PROCEDURE FOR SELECTING STARTING CONFORMATIONS FOR ENERGY MINIMIZATION OF NUCLEOSIDES AND NUCLEOTIDES

ABSTRACT

The purpose of this study was to carry out a thorough search of the conformational space of various adenine-containing nucleotides, applying a previously published searching procedure, known as the representative method. This method, which reduces the number of starting conformations required to explore all the important regions of conformational space, appears to be successful in finding all (or nearly all) the putative low-energy conformations of each molecule.     

ARTIST: an activated method in internal coordinate space for sampling protein energy landscapes

We present the first applications of an activated method in internal coordinate space for sampling all-atom protein conformations, the activation-relaxation technique for internal coordinate space trajectories (ARTIST). This method differs from all previous internal coordinate-based studies aimed at folding or refining protein structures in that conformational changes result from identifying and crossing well-defined saddle points connecting energy minima. Our simulations of four model proteins containing between 4 and 47 amino acids indicate that this method is efficient for exploring conformational space in both sparsely and densely packed environments, and offers new perspectives for applications ranging from computer-aided drug design to supramolecular assembly.     

On the multiple-minima problem in the conformational analysis of polypeptides. IV. Application of the electrostatically driven Monte Carlo method to the 20-residue membrane-bound portion of melittin

The conformational space of the membrane-bound portion of melittin has been searched using the electrostatically driven Monte Carlo (EDMC) method with the ECEPP/2 (empirical conformational energy program for peptides) algorithm. The former methodology assumes that a polypeptide or protein molecule is driven toward the native structure by the combined action of electrostatic interactions and stochastic conformational changes associated with thermal movements. The algorithm produces a Monte Carlo search in the conformational hyperspace of the polypeptide using electrostatic predictions and a random sampling technique, combined with local minimization of the energy function, to locate low-energy conformations. As a result of 8 test calculations on the 20-residue membrane-bound portion of melittin, starting from six arbitrary and two completely random conformations, the method was able to locate a very low-energy region of the potential with a well-defined structure for the backbone. In all of the cases under study, the method found a cluster of similar low-energy conformations that agree well with the structure deduced from x-ray diffraction experiments and with one computed earlier by the build-up procedure.     

Conformations of folded proteins in restricted spaces

A new method is presented to examine the complete range of folded topologies accessible in the compact state of globular proteins. The procedure is to generate all conformations, with volume exclusion, upon a lattice in a space restricted to the individual protein's known compact conformational space. Using one lattice point per residue, we find 10(2)-10(4) possible compact conformations for the five small globular proteins studied. Subsequently, these conformations are evaluated in terms of residue-specific, pairwise contact energies that favor nonbonded, hydrophobic interactions. Native structures for the five proteins are always found within the best 2% of all conformers generated. This novel method is simple and general and can be used to determine a small group of most favorable overall arrangements for the folding of specific amino acid sequences within a restricted space.     

MOLS sampling and its applications in structural biophysics

This review describes the MOLS method and its applications. This computational method has been developed in our laboratory primarily to explore the conformational space of small peptides and identify features of interest, particularly the minima, i.e., the low energy conformations. A systematic “brute-force” search through the vast conformational space for such features faces the insurmountable problem of combinatorial explosion, whilst other techniques, e.g., Monte Carlo searches, are somewhat limited in their region of exploration and may be considered inexhaustive. The MOLS method, on the other hand, uses a sampling technique commonly employed in experimental design theory to identify a small sample of the conformational space that nevertheless retains information about the entire space. The information is extracted using a technique that is a variant of the self-consistent mean field technique, which has been used to identify, for example, the optimal set of side-chain conformations in a protein. Applications of the MOLS method to understand peptide structure, predict the structures of loops in proteins, predict three-dimensional structures of small proteins, and arrive at the best conformation, orientation, and positions of a small molecule ligand in a protein receptor site have all yielded satisfactory results.     

