Prediction of peptide conformation: The adaptive simulated annealing approach

We report the application of the adaptive simulated annealing (ASA) method as a global optimization approach to biomolecular structure determination, using the ECEPP/2 (empirical conformation energy program for peptides) potential energy form. As applied to Met-enkephalin, our optimization results in a conformation that is in agreement with other studies. In addition, a dominant right-handed α-helical conformation is predicted for a 14-residue poly (L-alanine) model peptide in a limited search range. These results show that ASA is an efficient and robust algorithm for conformational analysis. © 1997 by John Wiley & Sons, Inc.     

Prediction of peptide conformation using a scale-transformed entropy sampling algorithm

An algorithm for predicting the lowest energy structure of a peptide has been developed. High-energy barriers on an energy surface can be easily overcome by logarithmically transforming the energy space. For efficient optimizations, the energy space is searched using a scale-transformed entropy sampling method, and conformations specific to a primary structure of the peptide are sampled with large weights. The efficiency of the present method is demonstrated by calculations on cholecystokinin octapeptide (CCK-8).     

Some approaches to the multiple-minima problem in the calculation of polypeptide and protein structures

Various methods are used to surmount the multiple-minima problem that is encountered in the multidimensional conformational energy surface of a polypeptide. A summary is given here of two of these methods: (i) The build-up procedure that is modified to include statistical data on the positional frequencies of occurrence of amino acid residues along the chain, and (ii) the diffusion equation method that smoothes out the potential surface, leaving only the potential well containing the global minimum.     

Control of peptide chain conformation by photoisomerising chromophores: Enzymes and model compounds

Literature data about enzymatic proteins and synthetic polymers containing azo or spirobenzopyran photochromic compounds are discussed.In enzymes, the catalytic activity can be photomodulated by means of the attached photochromic molecules as well as by microenvironmental changes when they are embedded in photoresponsive membranes. In synthetic polymers, large light-induced conformational changes can be obtained in solution, the most pronounced effects being observed in systems with labile fold structures.The mechanisms responsible for the conformational variations can be the changes in intramolecular and solvational interactions brought about both by the structural change of the chromophore after photoisomerisation and by the charge separation.The data about enzymes, when brought into correlation with those about model compounds, support the hypothesis that the above mechanisms are also operative in the photomodulation of enzyme activity.     

Synthesis of a cyclic peptide containing norlanthionine: effect of the thioether bridge on peptide conformation

Two diastereomeric analogues of ring C of nisin incorporating a novel norlanthionine residue have been synthesized via a triply orthogonal protecting group strategy. A full structural study was carried out by NMR, which elucidated the conformational properties of the two peptides and enabled the identity of each diastereoisomer to be proposed.     

A molecular mechanics-NMR pseudoenergy approach to the solution conformation of glycolipids

We present here a protocol for the determination of oligosaccharide solution conformation from a combination of molecular mechanics calculations and NMR distance constraints treated as pseudoenergies. As an illustration of our methodology we have chosen the determination of the solution conformation of the tetrasaccharide headgroup of the glycolipid globoside. In order to test the ability of our methodology to avoid becoming trapped in local minima, we have chosen three starting structures, well displaced from one another in conformational space. The structures obtained upon convergence of the calculations with distance constraint pseudoenergies were quite similar to one another. For two of the three glycosidic linkages in globoside, the results from the calculations were virtually identical for each of the three starting structures. We also apply our protocol to a model which allows for the existence of multiple conformers in an effort to explore the possibility of conformational flexibility in the oligosaccharide headgroup of globoside.     

Extended multicanonical method combined with thermodynamically optimized potential: application to the liquid-crystal transition of silicon

A novel method is proposed to study first-order phase transition in real materials. It is applied to the liquid-crystal transition of silicon successfully. It consists of two parts: a direct simulation of the transition by an extended multicanonical ensemble with an order parameter defined with structure factors that characterize the transition, and optimization of a model interatomic potential in terms of the ensemble from an accurate one. These provide a principle to project a first-principles approach on a model-based approach conserving thermodynamic properties of multiple phases.     

