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.     

Prodock: Software package for protein modeling and docking

A new software package, Prodock , for protein modeling and flexible docking is presented. The protein system is described in internal coordinates with an arbitrary level of flexiblity for the proteins or ligands. The protein is represented by an all-atom model with the Ecepp /3 or Amber IV force field, depending on whether the ligand is a peptidic molecule or not. Prodock is based on a new residue data dictionary that makes the programming easier and the definition of molecular flexibility more straigthforward. Two versions of the dictionary have been constructed for the Ecepp /3 and Amber IV geometry, respectively. The global optimization of the energy function is carried out with the scaled collective variable Monte Carlo method plus energy minimization. The incorporation of a local minimization during the conformational sampling has been shown to be very important for distinguishing low-energy nonnative conformations from native structures. To make the Monte Carlo minimization method efficient for docking, a new grid-based energy evaluation technique using Bezier splines has been incorporated. This article includes some techniques and simulation tools that significantly improve the efficiency of flexible docking simulations, in particular forward/backward polypeptide chain generation. A comparative study to illustrate the advantage of using quaternions over Euler angles for the rigid-body rotational variables is presented in this paper. Several applications of the program Prodock are also discussed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 412–427, 1999     

Analysis of the genetic algorithm method of molecular conformation determination

Many important problems in chemistry require knowledge of the 3-D conformation of a molecule. A commonly used computational approach is to search for a variety of low-energy conformations. Here, we study the behavior of the genetic algorithm (GA) method as a global search technique for finding these low-energy conformations. Our test molecule is cyclic hexaglycine. The goal of this study is to determine how to best utilize GAs to find low-energy populations of conformations given a fixed amount of CPU time. Two measures are presented that help monitor the improvement in the GA populations and their loss of diversity. Different hybrid methods that combine coarse GA global search with local gradient minimization are evaluated. We present several specific recommendations about trade-offs when choosing GA parameters such as population size, number of generations, rate of interaction between subpopulations, and combinations of GA and gradient minimization. In particular, our results illustrate why approaches that emphasize convergence of the GA can actually decrease its effectiveness as a global conformation search method. © John Wiley & Sons, Inc.     

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.     

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.     

H·(H2O)n clusters: microsolvation of the hydrogen atom via molecular ab initio gradient embedded genetic algorithm (GEGA)

A new version of the ab initio gradient embedded genetic algorithm (GEGA) program for finding the global minima on the potential energy surface (PES) of mixed clusters formed by molecules and atoms is reported. The performance of the algorithm is demonstrated on the neutral H·(H(2)O)(n) (n = 1-4) clusters, that is, a radical H atom solvated in 1-4 water molecules. These clusters are of a fundamental interest. The solvated hydrogen atom forms during photochemical events in water, or during scavenging of solvated electrons by acids, and transiently exists in biological systems and possibly in inclusion complexes in the deep ocean and in the ice shield of earth. The processes associated with its existence are intriguingly complex, however, and have been the subject of decades-long debates. Using GEGA, we explicate the apparently extreme structural diversity in the H·(H(2)O)(n) (n = 1-4) clusters. All considered clusters have four basic structural types: type I, where the H radical is weakly coordinated to the oxygen atom of one of the water molecules; type II, where H is weakly coordinated to a H atom of one of the water molecules; type III, consisting of H(2), the OH radical, and n - 1 H(2)O molecules; and type IV, consisting of H(3)O and n - 1 H(2)O. There are myriads of isomers of all four types. The lowest energy species of types I and II are the isoenergetic global minima. H·(H(2)O)(n) clusters appear to be a challenging case for GEGA because they have many shallow minima close in energy some of which are significantly less stable than the global minimum. Additionally, the global minima themselves have high structural degeneracy, they are only weakly bound, and they are prone to dissociation. GEGA performed exceptionally well in finding both the global and the low-energy local minima that were subsequently confirmed at higher levels of theory.     

Conformational analysis and flexibility of carbohydrates using the CICADA approach with MM3

The potential energy hypersurfaces (PES) of several carbohydrate molecules were studied with a new algorithm for conformational searches, CICADA (Channels in Conformational Space Analyzed by Driver Approach) interfaced with the molecular mechanics program MM3(92). The method requires (1) one or a few low-energy conformations as starting points; and (2) designation of the torsion angles important for understanding the conformational behavior of the molecule. The PES is explored by driving separately each selected torsion angle (in both directions) with a concomitant full-geometry optimization at each increment (except for the driven angle). When a minimum has been detected, the molecule is freely optimized, and the minima so detected are then stored if not encountered previously. The new minima serve as starting structures for further explorations. The results from CICADA permit prediction of relative and absolute flexibility and conformational softness for both the entire molecule as well as for individual group rotations and local minima. The carbohydrates analyzed were Me-α-D -glucopyranoside, β-D -GlcNAc(1-2)α-D -Man, and α-D -GalNAc(1-3)[α-L -Fuc(1-2)]Gal-O-Me. All the low-energy conformers along with the transition states and flexibilities features were characterized. CICADA found all minima and low-energy conversion pathways for the disaccharide that were found by a traditional grid search. In contrast to the grid search method, CICADA concentrates mostly on the exploration of the low-energy regions of the PES, thereby saving a significant amount of computational time. The performance of the method opens new routes for exploring conformational space of larger molecules, such as oligosaccharides. © 1995 by John Wiley & Sons, Inc.     

