Enkephalin: conformational analysis by means of empirical energy calculations

Critical Assessment of Methods for Predicting the 3D Structure of Proteins and Protein Complexes

Advances in a scientific discipline are often measured by small, incremental steps. In this review, we report on two intertwined disciplines in the protein structure prediction field, modeling of single chains and modeling of complexes, that have over decades emulated this pattern, as monitored by the community-wide blind prediction experiments CASP and CAPRI. However, over the past few years, dramatic advances were observed for the accurate prediction of single protein chains, driven by a surge of deep learning methodologies entering the prediction field. We review the mainscientific developments that enabled these recent breakthroughs and feature the important role of blind prediction experiments in building up and nurturing the structure prediction field. We discuss how the new wave of artificial intelligence-based methods is impacting the fields of computational and experimental structural biology and highlight areas in which deep learning methods are likely to lead to future developments, provided that major challenges are overcome.

Exploring Conformational Preferences of Leu-enkephalin Using the Conformational Search and Double-Hybrid DFT Energy Calculations

The conformational preferences of Leu-enkephalin (Leu-Enk) were explored by the conformational search and density functional theory (DFT) calculations. By a combination of low-energy conformers of each residue, the initial structures of the neutral Leu-Enk were generated and optimized using the ECEPP3 force field in the gas phase. These structures were reoptimized at the HF/3-21G(d) and M06-2X levels of theory with 6-31G(d) and 6-31+G(d) basis functions. We finally located the 139 structures with the relative energy <10 kcal mol-1 in the gas phase, from which the structures of the corresponding zwitterionic Leu-Enk were generated and reoptimized at the M06-2X/6-31+G(d) level of theory using the implicit solvation model based on density (SMD) in water. The conformational preferences of Leu-Enk were analyzed using Gibbs free energies corrected by single-point energies calculated at the double-hybrid DSD-PBEP86-D3BJ/def2-TZVP level of theory in the gas phase and in water. The neutral Leu-Enk dominantly adopted a folded structure in the gas phase stabilized by three H-bonds with a βII'-bend-like motif at the Gly3-Phe4 sequence and a close contact between the side chains of Phe4 and Leu5. The zwitterionic Leu-Enk exhibited a folded structure in water stabilized by three H-bonds with double β-bends such as a βII' bend at the Gly2-Gly3 sequence and a βI bend at the Gly3-Phe4 sequence. The calculated ensemble-averaged distance between CGly2 α and CLeu5 α of the zwitterionic Leu-Enk in water is consistent with the value estimated from the simulated annealing using the distance constraints derived from nuclear Overhauser effect spectroscopy (NOESY) spectra in water. Interestingly, the preferred conformations of the neutral and zwitterionic Leu-Enk are new folded structures not predicted by earlier computational studies. According to the refined model of the zwitterionic Leu-Enk bound to δ-opioid receptor (δOR), there were favorable interactions of the terminal charged groups of Leu-Enk with the side chains of charged residues of δOR as well as a favorable CAryl···H interaction of the Phe4 residue of Leu-Enk with Trp284 of δOR. Hence, these favorable interactions would induce the folded structure of the zwitterionic Leu-Enk with double β-bends isolated in water into the "bioactive conformation" like an extended structure when binding to δOR.

My 65 years in protein chemistry

This is a tour of a physical chemist through 65 years of protein chemistry from the time when emphasis was placed on the determination of the size and shape of the protein molecule as a colloidal particle, with an early breakthrough by James Sumner, followed by Linus Pauling and Fred Sanger, that a protein was a real molecule, albeit a macromolecule. It deals with the recognition of the nature and importance of hydrogen bonds and hydrophobic interactions in determining the structure, properties, and biological function of proteins until the present acquisition of an understanding of the structure, thermodynamics, and folding pathways from a linear array of amino acids to a biological entity. Along the way, with a combination of experiment and theoretical interpretation, a mechanism was elucidated for the thrombin-induced conversion of fibrinogen to a fibrin blood clot and for the oxidative-folding pathways of ribonuclease A. Before the atomic structure of a protein molecule was determined by x-ray diffraction or nuclear magnetic resonance spectroscopy, experimental studies of the fundamental interactions underlying protein structure led to several distance constraints which motivated the theoretical approach to determine protein structure, and culminated in the Empirical Conformational Energy Program for Peptides (ECEPP), an all-atom force field, with which the structures of fibrous collagen-like proteins and the 46-residue globular staphylococcal protein A were determined. To undertake the study of larger globular proteins, a physics-based coarse-grained UNited-RESidue (UNRES) force field was developed, and applied to the protein-folding problem in terms of structure, thermodynamics, dynamics, and folding pathways. Initially, single-chain and, ultimately, multiple-chain proteins were examined, and the methodology was extended to protein-protein interactions and to nucleic acids and to protein-nucleic acid interactions. The ultimate results led to an understanding of a variety of biological processes underlying natural and disease phenomena.

