Comparative analysis of protein-bound ligand conformations with respect to catalyst's conformational space subsampling algorithms

We examined the quality of Catalyst's conformational model generation algorithm via a large scale study based on the crystal structures of a sample of 510 pharmaceutically relevant protein-ligand complexes extracted from the Protein Data Bank (PDB). Our results show that the tested algorithms implemented within Catalyst are able to produce high quality conformers, which in most of the cases are well suited for in silico drug research. Catalyst-specific settings were analyzed, such as the method used for the conformational model generation (FAST vs BEST) and the maximum number of generated conformers. By setting these options for higher fitting quality, the average RMS values describing the similarity of experimental and simulated conformers were improved from an RMS of 1.06 with max. 50 FAST generated conformers to an RMS of 0.93 with max. 255 BEST generated conformers, which represents an improvement by 12%. Each method provides best fitting conformers with an RMS value<1.50 in more than 80% of all cases. We analyzed the computing time/quality ratio of various conformational model generation settings and examined ligands in high energy conformations. Furthermore, properties of the same ligands in various proteins were investigated, and the fitting qualities of experimental conformations from the PDB and the Cambridge Structural Database (CSD) were compared. One of the most important conclusions of former studies, the fact that bioactive conformers often have energy high above that of global minima, was confirmed.     

Relationship among ligand conformations in solution, in the solid state, and at the Hsp90 binding site: geldanamycin and radicicol

The unknown effects of a receptor's environment on a ligand's conformation presents a difficult challenge in predicting feasible bioactive conformations, particularly if the receptor is ill-defined. The primary hypothesis of this work is that a structure's conformational ensemble in solution presents viable candidates for protein binding. The experimental solution profile can be achieved with the NAMFIS (NMR analysis of molecular flexibility in solution) method, which deconvolutes the average NMR spectrum of small flexible molecules into individual contributing conformations with varying populations. Geldanamycin and radicicol are structurally different macrocycles determined by X-ray crystallography to bind to a common site on the cellular chaperone heat shock protein 90 (Hsp90). Without benefit of a receptor structure, NAMFIS has identified the bioactive conformers of geldanamycin and radicicol in CDCl3 solution with populations of 4% and 21%, respectively. Conversely, docking the set of NAMFIS conformers into the unliganded proteins with GLIDE followed by MM-GBSA scoring reproduces the experimental crystallographic binding poses.     

Computational protocols for prediction of solute NMR relative chemical shifts. a case study of L-tryptophan in aqueous solution

In this study, we have applied two different spanning protocols for obtaining the molecular conformations of L-tryptophan in aqueous solution, namely a molecular dynamics simulation and a molecular mechanics conformational search with subsequent geometry re-optimization of the stable conformers using a quantum mechanically based method. These spanning protocols represent standard ways of obtaining a set of conformations on which NMR calculations may be performed. The results stemming from the solute-solvent configurations extracted from the MD simulation at 300 K are found to be inferior to the results stemming from the conformations extracted from the MM conformational search in terms of replicating an experimental reference as well as in achieving the correct sequence of the NMR relative chemical shifts of L-tryptophan in aqueous solution. We find this to be due to missing conformations visited during the molecular dynamics run as well as inaccuracies in geometrical parameters generated from the classical molecular dynamics simulations.     

Predicting bioactive conformations and binding modes of macrocycles

Macrocyclic compounds experience increasing interest in drug discovery. It is often thought that these large and chemically complex molecules provide promising candidates to address difficult targets and interfere with protein–protein interactions. From a computational viewpoint, these molecules are difficult to treat. For example, flexible docking of macrocyclic compounds is hindered by the limited ability of current docking approaches to optimize conformations of extended ring systems for pose prediction. Herein, we report predictions of bioactive conformations of macrocycles using conformational search and binding modes using docking. Conformational ensembles generated using specialized search technique of about 70 % of the tested macrocycles contained accurate bioactive conformations. However, these conformations were difficult to identify on the basis of conformational energies. Moreover, docking calculations with limited ligand flexibility starting from individual low energy conformations rarely yielded highly accurate binding modes. In about 40 % of the test cases, binding modes were approximated with reasonable accuracy. However, when conformational ensembles were subjected to rigid body docking, an increase in meaningful binding mode predictions to more than 50 % of the test cases was observed. Electrostatic effects did not contribute to these predictions in a positive or negative manner. Rather, achieving shape complementarity at macrocycle-target interfaces was a decisive factor. In summary, a combined computational protocol using pre-computed conformational ensembles of macrocycles as a starting point for docking shows promise in modeling binding modes of macrocyclic compounds.     