Block-units method for conformational calculations of large nucleic acid chains. II. The two-hierarchical approach and its application to conformational arrangement of the unusual T psi C loop of rabbit tRNA(Val)

The two-level hierarchical methodology is suggested for conformational calculations of large fragments of nucleic acids. The method of the first level is intended for performing a fast screening of the conformational phase space. The high-level method may be used to refine structurally important conformations. The method of the first level is the block-units method, which has been developed specially for these purposes (see part I). It has been shown that the block-units method allows the satisfactory calculation of the structure parameters of the optimal conformations of polynucleotides. The results of the conformational rearrangement calculations of the T psi C loop of the tRNA(Phe) after modification of its sequence are represented.     

Conformational analysis of a 12-residue analogue of mastoparan and of mastoparan X.

We have investigated the conformational properties of a truncated analogue of mastoparan and of mastoparan X, both peptides from wasp venom. The electrostatically driven Monte Carlo method was used to explore the conformational space of these short peptides. The initial conformations used in this study, mainly random ones, led to alpha-helical conformations. The alpha-helical conformations thus found exhibit an amphipathic character. These results are in accord with experimental data from NMR and CD spectroscopy.     

三肽和四肽构象空间的可视化方法

研究蛋白质寡肽构象在构象空间中的分布情况,对提取寡肽模式并构建短肽库具有重要意义。通过构建一个保距映射,将以主链原子均方根距离(root mean square distance,RMSD)为距离测度的三肽构象空间变换为一维直线上的欧氏距离空间,从而直观地展现三肽构象的聚集情况,表明三肽主链构象可以用单一变量编码。应用该特性对四肽的构象空间加以分析,将四肽构象映射到三维空间中,从而以可视的方式描述四肽构象空间的聚集情况。对短肽构象空间的初步分析表明,短肽的聚集性和二级结构有着密切的联系。在四肽构象空间中存在有自然边界的离散区域(与螺旋等结构相关),也有一些区域(与折叠等结构有关)难以进一步划分。这种方法也为以可视方式分析高维空间中肽段的聚集性给出了一种可能的方案。     

Conformational states and folding pathways of peptides revealed by principal-independent component analyses

Principal component analysis is a powerful method for projecting multidimensional conformational space of peptides or proteins onto lower dimensional subspaces in which the main conformations are present, making it easier to reveal the structures of molecules from e.g. molecular dynamics simulation trajectories. However, the identification of all conformational states is still difficult if the subspaces consist of more than two dimensions. This is mainly due to the fact that the principal components are not independent with each other, and states in the subspaces cannot be visualized. In this work, we propose a simple and fast scheme that allows one to obtain all conformational states in the subspaces. The basic idea is that instead of directly identifying the states in the subspace spanned by principal components, we first transform this subspace into another subspace formed by components that are independent of one other. These independent components are obtained from the principal components by employing the independent component analysis method. Because of independence between components, all states in this new subspace are defined as all possible combinations of the states obtained from each single independent component. This makes the conformational analysis much simpler. We test the performance of the method by analyzing the conformations of the glycine tripeptide and the alanine hexapeptide. The analyses show that our method is simple and quickly reveal all conformational states in the subspaces. The folding pathways between the identified states of the alanine hexapeptide are analyzed and discussed in some detail.     

Sterics and solvation winnow accessible conformational space for unfolded proteins

The magnitude of protein conformational space is over-estimated by the traditional random-coil model, in which local steric restrictions arise exclusively from interactions between adjacent chain neighbors. Using a five-state model, we assessed the extent to which steric hindrance and hydrogen bond satisfaction, energetically significant factors, impose additional conformational restrictions on polypeptide chains, beyond adjacent residues. Steric hindrance is repulsive: the distance of closest approach between any two atoms cannot be less than the sum of their van der Waals radii. Hydrogen bond satisfaction is attractive: polar backbone atoms must form hydrogen bonds, either intramolecularly or to solvent water. To gauge the impact of these two factors on the magnitude of conformational space, we systematically enumerated and classified the disfavored conformations that restrict short polyalanyl backbone chains. Applying such restrictions to longer chains, we derived a scaling law to estimate conformational restriction as a function of chain length. Disfavored conformations predicted by the model were tested against experimentally determined structures in the coil library, a non-helix, non-strand subset of the PDB. These disfavored conformations are usually absent from the coil library, and exceptions can be uniformly rationalized.     

