates 10^{4} (median) conformers in its search, while BOA only requires 10^{2} energy evaluations to find top candidates. Despite using evaluating fewer conformers, 20–40% of the time BOA finds lower-energy conformations than a systematic Confab search for molecules with four or more rotatable bonds.

Complex macrocycle exploration: parallel, heuristic, and constraint-based conformer generation using ForceGen

ForceGen is a template-free, non-stochastic approach for 2D to 3D structure generation and conformational elaboration for small molecules, including both non-macrocycles and macrocycles. For conformational search of non-macrocycles, ForceGen is both faster and more accurate than the best of all tested methods on a very large, independently curated benchmark of 2859 PDB ligands. In this study, the primary results are on macrocycles, including results for 431 unique examples from four separate benchmarks. These include complex peptide and peptide-like cases that can form networks of internal hydrogen bonds. By making use of new physical movements (“flips” of near-linear sub-cycles and explicit formation of hydrogen bonds), ForceGen exhibited statistically significantly better performance for overall RMS deviation from experimental coordinates than all other approaches. The algorithmic approach offers natural parallelization across multiple computing-cores. On a modest multi-core workstation, for all but the most complex macrocycles, median wall-clock times were generally under a minute in fast search mode and under 2 min using thorough search. On the most complex cases (roughly cyclic decapeptides and larger) explicit exploration of likely hydrogen bonding networks yielded marked improvements, but with calculation times increasing to several minutes and in some cases to roughly an hour for fast search. In complex cases, utilization of NMR data to constrain conformational search produces accurate conformational ensembles representative of solution state macrocycle behavior. On macrocycles of typical complexity (up to 21 rotatable macrocyclic and exocyclic bonds), design-focused macrocycle optimization can be practically supported by computational chemistry at interactive time-scales, with conformational ensemble accuracy equaling what is seen with non-macrocyclic ligands. For more complex macrocycles, inclusion of sparse biophysical data is a helpful adjunct to computation.

Template-Based Method for Conformation Generation and Scoring for Congeneric Series of Ligands.

Physics-based prediction of protein-ligand binding affinities for a congeneric series of ligands in lead optimization requires their geometries as a first step. In this paper, we report a method that uses the 3D conformation of a lead compound in complex with a protein as a template to generate conformations of a series of related analog compounds. The method uses the Maximal Common Substructure (MCS) computed between lead and analog ligands to assign coordinates for the atoms shared between the ligands. For the differing atoms, a conformation generation procedure is implemented that results in a diversity of conformations. The generated conformations are sorted using a score based on the Molecular Mechanics and Generalized Born with Solvent Accessible Surface Area contribution (MM-GBSA) method. The accuracy of the generated conformations is tested retrospectively using a cross-validation approach applied to four data sets obtained from the Drug Design Data Resource (D3R) by measuring the RMSD of the top scored conformation with respect to the crystallographic pose. The scoring ability of the method is independently assessed using data for the same protein targets to test the rank ordering ability and separating active and inactive ligands. We tested the effect of protein flexibility during structural optimization and scoring approaches with and without strain energies. Retrospective validation on data sets comprising 4 targets shows that the method outperforms random selection for all targets and outperforms a molecular weight-based null model in 3 out of 4 targets in separating active and inactive compounds. Therefore, the presented method is expected to be of utility in lead optimization for rapidly screening analog ligands and generating initial conformations for use in more detailed physics-based binding affinity prediction methods.

Toward the elucidation of the mechanism for passive membrane permeability of cyclic peptides.

Toward the elucidation of the mechanism for passive membrane permeability of cyclic peptides.

Conformator: A Novel Method for the Generation of Conformer Ensembles.

Computer-aided drug design methods such as docking, pharmacophore searching, 3D database searching, and the creation of 3D-QSAR models need conformational ensembles to handle the flexibility of small molecules. Here, we present Conformator, an accurate and effective knowledge-based algorithm for generating conformer ensembles. With 99.9% of all test molecules processed, Conformator stands out by its robustness with respect to input formats, molecular geometries, and the handling of macrocycles. With an extended set of rules for sampling torsion angles, a novel algorithm for macrocycle conformer generation, and a new clustering algorithm for the assembly of conformer ensembles, Conformator reaches a median minimum root-mean-square deviation (measured between protein-bound ligand conformations and ensembles of a maximum of 250 conformers) of 0.47 Å with no significant difference to the highest-ranked commercial algorithm OMEGA and significantly higher accuracy than seven free algorithms, including the RDKit DG algorithm. Conformator is freely available for noncommercial use and academic research.

