A genetic algorithm for flexible molecular overlay and pharmacophore elucidation

Summary A genetic algorithm (GA) has been developed for the superimposition of sets of flexible molecules. Molecules are represented by a chromosome that encodes angles of rotation about flexible bonds and mappings between hydrogen-bond donor proton, acceptor lone pair and ring centre features in pairs of molecules. The molecule with the smallest number of features in the data set is used as a template, onto which the remaining molecules are fitted with the objective of maximising structural equivalences. The fitness function of the GA is a weighted combination of: (i) the number and the similarity of the features that have been overlaid in this way; (ii) the volume integral of the overlay; and (iii) the van der Waals energy of the molecular conformations defined by the torsion angles encoded in the chromosomes. The algorithm has been applied to a number of pharmacophore elucidation problems, i.e., angiotensin II receptor antagonists, Leu-enkephalin and a hybrid morphine molecule, 5-HT_1D agonists, benzodiazepine receptor ligands, 5-HT₃ antagonists, dopamine D₂ antagonists, dopamine reuptake blockers and FKBP12 ligands. The resulting pharmacophores are generated rapidly and are in good agreement with those derived from alternative means.     

An analytic ring closure condition for geometrical algorithm to search the conformational space

The recently reported geometrical algorithm to search the conformational space (GASCOS) scans conformational space exhaustively using an internal coordinate tree search. Using only geometrical operations and a set of criteria for eliminating chemically unreasonable atomic arrangements, the algorithm generates starting geometries for optimizations by molecular mechanics or by molecular orbital procedures. Up until now GASCOS has been used for linear structures, but an extension to cyclic structures is reported here.     

A CoMFA analysis with conformational propensity: An attempt to analyze the SAR of a set of molecules with different conformational flexibility using a 3D-QSAR method

CoMFA analysis, a widely used 3D-QSAR method, has limitations to handle a set of SAR data containing diverse conformational flexibility since it does not explicitly include the conformational entropic effects into the analysis. Here, we present an attempt to incorporate the conformational entropy effects of a molecule into a 3D-QSAR analysis. Our attempt is based on the assumption that the conformational entropic loss of a ligand upon making a ligand-receptor complex is small if the ligand in an unbound state has a conformational propensity to adopt an active conformation in a complex state. For a QSAR analysis, this assumption was interpreted as follows: a potent ligand should have a higher conformational propensity to adopt an `active-conformation'-like structure in an unbound state than an inactive one. The conformational propensity value was defined as the populational ratio, N<sub>active</sub>/N<sub>stable</sub>, of the number of energetically stable conformers, N<sub>stable</sub>, to the number of `active-conformation'-like structures, N_active. The latter number was calculated by counting the number of conformers that satisfied the structural parameters deduced from the active conformation. A set of SAR data of imidazoleglycerol phosphate dehydratase inhibitors containing 20 molecules with different conformational flexibility was used as a training set for developing a 3D structure-activity relationship by a CoMFA analysis with the conformational propensity value. This resulted in a cross-validated squared correlation coefficient of the CoMFA model with the conformational propensity value (R ² _cross = 0.640) higher than that of the standard CoMFA model (R ² _cross = 0.431). Then we evaluated the quality of the CoMFA models by predicting the inhibitory activity for a new molecule.     

PEPCAT—A new tool for conformational analysis of peptides

We report a new technique for the efficient analysis and visualization of peptide and protein conformations and conformational relationships, which we have implemented in a computer program called PEPCAT. PEPCAT (an abbreviation for Peptide Conformational Analysis Tool) provides a simple, graphical, and flexible framework that allows the user to define a specific structural feature or juxtaposition of amino acids and to follow the fate of the motif during a molecular dynamics simulation. Here we describe the PEPCAT analysis of the effects of environmental and chemical modifications on conformational preferences of a regulator of hemopoiesis, namely the pentapeptide pyro‐EEDCK, and of a conformational transition in the immunosuppressant drug cyclosporin A. PEPCAT, however, can be applied to the conformational analysis of peptides and proteins in general. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 446–461, 2000     

Low-mode conformational search elucidated: Application to C39H80 and flexible docking of 9-deazaguanine inhibitors into PNP

