Conformational sampling by a general linearized embedding algorithm

Linearized embedding is a variant on the usual distance geometry methods for finding atomic Cartesian coordinates given constraints on interatomic distances. Instead of dealing primarily with the matrix of interatomic distances, linearized embedding concentrates on properties of the metric matrix, the matrix of inner products between pairs of vectors defining local coordinate systems within the molecule. We developed a pair of general computer programs that first convert a given arbitrary conformation of any covalent molecule from atomic Cartesian coordinates representation to internal local coordinate systems enforcing rigid valence geometry and then generate a random sampling of conformers in terms of atomic Cartesian coordinates that satisfy the rigid local geometry and a given list of interatomic distance constraints. We studied the sampling properties of this linearized embedding algorithm vs. a standard metric matrix embedding program, DGEOM, on cyclohexane, cycloheptane, and a cyclic pentapeptide. Linearized embedding always produces exactly correct bond lengths, bond angles, planarities, and chiralities; it runs at least two times faster per structure generated, and is successful as much as four times as often at refining these structures to full agreement with the constraints. It samples the full range of allowed conformations broadly, although not perfectly uniformly. Because local geometry is rigid, linearized embedding's sampling in terms of torsion angles is more restricted than that of DGEOM, but it finds in some instances conformations missed by DGEOM. © 1992 by John Wiley & Sons, Inc.     

Modeling flexible pharmacophores with distance geometry, scoring, and bound stretching

The study of pharmacophores, i.e., of common features between different ligands, is important for the quantitative identification of "compatible" enzymes and binding species. A pharmacophore-based technique is developed that combines multiple conformations with a distance geometry method to create flexible pharmacophore representations. It uses a set of low-energy conformations combined with a new process we call bound stretching to create sets of distance bounds, which contain all or most of the low-energy conformations. The bounds can be obtained using the exact distances between pairs of atoms from the different low-energy conformations. To avoid missing conformations, we can take advantage of the triangle distance inequality between sets of three points to logically expand a set of upper and lower distance bounds (bound stretching). The flexible pharmacophore can be found using a 3-D maximal common subgraph method, which uses the overlap of distance bounds to determine the overlapping structure. A scoring routine is implemented to select the substructures with the largest overlap because there will typically be many overlaps with the maximum number of overlapping bounds. A case study is presented in which 3-D flexible pharmacophores are generated and used to eliminate potential binding species identified by a 2-D pharmacophore method. A second case study creates flexible pharmacophores from a set of thrombin ligands. These are used to compare the new method with existing pharmacophore identification software.     

Linearized embedding: A new metric matrix algorithm for calculating molecular conformations subject to geometric constraints

There are many methods in the literature for calculating conformations of a molecule subject to geometric constraints, such as those derived from two-dimensional NMR experiments. One of the most general ones is the EMBED algorithm, based on distance geometry, where all constraints except chirality are converted into upper and lower bounds on interatomic distances. Here we propose a variation on this where the molecule is assumed to have fixed bond lengths, vicinal bond angles and chiral centers; and these holonomic constraints are enforced separately from the experimental constraints by being built into the mathematical structure of the problem. The advantages of this approach are: (1) for molecules having large rigid groups of atoms, there are substantially fewer variables in the problem than all the atomic coordinates; (2) rigid groups achieve in the end more accurate local geometry (e.g., planar aromatic rings are truly planar, chiral centers always have their correct absolute chirality); (3) it is easier to detect inconsistencies between the holonomic and the experimental constraints; and (4) when generating a random sampling of conformers consistent with all constraints, the probability of achieving satisfactory structures tends to be greater.     

Calculation of conformations of organic molecules

The most stable conformation of the molecule has a minimum of potential energy that arises due to the competition between the tendency of the valency angles to take ideal values and that of non-bonded atoms to be situated at an equilibrium distance. The equilibrium distance is equal to the sum of intermolecular radii determined by measuring the distances between atoms of adjacent molecules in the crystal. This idea is suggested as underlying a method of computation that enables to solve two problems. Firstly, the structure of the molecule being known, it becomes possible to ascertain the points of the interaction curve of the non-bonded atoms and secondly, with the interaction curve known, one can calculate the optimal configuration of the molecule.

To illustrate the suggested theory the conformation of molecules of some cyclic hydrocarbons has been calculated. It is to be stressed that the investigation of the conformation of strained molecules affords the main means of studying the interaction of non-bonded atoms.     