A molecular mechanics force field for conformational analysis of aliphatic acyclic amines

An improved molecular mechanics force field for conformational and vibrational studies of aliphatic acyclic amines is developed. The resulting force field reproduces molecular structures adequately and provides a good fit for energy differences between conformers and barriers to internal rotation for a large number of amines. In addition, vibrational frequencies are calculated in good agreement with available experimental data. When compared with existent force fields for amines, the present force field is considerably more simple and gives rise to calculated properties in closer agreement with experiment.     

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.     

Cluster analysis of molecular conformations

We describe a method for locating clusters of geometrically similar conformers in ensembles of chemical conformations. We first calculate the pairwise interconformational distance matrix in either torsional or Cartesian space and then use an agglomerative, single-link clustering method to define a hierarchy of clusterings in the same space. Especially good clusterings are distinguished by high values of the separation ratio: the ratio of the shortest intercluster distance to the characteristic threshold distance defining the clustering. We also discuss other statistics. The method has been embodied in a program called XCluster, which can display the distance matrix, the hierarchy of clusterings, and the clustering statistics in a variety of formats. XCluster can also write out the clustered conformations for subsequent or simultaneous viewing with a molecular visualization program. We demonstrate the sorts of insight that this approach affords with examples obtained from conformational search and molecular dynamics procedures. © 1994 by John Wiley & Sons, Inc.     

Two-state folding observed in individual protein molecules

The folding dynamics of small proteins are often described in terms of a simple two-state kinetic model. Within this notion, the behavior of individual molecules is expected to be stochastic, with a protein molecule residing in either the unfolded or the folded state for extended periods of time, with intermittent rapid jumps across the free energy barrier. However, a direct observation of this bistable behavior has not been made to date. Rather, previous reports of folding trajectories of individual proteins have shown an unexpected degree of complexity. This raises the question whether the simple kinetic properties derived from classical experiments on large ensembles of molecules are reflected in the folding paths taken by individual proteins. Here we report single-molecule folding/unfolding trajectories observed by fluorescence resonance energy transfer for a protein that meets all criteria of a two state-system. The trajectories, measured on molecules immobilized in lipid vesicles, demonstrate the anticipated bistable behavior, with steplike transitions between folded and unfolded conformations. They further allow us to put an upper bound on the barrier crossing time.     

An unbounded systematic search of conformational space

A new method for searching internal coordinate conformational space systematically via a continuous-process procedure is described. Unlike previous systematic search methods, the new scheme generates torsionally remote conformers early in the search. It is also unbounded in that the extent of the search need not be specified at the outset. The search begins at low resolution (120° in torsion angle space) and then goes to higher and higher resolution as all points in space at a given resolution have been searched. The search may run without end or be terminated when new conformers cease to be found or when all space at some maximum allowable resolution has been explored. Conformational searches on several medium- and large-ring molecules using the new method are described and the results are compared with those from certain previously described search methods. It is found that the new method is significantly more efficient than previous procedures at finding all low energy conformers of organic molecules.     

Predictive in silico all-atom folding of a four-helix protein with a free-energy model

We report the predictive all-atom folding of the 60 amino acid four-helix bacterial ribosomal protein (BRP) L20 with a stochastic evolutionary optimization method in a free-energy force field. The energetically best, as well as six of the 10 lowest conformations, converge to a near-native structure. All of the 10 best energy conformations share the secondary structure elements of the native conformation, but differ in their tertiary alignment. The best conformation has a backbone root-mean-square deviation of 4.6 A to the native conformation and reproduces most distance constraints of the NMR experiment to 1.5 A resolution. Starting from random initial conditions, the native content of the simulated population increases more than 60-fold in the course of the simulation. These data demonstrate the feasibility of predictive unbiased all-atom protein folding with present day computational resources for the BRP L20.     

