Q-fit: a probabilistic method for docking molecular fragments by sampling low energy conformational space

A new method is presented that docks molecular fragments to a rigid protein receptor. It uses a probabilistic procedure based on statistical thermodynamic principles to place ligand atom triplets at the lowest energy sites. The probabilistic method ranks receptor binding modes so that the lowest energy ones are sampled first. This allows constraints to be introduced to limit the depth of the search leading to a computationally efficient method of sampling low energy conformational space. This is combined with energy minimization of the initial fragment placement to arrive at a low energy conformation for the molecular fragment. Two different search methods are tested involving (i) geometric hashing and (ii) pose clustering methods. Ten molecular fragments were docked that have commonly been used to test docking methods. The success rate was 8/10 and 10/10 for generating a close solution ranked first using the two different sampling procedures. In general, all five of the top ranked solutions reproduce the observed binding mode, which increases confidence in the predictions. A set of ten molecular fragments that have previously been identified as problematic were docked. Success was achieved in 3/10 and 4/10 using the two different methods. Again there is a high level of agreement between the two methods and again in the successful cases the top ranked solutions are correct whilst in the case of the failures none are. The geometric hashing and pose clustering methods are fast averaging 13 and 11 s per placement respectively using conservative parameters. The results are very encouraging and will facilitate the process of finding novel small molecule lead compounds by virtual screening of chemical databases.     

A model for the binding of low molecular weight inhibitors to the active site of thrombin

This paper describes the construction, validation and application of an active site model of the serine protease thrombin. Initial use was made of medium resolution X-ray crystallographic structures of thrombin complexed with low molecular weight, non-specific inhibitors to create a computationally useable active site shell of the enzyme. Molecular mechanics methods were then applied to dock known ligands into the active site region in order to derive a model that would accurately predict binding conformations. Validation of the modelling process was achieved by comparison of the predicted enzyme-bound conformations with their known, crystallographic binding conformations. The resultant model was used extensively for predictive purposes prior to obtaining confirmatory crystal data relating to a ligand possessing a novel and unexpected binding component complexed to thrombin. The data served both to confirm the accuracy of the binding site model and to provide information for the further refinement of the model.     

On the use of local basis sets for localized molecular orbitals

Two procedures are discussed for the direct variational optimization of localized molecular orbitals which are expanded in local subsets of the molecular basis set. It is shown that a Newton-Raphson approach is more efficient than an iterative diagonalization scheme. The effect of the basis-set truncation on the quality ofab-initio SCF results is investigated for Be, Li₂, HF, H₂O, NH₃, CH₄ and C₂H₆.     

Dynamics of the glycosidic bond: conformational space of lactose

The dynamics of the glycosidic bond of lactose was studied by a paramagnetic tagging‐based NMR technique, which allowed the collection of an unusually large series of NMR data for a single compound. By the use of distance‐ and orientation‐dependent residual dipolar couplings and pseudocontact shifts, the simultaneous fitting of the probabilities of computed conformations and the orientation of the magnetic susceptibility tensor of a series of lanthanide complexes of lactose show that its glycosidic bond samples syn/syn, anti/syn and syn/anti ?/ψ regions of the conformational space in water. The analysis indicates a higher reliability of pseudocontact shift data as compared to residual dipolar couplings with the presently available weakly orienting paramagnetic tagging technique. The method presented herein allows for an improved understanding of the dynamic behaviour of oligosaccharides.     

Reduction of the Search Space for the Folding of Proteins at the Level of Formation and Assembly of Secondary Structures: A New View on the Solution of Levinthal′s Paradox

The complete volume of the protein conformation space is, by many orders of magnitude, smaller at the level of secondary structure elements than that at the level of amino acid residues; the latter, according to Levinthal′s estimate, scales approximately as 10^{2 L}, with L being the number of residues in the chain, whereas the former, as demonstrated in this paper, scales no faster than ～L^N, with N being the number of the secondary structure elements, which is approximately equal to L/15. This drastic decrease in the exponent (L/15 instead of 2 L) explains why sampling of the conformation space does not contradict the ability of the protein chain to find its most stable fold.     