Unfolding the fold of cyclic cysteine-rich peptides

We propose a method to extensively characterize the native state ensemble of cyclic cysteine-rich peptides. The method uses minimal information, namely, amino acid sequence and cyclization, as a topological feature that characterizes the native state. The method does not assume a specific disulfide bond pairing for cysteines and allows the possibility of unpaired cysteines. A detailed view of the conformational space relevant for the native state is obtained through a hierarchic multi-resolution exploration. A crucial feature of the exploration is a geometric approach that efficiently generates a large number of distinct cyclic conformations independently of one another. A spatial and energetic analysis of the generated conformations associates a free-energy landscape to the explored conformational space. Application to three long cyclic peptides of different folds shows that the conformational ensembles and cysteine arrangements associated with free energy minima are fully consistent with available experimental data. The results provide a detailed analysis of the native state features of cyclic peptides that can be further tested in experiment.     

New developments of the electrostatically driven monte carlo method: Test on the membrane-bound portion of melittin

The electrostatically driven Monte Carlo (EDMC) method has been greatly improved by adding a series of new features, including a procedure for cluster analysis of the accepted conformations. This information is used to guide the search for the global energy minimum. Alternative procedures for generating perturbed conformations to sample the conformational space were also included. These procedures enhance the efficiency of the method by generating a larger number of low-energy conformations. The improved EDMC method has been used to explore the conformational space of a 20-residue polypeptide chain whose sequence corresponds to the membrane-bound portion of melittin. The ECEPP/3 (Empirical Conformational Energy Program for Peptides) algorithm was used to describe the conformational energy of the chain. After an exhaustive search involving 14 independent runs, the lowest energy conformation (LEC) (−91.0 kcal/mol) of the entire study was encountered in four of the runs, while conformations higher in energy by no more than 1.8 kcal/mol were found in the remaining runs with the exception of one of them (run 8). The LEC is identical to the conformation found recently by J. Lee, H.A. Scheraga, and S. Rackovsky [(1998) “Conformational Analysis of the 20-Residue Membrane-Bound Portion of Melittin by Conformational Space Annealing,” Biopolymers, Vol. 46, pp. 103–115] as the lowest energy conformation obtained in their study using the conformational space annealing method. These results suggest that this conformation corresponds to the global energy minimum of the ECEPP/3 potential function for this specific sequence; it also appears to be the conformation of lowest free energy. © 1998 John Wiley & Sons, Inc. Biopoly 46: 117–126, 1998     

Constructing ensembles of flexible fragments in native proteins by iterative stochastic elimination is relevant to protein-protein interfaces

We investigate the extent to which ensembles of flexible fragments (FF), generated by our loop conformational search method, include conformations that are near experimental and reflect conformational changes that these FFs undergo when binary protein-protein complexes are formed. Twenty-eight FFs, which are located in protein-protein interfaces and have different conformations in the bound structure (BS) and unbound structure (UbS) were extracted. The conformational space of these fragments in the BS and UbS was explored with our method which is based on the iterative stochastic elimination (ISE) algorithm. Conformational search of BSs generated bound ensembles and conformational search of UbSs produced unbound ensembles. ISE samples conformations near experimental (less than 1.05 A root mean square deviation, RMSD) for 51 out of the 56 examined fragments in the bound and unbound ensembles. In 14 out of the 28 unbound fragments, it also samples conformations within 1.05 A from the BS in the unbound ensemble. Sampling the bound conformation in the unbound ensemble demonstrates the potential biological relevance of the predicted ensemble. The 10 lowest energy conformations are the best choice for docking experiments, compared with any other 10 conformations of the ensembles. We conclude that generating conformational ensembles for FFs with ISE is relevant to FF conformations in the UbS and BS. Forming ensembles of the isolated proteins with our method prior to docking represents more comprehensively their inherent flexibility and is expected to improve docking experiments compared with results obtained by docking only UbSs.     