Decomposition kinetics of calcite: a new approach to the old problem

In addition to the results of our own experiments on the decompositions of calcite crystals under high-vacuum (10⁻⁸ bar) and low-vacuum (10⁻² bar) conditions, some data reported in the literature were used for the determination of the E parameters by the second- and third-law methods and discussion of the self-cooling effect on the results of these determinations. Analysis of these data supports the advantages of the third-law method compared with the second-law (and Arrhenius-plots) methods in relation to reliability of results obtained. The experimental values of the E parameters, obtained by different technique and under different conditions by the third-law method, are in excellent agreement with the theoretically predicted values based on the mechanism of congruent decomposition of CaCO₃ into gaseous species CO₂ and CaO with the simultaneous condensation of low-volatility CaO molecules. Indeed, the experimental values of the E parameters in the equimolar and isobaric modes of decomposition, obtained in this work under optimal conditions, are equal to 261 and 493 kJ mol⁻¹, respectively whereas the theoretical values at these temperatures equals to 253 and 505 kJ mol⁻¹. The application of the third-law method allowed to support the enormous influence of self-cooling on the results obtained by the usual second-law and Arrhenius-plots methods accepted in thermal analysis. The role of this effect is increased dramatically in the experiments performed under high-vacuum conditions. Contrary to the second-law method, the third-law method appears to be rather insensitive to reactant self-cooling in the process of decomposition and to the presence of gaseous product (CO₂) in the reactor.     

Efficiency of the multicanonical simulation method as applied to peptides of increasing size: the heptapeptide deltorphin

The advantage of the multicanonical (MUCA) simulation method of Berg and coworkers over the conventional Metropolis method is in its ability to move a system effectively across energy barriers thereby providing results for a wide range of temperatures. However, a MUCA simulation is based on weights (related to the density of states) that should be determined prior to a production run and their calculation is not straightforward. To overcome this difficulty a procedure has been developed by Berg that calculates the MUCA weights automatically. In a previous article (Ya?ar et al. J Comput Chem 2000, 14, 1251-1261) we extended this procedure to continuous systems and applied it successfully to the small pentapeptide Leu-enkephalin. To investigate the performance of the automated MUCA procedure for larger peptides, we apply it here to deltorphin, a linear heptapeptide with bulky side chains (H-Tyr(1)-D-Met(2)-Phe(3)-His(4)-Leu(5)-Met(6)-Asp(7)-NH(2)). As for Leu-enkephalin, deltorphin is modeled in vacuum by the potential energy function ECEPP. MUCA is found to perform well. A weak second peak is seen for the specific heat, which is given a special attention. By minimizing the energy of structures along the trajectory it is found that MUCA provides a good conformational coverage of the low energy region of the molecule. These latter results are compared with conformational coverage obtained by the Monte Carlo minimization method of Li and Scheraga.     

Effects of osmolytes on the helical conformation of model peptide: molecular dynamics simulation

Co-solvents such as glycerol and sorbitol are small organic molecules solvated in the cellular solutions that can have profound effects on the protein structures. Here, the molecular dynamics simulations and comparative structural analysis of magainin, as a peptide model, in pure water, 2,2,2-trifluoroethanol∕water, glycerol∕water, and sorbitol∕water are reported. Our results show that the peptide NMR structure is largely maintained its native structure in osmolytes-water mixtures. The simulation data indicates that the stabilizing effect of glycerol and sorbitol is induced by preferential accumulation of glycerol and sorbitol molecules around the nonpolar and aromatic residues. Thus, the presence of glycerol and sorbitol molecules decreases the interactions of water molecules with the hydrophobic residues of the peptide, and the alpha helical structure is stabilized.     