Quantum mechanical/molecular mechanical self-consistent Madelung potential method for treatment of polar molecular crystals

The self-consistent Madelung potential (SCMP) approach for calculating molecular wave functions for a subunit embedded in a symmetrical environment constituted by the copies of the subunit is implemented with semiempirical NDDO model Hamiltonians and supplemented with empirically parameterized dispersion–repulsion interaction potentials. This model yields sublimation enthalpies in good agreement with available experimental data for a series of molecular crystals, including imidazol, benzimidazole, urea, urethane, dicyaneamide, formamide, uracil, cytosine, maleic anhydride, succinic anhydride, and 1,3,5-triamino-2,4,6-trinitro-benzene. The SCMP-NDDO method, which avoids difficulties concerning the parametrization of charges in the molecular mechanics force fields, is proposed mainly for the treatment of molecular crystals with large unit cells. It might be particularly useful where important charge reorganization is expected under the effect of the crystal field. Charge distributions, obtained by the SCMP and the simple dielectric cavity self-consistent reaction field models, are compared and analyzed. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 38–50, 1998     

On the influence of charged side chains on the folding-unfolding equilibrium of beta-peptides: a molecular dynamics simulation study

The influence of charged side chains on the folding-unfolding equilibrium of beta-peptides was investigated by means of molecular dynamics simulations. Four different peptides containing only negatively charged side chains, positively charged side chains, both types of charged side chains (with the ability to form stabilizing salt bridges) or no charged side chains were studied under various conditions (different simulation temperatures, starting structures and solvent environment). The NMR solution structure in methanol of one of the peptides (A) has already been published; the synthesis and NMR analysis of another peptide (B) is described here. The other peptides (C and D) studied herein have hitherto not been synthesized. All four peptides A-D are expected to adopt a left-handed 3(14)-helix in solution as well as in the simulations. The resulting ensembles of structures were analyzed in terms of conformational space sampled by the peptides, folding behavior, structural properties such as hydrogen bonding, side chain-side chain and side chain-backbone interactions and in terms of the level of agreement with the NMR data available for two of the peptides. It was found that the presence of charged side chains significantly slows down the folding process in methanol solution due to the stabilization of intermediate conformers with side chain-backbone interactions. In water, where the solvent competes with the solute-solute polar interactions, the folding process to the 3(14)-helix is faster in the simulations.     

A method for conformational sampling of loops in proteins based on adiabatic decoupling and temperature or force scaling

A method for conformational Boltzmann sampling of loops in proteins in aqueous solution is presented that is based on adiabatic decoupling molecular dynamics (MD) simulation with temperature or force scaling. To illustrate the enhanced sampling, the loop from residues 33 to 43 in the bovine protein ribonuclease A is adiabatically decoupled from the rest of the protein and the solvent with a mass scaling factor s(m) =1000 and the sampling is enhanced with a scaling of the temperature using s(T) =2 or of the force using s(V) =0.667. Over 5 ns of simulation the secondary structure of the protein remains unaltered while a combined dihedral-angle conformational cluster analysis shows an increase of conformations outside the first most populated cluster of loop conformations for adiabatic decoupling MD with temperature scaling using s(T) =2 or force scaling using s(V) =0.667 compared to the standard MD simulation. The atom-positional root-mean-square fluctuations of the C(α) atoms of the loop show an increase in the movement of the loop as well, indicating that adiabatic decoupling MD with upscaling of the temperature or downscaling of the force is a promising method for conformational Boltzmann sampling.     

A conformational analysis method for understanding the energy landscapes of clusters.

A newly developed unbiased structural optimization method, named dynamic lattice searching (DLS), is proposed as an approach for conformational analysis of atomic/molecular clusters and used in understanding the energy landscape of large clusters. The structures of clusters are described in terms of the number of basic tetrahedron (BT) units they contain. We found that the hit numbers of different structural motifs in DLS runs is proportional to the number of BTs. A parameter T(max) is defined to limit the maximal number of atoms moved in a structural transition. Results show that T(max) is a key parameter for modulating the efficiency of the DLS method and has a great influence on the hit number of different motifs in DLS runs. Finally, the effect of potential range on the conformational distribution of the (Morse)(98) cluster is also discussed with different potential-range parameters.     