Molecular similarity based on atomic electrostatic potential

We propose a new similarity measure operating in the space spanned by the potential values, evaluated at atoms constituting the benzene ring and the COOH group in para-substituted benzoic acids and at benzene ring atoms in monosubstituted benzenes. The similarity measures are equivalent to the Euclidean distance between points in that space. Only the distances between the potentials at corresponding atoms in different molecules are included. The distances for benzene rings were very similar, regardless of whether they were calculated in para-substituted acids or in monosubstituted benzenes. As reference reactions, dissociation of benzoic acids and nitration of monosubstituted benzenes have been used. The effects of reduction of dimensionality of the potential space on the comparison of similarity measures with the free energies of the reference reactions have been investigated. It became obvious that the potentials at individual atoms in molecules of the acids and monosubstituted benzenes are mutually correlated to a high degree.     

A density functional study of uranyl monocarboxylates

We studied uranium(VI) monocarboxylate complexes by a relativistic density functional method using simple carboxylic acids as ligands, i.e. [UO2(OOCR)]+ (R = H, CH3, CH2CH3). These complexes exist in aqueous solution and, for R = CH3 and CH2CH3, may also be considered as models of uranyl complexated by humic substances. We investigated mono- and bidentate coordination modes. Short-range solvent effects were accounted for explicitly via aqua ligands of the first hydration shell and long-range electrostatic interactions were described via a polarizable continuum model. The calculated results for the uranyl U=O bond, the bond to aqua ligands, and the averaged uranium distances to equatorial oxygen atoms, U-Oeq, agreed quite well with EXAFS-derived interatomic distances. However, the uranyl-carboxylate bond was calculated to be notably shorter than the experimentally determined value. Experimental differences between mono- and bidentate coordination, obtained mainly from crystal structures, were qualitatively reproduced for the U-C distance but not for the average bond length, U-Oeq. We discuss these discrepancies between calculated and experimental results in some detail and suggest changes in the coordination number rather than variations of the coordination geometry as the main source of the experimentally observed variation of the U-Oeq distance.     

蒙特卡洛模拟退火与距离限制相结合的方法在多肽溶液构象分析中的应用

多维核磁共振技术的飞速发展议得其在生物大分子结构测定方面的应用已经达到可以与【射线晶体学并驾齐驱的地步．蛋白质结构堆积紧密，较适合于用核磁共振方法给出确定的结构．与蛋白质不同的是多肽的柔性较大，在溶液中可能存在多种构象，核磁共振实验给出的只是平均信息＊．利用核磁，（振数据构建分子结构模型常用的方法有距离几何、分子动力学等，在由核磁共振NOESZ得到的距离信息足够多时可以给出较好的结果问．由于多肽本身的特点：柔性较大，由核磁共振得到的距离信息较少等，利用距离几何、分子动力学方法进行构象搜索时容易陷入…     

Improvements to the distance geometry algorithm for conformational sampling of cyclic structures

Modifications to the distance geometry algorithm as embodied in the program DGEOM have been made to improve sampling capabilities. Specifically, torsion angle sampling replaces distance sampling for 1,4 atomic relationships and correlated distance sampling is disabled. The effects of these modifications are illustrated by comparing the different sets of conformations produced for butane. In addition, these changes are shown to increase the conformational sampling of two medium-sized rings, cycloheptadecane and caprylolactam. The current results for these molecules are compared to those of other conformational searching methods.     

蒙特卡洛模拟退火与距离限制相结合的方法——在多肽溶液构象分析中的应用

Distance geometry and molecular dynamics are currently employed in determining molecular structures with interatomic distances from NMR NOESY experiment. Because of the flexibility of peptide, distances obtained from NMR are usually not sufficient to confine its structure. Both distance geometry and molecular dynamics will bias in the conformational space at this circumstance. Constraint Monte Carlo simulated annealing was established to solve this problem. Distance constraints were included into the ECEPP/2 force field by introducing a harmonic energy term. Conformational analysis of a pentapeptide with eight interatomic distances from NMR was carried out as a test. By comparison of the 100 conformers obtained from constraint simulated annealing and the 100 conformers from distance geometry calculation, it was found that constraint simulated annealing can cover the outcomes of distance geometry and at the same time give more con-formers fitting to the experimental data. The result shows that constraint Monte-Carlo simulated annealing is more valid in constructing peptide structures from NMR distances than currently employed methods when no sufficient distances from NMR are available.     