We previously described a new conformational search method, termed low-mode search (LMOD), and discussed its utility for conformational searches performed on cycloalkanes and a cyclic penta-peptide. 1 In this report, we discuss a rigorous implementation of mode following (c-LMOD) for conformational searching, and we demonstrate that for a conformational search involving cycloheptadecane, this rigorous implementation is capable of finding all of the previously known structures. To the best of our knowledge, this is the first computational proof that mode following can be used for conformational searches conducted on a complex molecular system. We show, however, that, as expected, it is generally inefficient to perform a conformational search in this manner. Nonetheless, c-LMOD has been shown to be an excellent method for conducting conformational analyses involving conformational interconversions, where the location of saddle points is important. We also describe refinement to our original LMOD procedure (l-LMOD) and discuss its utility for a difficult conformational search problem, namely locating the global minimum energy conformation of C₃₉H₈₀. For this search, l-LMOD combined with limited torsional Monte Carlo movement was able to locate the lowest energy structures yet reported, and significantly outperformed a pure torsional Monte Carlo and a genetic algorithm-based search. Furthermore, we also demonstrate the utility of l-LMOD combined with random translation/rotation of a ligand for the extremely difficult problem of docking flexible ligands into flexible protein binding sites on a system that includes 9-deaza-guanine-based inhibitors docked into the flexible biding site of PNP. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1671–1684, 1999     

HUNTER: A conformational search program for acyclic to polycyclic molecules with special emphasis on stereochemistry

A new conformational search program, HUNTER, connected with the force fields MMP2 and MM3(92) is presented. The program accepts all types of molecules with most different substructures, considers stereochemical facts, and covers conformational space efficiently and completely. The most important facilities are an automated analysis of the stereochemistry including topographical facts, a separate perturbation of the acyclic and cyclic parts of the molecule using modified corner flapping, and an incremental rotation around single bonds with fixed flap and rotation angles, respectively; an exclusion of high energy structures by simulated annealing; the choice of the conformer lowest in energy, which is new as an initial structure for the next sampling run; and the use of a reduced set of dihedral angles to define a conformation. A specifically devised graphic interface, SERVANT, is used to feed in and control all informations necessary for a program run and to visualize the results. Most of the parameters are user-defined and thereby allow a flexible search, including a search for the most stable diastereomer. The efficiency of the different parameter sets was tested in calculation with cycloundecane ( 12 ), (Z)-oct-3-ene ( 13 ), and sipholenol-A monoacetate ( 14 ). The best performance regarding the number of different low-energy conformers was achieved with 60° ( 14 ) and 90° flaps ( 12 ), respectively, including substituent correction for the cyclic parts, and with 105° ( 14 ) and 120° rotations ( 13 ), respectively, for the acyclic parts. In comparison to the stochastic search routine implemented in MM3(92), HUNTER performed two ( 12 ) to six ( 14 ) times better. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1264–1281, 1997     

Methodological developments and strategies for a fast flexible superposition of drug-size molecules

An alternative to experimental high through-put screening is the virtual screening of compound libraries on the computer. In absence of a detailed structure of the receptor protein, candidate molecules are compared with a known reference by mutually superimposing their skeletons and scoring their similarity. Since molecular shape highly depends on the adopted conformation, an efficient conformational screening is performed using a knowledge-based approach. A comprehensive torsion library has been compiled from crystal data stored in the Cambridge Structural Database. For molecular comparison a strategy is followed considering shape associated physicochemical properties in space such as steric occupancy, electrostatics, lipophilicity and potential hydrogen-bonding. Molecular shape is approximated by a set of Gaussian functions not necessarily located at the atomic positions. The superposition is performed in two steps: first by a global alignment search operating on multiple rigid conformations and then by conformationally relaxing the best scored hits of the global search. A normalized similarity scoring is used to allow for a comparison of molecules with rather different shape and size. The approach has been implemented on a cluster of parallel processors. As a case study, the search for ligands binding to the dopamine receptor is given.     

Application of vibronic spectroscopy to conformational analysis. Investigations of molecules of carbonyl compounds

Application of vibronic spectroscopy to the conformational analysis of molecules in the ground and excited electronic states is reviewed. The basic concepts of the method as well as its methodological and technical aspects are discussed. The abilities of vibronic spectroscopy are exemplified by the results obtained for molecules of carbonyl compounds.The review is based on a report at the Vibrational Spectroscopy Conference dedicated to the 80th birthday of B. I. Stepanov (Minsk, Belarus', October 3–5, 1993).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 783–791, May, 1994.This work was performed with the partial financial support of the Russian.Universities State Program.     

Self-organizing superimposition algorithm for conformational sampling

A novel self-organizing algorithm for conformational sampling is introduced, in which precomputed conformations of rigid fragments are used as templates to enforce the desired geometry. Starting from completely random coordinates, the algorithm repeatedly superimposes the templates to adjust the positions of the atoms, thereby gradually refining the conformation of the molecule. Combined with pair-wise adjustments of the atoms to resolve steric clashes, conformations that satisfy all geometric constraints can be generated from this procedure. The algorithm is demonstrated to achieve good performance and promises potential applications on more challenging modeling problems.     

