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.     

Conformation‐Family Monte Carlo (CFMC): An Efficient Computational Method for Identifying the Low‐Energy States of a Macromolecule

A highly efficient method, Conformation‐Family Monte Carlo (CFMC), has been developed for searching the conformational space of a macromolecule and identifying its low‐energy conformations. This method maintains a database of low‐energy conformations that are clustered into families. The conformations in this database are improved iteratively by a Metropolis‐type Monte Carlo procedure, together with energy minimization, in which the search is biased towards investigating the regions of the lowest‐energy families. The CFMC method has the advantages of our earlier potential‐smoothing methods (in that it `coarse‐grains' the conformational space and exploits information about nearby low‐energy states), but avoids their disadvantages (such as the displacement of the global minimum at large smoothings). The CFMC method is applied to a test protein, domain B of Staphylococcal protein A. Independent CFMC runs yielded the same low‐energy families of conformations from random starts, indicating that the thermodynamically relevant conformational space of this protein has been explored thoroughly. The CFMC method is highly efficient, performing as well as or better than competing methods, such as Monte Carlo with minimization, conformational‐space annealing, and the self‐consistent basin‐to‐deformed‐basin method.     

Quantum theory of the structure and bonding in proteins: Part 4. The question of the quality of the basis set and of the stability of the extended forms

The conformational energy map of the molecule NH₂CH₂CHO is constructed using both the long basis set and the short basis set of the GAUSSIAN 70 package. It is shown that the two maps are qualitatively the same but that there are quantitative differences between them. Analysis of these and other results suggests that the stability of the extended planar structure is due in the main to the minimization of torsional barriers about the two single bonds of the backbone of the protein chain.There is broad general agreement between the semi-empirical method and its results as used by Scheraga and his colleagues on the one hand and our results from the ab initio computations on the other. Both methods suggest that the details of the conformations of these small peptides, treated as isolated molecules, are determined by hydrogen bonds and torsional barriers.     

Determination of the major solution conformation of tyrocidine A,using molecular mechanics energy minimization and NMR-derived distance and torsion angle constraints

Molecular mechanics energy calculations coupled with nuclear magnetic resonance-determined distance and torsion angle constraints have been used to determine the three-dimensional structure of tyrocidine A, a cyclic decapeptide which exists largely as a single conformation in solution. Two open-chain polyalanine models were used to represent separate halves of the peptide backbone and a combinatorial method of searching conformation space used to generate candidate structures consistent with experimental distance constraints. These structures were energy-minimized using the AMBER molecular mechanics forcefield and the resulting conformations classified by factor analysis of their Cartesian coordinates. Representative low-energy conformers of the two halves of the backbone were fused together and two candidate conformations of the completed backbone refined by further minimization using both distance and torsional constraints. Side chains were then added as their experimentally preferred rotamers and the whole molecule minimized without constraints to give the final model structure. This shows type II' and III ß turns at residues 4–5 and 9–10, respectively, coupled by twisted antiparallel strands which show hydrogen bonds between all four pairs of opposing peptide groups. The backbone conformation of residues 2–6 closely resembles that found in the crystal structure of gramicidin S.     

Efficiency of simulated annealing for peptides with increasing geometrical restrictions

Simulated annealing (SA) is a popular global minimizer that can conveniently be applied to complex macromolecular systems. Thus, a molecular dynamics or a Monte Carlo simulation starts at high temperature, which is decreased gradually, and the system is expected to reach the low-energy region on the potential energy surface of the molecule. However, in many cases this process is not efficient. Alternatively, the low-energy region can be reached more effectively by minimizing the energy of selected molecular structures generated along the simulation pathway. The efficiency of SA to locate energy-minimized structures within 5 kcal/mol above the global energy minimum is studied as applied to three peptide models with increasing geometrical restrictions: (1) The linear pentapeptide Leu-enkephalin described by the ECEPP potential, (2) a cyclic hexapeptide described by the GROMOS force field energy E_GRO alone, and (3) the same cyclic peptide with E_GRO combined with a restraining potential based on 31 proton–proton restraints obtained from nuclear magnetic resonance (NMR) experiments. The efficiency of SA is compared to that of the Monte Carlo minimization (MCM) method of Li and Scheraga, and to our local torsional deformations (LTD) method for the conformational search of cyclic molecules. The results for the linear peptide show that SA provides a relatively weak guidance towards the most stable energy region; as expected, this guidance increases for the cyclic peptide and the cyclic peptide with NMR restraints. However, in general, MCM and LTD are significantly more efficient than SA as generators of low-energy minimized structures. This suggests that LTD might provide a better search tool than SA in structure determination of protein regions for which a relatively small number of restraints are provided by NMR. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1659–1670, 1999     