Combined Ligand and Fragment‐based Drug Design of Selective Histone Deacetylase – 6 Inhibitors

Histone deacetylase 6 (HDAC6) is unique hydrolase within HDAC family, having pleiotropic deacetylase activity against α-tubulin, cortactin and dynein. Comprehensively, HDAC6 controls cell motility, apoptosis and protein folding, whereas alterations in its structure and function are related to the pathogenesis of cancer, neurodegeneration and inflammation. To define structural motifs which guide HDAC6 selectivity, we developed and compared three-dimensional Quantitative Structure-Activity Relationship (3D-QSAR) models for HDAC1 and HDAC6 inhibitors. The reduction of the bias in conformer generation was supported by virtual docking study by using crystal structures of human HDAC1 and HDAC6 isoforms. Following these findings, the combined ligand-based and fragment-based drug design methodologies were used in the design of selective HDAC6 inhibitors. Group of the most promising novel ligands was selected based on the predicted HDAC6 selectivity, pharmacokinetic profile, synthetic tractability, and in silico cytotoxicity against the wide range of human cancer cell lines.

Stress induced «railway for pre-ribosome export» structure as a new model for studying eukaryote ribosome biogenesis

The article presents the details of the process of structural organization, formation and disassembly of the nucleolus, chromatin condensation during the passage of the cell cycle studied by the method of classical transmission electron microscopy (TEM) in the cells of the meristematic zone of the wheat root. The transformations of peripheral chromosome material (PCM) in telophase, the transformations of the nucleolar nucleolonema in the interphase and prophase, and the chromatin transformations (condensation and decondensation) were studied and analyzed under the conditions of the geomagnetic field, weakened magnetic field and static magnetic field. Using an analysis of the dynamics of structural transformations of proliferating nuclei, we observed a disturbance in the formation of the chromonema and condensed chromatin in the middle interphase, a change in the structural organization of the nucleolus during the transition from late interphase to prophase, as well as a change in the structure of PCM, pre-nucleolus and chromatin in telophase. A schema for the generation of a specific conformation of nucleolonema and chromonema and its influence on the structural organization of chromosomes in anaphase and telophase was proposed. The nature of this structure is discussed. Possible mechanisms of the effect of magnetic field on the nuclear compartment, regulation of chromatin decompactization, export of pre-ribosomal particles under stress, and the fine structure of the nucleolonema are considered.

Energy windows for computed compound conformers: covering artefacts or truly large reorganization energies?

The generation of 3D conformers of small molecules underpins most computational drug discovery. Thus, the conformer quality is critical and depends on their energetics. A key parameter is the empirical conformational energy window (ΔEw), since only conformers within ΔEw are retained. However, ΔEw values in use appear unrealistically large. We analyze the factors pertaining to the conformer energetics and ΔEw. We argue that more attention must be focused on the problem of collapsed low-energy conformers. That is due to artificial intramolecular stabilization and occurs even with continuum solvation. Consequently, the conformational energy of extended bioactive structures is artefactually increased, which inflates ΔEw. Thus, this Perspective highlights the issues arising from low-energy conformers and suggests improvements via empirical or physics-based strategies.

Subtleties of nonrelativistic reduction and applications

Various subtleties and problems associated with nonrelativistic (NR) reduction of a scalar field theory to the Schroedinger theory are discussed. Contrary to the usual approaches that discuss the mapping among the equations of motion or the actions, we highlight the mapping among the space time generators. Using a null reduction we show the embedding of the conformal generators of the Schroedinger theory to that of a complex scalar theory in one higher dimension. As applications we reveal the conformal symmetry in hydrodynamics and the obtention of NR diffeomorphism symmetry from the relativistic one. A geometrical connection based on Horava–Lifshitz and Newton–Cartan spacetime is discussed.

TANGO: A high through-put conformation generation and semiempirical method-based optimization tool for ligand molecules.