A versatile method for systematic conformational searches: application to CheY

A novel molecular structure prediction method, the Z Method, is described. It provides a versatile platform for the development and use of systematic, grid‐based conformational search protocols, in which statistical information (i.e., rotamers) can also be included. The Z Method generates trial structures by applying many changes of the same type to a single starting structure, thereby sampling the conformation space in an unbiased way. The method, implemented in the CHARMM program as the Z Module, is applied here to an illustrative model problem in which rigid, systematic searches are performed in a 36‐dimensional conformational space that describes the relative positions of the 10 secondary structural elements of the protein CheY. A polar hydrogen representation with an implicit solvation term (EEF1) is used to evaluate successively larger fragments of the protein generated in a hierarchical build‐up procedure. After a final refinement stage, and a total computational time of about two‐and‐a‐half CPU days on AMD Opteron processors, the prediction is within 1.56 Å of the native structure. The errors in the predicted backbone dihedral angles are found to approximately cancel. Monte Carlo and simulated annealing trials on the same or smaller versions of the problem, using the same atomic model and energy terms, are shown to result in less accurate predictions. Although the problem solved here is a limited one, the findings illustrate the utility of systematic searches with atom‐based models for macromolecular structure prediction and the importance of unbiased sampling in structure prediction methods. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Geometric algorithms for the conformational analysis of long protein loops

The efficient filtering of unfeasible conformations would considerably benefit the exploration of the conformational space when searching for minimum energy structures or during molecular simulation. The most important conditions for filtering are the maintenance of molecular chain integrity and the avoidance of steric clashes. These conditions can be seen as geometric constraints on a molecular model. In this article, we discuss how techniques issued from recent research in robotics can be applied to this filtering. Two complementary techniques are presented: one for conformational sampling and another for computing conformational changes satisfying such geometric constraints. The main interest of the proposed techniques is their application to the structural analysis of long protein loops. First experimental results demonstrate the efficacy of the approach for studying the mobility of loop 7 in amylosucrase from Neisseria polysaccharea. The supposed motions of this 17-residue loop would play an important role in the activity of this enzyme.     

Applications of simulated annealing to the conformational analysis of flexible molecules

We describe in this article our solution to the global minimum problem which uses the simulated annealing algorithm of Kirkpatrick. This method is a Metropolis (e-ΔE/kT) Monte Carlo sampling of conformation space with simultaneous constraint of the search by lowering the temperature T so that the search converges on the global minimum. The Anneal-Conformer program has been extensively tested with peptides and organic molecules using either the Amber or MM2 force fields. A history file of the simulated annealing process allows reconstruction of the random walk in conformation space for subsequent examination. Thus plots of distance and dihedral angle changes during the search for the global minimum can be examined to deduce molecular shape and flexibility. A separate program Conf-Gen reads the history file and extracts all low energy conformations visited during the run.     

Parameterization of OPLS-AA force field for the conformational analysis of macrocyclic polyketides

The parameters for the OPLS-AA potential energy function have been extended to include some functional groups that are present in macrocyclic polyketides. Existing OPLS-AA torsional parameters for alkanes, alcohols, ethers, hemiacetals, esters, and ketoamides were improved based on MP2/aug-cc-pVTZ and MP2/aug-cc-pVDZ calculations. Nonbonded parameters for the sp(3) carbon and oxygen atoms were refined using Monte Carlo simulations of bulk liquids. The resulting force field predicts conformer energies and torsional barriers of alkanes, alcohols, ethers, and hemiacetals with an overall RMS deviation of 0.40 kcal/mol as compared to reference data. Densities of 19 bulk liquids are predicted with an average error of 1.1%, and heats of vaporization are reproduced within 2.4% of experimental values. The force field was used to perform conformational analysis of smaller analogs of the macrocyclic polyketide drug FK506. Structures that adopted low-energy conformations similar to that of bound FK506 were identified. The results show that a linker of four ketide units constitutes the shortest effector domain that allows binding of the ketide drugs to FKBP proteins. It is proposed that the exact chemical makeup of the effector domain has little influence on the conformational preference of tetraketides.     

Tork: Conformational analysis method for molecules and complexes

A conformational search method for organic molecules and bimolecular complexes is presented. The method, termed Tork, uses normal-mode analysis in bond-angle-torsion coordinates and focuses on a key subset of torsional coordinates to identify natural molecular motions that lead the initial conformation to new energy minima. New conformations are generated via distortion along these modes and their pairwise combinations, followed by energy minimization. For complexes, special treatment is accorded to the six coordinates that specify the position and orientation of one molecule relative to the other. Tests described here show that Tork is highly efficient for cyclic, acyclic, and mixed single molecules, as well as for host-guest complexes.     