Conformational analysis of a stereochemically complete set of cis-enediol peptide analogues

A conformational analysis of a stereochemically complete set of peptide analogues based on a cis-enediol unit is presented. The cis-enediol unit, which can replace a two or a three amino acid segment of a peptide, contains two "side chains", four asymmetrical carbon atoms, and six free dihedral angles. To determine the accessible conformational space, the molecules are divided into three fragments, each containing two free dihedral angles. The energy surfaces are computed for all dihedral angle values, and the possible conformations of the cis-enediol unit analogues are built using all combinations of the surface minima. Such a "build-up" procedure, which is very fast, is able to reproduce 75% of the minima obtained from a full dihedral angle exploration of the conformational space. The cis-enediol unit minima are compared with the corresponding di- and tripeptide minima; all peptide minima can be closely matched by a cis-enediol unit minimum of low energy (less than 2.2 kcal/mol above the lowest energy conformer). However, there are low energy minima of the cis-enediol unit that have no corresponding minima in peptides. The results are shown to depend strongly on the chirality of the analogues. The ability of each of the stereoisomers to mimic natural peptides, evaluated by the present approach, is correlated with its experimental activity in a renin inhibition assay.     

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.     

A Monte Carlo pharmacophore generation procedure: Application to the human PAF receptor

Summary A novel pharmacophore definition procedure is described, which uses a Monte Carlo method to superimpose molecules. Pharmacophore space is searched by a technique similar to high temperature annealing. Subsequent refinement of candidate pharmacophores by energy minimization produces low-energy conformations that may be involved in receptor binding. The method has been applied to compounds that bind to the human platelet-activating factor (PAF) receptor. Alternative binding site models for the PAF receptor are presented and discussed.A preliminary account of this work has been published elsewhere [1].     

The energy well connection graph: a use of curvilinear coordinates to achieve dimension reduction for graph representation of molecular conformation energy data

In the conformation space of a flexible molecule, curvilinear coordinate paths connecting conformations of segments of the given molecule are used to reduce the number of variables required for describing barriers between preferred conformations of the molecule as a whole. The technique is applied to a hypothetical example, then to m-trinuoromethyl-N-ethyl-amphetamine (fenfluramine), and to N-methyl-3-phenyl-3-(o-methoxyphenoxy)-propylamine (nisoxetine). In the latter example, the number of variables is thus reduced from six to three. In all three examples, a graph representation of low-energy well connection is achieved. The limit of easy comprehension has thus been moved back from about three torsion angles to three effective segments. Within this limit the procedure leads to a quantitative diagram, which is no harder to read than a contour map, showing the barriers to low-energy interconnection among the favorable conformations of a moderately complex molecule.     

Partition potential for hydrogen bonding in formic acid dimers

The ground-state energy and density of 4 low-energy conformations of the formic acid dimer were calculated via partition density functional theory (PDFT). The differences between isolated and PDFT monomer densities display similar deformation patterns for primary and secondary hydrogen bonds (HBs) among all 4 dimers. In contrast, the partition potential shows no transferable features in the bonding regions. These observations highlight the global character of the partition potential and the cooperative effect that occurs when a dimer is bound via more than 1 HB. We also provide numerical confirmation of the intuitive (but unproven) observation that fragment deformation energies are larger for systems with larger binding energies.     

Powerful simulated-annealing algorithm locates global minimum of protein-folding potentials from multiple starting conformations

Protein-folding potentials, designed with the explicit goal that the global energy minimum correspond to crystallographically observed conformations of protein molecules, may offer great promise toward calculating native protein structures. Achieving this promise, however, depends on finding an effective means of dealing with the multiple-minimum problem inherent in such potentials. In this study, a protein-folding-potential test system has been developed that exhibits the properties of general protein-folding potentials yet has a unique well-defined global energy minimum corresponding to the crystallographically determined conformation of the test molecule. A simulated-annealing algorithm is developed that locates the global minimum of this potential in four of eight test runs from random starting conformations. Exploration of the energy-conformation surface of the potential indicates that it contains the numerous local minima typical of protein-folding potentials and that the global minimum is not easily located by conventional minimization procedures. When the annealing algorithm is applied to a previously developed actual folding potential to analyze the conformation of avian pancreatic polypeptide, a new conformer is located that is lower in energy than any conformer located in previous studies using a variety of minimization techniques.     