Lead optimization is one of the crucial steps in the drug discovery pipeline. After identifying the lead molecule and obtaining its 2D geometry, understanding the best conformation it would attain in 3D still remains one of the most challenging steps in drug discovery. There have been multiple methods and algorithms that are directed toward achieving best conformation for the lead molecules. TANGO focuses on conformation generation and its optimization using semiempirical energy calculations. The conformation generation is based on torsion angle rotation of the exocyclic bonds. The energy calculations are performed using MOPAC. The unique feature of this tool lies in the implementation of Message Passing Interface (MPI) for conformation generation and semiempirical-based optimization. A well-defined architecture handling the input and output generation has been used. The master and slave approach to handle operations involved in torsion angle rotation and energy calculations has helped in load balancing the process of conformation generation. The benchmarking results suggest that TANGO scales significantly well across eight nodes with each node utilizing 16 cores. This tool may prove to very useful in high throughput generation of semiempirically optimized small molecule conformations. The use of semiempirical methods for optimization generates a conformational ensemble thereby helping to obtain stable and alternate stable conformers for a given ligand molecule. © 2018 Wiley Periodicals, Inc.

Shape similarity guided pose prediction: lessons from D3R Grand Challenge 3.

To extend the utility of ligand 3D shape similarity into pose prediction and virtual screening, we have previously developed CDVS and PoPSS methods. Both of them utilize ligand 3D shape similarity with the crystallographic ligands to improve pose prediction. While CDVS utilizes shape similarity to select suitable receptor structures for molecular docking, PoPSS places a ligand conformation of the highest shape similarity with crystal ligands into the target protein binding pocket which is then refined by side-chain repacking and Monte Carlo energy minimization. Analyses of PoPSS revealed some drawbacks in ligand conformation generation and the scoring scheme used. Moreover, as PoPSS does not sample the ligand conformation after placing it in the binding pocket, it relies solely on conformation generation methods to produce native like conformations. To address these limitations of PoPSS method, we report here a modified approach named as PoPSS-Lite, where side-chain repacking was replaced by a simple grid-based energy minimization. This modification also allowed the sampling of terminal functional groups while keeping the core scaffold fixed. Furthermore, shape similarity calculations were improved by increasing the number of ligand conformations and using a different similarity metric. The performance of PoPSS-Lite was prospectively evaluated in D3R GC3. Comparison of PoPSS-Lite demonstrated superior performance over PoPSS and CDVS with lower mean and median RMSDs. Furthermore, comparison with other D3R GC3 pose prediction submissions revealed top performance for PoPSS-Lite. Our D3R GC3 result extends our perspective that ligand 3D shape similarity with known crystallographic information can be successfully used to predict the binding pose of ligands with unknown binding modes. Our D3R GC3 results further highlight the necessity for improvement in conformer generation methods in order to improve shape similarity guided pose prediction.

Conformational Sampling of Small Molecules With iCon: Performance Assessment in Comparison With OMEGA.

Herein we present the algorithm and performance assessment of our newly developed conformer generator iCon that was implemented in LigandScout 4.0. Two data sets of high-quality X-ray structures of drug-like small molecules originating from the Protein Data Bank (200 ligands) and the Cambridge Structural Database (481 molecules) were used to validate iCon's performance in the reproduction of experimental conformations. OpenEye's conformer generator OMEGA was subjected to the same evaluation and served as a reference software in this analysis. We tested several setting patterns in order to identify the most suitable and efficient ones for conformational sampling with iCon; equivalent settings were also tested on OMEGA in order to compare the results obtained from the two programs and better assess iCon's performance. Overall, this study proved that iCon is able to generate reliable representative conformational ensembles of drug-like small molecules, yielding results comparable to those showed by OMEGA, and thus is ready to serve as a valuable tool for computer-aided drug design.

Hierarchical Flexible Peptide Docking by Conformer Generation and Ensemble Docking of Peptides.

Given the importance of peptide-mediated protein interactions in cellular processes, protein-peptide docking has received increasing attention. Here, we have developed a Hierarchical flexible Peptide Docking approach through fast generation and ensemble docking of peptide conformations, which is referred to as HPepDock. Tested on the LEADS-PEP benchmark data set of 53 diverse complexes with peptides of 3-12 residues, HPepDock performed significantly better than the 11 docking protocols of five small-molecule docking programs (DOCK, AutoDock, AutoDock Vina, Surflex, and GOLD) in predicting near-native binding conformations. HPepDock was also evaluated on the 19 bound/unbound and 10 unbound/unbound protein-peptide complexes of the Glide SP-PEP benchmark and showed an overall better performance than Glide SP-PEP+MM-GBSA and FlexPepDock in both bound and unbound docking. HPepDock is computationally efficient, and the average running time for docking a peptide is ∼15 min with the range from about 1 min for short peptides to around 40 min for long peptides.