Reconstructing the free-energy landscape of Met-enkephalin using dihedral principal component analysis and well-tempered metadynamics

Well-Tempered Metadynamics (WTmetaD) is an efficient method to enhance the reconstruction of the free-energy surface of proteins. WTmetaD guarantees a faster convergence in the long time limit in comparison with the standard metadynamics. It still suffers, however, from the same limitation, i.e., the non-trivial choice of pertinent collective variables (CVs). To circumvent this problem, we couple WTmetaD with a set of CVs generated from a dihedral Principal Component Analysis (dPCA) on the Ramachandran dihedral angles describing the backbone structure of the protein. The dPCA provides a generic method to extract relevant CVs built from internal coordinates, and does not depend on the alignment to an arbitrarily chosen reference structure as usual in Cartesian PCA. We illustrate the robustness of this method in the case of a reference model protein, the small and very diffusive Met-enkephalin pentapeptide. We propose a justification a posteriori of the considered number of CVs necessary to bias the metadynamics simulation in terms of the one-dimensional free-energy profiles associated with Ramachandran dihedral angles along the amino-acid sequence.

Transition pathway and its free-energy profile: a protocol for protein folding simulations

We propose a protocol that provides a systematic definition of reaction coordinate and related free-energy profile as the function of temperature for the protein-folding simulation. First, using action-derived molecular dynamics (ADMD), we investigate the dynamic folding pathway model of a protein between a fixed extended conformation and a compact conformation. We choose the pathway model to be the reaction coordinate, and the folding and unfolding processes are characterized by the ADMD step index, in contrast to the common a priori reaction coordinate as used in conventional studies. Second, we calculate free-energy profile as the function of temperature, by employing the replica-exchange molecular dynamics (REMD) method. The current method provides efficient exploration of conformational space and proper characterization of protein folding/unfolding dynamics from/to an arbitrary extended conformation. We demonstrate that combination of the two simulation methods, ADMD and REMD, provides understanding on molecular conformational changes in proteins. The protocol is tested on a small protein, penta-peptide of met-enkephalin. For the neuropeptide met-enkephalin system, folded, extended, and intermediate sates are well-defined through the free-energy profile over the reaction coordinate. Results are consistent with those in the literature.

Ligand Binding Pathway Elucidation for Cryptophane Host-Guest Complexes

Modeling binding pathways can provide insight into molecular recognition, including kinetic mechanisms, barriers to binding, and gating effects. This work represents a novel computational approach, Hopping Minima, for the determination of conformational transitions of single molecules as well as binding pathways for molecular complexes. The method begins by thoroughly sampling a set of conformational minima for a molecular system. The natural motions of the system are modeled using the normal modes of the sampled minima. The natural motions are utilized to connect conformational minima and are finally combined to form association/binding pathways in the case of molecular complexes. We provide an implementation and example application of the method using alanine dipeptide and a set of chemical host-guest systems: two cryptophane hosts with two guest cations, trimethylammonium and tetramethylammonium. Our results demonstrate that conformational transitions can be modeled and extended to find binding pathways as well as energetic information relevant to the minimum conformations involved. This approach has advantages over simulation-based methods for studying systems with slow binding processes and can help design molecules with preferred binding kinetics.