Non-natural amino acids as modulating agents of the conformational space of model glycopeptides

The synthesis and conformational analysis in aqueous solution of different alpha-methyl-alpha-amino acid diamides, derived from serine, threonine, beta-hydroxycyclobutane-alpha-amino acids, and their corresponding model beta-O-glucopeptides, are reported. The study reveals that the presence of an alpha-methyl group forces the model peptides to adopt helix-like conformations. These folded conformations are especially significant for cyclobutane derivatives. Interestingly, this feature was also observed in the corresponding model glucopeptides, thus indicating that the alpha-methyl group and not the beta-O-glucosylation process largely determines the conformational preference of the backbone in these structures. On the other hand, atypical conformations of the glycosidic linkage were experimentally determined. Therefore, when a methyl group was located at the Cbeta atom with an R configuration, the glycosidic linkage was rather rigid. Nevertheless, when the S configuration was displayed, a significant degree of flexibility was observed for the glycosidic linkage, thus showing both alternate and eclipsed conformations of the psi(s) dihedral angle. In addition, some derivatives exhibited an unusual value for the phi(s) angle, which was far from a value of -60 degrees expected for a conventional beta-O-glycosidic linkage. In this sense, the different conformations exhibited by these molecules could be a useful tool in obtaining systems with conformational preferences "à la carte".     

A molecular mechanics and semiempirical conformational analysis of the herbicide diuron inhibitor of photosystem II

The potential energy surface (PES) for the herbicide diuron (DCMU), a photosystem II inhibitor, has been extensively investigated using the quantum-mechanical semiempirical molecular orbital methods AM1 and PM3 and molecular mechanics method. A detailed conformational search has been carried out which revealed the occurrence of four genuine minimum energy structures. The relative stability of the conformers and rotational barriers to conformational interconversion were evaluated using distinct theoretical approaches. The results showed that thetrans form of the diuron molecule is more stable than thecis form in all methods, and so it may possibly be the biologically active isomer.     

A new method for the derivation of exact vibration-rotational kinetic energy operator in internal coordinates

An efficient angular momentum method is presented and used to derive analytic expressions for the vibration-rotational kinetic energy operator of polyatomic molecules.The vibration-rotational kinetic energy operator is expressed in terms of the total angular momentum operator J,the angular momentum operator J and the momentum operator p conjugate to Z in the molecule-fixed frame Not only the method of derivation is simpler than that in the previous work,but also the expressions ot the kinetic energy operators arc more compact.Particularly,the operator is easily applied to different vibrational or rovibrational problems of the polyatomic molecules by variations of matrix elements Gn of a mass-dependent constant symmetric matrix     

DMC: A multifunctional hybrid dynamics/Monte Carlo simulation algorithm for the evaluation of conformational space

A hybrid conformational search algorithm (DMC) is described that combines a modified form of molecular dynamics with Metropolis Monte Carlo sampling, using the COSMIC(90) force field. Trial configurations are generated by short bursts of high-temperature dynamics in which the initial kinetic energy is focused into single bond rotations or alternatively into “corner-flapping” motions in ring systems. Constant temperature and simulated annealing search protocols have been applied to the conformational analysis of several model hydrocarbons (cyclopentane, cyclohexane, cycloheptane, cyclooctane, cycloheptadecane, decane, and tetradecane), and the performance compared with conventional molecular dynamics and Monte Carlo sampling methods. Optimum Metropolis sampling temperatures have been determined and range from 1000–2000 K for acyclic molecules to 3000 K for cyclic systems. Simulated annealing runs are most successful at locating the global minimum when cooling slowing from these optimum temperatures.     

Correlation-function potential-harmonic and generalized Laguerre function method for directly solving Schrodinger equations of atoms

The potential-harmonic and generalized Laguerre function method (PHGLF) was modified into the correlation-function potential-harmonic and generalized Laguerre function method (CFPHGLF). The eigenenergies for 21S, 31S and 41S states of helium-like systems from the CFPHGLF are much more accurate than those from the previous PHGLF, but the eigenenergy for the 11S is not as good as that from the PHGLF method. The results indicate that the electron-nucleus cusp plays more important role than the electron-electron cusp and the cluster structure for the loosely bound excited states, and that the electron-electron cusp is absolutely essential for the tightly bound ground state.     

Molecular simulation of alkyl monolayers on the Si(111)surface

The structure of twelve-carbon monolayers on the H-terminated Si(111) surface is investigated by molecular simulation method. The best substitution percent on Si(111) surface obtained via molecular mechanics calculation is equal to 50%, and the (8×8) simulated cell can be used to depict the structure of alkyl monolayer on Si surface. After two-dimensional cell containing alkyl chains and four-layer Si(111) crystal at the substitution 50% is constructed, the densely packed and well-ordered monolayer on Si(111) surface can be shown through energy minimization in the suitable-size simulation cell. These simulation results are in good agreement with the experiments. These conclusions show that molecular simulation can provide otherwise inaccessible mesoscopic information at the molecular level, and can be considered as an adjunct to experiments.     