MC(JBW): Simple but smart Monte Carlo algorithm for free energy simulations of multiconformational molecules

Many of the most common molecular simulation methods, including Monte Carlo (MC) and molecular or stochastic dynamics (MD or SD), have significant difficulties in sampling the space of molecular potential energy surfaces characterized by multiple conformational minima and significant energy barriers. In such cases improved sampling can be obtained by special techniques that lower such barriers or somehow direct search steps toward different low energy regions of space. We recently described a hybrid MC/SD algorithm [MC(JBW)/SD] incorporating such a technique that directed MC moves of selected torsion and bond angles toward known low energy regions of conformational space. Exploration of other degrees of freedom was left to the SD part of the hybrid algorithm. In the work described here, we develop a related but simpler simulation algorithm that uses only MC to sample all degrees of freedom (e.g., stretch, bend, and torsion). We term this algorithm MC(JBW). Using simulations on various model potential energy surfaces and on simple molecular systems (n-pentane, n-butane, and cyclohexane), MC(JBW) is shown to generate ensembles of states that are indistinguishable from the canonical ensembles generated by classical Metropolis MC in the limit of very long simulations. We further demonstrate the utility of MC(JBW) by evaluating the room temperature free energy differences between conformers of various substituted cyclohexanes and the larger ring hydrocarbons cycloheptane, cyclooctane, cyclononane, and cyclodecane. The results compare favorably with available experimental data and results from previously reported MC(JBW)/SD conformational free energy calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1736–1745, 1998     

Estimation of active conformations of drugs by a new molecular superposing procedure

We have developed a new program, SUPERPOSE, to superpose two molecules based on the physicochemical properties of functional atoms within individual molecules. SUPERPOSE treats a pseudo-molecule consisting of functional atoms instead of a real molecule. Four types of physicochemical properties – hydrophobicity, presence of a hydrogen-bonding donor, presence of a hydrogen-bonding acceptor and presence of a hydrogen-bonding donor/acceptor – were supposed and a score was given to each overlap. When functional atoms with the same physicochemical properties were overlapped, points were added to the score, and when the functional atoms with different physicochemical properties were overlapped, points were subtracted. We applied SUPERPOSE to 12 pairs of 24 enzyme inhibitors and found that the best scored overlay for each inhibitor pair could successfully reproduce the superposition obtained from X-ray crystallography. Next, we applied SUPERPOSE to estimate the active conformations of the thrombin inhibitors MQPA, 4-TAPAP and NAPAP. Superpositions of conformers sampled by the high-temperature molecular dynamics calculation with respect to the three inhibitors were performed, and 13 sets of conformers having the best common overlay to the three inhibitors were selected. One among 13 sets was consistent with the superposition of the active conformations derived from the X-ray crystallography of the thrombin–inhibitor complexes.     

Conformational analysis of macrocycles: comparing general and specialized methods

Macrocycles represent an important class of medicinally relevant small molecules due to their interesting biological properties. Therefore, a firm understanding of their conformational preferences is important for drug design. Given the importance of macrocycle-protein modelling in drug discovery, we envisaged that a systematic study of both classical and recent specialized methods would provide guidance for other practitioners within the field. In this study we compare the performance of the general, well established conformational analysis methods Monte Carlo Multiple Minimum (MCMM) and Mixed Torsional/Low-Mode sampling (MTLMOD) with two more recent and specialized macrocycle sampling techniques: MacroModel macrocycle Baseline Search (MD/LLMOD) and Prime macrocycle conformational sampling (PRIME-MCS). Using macrocycles extracted from 44 macrocycle-protein X-ray crystallography complexes, we evaluated each method based on their ability to (i) generate unique conformers, (ii) generate unique macrocycle ring conformations, (iii) identify the global energy minimum, (iv) identify conformers similar to the X-ray ligand conformation after Protein Preparation Wizard treatment (X-rayppw), and (v) to the X-rayppw ring conformation. Computational speed was also considered. In addition, conformational coverage, as defined by the number of conformations identified, was studied. In order to study the relative energies of the bioactive conformations, the energy differences between the global energy minima and the energy minimized X-rayppw structures and, the global energy minima and the MCMM-Exhaustive (1,000,000 search steps) generated conformers closest to the X-rayppw structure, were calculated and analysed. All searches were performed using relatively short run times (10,000 steps for MCMM, MTLMOD and MD/LLMOD). To assess the performance of the methods, they were compared to an exhaustive MCMM search using 1,000,000 search steps for each of the 44 macrocycles (requiring ca 200 times more CPU time). Prior to our analysis, we also investigated if the general search methods MCMM and MTLMOD could also be optimized for macrocycle conformational sampling. Taken together, our work concludes that the more general methods can be optimized for macrocycle modelling by slightly adjusting the settings around the ring closure bond. In most cases, MCMM and MTLMOD with either standard or enhanced settings performed well in comparison to the more specialized macrocycle sampling methods MD/LLMOD and PRIME-MCS. When using enhanced settings for MCMM and MTLMOD, the X-rayppw conformation was regenerated with the greatest accuracy. The, MD/LLMOD emerged as the most efficient method for generating the global energy minima.     