De novo structure prediction and experimental characterization of folded peptoid oligomers

Peptoid molecules are biomimetic oligomers that can fold into unique three-dimensional structures. As part of an effort to advance computational design of folded oligomers, we present blind-structure predictions for three peptoid sequences using a combination of Replica Exchange Molecular Dynamics (REMD) simulation and Quantum Mechanical refinement. We correctly predicted the structure of a N-aryl peptoid trimer to within 0.2 Å rmsd-backbone and a cyclic peptoid nonamer to an accuracy of 1.0 Å rmsd-backbone. X-ray crystallographic structures are presented for a linear N-alkyl peptoid trimer and for the cyclic peptoid nonamer. The peptoid macrocycle structure features a combination of cis and trans backbone amides, significant nonplanarity of the amide bonds, and a unique "basket" arrangement of (S)-N(1-phenylethyl) side chains encompassing a bound ethanol molecule. REMD simulations of the peptoid trimers reveal that well folded peptoids can exhibit funnel-like conformational free energy landscapes similar to those for ordered polypeptides. These results indicate that physical modeling can successfully perform de novo structure prediction for small peptoid molecules.

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.

Methionine enkephalin and isosteric analogues. I. Synthesis on a phenolic resin support

An efficient synthesis of methionine enkephalin using a phenolic resin support is described. Analogues modified at their C-termini, such as peptide acids, amides, methyl esters and compounds formed by their reduction, were prepared conveniently from common peptide phenyl ester resins. The resin was used in the synthesis of complex isosterically modified analogues designed to investigate the role of peptide backbone plays in receptor interaction. Free hexapeptide phenyl ester resins underwent intramolecular aminolysis liberating the corresponding cyclic peptides.

Exploring conformational space using a mean field technique with MOLS sampling

The computational identification of all the low energy structures of a peptide given only its sequence is not an easy task even for small peptides,due to the multiple-minima problem and combinatorial explosion. We have developed an algorithm, called the MOLS technique,that addresses this problem, and have applied it to a number of different aspects of the study of peptide and protein structure. Conformational studies of oligopeptides, including loop sequences in proteins have been carried out using this technique. In general the calculations identified all the folds determined by previous studies,and in addition picked up other energetically favorable structures. The method was also used to map the energy surface of the peptides. In another application, we have combined the MOLS technique, using it to generate a library of low energy structures of an oligopeptide, with a genetic algorithm to predict protein structures. The method has also been applied to explore the conformational space of loops in protein structures.Further, it has been applied to the problem of docking a ligand in its receptor site, with encouraging results.

Structural characterization of methionine and leucine enkephalins by hydrogen/deuterium exchange and electrospray ionization tandem mass spectrometry

Conformational changes in two endogenous opioid active pentapeptides methionine enkephalin (Met-enk) and leucine enkephalin (Leu-enk) induced by trifluoroethanol (TFE) were identified using hydrogen/deuterium exchange (HDX), coupled with electrospray ionization (ESI) mass spectrometry. The exchange features in individual amino acid residues were characterized by acquiring tandem mass spectra of the deuterated peptides. The exact identity of the labile hydrogens involved in HDX reveals that the monomer forms of both peptides adopt an unfolded conformation in aqueous solvent, but prefer the 5-->2 beta-turn secondary structure under the membrane-mimetic environment. The ESI mass spectra of Met-enk and Leu-enk also reveal that the dimer structure of these peptides coexists with the monomer conformation. The extent of the dimer structure is dependent on the peptide concentration and nature of the solvent. The non-polar solvents facilitate the dimer formation.

Conformational studies on enkephalins using the MOLS technique

Conformational studies of two linear enkephalin molecules, Met-enkephalin and Leu-enkephalin, have been carried using the mutually orthogonal Latin squares (MOLS) technique with the ECEPP/3 force field. This technique was developed recently in our laboratory to perform an unbiased search of the conformational space of peptides and to locate low energy conformations. The present study identified all the folds predicted by other studies, and in addition picked up other energetically favorable structures. The results suggest that the peptide backbone exists as a mixture of folded and unfolded forms (approximately 50% each). The study also provides information on the distribution of the low energy conformations that we have classified on the basis of structural motifs, backbone hydrogen-bonding patterns, and root mean square deviations in atomic positions.