Multiple sequence alignment algorithm based on a dispersion graph and ant colony algorithm

In this article, we describe a representation for the processes of multiple sequences alignment (MSA) and used it to solve the problem of MSA. By this representation, we took every possible aligning result into account by defining the representation of gap insertion, the value of heuristic information in every optional path and scoring rule. On the basis of the proposed multidimensional graph, we used the ant colony algorithm to find the better path that denotes a better aligning result. In our article, we proposed the instance of three‐dimensional graph and four‐dimensional graph and advanced a special ichnographic representation to analyze MSA. It is yet only an experimental software, and we gave an example for finding the best aligning result by three‐dimensional graph and ant colony algorithm. Experimental results show that our method can improve the solution quality on MSA benchmarks. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

CAMERRA: An analysis tool for the computation of conformational dynamics by evaluating residue–residue associations

A computational method which extracts the dominant motions from an ensemble of biomolecular conformations via a correlation analysis of residue–residue contacts is presented. The algorithm first renders the structural information into contact matrices, then constructs the collective modes based on the correlated dynamics of a selected set of dynamic contacts. Associated programs can bridge the results for further visualization using graphics software. The aim of this method is to provide an analysis of conformations of biopolymers from the contact viewpoint. It may assist a systematical uncovering of conformational switching mechanisms existing in proteins and biopolymer systems in general by statistical analysis of simulation snapshots. In contrast to conventional correlation analyses of Cartesian coordinates (such as distance covariance analysis and Cartesian principal component analysis), this program also provides an alternative way to locate essential collective motions in general. Herein, we detail the algorithm in a stepwise manner and comment on the importance of the method as applied to decoding allosteric mechanisms. © 2018 Wiley Periodicals, Inc.     

Efficiency of tabu‐search‐based conformational search algorithms

Efficient conformational search or sampling approaches play an integral role in molecular modeling, leading to a strong demand for even faster and more reliable conformer search algorithms. This article compares the efficiency of a molecular dynamics method, a simulated annealing method, and the basin hopping (BH) approach (which are widely used in this field) with a previously suggested tabu‐search‐based approach called gradient only tabu search (GOTS). The study emphasizes the success of the GOTS procedure and, more importantly, shows that an approach which combines BH and GOTS outperforms the single methods in efficiency and speed. We also show that ring structures built by a hydrogen bond are useful as starting points for conformational search investigations of peptides and organic ligands with biological activities, especially in structures that contain multiple rings. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A parallel tabu search for conformational energy optimization of oligopeptides

We have developed and implemented a tabu search heuristic (TS) to determine the best energy minimum for oligopeptides. Our test molecule was Met‐enkephalin, a pentapetide that over the years has been used as a validation model for many global optimizers. The test potential energy function was ECEPP/3. Our tabu search implementation is based on assigning integer values to the variables to be optimized, and in facilitating the diversification and intensification of the search. The final output from the TS is treated with a local optimizer, and our best result competes both in quality and CPU time with those reported in the literature. The results indicate that TS is an efficient algorithm for conformational searches. We present a parallel TS version along with experimental results that show that this algorithm allows significant increases in speed. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 147–156, 2000     

Synthesis and conformational analysis of macrocyclic dihydroxystilbenes linked between the para-para positions

A new family of diphenylethanes has been synthesized as conformationally restricted analogues of antimitotic combretastatins. The two phenyl rings are linked between the para-phenolic positions through a 3-oxapentamethylene or hexamethylene chain. The key macrocyclization step was achieved in moderate yields by using an intramolecular McMurry pinacol coupling of linked aromatic dialdehydes, except for the nitro-substituted compounds. The relative stereochemistry of the isomeric pinacols was determined by a combination of spectroscopic, chemical derivatization, and molecular-modeling approaches. The NMR spectra of these compounds (with a polyoxygenated crownophane skeleton) indicate severe conformational restrictions relative to their parent combretastatins; the rotation of the phenyl rings is hampered by interactions of their substituents and the linker and the conformational restrictions imposed by the substituted bridge.     

A genetic algorithm encoded with the structural information of amino acids and dipeptides for efficient conformational searches of oligopeptides

The genetic algorithm (GA) is an intelligent approach for finding minima in a highly dimensional parametric space. However, the success of GA searches for low energy conformations of biomolecules is rather limited so far. Herein an improved GA scheme is proposed for the conformational search of oligopeptides. A systematic analysis of the backbone dihedral angles of conformations of amino acids (AAs) and dipeptides is performed. The structural information is used to design a new encoding scheme to improve the efficiency of GA search. Local geometry optimizations based on the energy calculations by the density functional theory are employed to safeguard the quality and reliability of the GA structures. The GA scheme is applied to the conformational searches of Lys, Arg, Met‐Gly, Lys‐Gly, and Phe‐Gly‐Gly representative of AAs, dipeptides, and tripeptides with complicated side chains. Comparison with the best literature results shows that the new GA method is both highly efficient and reliable by providing the most complete set of the low energy conformations. Moreover, the computational cost of the GA method increases only moderately with the complexity of the molecule. The GA scheme is valuable for the study of the conformations and properties of oligopeptides. © 2016 Wiley Periodicals, Inc.