Flexible protein‐protein docking based on Best‐First search algorithm

We developed a new high resolution protein‐protein docking method based on Best‐First search algorithm that loosely imitates protein‐protein associations. The method operates in two stages: first, we perform a rigid search on the unbound proteins. Second, we search alternately on rigid and flexible degrees of freedom starting from multiple configurations from the rigid search. Both stages use heuristics added to the energy function, which causes the proteins to rapidly approach each other and remain adjacent, while optimizing on the energy. The method deals with backbone flexibility explicitly by searching over ensembles of conformations generated before docking. We ran the rigid docking stage on 66 complexes and grouped the results into four classes according to evaluation criteria used in Critical Assessment of Predicted Interactions (CAPRI; “high,” “medium,” “acceptable,” and “incorrect”). Our method found medium binding conformations for 26% of the complexes and acceptable for additional 44% among the top 10 configurations. Considering all the configurations, we found medium binding conformations for 55% of the complexes and acceptable for additional 39% of the complexes. Introducing side‐chains flexibility in the second stage improves the best found binding conformation but harms the ranking. However, introducing side‐chains and backbone flexibility improve both the best found binding conformation and the best found conformation in the top 10. Our approach is a basis for incorporating multiple flexible motions into protein‐protein docking and is of interest even with the current use of a simple energy function. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Extensive conformational searches of 13 representative dipeptides and an efficient method for dipeptide structure determinations based on amino acid conformers

Conformations of peptides are the basis for their property studies and the predictions of peptide structures are highly important in life science but very complex in practice. Here, thorough searches on the potential energy surfaces of 13 representative dipeptides by considering all possible combinations of the bond rotational degrees of freedom are performed using the density functional theory based methods. Careful analyses of the conformers of the 13 dipeptides and the corresponding amino acids reveal the connections between the structures of dipeptide and amino acids. A method for finding all important dipeptide conformers by optimizing a small number of trial structures generated by suitable superposition of the parent amino acid conformations is thus proposed. Applying the method to another eight dipeptides carefully examined by others shows that the new approach is both highly efficient and reliable by providing the most complete ensembles of dipeptide conformers and much improved agreements between the theoretical and experimental IR spectra. The method opens the door for the determination of the stable structures of all dipeptides with a manageable amount of effort. Preliminary result on the applicability of the method to the tripeptide structure determination is also presented. The results are the first step towards proving Anfinsen's hypothesis by revealing the relationships between the structures of the simplest peptide and its constituting amino acids. It implies that the structures of peptides are not only determined by their amino acid sequences, but also closely linked with the amino acid conformations. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

A Method for Multiconformational Modeling of the Three‐Dimensional Shape of a Molecule

A method for multiconformational modeling of the threedimensional shape of a molecule is proposed that includes search for conformers, their optimum superposition, and analysis of spatial features of the resulting structure. The method allows one to determine features of various molecular conformations of compounds under study, to assess the contributions of conformers to particular properties of the substance, to evaluate the space occupied by the molecule, and to compare the average size of the multiconformational model of the molecule with the sizes of the most stable conformations. The potentials of the model are illustrated by density calculations for 137 organic liquids.     

Generating conformer ensembles using a multiobjective genetic algorithm

The task of generating a nonredundant set of low-energy conformations for small molecules is of fundamental importance for many molecular modeling and drug-design methodologies. Several approaches to conformer generation have been published. Exhaustive searches suffer from the exponential growth of the search space with increasing degrees of conformational freedom (number of rotatable bonds). Stochastic algorithms do not suffer as much from the exponential increase of search space and provide a good coverage of the energy minima. Here, the use of a multiobjective genetic algorithm in the generation of conformer ensembles is investigated. Distance geometry is used to generate an initial conformer, which is then subject to geometric modifications encoded by the individuals of the genetic algorithm. The geometric modifications apply to torsion angles about rotatable bonds, stereochemistry of double bonds and tetrahedral chiral centers, and ring conformations. The geometric diversity of the evolving conformer ensemble is preserved by a fitness-sharing mechanism based on the root-mean-square distance of the atomic coordinates. Molecular symmetry is taken into account in the distance calculation. The geometric modifications introduce strain into the structures. The strain is relaxed using an MMFF94-like force field in a postprocessing step that also removes conformational duplicates and structures whose strain energy remains above a predefined window from the minimum energy value found in the set. The implementation, called Balloon, is available free of charge on the Internet ( http://www.abo.fi/~mivainio/balloon/).