Application of evolutionary algorithm methods to polypeptide folding: comparison with experimental results for unsolvated Ac-(Ala-Gly-Gly)5-LysH+

We present an evolutionary method for finding the low-energy conformations of polypeptides. The application, called FOLDAWAY,is based on a generic framework and uses several evolutionary operators as well as local optimization to navigate the complex energy landscape of polypeptides. It maintains two complementary representations of the structures and uses the CHARMM force field for evaluating the energies. The method is applied to unsolvated Met-enkephalin and Ac-(Ala-Gly-Gly)(5)-Lys(+)H(+). Unsolvated Ac-(Ala-Gly-Gly)(5)-Lys(+)H(+) has been the object of recent experimental studies using ion mobility measurements. It has a flat energy landscape where helical and globular conformations have similar energies. FOLDAWAY locates several large groups of structures not found in previous molecular dynamics simulations for this peptide, including compact globular conformations, which are probably present in the experiments. However, the relative energies of the different conformations found by FOLDAWAY do not accurately match the relative energies expected from the experimental observations.

Atomically detailed folding simulation of the B domain of staphylococcal protein A from random structures

The conformational space of the 10-55 fragment of the B-domain of staphylococcal protein A has been investigated by using the electrostatically driven Monte Carlo (EDMC) method. The ECEPP/3 (empirical conformational energy program for peptides) force-field plus two different continuum solvation models, namely SRFOPT (Solvent Radii Fixed with atomic solvation parameters OPTimized) and OONS (Ooi, Oobatake, Némethy, and Scheraga solvation model), were used to describe the conformational energy of the chain. After an exhaustive search, starting from two different random conformations, three of four runs led to native-like conformations. Boltzmann-averaged root-mean-square deviations (RMSD) for all of the backbone heavy atoms with respect to the native structure of 3.35 A and 4.54 A were obtained with SRFOPT and OONS, respectively. These results show that the protein-folding problem can be solved at the atomic detail level by an ab initio procedure, starting from random conformations, with no knowledge except the amino acid sequence. To our knowledge, the results reported here correspond to the largest protein ever folded from a random conformation by an initial-value formulation with a full atomic potential, without resort to knowledge-based information.

Enhanced sampling of the molecular potential energy surface using mutually orthogonal latin squares: application to peptide structures

The computational identification of the optimal three-dimensional fold of even a small peptide chain from its sequence, without reference to other known structures, is a complex problem. There have been several attempts at solving this by sampling the potential energy surface of the molecule in a systematic manner. Here we present a new method to carry out the sampling, and to identify low energy conformers of the molecule. The method uses mutually orthogonal Latin squares to select (of the order of) n(2) points from the multidimensional conformation space of size m(n), where n is the number of dimensions (i.e., the number of conformational variables), and m specifies the fineness of the search grid. The sampling is accomplished by first calculating the value of the potential energy function at each one of the selected points. This is followed by analysis of these values of the potential energy to obtain the optimal value for each of the n-variables separately. We show that the set of the n-optimal values obtained in this manner specifies a low energy conformation of the molecule. Repeated application of the method identifies other low energy structures. The computational complexity of this algorithm scales as the fourth power of the size of the molecule. We applied this method to several small peptides, such as the neuropeptide enkephalin, and could identify a set of low energy conformations for each. Many of the structures identified by this method have also been previously identified and characterized by experiment and theory. We also compared the best structures obtained for the tripeptide (Ala)(3) by the present method, with those obtained by an exhaustive grid search, and showed that the algorithm is successful in identifying all the low energy conformers of this molecule.

Conformational studies of cyclic enkephalin analogues with L- or D-proline in position 3

