A Central Partition of Molecular Conformational Space. III. Combinatorial Determination of the Volume Spanned by a Molecular System

In the first work of this series (Gabarro-Arpa, Comp. Biol. Chem. 27 (2003) 153–159) it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the space into a hierarchical set of cells that can be encoded by the face lattice poset of the arrangement. The model however, lacked explicit rotational symmetry, which made impossible to distinguish rotated structures in conformational space. This problem was solved in a second work (Gabarro-Arpa, Proc. 26th Ann. Int. Conf. of the IEEE EMBS (San Franciso, 2004) 3007–3010) by sorting the elementary 3-dimensional components of the molecular system into a set of morphological classes that can be properly oriented in a standard 3-D reference frame. This also made possible to find a solution to the problem that is being addressed in the present work: for a molecular system immersed in a heat bath we want to enumerate the subset of cells in conformational space that are visited by the molecule in its thermal wandering. If each visited cell is a vertex on a graph with edges to the adjacent cells, here it is explained how such graph can be built.     

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.     

RNA unrestrained molecular dynamics ensemble improves agreement with experimental NMR data compared to single static structure: a test case

Nuclear magnetic resonance (NMR) provides structural and dynamic information reflecting an average, often non-linear, of multiple solution-state conformations. Therefore, a single optimized structure derived from NMR refinement may be misleading if the NMR data actually result from averaging of distinct conformers. It is hypothesized that a conformational ensemble generated by a valid molecular dynamics (MD) simulation should be able to improve agreement with the NMR data set compared with the single optimized starting structure. Using a model system consisting of two sequence-related self-complementary ribonucleotide octamers for which NMR data was available, 0.3 ns particle mesh Ewald MD simulations were performed in the AMBER force field in the presence of explicit water and counterions. Agreement of the averaged properties of the molecular dynamics ensembles with NMR data such as homonuclear proton nuclear Overhauser effect (NOE)-based distance constraints, homonuclear proton and heteronuclear ¹H–³¹P coupling constant (J) data, and qualitative NMR information on hydrogen bond occupancy, was systematically assessed. Despite the short length of the simulation, the ensemble generated from it agreed with the NMR experimental constraints more completely than the single optimized NMR structure. This suggests that short unrestrained MD simulations may be of utility in interpreting NMR results. As expected, a 0.5 ns simulation utilizing a distance dependent dielectric did not improve agreement with the NMR data, consistent with its inferior exploration of conformational space as assessed by 2-D RMSD plots. Thus, ability to rapidly improve agreement with NMR constraints may be a sensitive diagnostic of the MD methods themselves.     

Conformational Preferences of a β‐Octapeptide as Function of Solvent and Force‐Field Parameters

The ability to design properly folded β‐peptides with specific biological activities requires detailed insight into the relationship between the amino acid sequence and the secondary and/or tertiary structure of the peptide. One of the most frequently used spectroscopic techniques for resolving the structure of a biomolecule is NMR spectroscopy. Because only signal intensities and frequencies are recorded in the experiment, a conformational interpretation of the recorded data is not straightforward, especially for flexible molecules. The occurrence of conformational and/or time averaging, and the limited amount and accuracy of experimental data hamper the precise conformational determination of a biomolecule. In addition, the relation between experimental observables with the underlying conformational ensemble is often only approximately known, thereby aggravating the difficulty of structure determination of biomolecules. The problematic aspects of structure refinement based on NMR nuclear Overhauser effect (NOE) intensities and ³J‐coupling data are illustrated by simulating a β‐octapeptide in explicit MeOH and H₂O as solvents using three different force fields. NMR Data indicated that this peptide would fold into a 3₁₄‐helix in MeOH and into a hairpin in H₂O. Our analysis focused on the conformational space visited by the peptide, on structural properties of the peptide, and on agreement of the MD trajectories with available NMR data. We conclude that 1) although the 3₁₄‐helical structure is present when the peptide is solvated in MeOH, it is not the only relevant conformation, and that 2) the NMR data set available for the peptide, when solvated in H₂O, does not provide sufficient information to derive a single secondary structure, but rather a multitude of folds that fulfill the NOE data set.     