Geometrically feasible binding modes of a flexible ligand molecule at the receptor site

A very efficient algorithm for determining the geometrically feasible binding modes of a flexible ligand molecule at the receptor site is presented. It is based on distance geometry but maintains the requirements of three dimensions. The distance geometry manipulation can superimpose two bodies without explicitly calculating the necessary rigid rotation and translation. The whole conformation space of a flexible molecule can be efficiently examined by considering only a finite number of conformational points. The method is suitable only when the criterion for superposition is some minimum distance limit. It cannot, however, give the exact distance between two points in two different bodies.     

Nature of the coordination bond in the GeCl4-trimethylamine complex

Quantum-chemical computations were performed for the GeCl₄ ← N(CH₃)₃ system using the MP2/6-31G(d) method with total optimization of its geometry and at different fixed Ge…N distances (from 2.0 to 4.5 Å). The coordination bond in the complex results from the involvement of different AOs of Ge and N atoms (along with other atoms in the molecule) in the formation of a number of MOs. The number of these MOs increases with decreasing Ge…N distance, thus reducing the total energy of a molecule and stabilizing it. The coordination bond and the covalent bond are of the same nature. When the distance between the components of the system is reduced, the partial negative charges of N, C, and all Cl atoms increase; the partial positive charges of Ge and H increase as well.     

A self-organizing algorithm for molecular alignment and pharmacophore development

We present a method for simultaneous three-dimensional (3D) structure generation and pharmacophore-based alignment using a self-organizing algorithm called Stochastic Proximity Embedding (SPE). Current flexible molecular alignment methods either start from a single low-energy structure for each molecule and tweak bonds or torsion angles, or choose from multiple conformations of each molecule. Methods that generate structures and align them iteratively (e.g., genetic algorithms) are often slow. In earlier work, we used SPE to generate good-quality 3D conformations by iteratively adjusting pairwise distances between atoms based on a set of geometric rules, and showed that it samples conformational space better and runs faster than earlier programs. In this work, we run SPE on the entire ensemble of molecules to be aligned. Additional information about which atoms or groups of atoms in each molecule correspond to points in the pharmacophore can come from an automatically generated hypothesis or be specified manually. We add distance terms to SPE to bring pharmacophore points from different molecules closer in space, and also to line up normal/direction vectors associated with these points. We also permit pharmacophore points to be constrained to lie near external coordinates from a binding site. The aligned 3D molecular structures are nearly correct if the pharmacophore hypothesis is chemically feasible; postprocessing by minimization of suitable distance and energy functions further improves the structures and weeds out infeasible hypotheses. The method can be used to test 3D pharmacophores for a diverse set of active ligands, starting from only a hypothesis about corresponding atoms or groups.     

Kinetic parameters and geometry of the transition state of acyl radical decarbonylation

Experimental data on acyl radical decomposition reactions (RC^·O → R^· + CO, where R = alkyl or aryl) are analyzed in terms of the intersecting parabolas method. Kinetic parameters characterizing these reactions are calculated. The transition state of methyl radical addition to CO at the C atoms is calculated using the DFT method. A semiempirical algorithm is constructed for calculating the transition state geometry for the decomposition of acyl radicals and for the reverse reactions of R^· addition to CO. Kinetic parameters (activation energy and rate constant) and geometry (interatomic distances in the transition state) are calculated for 18 decomposition reactions of structurally different acyl radicals. A linear correlation between the interatomic distance r ^#(C…C) (or r ^#(C…O)) in the transition state the enthalpy of the reaction (δH _e) is established for acyl decomposition reactions (at br _e = const). A comparative analysis of the enthalpies, activation energies, and interatomic distances in the transition state is carried out for the decomposition and formation of acyl, carboxyl, and formyl radicals.     

Adsorption of benzene, fluorobenzene and meta-di-fluorobenzene on Cu(110): a computational study

We modelled the adsorption of benzene, fluorobenzene and meta-di-fluorobenzene on Cu(110) by Density Functional Theory. We found that the adsorption configuration depends on the coverage. At high coverage, benzene assumes a tilted position, while at low coverage a horizontal slightly distorted geometry is favoured. Functionalizing the benzene ring with one or two fluorine atoms weakens the bonding to the surface. A rotation is induced, which decreases the distance of the fluorine atom from the surface. STM simulations reveal that details about both, benzene adsorption geometry and fluorine position, can be only detected at short tip-surface distances.     