Generic shapes for the conformation analysis of macrocyclic structures

A new algorithm for the systematic generation of conformations of macrocyclic systems is presented. The procedure is based on the concept of generic shapes that are found in such structures. These shapes are characterized by a selection of harmonics which occur in an approximate Fourier representation of the atomic coordinates of the rings. Following a fixed protocol, a limited set of in-plane and out-of-plane circular harmonics is used to define an ensemble of generic ring shapes. These generic shapes are used as start structures for energy minimizations by a given force-field method. To account for the possibility of having several final conformations originating from the same generic shape, the corresponding initial structure is taken several times and subjected to a randomization step before minimization. The resulting conformations that fall within a preset low-energy band are collected and screened for duplicates and enantiomers. The efficiency of this procedure (ratio between the number of accepted conformations and the total number of energy minimizations) depends on the flexibility of the macrocyclic system. The efficiency is generally quite high for very flexible rings. According to the proposed protocol, the number of generic shapes used as start structures grows as the square of N(lnN), where N is the ring size. The algorithm lends itself to conformational analyses of medium-size and large rings as well as of loops spanned between fixed structural units.     

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.     

MM3 Modeling of Ribose and 2-Deoxyribose Ring Puckering

ABSTRACT

Conformational energy maps for furanosyl and pyranosyl rings of α- and β-ribose and 2-deoxyribose were generated with the molecular mechanics program MM3. For the furanosyl tautomers, low-energy Northern and Southern minima were found. For the pyranosyl rings, lowest-energy minima corresponded to chair forms. Hydrogen-hydrogen coupling constants for the minimal-energy conformers were calculated based on Karplus equations. Computational and experimental results indicate that several tautomeric forms of ribose and 2-deoxyribose exist in multiple conformations in solution. Ring conformations of related crystal structures have energies within ～2 kcal/mol of the calculated global minima.     

Conformational energy analysis of substituted diphenylethanes: Part II. Empirical energy calculations on stilbene dihalogenides

The geometry and energy of the stable conformations of the isomeric forms of 1,2-halogeno-1,2-diphenylethanes have been obtained by means of empirical energy functions. A minimization of the conformational energy with respect to the torsion angles and the valence angles around the asymmetrically substituted carbon atoms has been carried out. The evaluated populations of the stable conformations showed good agreement with available experimental data. CNDO/2 calculations on the low-energy conformations of the isomeric forms of 1,2-difluoro-, 1,2-fluorochloro-, and 1,2-dichlorodiphenylethane have been carried out. These yielded improved estimates of the dipole moments for the dichloro isomers.     

Polymer-monovalent salt-induced DNA compaction studied via single-molecule microfluidic trapping

Polymer-monovalent salt-induced single-molecule DNA compaction/condensation in a microfluidic stagnation point flow was studied by analyzing both DNA compaction images and time trajectories. For the whole DNA compaction process we observed three successive steps: Step I, a relaxation process of the stretched DNA that occurs slowly along the whole DNA chain, Step II, nucleus formation and growth, and Step III, corresponding to a rapid compaction of the chain. A memory effect was observed between Steps I and III, and a new (intruder-induced) nucleation mode was observed for the first time. This study extends the use of the microfluidic stagnation point flow, which we have previously used for sequence detection and to measure enzyme kinetics site-specifically.     

Molecular modelling prediction of ligand binding site flexibility

We have investigated the efficacy of generating multiple sidechain conformations using a rotamer library in order to find the experimentally observed ligand binding site conformation of a protein in the presence of a bound ligand. We made use of a recently published algorithm that performs an exhaustive conformational search using a rotamer library to enumerate all possible sidechain conformations in a binding site. This approach was applied to a dataset of proteins whose structures were determined by X-ray and NMR methods. All chosen proteins had two or more structures, generally involving different bound ligands. By taking one of these structures as a reference, we were able in most cases to successfully reproduce the experimentally determined conformations of the other structures, as well as to suggest alternative low-energy conformations of the binding site. In those few cases where this procedure failed, we observed that the bound ligand had induced a high-energy conformation of the binding site. These results suggest that for most proteins that exhibit limited backbone motion, ligands tend to bind to low energy conformations of their binding sites. Our results also reveal that it is possible in most cases to use a rotamer search-based approach to predict alternative low-energy protein binding site conformations that can be used by different ligands. This opens the possibility of incorporating alternative binding site conformations to improve the efficacy of docking and structure-based drug design algorithms.     

Quantum-Chemical and semiclassical calculations of intermolecular interactions of phospholipids

By use of empirical 0–1–6–12 atom–atom potential functions and the PCILOCC method intra- and intermolecular interactions of glycero–phosphoryl–ethanolamine model head groups in a planar layer crystal were calculated. Starting from investigations of the two-dimensional energy-contour diagrams the minima of energy as a function of all head group torsion angles were calculated using a gradient procedure. Within an interval of 15 kcal/mol above the energy of the global minimum we obtained about 30 local minima. These results demonstrate a high flexibility of the investigated phosphorylethanolamine head group in agreement with experiment. The ethanolamine moiety exists in enantiomeric conformations. With the torsion angles of the 0–1–6–12 energy minimization procedure PCILOCC calculations were carried out. These calculations yield the x-ray conformation as the most stable one (unit-cell stabilization energy = ?36.3 kcal/mol). The PCILOCC as well as the potential function calculations show that the conformation of phospholipid head groups in layer crystals is determined by intramolecular as well as by intermolecular interactions with neighboring phospholipid molecules.