Some dimension problems in molecular databases

Molecular databases obtained either by combinatorial chemistry tools or by more traditional methods are usually organized according to a set of molecular properties. A database may be regarded as a multidimensional collection of points within a space spanned by the various molecular properties of interest, the property space. Some properties are likely to be more important than others, those considered important form the essential dimensions of the molecular database. How many properties are essential, this depends on the molecular problem addressed, however, the search in property space is usually limited to a few dimensions. Two types of search strategies are related either to search by property or search by lead compound. The first case corresponds to a lattice model, where the search is based on sets of adjacent blocks, usually hypercubes in property space, whereas lead-based searches in databases can be regarded as search around a center in property space. A natural model for lead-based searches involves a hyperspherical model. In this contribution a theoretical optimum dimension is determined that enhances the effectiveness of lead-based searches in property space of molecular databases.     

Molecular modeling of polymers: I. Correct and efficient enumeration of intrachain conformational energetics

Polymer conformational analyses can require being able to model the intramolecular energetics of a very long (infinite) chain employing calculations carried out on a relatively short chain sequence. A method to meet this need, based upon symmetry considerations and molecular mechanics energetics, has been developed. Given N equivalent degrees of freedom in a linear polymer chain, N unique molecular groups are determined within the chain. A molecular unit is defined as a group of atoms containing backbone rotational degrees of conformational freedom on each of its ends. The interaction of these N molecular groups, each with a finite number of nearest neighbors, properly describe the intramolecular energetics of a long (infinite) polymer chain. Thus, conformational energetics arising from arbitrarily distant neighbor interactions can be included in the estimation of statistical and thermodynamic properties of a linear polymeric system. This approach is called the polymer reduced interaction matrix method (PRIMM) and the results of applying it to isotactic polystyrene (I-PS) are presented by way of example.     

Electronic structure and molecular conformation of furan and pyrrole azomethines. An ab initio molecular orbital study

STO-3G minimal basis set ab initio molecular orbital calculations were employed to study the electronic structure and conformational preferences in furan-2-N-methylmethyleneimide ( 1 ) and pyrrole-2-N-methylmethyleneimide ( 2 ). The theoretical results were examined by comparison with the parent molecular systems through a population analysis and molecular orbital interactions considerations. The OCCN-trans and the NCCN-cis forms were found to be the most stable structures in 1 and 2 , respectively. Comparisons were made with available experimental data. The theoretical results indicate thatπ-electron interactions and molecular orbital interactions are not significant factors in determining the conformational preferences which most likely depend on dipole-dipole interactions.     

Computer Simulation of Molecular Dynamics: Methodology,Applications, and Perspectives in Chemistry

During recent decades it has become feasible to simulate the dynamics of molecular systems on a computer. The method of molecular dynamics (MD) solves Newton's equations of motion for a molecular system, which results in trajectories for all atoms in the system. From these atomic trajectories a variety of properties can be calculated. The aim of computer simulations of molecular systems is to compute macroscopic behavior from microscopic interactions. The main contributions a microscopic consideration can offer are (1) the understanding and (2) interpretation of experimental results, (3) semiquantitative estimates of experimental results, and (4) the capability to interpolate or extrapolate experimental data into regions that are only difficultly accessible in the laboratory. One of the two basic problems in the field of molecular modeling and simulation is how to efficiently search the vast configuration space which is spanned by all possible molecular conformations for the global low (free) energy regions which will be populated by a molecular system in thermal equilibrium. The other basic problem is the derivation of a sufficiently accurate interaction energy function or force field for the molecular system of interest. An important part of the art of computer simulation is to choose the unavoidable assumptions, approximations and simplifications of the molecular model and computational procedure such that their contributions to the overall inaccuracy are of comparable size, without affecting significantly the property of interest. Methodology and some practical applications of computer simulation in the field of (bio)chemistry will be reviewed.     