Hydration force between model hydrophilic surfaces: computer simulations

We performed molecular dynamics simulations to study the interactions between model hydrophilic plates made of carbon atoms distributed on a hexagonal lattice. Although neutral, the plates carry equal amounts of positive and negative charges to represent physical dipoles. Using the thermodynamic perturbation theory we calculated the potential of mean force (PMF) acting between the plates as a function of the distance between these plates. We observed that, at distances when more than one water layer can be found between the plates, the contribution of water into the PMF can be either attractive or repulsive depending on the correlation between the charges situated on the plates.     

Mapping the intramolecular signal propagation pathways in protein using Bayesian change point analysis of atomic motions

We propose to use change points of atomic positions in the molecular dynamics trajectory as indicators of the propagating signals in protein. We designate these changes as signals because they can propagate within the molecule in the form of “perturbation wave”, transmit energy or information between different parts of protein, and serve as allosteric signals. We found that change points can distinguish between thermal fluctuations of atoms (noise) and signals in a protein despite the differences in the motility of amino acid residues. Clustering of the spatially close residues that were experiencing change points close in time, allowed us to map pathways of signal propagation in a protein at the atomic level of resolution. We propose a potential mechanism for the origin of the signal and its propagation that relies on the autonomic coherence resonance in atomic fluctuations. According to this mechanism, random synchronization of fluctuations of neighboring atoms results in a resonance, which increases amplitude of vibration of these atoms. This increase can be transmitted to the atoms colliding with the resonant atoms, leading to the propagating signal. The wavelet-based coherence analysis of the inter-atomic distances between carbon-alpha atoms and surrounding atoms for the residue pairs that belong to the same communication pathway allowed us to find time periods with temporarily locked phases, confirming the occurrence of conditions for resonance. Analysis of the mapped pathways demonstrated that they form a network that connects different regions of the protein.     

Constrained optimization in delocalized internal coordinates

Using the recently introduced delocalized internal coordinates, in conjunction with the classical method of Lagrange multipliers, an algorithm for constrained optimization is presented in which the desired constraints do not have to be satisfied in the starting geometry. The method used is related to a previous algorithm by the same author for constrained optimization in Cartesian coordinates [J. Comput. Chem., 13 , 240 (1992)], but is simpler and far more efficient. Any internal (distance or angle/torsion) constraint can be imposed between any atoms in the system whether or not the atoms involved are formally bonded. Imposed constraints can be satisfied exactly. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 :1079–1095, 1997     

How far do electrons move? A semiempirical investigation of thermal electron-transfer distances in cationic bis(hydrazine) and bis(hydrazyl) mixed-valence compounds.

A computational approach for estimating thermal electron-transfer reaction distances in symmetrical mixed-valence compounds is described and applied to a series of bis(hydrazine) and bis(hydrazyl) radical cations and derivatives, some of which have been investigated experimentally by Nelsen and co-workers. Ground-state semiempirical charge distributions are obtained by using optimized reactant geometries. Advantage is then taken of the approximate C(2) symmetry, or the approximate mirror symmetry, of each of the targeted compounds, and the inherent degeneracy of the corresponding electron-transfer reactions, such that the change in dipole moment (Delta-mu) upon charge transfer can be estimated from an appropriately distance-weighted sum of charge differences between approximately symmetry-equivalent atoms found on the donor and acceptor sides of the molecule. Delta-mu can then be related directly to the effective one-electron-transfer distance. We find that calculated adiabatic electron-transfer distances can differ appreciably from the geometric donor-site/acceptor-site separation distances. Furthermore, for a fixed geometric separation distance, the effective electron-transfer distance can vary considerably, depending on chemical substituent composition and/or isomeric configuration. Further advantage is taken of the approximate donor-site/acceptor-site symmetry, in the context of a Newton-Cave type analysis, to establish the relative importance of electronic delocalization effects versus self-polarization and inductive effects in diminishing or enhancing effective one-electron-transfer distances.     

环十二肽溶液构象的二维核磁共振研究

利用二维核磁共振方法及距离几何计算研究了在片段组装法全新蛋白质合成中用作底座分子的环十二肽的溶液构象. 研究结果表明在环十二肽分子主链中包含四个转角结构,四个赖氨酸侧链均位于环的同一侧.环肽的构象为以环肽为模板组装四螺旋束分子提供了有利的条件