The conformation of a series of cyclic enkephalin analogues of a general formula X(1)-cyclo[Y(2)-Z(3)-Nal(4)-Leu(5)] (Nal: beta-(2-naphthyl)alanine), where X = Tyr, Phe, or Phe(NO(2)), Y = D-Dab or L-Dab (Dab: 2,4-diaminobutyric acid), and Z = D-Pro or L-Pro, was studied by means of NMR spectroscopy and theoretical conformational analysis with the Empirical Conformational Energy Program for Peptides and Proteins force field plus solvation. The NMR measurements were performed in dimethyl sulfoxide solution. The nuclear Overhauser effect intensities and coupling constants were used to compute the statistical weights of the conformations of the ensemble generated in global conformational searches. The purpose of this study was to determine whether introducing the D- or L-proline residue in position 3 can produce peptides with both rigid backbone and significant separation of the pharmacophore groups in position 1 and 4 (as required for high affinity for the mu-type opioid receptors). It was found that the analogues with D-Dab in position 2 and D-Pro in position 3 possess a stable type II' beta-turn at positions 3 and 4, which rigidifies the cyclic backbone; this finding was confirmed by independent measurements of the temperature coefficients of the amide protons, which indicated very significant screening of the Leu(5) amide proton from the solvent. However, these analogues were found to possess a short interchromophore distance. The analogues containing both Dab and Pro in the L-configuration are characterized by a larger interchromophore distance; however, they do not possess a stable beta-turn and have therefore a higher conformational flexibility. The modifications proposed in this work are therefore not likely to lead to enkephalin analogues with a high affinity for the mu-receptors.

Long time dynamics of Met-enkephalin: comparison of explicit and implicit solvent models

Met-enkephalin is one of the smallest opiate peptides. Yet, its dynamical structure and receptor docking mechanism are still not well understood. The conformational dynamics of this neuron peptide in liquid water are studied here by using all-atom molecular dynamics (MD) and implicit water Langevin dynamics (LD) simulations with AMBER potential functions and the three-site transferable intermolecular potential (TIP3P) model for water. To achieve the same simulation length in physical time, the full MD simulations require 200 times as much CPU time as the implicit water LD simulations. The solvent hydrophobicity and dielectric behavior are treated in the implicit solvent LD simulations by using a macroscopic solvation potential, a single dielectric constant, and atomic friction coefficients computed using the accessible surface area method with the TIP3P model water viscosity as determined here from MD simulations for pure TIP3P water. Both the local and the global dynamics obtained from the implicit solvent LD simulations agree very well with those from the explicit solvent MD simulations. The simulations provide insights into the conformational restrictions that are associated with the bioactivity of the opiate peptide dermorphin for the delta-receptor.

Synthesis of cyclic dipeptide templates, their incorporation into peptides and studies on their conformational and biological properties

This study investigated the diastereoselective synthesis of three dipeptide templates 1, 2 and 3, which may be regarded as conformationally restricted analogs of H-Gly-Xaa-OH, in which Xaa constitutes an aromatic amino acid. Bond formation between alpha-C of Gly and the aromatic moiety was achieved by proton-catalyzed intramolecular electrophilic aromatic substitution. The absolute configuration of the dipeptide templates was determined by single-crystal X-ray crystallography or by nuclear Overhauser enhancement measurements. A protective group strategy was elaborated to allow their incorporation into peptide sequences by liquid phase as well as by solid-phase peptide synthesis. The templates were used to generate an enkephalin analog 15, a modified peptidic neurokinin antagonist 20 and two dermorphin derivatives (24 and 33). Molecular dynamic simulations with 15 and 20 revealed the preference for a turn-like motif for 15. The biological activity, as investigated by respective receptor binding and functional assays, was strongly diminished with all four derivatives, indicating that their receptor-relevant molecular geometries lie outside the examined conformational space.

Conformational analysis of [Met5]-enkephalin: solvation and ionization considerations

[Met5]-Enkephalin has the sequence Tyr-Gly-Gly-Phe-Met. Only the extended conformation of the peptide has been observed by X-ray crystallography. Nuclear magnetic resonance spectroscopy supports the presence of a turn at Gly 3 and Phe 4 in dimethyl sulfoxide. In this study, the peptide conformational states and thermodynamic properties are understood in terms of ionization state and solvent environment. In the calculation, final conformations obtained from multiple independent Monte Carlo simulated annealing conformational searches are starting points for molecular dynamics simulations. In an aqueous environment given by the use of solvation free energy and the zwitterionic state, dominant structural motifs computed are G-P Type II' bend, G-G Type II' bend, and G-G Type I' bend motifs, in order of increasing free energy. In the calculation of the peptide with neutral N- and C-termini and solvation free energy, the extended conformer dominates (by at least a factor of 2.5), and the conformation of another low free energy conformer superimposes well on the pharmacophoric groups of morphine. Neutralization of charge and solvation induce and stabilize the extended conformation, respectively. A mechanism of inter-conversion between the extended conformer and three bent conformers is supported by phi/psi-scatter plots, and by the conformer relative free energies. An estimate of the entropy change of receptor unbinding is 8.3 cal K-1 mol-1, which gives rise to a -2.5 kcal/mol entropy contribution to the free energy of unbinding at 25 degrees C. The conformational analysis methodology described here should be useful in studies on short peptides and flexible protein surface loops that have important biological implications.