An approach to the multiple-minima problem in protein folding by relaxing dimensionality. Tests on enkephalin

An algorithm for locating the region in conformational space containing the global energy minimum of a polypeptide is described. Distances are used as the primary variables in the minimization of an objective function that incorporates both energetic and distance-geometric terms. The latter are obtained from geometry and energy functions, rather than nuclear magnetic resonance experiments, although the algorithm can incorporate distances from nuclear magnetic resonance data if desired. The polypeptide is generated originally in a space of high dimensionality. This has two important consequences. First, all interatomic distances are initially at their energetically most favorable values; i.e. the polypeptide is initially at a global minimum-energy conformation, albeit a high-dimensional one. Second, the relaxation of dimensionality constraints in the early stages of the minimization removes many potential energy barriers that exist in three dimensions, thereby allowing a means of escaping from three-dimensional local minima. These features are used in an algorithm that produces short trajectories of three-dimensional minimum-energy conformations. A conformation in the trajectory is generated by allowing the previous conformation in the trajectory to evolve in a high-dimensional space before returning to three dimensions. The resulting three-dimensional structure is taken to be the next conformation in the trajectory, and the process is iterated. This sequence of conformations results in a limited but efficient sampling of conformational space. Results for test calculations on Met-enkephalin, a pentapeptide with the amino acid sequence H-Tyr-Gly-Gly-Phe-Met-OH, are presented. A tight cluster of conformations (in three-dimensional space) is found with ECEPP energies (Empirical Conformational Energy Program for Peptides) lower than any previously reported. This cluster of conformations defines a region in conformational space in which the global-minimum-energy conformation of enkephalin appears to lie.     

Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm

We describe an algorithm which enables us to search the conformational space of the side chains of a protein to identify the global minimum energy combination of side chain conformations as well as all other conformations within a specified energy cutoff of the global energy minimum. The program is used to explore the side chain conformational energy surface of a number of proteins, to investigate how this surface varies with the energy model used to describe the interactions within the system and the rotamer library. Enumeration of the rotamer combinations enables us to directly evaluate the partition function, and thus calculate the side chain contribution to the conformational entropy of the folded protein. An investigation of these conformations and the relationships between them shows that most of the conformations near to the global energy minimum arise from changes in side chain conformations that are essentially independent; very few result from a concerted change in conformation of two or more residues. Some of the limitations of the approach are discussed. Proteins 33:227–239, 1998. © 1998 Wiley-Liss, Inc.     

Conformational space exploration of Met- and Leu-enkephalin using the MOLS method, molecular dynamics, and Monte Carlo simulation--a comparative study

We report here a comparative study of the molecular conformational energy landscape generated using the mutually orthogonal Latin squares (MOLS) method, molecular dynamics (MD), and Monte Carlo (MC) simulation. The MOLS method, as described earlier from our laboratory, uses an experimental design technique to rapidly and exhaustively sample the low energy conformations of a molecule. MD and MC simulations have been used to perform similar tasks. In the comparison reported here, the three methods were applied to a pair of neuropeptides, namely Met- and Leu-enkephalin. A set of 1500 conformations of these enkephalins were generated using these methods with CHARMM22 force field, and the resulting samples were analyzed to determine the extent and nature of coverage of the conformational space. The results indicate that the MOLS method samples a larger number of possible conformations and identifies conformations closer to the experimental structures than the MD and MC simulations.     