A fast and efficient method to generate biologically relevant conformations

Summary Mutual binding between a ligand of low molecular weight and its macromolecular receptor demands structural complementarity of both species at the recognition site. To predict binding properties of new molecules before synthesis, information about possible conformations of drug molecules at the active site is required, especially if the 3D structure of the receptor is not known. The statistical analysis of small-molecule crystal data allows one to elucidate conformational preferences of molecular fragments and accordingly to compile libraries of putative ligand conformations. A comparison of geometries adopted by corresponding fragments in ligands bound to proteins shows similar distributions in conformation space. We have developed an automatic procedure that generates different conformers of a given ligand. The entire molecule is decomposed into its individual ring and open-chain torsional fragments, each used in a variety of favorable conformations. The latter ones are produced according to the library information about conformational preferences. During this building process, an extensive energy ranking is applied. Conformers ranked as energetically favorable are subjected to an optimization in torsion angle space. During minimization, unfavorable van der Waals interactions are removed while keeping the open-chain torsion angles as close as possible to the experimentally most frequently observed values. In order to assess how well the generated conformers map conformation space, a comparison with experimental data has been performed. This comparison gives some confidence in the efficiency and completeness of this approach. For some ligands that had been structurally characterized by protein crystallography, the program was used to generate sets of some 10 to 100 conformers. Among these, geometries are found that fall convincingly close to the conformations actually adopted by these ligands at the binding site.     

A knowledge-based approach to generating diverse but energetically representative ensembles of ligand conformers

This paper describes a new and efficient stochastic conformational sampling method for generating a range of low-energy molecule conformations. Sampling can be tailored to a specific structural domain (e.g., peptides) by extracting torsional profiles from specific datasets and subsequently applying them to target molecules outside the reference set. The programs that handle creation of the knowledge-based torsional profiles and conformer generation per se are separate and so can be used independently or sequentially, depending on the task at hand. The conformational ensembles produced are contrasted with those generated using local minimization approaches. They are also quantitatively compared with a broader range of techniques in terms of speed and the ability to reproduce bound ligand conformations found in complexes with proteins.     

An exploration of a novel strategy for superposing several flexible molecules

Summary This paper describes a computational strategy for the superposition of a set of flexible molecules. The combinatorial problems of searching conformational space and molecular matching are reduced drastically by the combined use of simulated annealing methods and cluster analysis. For each molecule, the global minimum of the conformational energy is determined by annealing and the search trajectory is retained in a history file. All the significantly different low-energy conformations are extracted by cluster analysis of data in the history file. Each pair of molecules, in each of their significantly different conformations, is then matched by simulated annealing, using the difference-distance matrix as the objective function. A set of match statistics is then obtained, from which the best match taken from all different conformations can be found. The molecules are then superposed either by reference to a base molecule or by a consensus method. This strategy ensures that as wide a range of conformations as possible is considered, but at the same time that the smallest number of significantly different conformations is used. The method has been tested on a set of six angiotensin II antagonists with between 7–11 rotatable bonds.     

Analyse conformationnelle théorique des molécules de benzylidène-aniline, stilbène et azobenzène : Partie II. Résultats de la méthode PCILO et ajustement d''un potentiel empirique

A conformational study of the benzylidene-aniline stilbene and azobenzene isoelectronic molecules has been carried out by the PCILO method in terms of torsional angles, bond lengths and valence angles. Initially, the conditions of application of this method to highly conjugated molecules were defined. The optimized geometries are in good agreement with those determined in the gas phase. Furthermore the rotation around a Ф—N or Ф—C bond can be specifically related to the variation of the second-order correction to the energy. This term was used to adjust the torsional potential in an empirical method adapted to this kind of molecule and able to account for both theoretical and experimental results.     