A method for determining the mean translational energy of particles desorbed from solid surfaces

A method for determinig the mean molecular translational energy in gas flows of low intensity (10¹²–10¹⁴ molec. s^–1) has been proposed. The method was verified using various gases (H₂, N₂, O₂, and CO₂ flowing into a vacuum out of a heated capillary. The translational energies were determined for CO and N₂ molecules desorbing from the surface of polycrystalline Ir. The translational temperature (T _tr) measured for CO equals 650±90 K and almost coincides with the surface temperature (T _s = 600 K). In the case of nitrogen molecules,T _tr = 4600±500 K atT _s = 500 K. The method proposed is applicable to the determination of the spatial distribution of molecular beam particles.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 30–34, January, 1995.The authors express their gratitude to A. V. Sklyarov for fruitful discussions during the elaboration of the theoretical basis and technical realization of the method.The reseach was carried out with the partial financial support of the International Science Foundation (Grant MBN 000).     

A molecular model for the active site of S-adenosyl-l-homocysteine hydrolase

Summary S-adenosyl-l-homocysteine hydrolase (AdoHcy hydrolase, EC 3.3.1.1.), a specific target for antiviral drug design, catalyzes the hydrolysis of AdoHcy to adenosine (Ado) and homocysteine (Hcy) as well as the synthesis of AdoHcy from Ado and Hcy. The enzyme isolated from different sources has been shown to contain tightly bound NAD⁺.Based on the 2.0 Å-resolution X-ray crystal structure of dogfish lactate dehydrogenase (LDH), which is functionally homologous to AdoHcy hydrolase, and the primary sequence of rat liver AdoHcy hydrolase, we have derived a molecular model of an extended active site for AdoHcy hydrolase. The computational mutation was performed using the software MUTAR (Yeh et al., University of Kansas, Lawrence), followed by molecular mechanics optimizations using the programs AMBER (Singh et al., University of California, San Francisco) and YETI (Vedani, University of Kansas). Solvation of the model structure was achieved by use of the program SOLVGEN (Jacober, University of Kansas); 56 water molecules were explicitly included in all refinements. Some of these may be involved in the catalytic reaction.We also studied a model of the complex of AdoHcy hydrolase with NAD⁺, as well as the ternary complexes of the redox reaction catalyzed by AdoHcy hydrolase and has been used to differentiate the relative binding strength of inhibitors.     

Molecular simulation of alkyl monolayers on the Si(lll) surface

The structure of twelve-carbon monolayers on the H-terminated Si(111) surface is investigated by molecular simulation method. The best substitution percent on Si(111) surface obtained via molecular mechanics calculation is equal to 50%, and the (8 ε 8) simulated cell can be used to depict the structure of alkyl monolayer on Si surface. After two-dimensional cell containing alkyl chains and four-layer Si(111) crystal at the substitution 50% is constructed, the densely packed and well-ordered monolayer on Si(111) surface can be shown through energy minimization in the suitable-size simulation cell. These simulation results are in good agreement with the experiments. These conclusions show that molecular simulation can provide otherwise inaccessible mesoscopic information at the molecular level, and can be considered as an adjunct to experiments.     

1H‐Azepine‐4‐amino‐4‐carboxylic Acid: A New α,α‐Disubstituted Ornithine Analogue Capable of Inducing Helix Conformations in Short Ala‐Aib Pentapeptides

A very efficient synthesis of orthogonally protected 1H‐azepine‐4‐amino‐4‐carboxylic acid, abbreviated as Azn, a conformationally restricted analogue of ornithine, was realized. It was obtained on a gram scale in good overall yield in five steps, three of which did not require isolation of the intermediates, starting from the readily available 1‐amino‐4‐oxo‐cyclohexane‐4‐carboxylic acid. Both enantiomers were used for the preparation of pentapeptide models containing Ala, Aib, and Azn. Conformational studies using both spectroscopic techniques (NMR, CD) and molecular dynamics on model 5‐mer peptides showed that the (R)‐Azn isomer possesses a marked helicogenic effect.     

General methodology in two dimensions for classical simulation of reactive and nonreactive events on ab initio potential energy surfaces

A completely general two-dimensional (2D) methodology for the classical simulation of reactive and nonreactive events on ab initio potential energy surfaces is introduced and tested. The methodology requires the minimum amount of information given a priori—geometries and energies at these geometries. From a list of ab initio geometries and energies, simulations may be executed and a distribution of outcomes obtained. The method introduced attempts a local approach at simulating the dynamics of the system, rather than a global analytic fit to the potential energy surface. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1431–1444, 1998