Multiple sequence alignment by conformational space annealing

We present a new method for multiple sequence alignment (MSA), which we call MSACSA. The method is based on the direct application of a global optimization method called the conformational space annealing (CSA) to a consistency-based score function constructed from pairwise sequence alignments between constituting sequences. We applied MSACSA to two MSA databases, the 82 families from the BAliBASE reference set 1 and the 366 families from the HOMSTRAD set. In all 450 cases, we obtained well optimized alignments satisfying more pairwise constraints producing, in consequence, more accurate alignments on average compared with a recent alignment method SPEM. One of the advantages of MSACSA is that it provides not just the global minimum alignment but also many distinct low-lying suboptimal alignments for a given objective function. This is due to the fact that conformational space annealing can maintain conformational diversity while searching for the conformations with low energies. This characteristics can help us to alleviate the problem arising from using an inaccurate score function. The method was the key factor for our success in the recent blind protein structure prediction experiment.     

Using robotics to fold proteins and dock ligands

The problems of protein folding and ligand docking have been explored largely using molecular dynamics or Monte Carlo methods. These methods are very compute intensive because they often explore a much wider range of energies, conformations and time than necessary. In addition, Monte Carlo methods often get trapped in local minima. We initially showed that robotic motion planning permitted one to determine the energy of binding and dissociation of ligands from protein binding sites (Singh et al., 1999). The robotic motion planning method maps complicated three-dimensional conformational states into a much simpler, but higher dimensional space in which conformational rearrangements can be represented as linear paths. The dimensionality of the conformation space is of the same order as the number of degrees of conformational freedom in three-dimensional space. We were able to determine the relative energy of association and dissociation of a ligand to a protein by calculating the energetics of interaction for a few thousand conformational states in the vicinity of the protein and choosing the best path from the roadmap. More recently, we have applied roadmap planning to the problem of protein folding (Apaydin et al., 2002a). We represented multiple conformations of a protein as nodes in a compact graph with the edges representing the probability of moving between neighboring states. Instead of using Monte Carlo simulation to simulate thousands of possible paths through various conformational states, we were able to use Markov methods to calculate the steady state occupancy of each conformation, needing to calculate the energy of each conformation only once. We referred to this Markov method of representing multiple conformations and transitions as stochastic roadmap simulation or SRS. We demonstrated that the distribution of conformational states calculated with exhaustive Monte Carlo simulations asymptotically approached the Markov steady state if the same Boltzman energy distribution was used in both methods. SRS permits one to calculate contributions from all possible paths simultaneously with far fewer energy calculations than Monte Carlo or molecular dynamics methods. The SRS method also permits one to represent multiple unfolded starting states and multiple, near-native, folded states and all possible paths between them simultaneously. The SRS method is also independent of the function used to calculate the energy of the various conformational states. In a paper to be presented at this conference (Apaydin et al., 2002b) we have also applied SRS to ligand docking in which we calculate the dynamics of ligand-protein association and dissociation in the region of various binding sites on a number of proteins. SRS permits us to determine the relative times of association to and dissociation from various catalytic and non-catalytic binding sites on protein surfaces. Instead of just following the best path in a roadmap, we can calculate the contribution of all the possible binding or dissociation paths and their relative probabilities and energies simultaneously.     

Topography of the active site of the noradrenaline neuronal membrane carrier based on the theoretical conformation analysis of inhibitors of neuronal catecholamine uptake

All equilibrium conformations for nine ligands, essentially different in structure, of the noradrenaline carrier through the synaptosomal membrane of rat hypothalamus were calculated by semi-empirical method. Among these compounds were amphetamine, methylphenidate, tricyclic antidepressants. The conformational energy minimization was performed in the space of torsional and bond angles. Geometrical characteristics of the conformers were determined in the cartesian coordinate system fixed relative to the benzene ring and nitrogen atom of the ligand. The selection of biologically active (productive) conformations was made according to the following criteria: 1) low conformational energy; 2) similarity of the nitrogen atoms and phenyl rings spatial disposition in all ligands; 3) accessibility for intermolecular interactions of the same sides of functional groupings in all ligands. The above criteria enabled the productive conformations for all ligands to be chosen unambiguously. The productive conformation of noradrenaline was found to have the Ph-C-C-N fragment in perpendicular trans-conformation. A topographic model for the carrier active site was suggested, its components being the nucleophilic and two arylophilic groups situated against the most accessible sides of the functional moieties of the productively bound ligands.