Synthesis and structural study of carbocyclic analogues of 1,2-disubstituted nucleosides

The compounds (±)-cis- and (±)-trans-9-[(2-hydroxymethyl) cyclopentyl]guanine (1 and 2 respectively) were efficiently synthesized by the construction of the purine base on the primary amino group of cis- and trans-2-aminocyclopentylmethanol. The 3D structures of these two 1,2-disubstituted carbanucleosides in DMSO were determined using molecular dynamics calculations with experimental NMR restraints on the basis of the information obtained from a ROESY spectrum. These structures were compared with those obtained in vacuo using molecular dynamics and AM1 semiempirical calculations. The global structures of the two compounds are very similar in the two environments studied, meaning that the structural determination in the gas phase can be extrapolated to molecular simulation studies in solution for compounds of this type.     

A Method to Explore Protein Side Chain Conformational Variability Using Experimental Data

Experimentally measured values of molecular properties or observables of biomolecules such as proteins are generally averages over time and space, which do not contain su?cient information to determine the underlying conformational distribution of the molecules in solution. The relationship between experimentally measured NMR ³J‐coupling values and the corresponding dihedral angle values is a particularly complicated case due to its nonlinear, multiple‐valued nature. Molecular dynamics (MD) simulations at constant temperature can generate Boltzmann ensembles of molecular structures that are free from a priori assumptions about the nature of the underlying conformational distribution. They suffer, however, from limited sampling with respect to time and conformational space. Moreover, the quality of the obtained structures is dependent on the choice of force ?eld and solvation model. A recently proposed method that uses time‐averaging with local‐elevation (LE) biasing of the conformational search provides an elegant means of overcoming these three problems. Using a set of side chain ³J‐coupling values for the FK506 binding protein (FKBP), we ?rst investigate the uncertainty in the angle values predicted theoretically. We then propose a simple MD‐based technique to detect inconsistencies within an experimental data set and identify degrees of freedom for which conformational averaging takes place or for which force ?eld parameters may be de?cient. Finally, we show that LE MD is the best method for producing ensembles of structures that, on average, ?t the experimental data.     

Pattern recognition in the prediction of protein structure. II. Chain conformation from a probability-directed search procedure

A procedure that finds the most probable conformational states of a protein chain is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. The conformation of the entire chain is represented by a sequence of single-residue conformational states; the distinct conformations in this representation are called “chain-states.” The first article in this series described a procedure that computes tripeptide conformational probabilities from the amino acid sequence using pattern recognition techniques. The procedure described in this article uses the tripeptide probabilities to estimate the probabilities of the chain-states. The chain-state probability estimator is a product of conditional and marginal probabilities (obtained from the tripeptide probabilities), with a penalty factor to eliminate conformations containing α-helices and ?-strands of excessive length. The probability estimator considers short-range conformational information, medium-range sequence information and some simple long-range information (through the restrictions on helix and strand lengths). Energy minimization calculations can be carried out in the region of conformational space corresponding to a particular chain-state. By selecting the most probable chain-states, the search can be focused on the most probable, or “important,” regions of the conformational space. These energy calculations are described in the third article of the series. The complete procedure described by the three articles is called PRISM, for pattern recognition-based importance sampling minimization.     

Localized Orbitals vs. Pseudopotential-Plane Waves Basis Sets: Performances and Accuracy for Molecular Magnetic Systems

 Density functional theory, in combination with a) a careful choice of the exchange-correlation part of the total energy and b) localized basis sets for the electronic orbitals, has become the method of choice for calculating the exchange-couplings in magnetic molecular complexes. Orbital expansion on plane waves can be seen as an alternative basis set especially suited to allow optimization of newly synthesized materials of unknown geometries. However, little is known on the predictive power of this scheme to yield quantitative values for exchange coupling constants J as small as a few hundredths of eV (50–300 cm⁻¹). We have used density functional theory and a plane waves basis set to calculate the exchange couplings J of three homodinuclear Cu-based molecular complexes with experimental values ranging from +40 cm⁻¹ to −300 cm⁻¹. The plane waves basis set proves as accurate as the localized basis set, thereby suggesting that this approach can be reliably employed to predict and rationalize the magnetic properties of molecular-based materials. Corresponding author. E-mail: Carlo.Massobrio@ipcms.u-strasbg.fr Received August 5, 2002; accepted August 9, 2002     