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     

Fast 3D molecular superposition and similarity search in databases of flexible molecules

We present a new method (fFLASH) for the virtual screening of compound databases that is based on explicit three-dimensional molecular superpositions. fFLASH takes the torsional flexibility of the database molecules fully into account, and can deal with an arbitrary number of conformation-dependent molecular features. The method utilizes a fragmentation-reassembly approach which allows for an efficient sampling of the conformational space. A fast clique-based pattern matching algorithm generates alignments of pairs of adjacent molecular fragments on the rigid query molecule that are subsequently reassembled to complete database molecules. Using conventional molecular features (hydrogen bond donors and acceptors, charges, and hydrophobic groups) we show that fFLASH is able to rapidly produce accurate alignments of medium-sized drug-like molecules. Experiments with a test database containing a diverse set of 1780 drug-like molecules (including all conformers) have shown that average query processing times of the order of 0.1 seconds per molecule can be achieved on a PC.     

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     

Conformational search using a molecular dynamics–minimization procedure: Applications to clusters of coulombic charges,Lennard–Jones particles,and waters

A new conformational search method, molecular dynamics–minimization (MDM), is proposed, which combines a molecular dynamics sampling strategy with energy minimizations in the search for low-energy molecular structures. This new method is applied to the search for low energy configurations of clusters of coulombic charges on a unit sphere, Lennard–Jones clusters, and water clusters. The MDM method is shown to be efficient in finding the lowest energy configurations of these clusters. A closer comparison of MDM with alternative conformational search methods on Lennard–Jones clusters shows that, although MDM is not as efficient as the Monte Carlo–minimization method in locating the global energy minima, it is more efficient than the diffusion equation method and the method of minimization from randomly generated structures. Given the versatility of the molecular dynamics sampling strategy in comparison to Monte Carlo in treating molecular complexes or molecules in explicit solution, one anticipates that the MDM method could be profitably applied to conformational search problems where the number of degrees of freedom is much greater. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 60–70, 1998     

QXP: Powerful, rapid computer algorithms for structure-based drug design

New methods for docking, template fitting and building pseudo-receptors are described. Full conformational searches are carried out for flexible cyclic and acyclic molecules. QXP (quick explore) search algorithms are derived from the method of Monte Carlo perturbation with energy minimization in Cartesian space. An additional fast search step is introduced between the initial perturbation and energy minimization. The fast search produces approximate low-energy structures, which are likely to minimize to a low energy. For template fitting, QXP uses a superposition force field which automatically assigns short-range attractive forces to similar atoms in different molecules. The docking algorithms were evaluated using X-ray data for 12 protein–ligand complexes. The ligands had up to 24 rotatable bonds and ranged from highly polar to mostly nonpolar. Docking searches of the randomly disordered ligands gave rms differences between the lowest energy docked structure and the energy-minimized X-ray structure, of less than 0.76 Å for 10 of the ligands. For all the ligands, the rms difference between the energy-minimized X-ray structure and the closest docked structure was less than 0.4 Å, when parts of one of the molecules which are in the solvent were excluded from the rms calculation. Template fitting was tested using four ACE inhibitors. Three ACE templates have been previously published. A single run using QXP generated a series of templates which contained examples of each of the three. A pseudo-receptor, complementary to an ACE template, was built out of small molecules, such as pyrrole, cyclopentanone and propane. When individually energy minimized in the pseudo-receptor, each of the four ACE inhibitors moved with an rms of less than 0.25 Å. After random perturbation, the inhibitors were docked into the pseudo-receptor. Each lowest energy docked structure matched the energy-minimized geometry with an rms of less than 0.08 Å. Thus, the pseudo-receptor shows steric and chemical complementarity to all four molecules. The QXP program is reliable, easy to use and sufficiently rapid for routine application in structure-based drug design.     

Energy-directed tree search: an efficient systematic algorithm for finding the lowest energy conformation of molecules

We present a new systematic algorithm, energy-directed tree search (EDTS), for exploring the conformational space of molecules. The algorithm has been designed to reliably locate the global minimum (or, in the worst case, a structure within 4 kJ mol(-1) of this species) at a fraction of the cost of a full conformational search, and in this way extend the range of chemical systems for which accurate thermochemistry can be studied. The algorithm is inspired by the build-up approach but is performed on the original molecule as a whole, and objectively determines the combinations of torsional angles to optimise using a learning process. The algorithm was tested for a set of 22 large molecules, including open- and closed-shell species, stable structures and transition structures, and neutral and charged species, incorporating a range of functional groups (such as phenyl rings, esters, thioesters and phosphines), and covering polymers, peptides, drugs, and natural products. For most of the species studied the global minimum energy structure was obtained; for the rest the EDTS algorithm found conformations whose total electronic energies are within chemical accuracy from the true global minima. When the conformational space is searched at a resolution of 120 degrees , the cost of the EDTS algorithm (in its worst-case scenario) scales as 2(N) for large N (where N is the number of rotatable bonds), compared with 3(N) for the corresponding systematic search.     

