Prediction of the conformational requirements for binding to the κ-opioid receptor and its subtypes. I. Novel α-helical cyclic peptides and their role in receptor selectivity

A conformational search of two similar κ-selective cyclic Dynorphin A (Dyn A) analogues is presented. Dyn A_1–11-NH₂( 1 ) and Dyn A_1–11-NH₂ ( 2 ) are not only highly potent κ-selective peptides but they also exhibit exceptional selectivity for κ receptors in the central (brain) vs. the peripheral (ileum) systems. Molecular mechanics systematic searching of the conformational preferences of the cyclic moieties of 1 and 2 produced 741 and 1003 starting ring structures, which were minimized at two dielectric constants of 2.0 and 80.0 in the AMBER force field. By rms superimposition, these low energy structures were grouped into conformational families for each ring system minimized at each dielectric. Comparison of the lowest energy structure of each of these families demonstrated that two (labeled A and B) were found as low energy ring systems for both 1 and 2 after minimization at either dielectric constant. These two structures are thus predicted to be the putative binding conformations for Dynorphin A at receptors in the brain. Interestingly, one of these putative binding structures exhibited an α-helical conformation in the disulfide bridged ring that has not been observed for small cyclic peptides of this nature before. Molecular dynamics simulation of the helical binding structures indicated that the helical configuration in 2 is lower in energy and is more confor-mationally stable than that of 1 . We correlate this with the increased selectivity and potency of 2 for κ receptors in the brain compared to the periphery, implying that this may be due to an α-helical conformation in the cyclized address or helical induction in the message sequence. © 1994 John Wiley & Sons, Inc.     

Comparison of Protein Models Minimized by the All-Atom and United-Atom Models in the AMBER Force Field: Correlation of RMS deviation with the Crystallographic R Factor and Size

Abstract

We performed energy minimization of 25 protein structures, which vary significantly in their size, secondary structural content and crystallographic R factor, in the AMBER force field. We used an unconstrained path and the conjugate gradients algorithm. To determine the reliability of the united-atom approximation, we minimized all the proteins using both the all-atom and united-atom models. The RMS deviations of the minimized structures were plotted as a function of the crystallographic R factors of the initial structures. For the all-atom models, we found a strong linear relationship between the RMS deviations and the R factors (correlation coefficient of 0.78). The RMS deviations of protein structures minimized using united-atom models showed a wider range of distribution and had a correlation coefficient with the R factors of only 0.52. The RMS deviations decrease with an increase in the size of the protein, probably due to the decreased ratio of surface area to volume with increasing size of the protein. The surface atoms and residues showed higher RMS deviations than those in the interior of the protein. Even in these plots the united-atom models show a wide range of distribution of data points. From these results, we recommend the use of all-atom models for energy minimization of proteins in the AMBER force field.     

Molecular Modeling of Proteins: A Strategy for Energy Minimization by Molecular Mechanics in the AMBER Force Field

Abstract

Energy minimization is an important step in molecular modeling of proteins. In this study, we sought to develop a minimization strategy which would give the best final structures with the shortest computer time in the AMBER force field. In the all-atom model, we performed energy minimization of the melittin (mostly α-helical) and cardiotoxin (mostly β-sheet and β-turns) crystal structures by both constrained and unconstrained pathways. In the constrained path, which has been recommended in the energy minimization of proteins, hydrogens were relaxed first, followed by the side chains of amino acid residues, and finally the whole molecule. Despite the logic of this approach, however, the structures minimized by the unconstrained path fit the experimental structures better than those minimized by constrained paths. Moreover, the unconstrained path saved considerable computer time. We also compared the effects of the steepest descents and conjugate gradients algorithms in energy minimization. Previously, steepest descents has been used in the initial stages of minimization and conjugate gradients in the final stages of minimization. We therefore studied the effect on the final structure of performing an initial minimization by steepest descents. The structures minimized by conjugate gradients alone resembled the structures minimized initially by the steepest descents and subsequently by the conjugate gradients algorithms. Thus an initial minimization using steepest descents is wasteful and unnecessary, especially when starting from the crystal structure. Based on these results, we propose the use of an unconstrained path and conjugate gradients for energy minimization of proteins. This procedure results in low energy structures closer to the experimental structures, and saves about 70–80% of computer time. This procedure was applied in building models of lysozyme mutants. The crystal structure of native T₄ lysozyme was mutated to three different mutants and the structures were minimized. The minimized structures closely fit the crystal structures of the respective mutants (< 0.3 Å root-mean-square, RMS, deviation in the position of all heavy atoms). These results confirm the efficiency of the proposed minimization strategy in modeling closely related homologs. To determine the reliability of the united atom approximation, we also performed all of the above minimizations with united atom models. This approximation gave structures with similar but slightly higher RMS deviations than the all-atom model, but gave further savings of60-70% in computer time. However, we feel further investigation is essential to determine the reliability of this approximation. Finally, to determine the limitation of the procedure, we built the melittin molecule interactively in an α-helical conformation and this model showed an RMS deviation greater than 2.8 Å when compared to the melittin crystal structure. This model was minimized by various strategies. None of the minimized structures converged towards the crystal structure. Thus, although the proposed method seems to give valid structures starting from closely related crystal structures, it cannot predict the native structure when the starting structure is far from the native structure. From these results, we recommend the use of the proposed strategy of minimizing by an unconstrained path using the conjugate gradients algorithm, but only for modeling of closely related structural homologs of proteins.     