Molecular dynamics simulations of Leu-enkephalin in water and DMSO

The structure of Leu-enkephalin (L-Enk) and Met-enkephalin (M-Enk) have frequently been studied, in particular by nuclear magnetic resonance spectroscopy. After more than 20 years of research, it was concluded that enkephalins have no preferred structure in aqueous solution, but that they may have in other solvents. We have performed molecular dynamics simulations of zwitterionic L-Enk in water, and zwitterionic as well as neutral L-Enk dimethyl sulfoxide (DMSO). In water the peptide is very flexible, although there seems to be a preference for compact conformations. In DMSO, the peptide forms a clear salt bridge in the zwitterionic form, but has no preferred conformation in the neutral form. This difference in conformation may provide an explanation for measurements in DMSO in which multiple conformations were found to exist. In this paper we introduce a new formulation for a dihedral angle autocorrelation function, and apply it to study side-chain dynamics in L-Enk. We find that the side-chain dynamics of the large Tyr and Phe residues cannot be adequately sampled in 2.0-ns simulations, while this does seem to be possible for the smaller Leu side chain.

A topographical model of mu-opioid and brain somatostatin receptor selective ligands. NMR and molecular dynamics studies

We have refined the 1H NMR-based conformations of the mu-opioid receptor selective peptides related to somatostatin of general formula Xxx-Yyy1-Cys-Zzz-D-Trp-Lys(Orn)5-Thr-Pen-Thr8- NH2, where Xxx, Yyy, Zzz are 0, D-Phe and Tyr for 1; 0, D-Tic and Tyr for 2; Gly, D-Tic and Tyr for 3; and 0, D-Phe and Tic for 4, respectively, (Kazmierski et al., J. Am. Chem. 113, 2275-2283), using a molecular-dynamics approach. We present evidence that the NMR data are compatible with beta II'-, gamma- and gamma'-turns for the central tetrapeptide Tyr-D-Trp-Lys/Orn-Thr. Based on detailed structural and topographical considerations, we suggest that the mu-opioid receptor selectivity of 2 is due to a particular spatial arrangement of aromatic side chains of D-Tic1 and Tyr3 (7.5 A), and that the opioid receptor recognition domain is located in the N-terminal part of the peptide while the somatostatin receptor recognition domain is determined by the central, turn forming part of this class of cyclic peptides. A model for a mu-opioid selective ligand has emerged from these studies that shows excellent structural similarities to rigid opioid alkaloids.

Investigation of conformational equilibrium of polypeptides by internal coordinate stochastic dynamics. Met5-enkephalin

The equilibrium population of different conformational states of a polypeptide can in principle be obtained by a very long molecular dynamics simulation. The method of internal coordinate molecular dynamics earlier developed in this laboratory (A.K. Mazur and R.A. Abagyan J. Biomol. Struct. Dyn. 6,833 (1989)) allows one to use time steps much larger than usual for computing molecular trajectories. It is shown here that the sampling of the conformational space can be additionally enhanced by adding a random component to the set of forces applied to atoms. We describe the algorithms by which the random force is introduced and also a special method which excludes the fast rotation of polar hydrogens from equations of motion but keeps them movable. As a result the task stated in the title becomes realistic. Internal coordinate stochastic dynamics is applied for scanning the conformational space of the pentapeptide Met5-enkephalin which is a common test example widely used in theoretical studies. A large number of conformational transitions is observed during the 20 ns simulation starting from the global energy minimum thus allowing us to arrive at a nearly Boltzmann distribution of populations of conformational states. A few states are found which are distinguished by high apparent configurational entropy which turn out to correspond well to experimentally observed conformations of enkephalins.