On the investigation of the low-energy conformational space of molecules

A new perspective on traditional energy minimization problems is provided by a connection between statistical thermodynamics and combinatorial optimization (finding the minimum of a function depending on many variables). The joint use of a new method for uncovering the global minimum of intramolecular potential energy functions, based on following the asymptotic behavior of a system of stochastic differential equations, and an iterative-improvement technique, whereby a search for relative minima is made by carrying out local quasi-Newton minimizations starting from many distinct points of the energy hypersurface, proved most effective for investigating the low-energy conformational space of molecules.     

Conformational analysis of oligosaccharides in solution

A complete understanding of the role of carbohydrates in biological systems is to a large extent dependent on the information available about the equilibrium mixture and about the preferred conformation of the carbohydrate molecules in solution. The conformational analysis offers a tool which can determine all possible conformations which influence the solution behavior of carbohydrates. This paper attempts to survey the progress in the theoretical conformational analysis of saccharides in solution. The conformational analysis will be discussed in detail both with respect to the strategy for the investigation of conformational properties but also with regard to the quality of the method used for calculations of the energy of the isolated molecule and free energy of solvation. Finally, examples will be given to illustrate how the methods of conformational analysis can be used to estimate the solution behavior of cyclic model compounds of carbohydrates 2-methoxytetrahydropyran, monosaccharide D -glucopyranose, and two disaccharides; β-maltose and β-cellobiose.     

Implementation and use of the method of prudent ascent in conformational analysis using molecular mechanics

In two-dimensional conformational analysis the current practice is to perform an energy minimization for all possible combinations of two dihedral angles in the molecule, in a fixed order, and apply a certain dihedral angle step-size. A newly developed method is presented in which the order of the evaluation points on the energy-surface is not fixed, but is dependent on all previous results in a way which we call “the method of prudent ascent.” In this method the most promising calculation is carried out first, thus minimizing the risk of atomic collisions. In order to be able to take care of the many additional degrees of conformational freedom present in, e.g., carbohydrate molecules, all minimizations are performed using a set of different promising starting conformations on the basis of previous calculations, and only the lowest energy result for each point is saved. An application of the method to conformational analysis of methyl-cellobiose and the artificial sweetener trichlorogalactosucrose is also presented.     

Protein structure prediction using a combination of sequence homology and global energy minimization I. Global energy minimization of surface loops

A procedure has been developed for global energy minimization of surface loops of proteins in the presence of a fixed core. The ECEPP potential function has been modified to allow more accurate representations of hydrogen bond interactions and intrinsic torsional energies. A computationally efficient representation of hydration free energy has been introduced. A local minimization procedure has been developed that uses a cutoff distance, minimization with respect to subsets of degrees of freedom, analytical second derivatives, and distance constraints between rigid segments to achieve efficiency in applications to surface loops. Efficient procedures have been developed for deforming segments of the initial backbone structure and for removing overlaps. Global energy minimization of a surface loop is accomplished by generating a sequence (or a trajectory) of local minima, the component steps of which are generated by searching collections of local minima obtained by deforming seven-residue segments of the surface loop. The search at each component step consists of the following calculations: (1) A large collection of backbone structures is generated by deforming a seven-residue segment of the initial backbone structure. (2) A collection of low-energy backbone structures is generated by applying local energy minimization to the resulting collection of backbone structures (interactions involving side chains that will be searched in this component step are not included in the energy). (3) One low-energy side-chain structure is generated for each of the resulting low-energy backbone structures. (4) A collection of low-energy local minima is generated by applying local energy minimization to the resulting collection of structures. (5) The local minimum with the lowest energy is retained as the next point of the trajectory. Applications of our global search procedure to surface segments of bovine pancreatic trypsin inhibitor (BPTI) and bovine trypsin suggest that component-step searches are reasonably complete. The computational efficiency of component-step searches is such that trajectories consisting of about 10 component steps are feasible using an FPS-5200 array processor. Our procedure for global energy minimization of surface loops is being used to identify and correct problems with the potential function and to calculate protein structure using a combination of sequence homology and global energy minimization.