Conformations and Structures of Two Novel Upper Rim Disubstituted Derivatives of Tetra-O-alkylcalix[4]arene: The Effect of Substituents

Two new calix[4]arene derivatives, 5,17-dinitro-26,28-dimethyoxy-25,27-dipropoxycalix[4]arene (4) and 5,17-diamino-26,28-dimethyoxy-25,27-dipropoxycalix[4]arene (5), have been synthesized and fully characterized. The ¹H NMR spectra measured in different solvents and temperatures indicated that the dominant conformer is partial cone for 4 and cone for 5, though there are some variations in relative ratio of partial cone to cone conformers. The structures of partial cone 4 and cone 5 are determined by X-ray crystallography. The different conformational behavior in compounds 4 and 5 is governed by the two substituents at the upper rim. The repulsion of the dipole due to the p-nitro substituents and weak interaction between methoxy group and the inverted anisole ring in the 4 may be responsible for stabilizing the partial cone conformation.This revised version was published online in July 2005 with a corrected issue number.     

MM3 Conformational Analysis and X‐ray Crystal Structure of 2,3,4,5‐Tetra‐O‐Acetyl‐N,N′‐Dimethyl‐D‐Glucaramide as a Conformational Model for the d‐Glucaryl Unit of Poly(Alkylene 2,3,4,5‐Tetra‐O‐Acetyl‐d‐Glucaramides)

This report describes the MM3 conformational analysis and X‐ray crystal structure of tetra‐O‐acetyl‐N,N′‐dimethyl‐d‐glucaramide as a conformational model for the D‐glucaryl monomer unit of poly(alkylene tetra‐O‐acyl‐d‐glucaramides). The driving force for this study was to determine the conformational preferences for the diacid unit as a function of the increasing steric bulk of pendant O‐acyl groups: acetyl, propanoyl, 2‐methylpropanoyl, and 2,2‐dimethylpropanoyl. The model dialkyl d‐glucaramides all displayed a large vicinal proton coupling between the central backbone glucaryl hydrogens, indicating an essentially fixed anti conformational arrangement of these protons. The MM3 molecular mechanics program was then applied to calculate the corresponding low‐energy conformations of the structurally simplest of these molecules, tetra‐O‐acetyl‐N,N′‐dimethyl‐d‐glucaramide (4). Given the large number of dihedral angles to be considered and the apparent rigidity of these molecules around the central carbons of the glucaryl backbone, a number of conformational approximations based upon model compounds were applied regarding the rotameric disposition of the pendant O‐acetyl and terminal N‐methyl groups. The calculated, and dominant, lowest energy conformer has a sickle structure very similar to the global minimum conformation previously calculated for unprotected d‐glucaramide. The x‐ray crystal structure data from 4 indicated an extended conformation in the solid state and gave solid‐state torsion angle information that was comparable to that obtained computationally.     

Symbolic representation of the molecular conformation of calixarenes

In calixarene chemistry there is a continuous search for new shaping units or substructures useful for molecular recognition or for the binding of ions. The problem of assigning their molecular conformations cannot be dealt with by the use of the dihedral angles as done until now, because this method contains intrinsic ambiguities. The new approach, proposed here, is based on the use of the set ofn pairs of torsion angles (conformational parameters) which involve the flexible part of the calixarene and it is free of ambiguities. Moreover, knowledge of the set of conformational parameters allows one to build straightforwardly three-dimensional molecular models. A symbolic representation of the molecular conformation of any calix[n]arene may be obtained by combining the Schöenflies symbol of the molecular symmetry together with the signs of the conformational parameters.