Enkephalin is a competitive antagonist of cholecystokinin in the gastrointestinal tract, as predicted from prior conformational analysis

Prior calculations based on ECEPP (Empirical Conformational Energies for Peptides Program) of the low energy minima for cholecystokinin (CCK) and Met-enkephalin have demonstrated that significant structural features of these two peptides are identical. This result suggested the possibility that Met-enkephalin, as well as other enkephalin analogues of similar structure, could associate with receptors for CCK. To test this theoretical result, we examined the ability of Met-enkephalin and its analogues to bind to peripheral CCK receptors in the rat gastrointestinal tract; in particular, we measured the ability of the opiate peptide to inhibit the effects of CCK in a physiological assay system which we have previously characterized: CCK-induced contraction of the isolated rat pyloric sphincter. We find that Met-enkephalin is an antagonist of the CCK-8-induced contraction, with a IC50 of 110 nM. Furthermore, antibodies against CCK were found to cross-react with Met-enkephalin and its analogues in a manner which suggests a distinct structure-activity relationship. These experimental results strongly support the theoretical results of conformational analysis showing structural similarity between enkephalin and CCK. They further suggest that enkephalins could modulate the response of CCK systems under physiological conditions.

Variable ranges of interactions in polypeptide conformations with a method to complement molecular modeling

Formulations of conformational weights for helix-coil transitions can be extended to substantially more complex situations than are usually pursued. General rules for matrix multiplication that depend parametrically on the interaction ranges and numbers of rotamers of residues are presented. The orders of the matrices of statistical weights can be increased with chain length, so that an individual matrix element can represent any specified single conformation, as needed. By the appropriate choice of interaction ranges and numbers of available conformers, approximations can be introduced in which: (1) an average of the conformations of any chain segment is obtained, (2) specific residue-residue interactions are excluded, or (3) the conformation of a part of the chain is restricted or fixed. The method is appropriate for treating specific interactions in peptides and could be used together with available experimental information to develop models of conformational transitions. As such, the methods represent a class of calculations aimed at more rigorous calculations built around known features of a molecule. The aim is to facilitate calculations that bridge the gap between nonquantitative molecular model building and more rigorous but less directed molecular mechanics calculations. The method can directly include any desired longer range of interactions, if the interaction range is not too long to make impossible the manipulation of the requisite matrices. An outline is presented of an application to treat salt bridges in the C peptide of ribonuclease A.

Characterization of low-energy conformational domains for Met-enkephalin

An extensive exploration of the conformational hypersurface of Met-enkephalin has been carried out, in order to characterize different low-energy conformational domains accessible to this pentapeptide. The search strategy used consisted of two steps. First, systematic nested rotations were performed using the ECEPP potential. Ninety-two low-energy structures were found and minimized using the CHARMm potential. High and low-temperature molecular dynamics trajectories were then computed for the lowest energy structures in an interative fashion until no lower energy conformers could be found. The same search strategy was used in these studies simulating three different environments, a distance-dependent dielectric epsilon = r, and two constant dielectrics epsilon = 10 and epsilon = 80. The lowest energy structure found in a distance-dependent dielectric is a Gly-Gly beta-II'-type turn. All other structures found for epsilon = r within 10 kcal/mol of this lowest energy structure are also bends. In the more polar environments, the density of conformational states is significantly larger compared to the apolar media. Moreover, fewer hydrogen bonds are formed in the more polar environments, which increases the flexibility of the peptide and results in less structured conformers. Comparisons are made with previous calculations and experimental results.

Constrained optimization and protein structure determination

Energy minimization is one of the main approaches to the computational determination of macromolecular structure. Due to the approximations in the empirical free-energy functions and due to the computational difficulties in locating their global minima, the problem is at present intractable when the only information available is the sequence of subunits forming the molecule. A less-demanding problem in terms of both physics and mathematics is constrained optimization, which uses additional but incomplete experimental information such as distances between certain atoms. This paper reviews methods for generating molecular structure using bond lengths and angles as variables and shows how the structure can be fully specified in terms of local geometry. The analysis permits precise statements to be made about the minimum set of distances that specify a unique structure without recourse to energy minimization. We then discuss the complementary situation, i.e., structure prediction with energy minimization based only on sequence information. Finally, we show how distance constraints can be incorporated into energy minimization methods.