A combinatorial approach to the electron correlation problem

Starting from a path-integral formulation of quantum statistical mechanics expressed in a space of Slater determinants, we develop a method for the Monte Carlo evaluation of the energy of a correlated electronic system. The path-integral expression for the partition function is written as a contracted sum over graphs. A graph is a set of distinct connected determinants on which paths can be represented. The weight of a graph is given by the sum over exponentially large numbers of paths which visit the vertices of the graph. We show that these weights are analytically computable using combinatorial techniques, and they turn out to be sufficiently well behaved to allow stable Monte Carlo simulations in which graphs are stochastically sampled according to a Metropolis algorithm. In the present formulation, graphs of up to four vertices have been included. In a Hartree-Fock basis, this allows for paths which include up to sixfold excitations relative to the Hartree-Fock determinant. As an illustration, we have studied the dissociation curve of the N(2) molecule in a VDZ basis, which allows comparison with full configuration-interaction calculations.     

A finite-difference approach to the electron correlation problem

A variant of the transcorrelated method of Boys and Handy employing finite differences is presented. It is based upon the following two properties of the transcorrelated Hamiltonian operator C^?1HC: (1) C^?1HC possesses an energy eigenvalue spectrum which is identical to that associated with H itself; and (2) if \documentclass{article}\pagestyle{empty}\begin{document}$$ C \equiv \begin{array}{*{20}c} \pi & {e^{r_{ij} /2} } \\ {i > j} & {} \\ \end{array} $$\end{document} then C^?1HC is free of the singularities of H at the points where the interelectron separation r_ij is zero. A bivariational principle for approximating the eigenvalues and the left and right eigenfunctions of C^?1HC is introduced and the resulting set of coupled integro-differential equations are solved in finite-difference form by means of a coupled self-consistent field, Newton Raphson algorithm. As a preliminary test of the method, a calculation of the ground-state energy of the helium atom is presented.     

MCDOCK: A Monte Carlo simulation approach to the molecular docking problem

Prediction of the binding mode of a ligand (a drug molecule) to its macromolecular receptor, or molecular docking, is an important problem in rational drug design. We have developed a new docking method in which a non-conventional Monte Carlo (MC) simulation technique is employed. A computer program, MCDOCK, was developed to carry out the molecular docking operation automatically. The current version of the MCDOCK program (version 1.0) allows for the full flexibility of ligands in the docking calculations. The scoring function used in MCDOCK is the sum of the interaction energy between the ligand and its receptor, and the conformational energy of the ligand. To validate the MCDOCK method, 19 small ligands, the binding modes of which had been determined experimentally using X-ray diffraction, were docked into their receptor binding sites. To produce statistically significant results, 20 MCDOCK runs were performed for each protein–ligand complex. It was found that a significant percentage of these MCDOCK runs converge to the experimentally observed binding mode. The root-mean-square (rms) of all non-hydrogen atoms of the ligand between the predicted and experimental binding modes ranges from 0.25 to 1.84 Å for these 19 cases. The computational time for each run on an SGI Indigo2/R10000 varies from less than 1 min to 15 min, depending upon the size and the flexibility of the ligands. Thus MCDOCK may be used to predict the precise binding mode of ligands in lead optimization and to discover novel lead compounds through structure-based database searching.     

Prediction of the global energy minimum conformation of polypeptides by the High Directional Monte Carlo procedure

Abstract

A new Monte Carlo sampling scheme, namely High Directional Monte Carlo procedure, is used to obtain the global energy minimum conformations of polypeptides such as enkephalin and melittin. The resultant structures of enkephalin and melittin agree well with previous results of theoretical and experimental studies. Particularly, it is shown that some important parts in the conformation, such as the hinge region that principally determines the tertiary structure of proteins, are correctly described by the new method. The resultant structures are compared with those of other works and their stereoscopic views are shown.     

From linear combinations to integrals: A new approach to the basis function problem

A new formalism is presented, based upon the finite element method, that permits a dual representation of orbitals in terms of exponential or Gaussian functions as both an integral over the space of exponential parameters and as a linear combination of basis functions. The method has been implemented for the atomic Hartree–Fock problem using exponential functions and test calculations made for atoms ranging from B to Cl. Accurate and consistent results can be obtained for a variety of atoms in a simple way using computational schemes that are systematic and hierarchic in nature. The new formalism is promising for any method where the calculation of integrals is not a major problem, such as some approaches of the density functional method and the pseudospectral formulation of ab initio methods. © 1992 by John Wiley & Sons, Inc.