Zooming in on AdS3/CFT2 near a BPS bound

Any (d + 1)-dimensional CFT with a U(1) flavor symmetry, a BPS bound and an exactly marginal coupling admits a decoupling limit in which one zooms in on the spectrum close to the bound. This limit is an Inönü-Wigner contraction of so(2, d+1)⊕u(1) that leads to a relativistic algebra with a scaling generator but no conformal generators. In 2D CFTs, Lorentz boosts are abelian and by adding a second u(1) we find a contraction of two copies of sl(2, ℝ) ⊕ u(1) to two copies of P2c, the 2-dimensional centrally extended Poincaré algebra. We show that the bulk is described by a novel non-Lorentzian geometry that we refer to as pseudo-Newton-Cartan geometry. Both the Chern-Simons action on sl(2, ℝ) ⊕ u(1) and the entire phase space of asymptotically AdS3 spacetimes are well-behaved in the corresponding limit if we fix the radial component for the u(1) connection. With this choice, the resulting Newton-Cartan foliation structure is now associated not with time, but with the emerging holographic direction. Since the leaves of this foliation do not mix, the emergence of the holographic direction is much simpler than in AdS3 holography. Furthermore, we show that the asymptotic symmetry algebra of the limit theory consists of a left- and a right-moving warped Virasoro algebra.

Efficient flexible backbone protein–protein docking for challenging targets

Binding-induced conformational changes challenge current computational docking algorithms by exponentially increasing the conformational space to be explored. To restrict this search to relevant space, some computational docking algorithms exploit the inherent flexibility of the protein monomers to simulate conformational selection from pre-generated ensembles. As the ensemble size expands with increased flexibility, these methods struggle with efficiency and high false positive rates. Here, we develop and benchmark RosettaDock 4.0, which efficiently samples large conformational ensembles of flexible proteins and docks them using a novel, six-dimensional, coarse-grained score function. A strong discriminative ability allows an eight-fold higher enrichment of near-native candidate structures in the coarse-grained phase compared to RosettaDock 3.2. It adaptively samples 100 conformations each of the ligand and the receptor backbone while increasing computational time by only 20-80%. In local docking of a benchmark set of 88 proteins of varying degrees of flexibility, the expected success rate (defined as cases with ≥50% chance of achieving 3 near-native structures in the 5 top-ranked ones) for blind predictions after resampling is 77% for rigid complexes, 49% for moderately flexible complexes and 31% for highly flexible complexes. These success rates on flexible complexes are a substantial step forward from all existing methods. Additionally, for highly flexible proteins, we demonstrate that when a suitable conformer generation method exists, the method successfully docks the complex. As a part of the Rosetta software suite, RosettaDock 4.0 is available at https://www.rosettacommons.org to all non-commercial users for free and to commercial users for a fee. Supplementary data are available at Bioinformatics online.

Peptidic Macrocycles - Conformational Sampling and Thermodynamic Characterization.

Macrocycles are of considerable interest as highly specific drug candidates, yet they challenge standard conformer generators with their large number of rotatable bonds and conformational restrictions. Here, we present a molecular dynamics-based routine that bypasses current limitations in conformational sampling and extensively profiles the free energy landscape of peptidic macrocycles in solution. We perform accelerated molecular dynamics simulations to capture a diverse conformational ensemble. By applying an energetic cutoff, followed by geometric clustering, we demonstrate the striking robustness and efficiency of the approach in identifying highly populated conformational states of cyclic peptides. The resulting structural and thermodynamic information is benchmarked against interproton distances from NMR experiments and conformational states identified by X-ray crystallography. Using three different model systems of varying size and flexibility, we show that the method reliably reproduces experimentally determined structural ensembles and is capable of identifying key conformational states that include the bioactive conformation. Thus, the described approach is a robust method to generate conformations of peptidic macrocycles and holds promise for structure-based drug design.