A Fourier transform infrared spectroscopic (FTIR) study of porcine and bovine pancreatic phospholipase A2 and their interaction with substrate analogues and a transition-state inhibitor

Fourier transform infrared spectroscopy has been used to investigate the secondary structure of porcine and bovine pancreatic phospholipase A2 (PLA2) and the zymogen of porcine PLA2, prophospholipase A2 (proPLA2), in both H2O and D2O media. Detailed qualitative analysis was made of these proteins using second derivative and deconvolution techniques. Quantitative studies of the proteins in solution made using Factor Analysis gave average values of 54% alpha-helix, 15% beta-sheet and 23% beta-turns. These values agree well with the secondary structures deduced from previous studies of single crystals using X-ray techniques. No significant differences in secondary structure were observed for porcine pancreatic (pro)phospholipase A2 in the presence or absence of Ca2+ ions, or in the temperature range 10-45 degrees C. The binding of the non-degradable phospholipid analogue, n-alkylphosphocholine, in monomeric form produced no significant difference in the secondary structure of either enzyme. Conformational differences were, however, observed between the enzyme lyophilised in a solid film and in aqueous solution. The change is probably due to the formation of beta-sheet upon hydration, coupled with a loss of random structures. Conformational differences in both porcine and bovine pancreatic PLA2 were observed on binding to n-alkylphosphocholine micelles. This change may be due to a small increase in the alpha-helical structure and a decrease in the beta-sheet, and/or possibly beta-turn content. Similar conformational changes were observed for the interaction of porcine and bovine PLA2 with the substrate analogue inhibitor 1-heptanoyl-2-heptanoylamino-2-deoxy-sn-glycero-3-phospho glycol in micellar form.     

Multibilayer structure of dimyristoylphosphatidylcholine dihydrate as determined by energy minimization

Complete energy minimization was carried out on the multibilayer crystal structure of 1,2-dimyristoyl-sn-glycero-3-phosphocholine dihydrate (DMPC.2H2O), starting from the X-ray structure determination reported by Pearson and Pascher (1979) Nature 281, 499-501. The asymmetric unit contains two nonidentical DMPC molecules and four water molecules. Minimization removed the acyl chain disorder present in the X-ray structure and caused the carbon planes of the acyl chains to become mutually parallel. Two energy-minimized structures (structures I and II) were found which mainly differed in the hydrogen-bonding arrangement of the waters of hydration. In structure I as in the X-ray structure, one of the water molecules forms a hydrogen-bonded bridge between successive bilayers; but in structure II, all hydrogen bonds are satisfied on the same bilayer. Structure II corresponds to the global energy minimum and is also a suitable structure for single bilayers. The lattice constants and cell volume of the minimized structures are close to the experimental values. The electrostatic force between DMPC bilayers is attractive. The mean hydration energy of the water is -14.2 kcal/mol, which is 2.5 kcal/mol lower than the binding energy of ice.     

Adaptability of restrained molecular dynamics for tertiary structure prediction: application to Crotalus atrox venom phospholipase A2

In order to assess the adaptability and/or applicability of the restrained molecular dynamics (RMD) simulation for building a possible tertiary structure of a protein from the X-ray crystal structure of a family reference protein, the tertiary structure prediction of Crotalus atrox venom phospholipase A2 (PLA2) was attempted based on the X-ray crystal structure of bovine pancreatic PLA2. For the formation of secondary and tertiary structures from the fully extended starting structure, the RMD simulation with interatomic distance restraints and torsion angle restraints, which were derived from homologous amino acid sequence regions in the reference protein, was carried out until the molecular system was fully equilibrated. The predicted tertiary structure of C. atrox venom PLA2 was compared with its X-ray crystal structure, and furthermore the utility of this method was discussed by reference to the similar tertiary structure prediction of beta-trypsin from the X-ray crystal structure of an elastase.     

Fold helical proteins by energy minimization in dihedral space and a DFIRE-based statistical energy function

Statistical energy functions are discrete (or stepwise) energy functions that lack van der Waals repulsion. As a result, they are often applied directly to a given structure (native or decoy) without further energy minimization being performed to the structure. However, the full benefit (or hidden defect) of an energy function cannot be revealed without energy minimization. This paper tests a recently developed, all-atom statistical energy function by energy minimization with a fixed secondary helical structure in dihedral space. This is accomplished by combining the statistical energy function based on a distance-scaled finite ideal-gas reference (DFIRE) state with a simple repulsive interaction and an improper torsion energy function. The energy function was used to minimize 2000 random initial structures of 41 small and medium-sized helical proteins in a dihedral space with a fixed helical region. Results indicate that near-native structures for most studied proteins can be obtained by minimization alone. The average minimum root-mean-squared distance (rmsd) from the native structure for all 41 proteins is 4.1 A. The energy function (together with a simple clustering of similar structures) also makes a reasonable selection of near-native structures from minimized structures. The average rmsd value and the average rank for the best structure in the top five is 6.8 A and 2.4, respectively. The accuracy of the structures sampled and the structure selections can be improved significantly with the removal of flexible terminal regions in rmsd calculations and in minimization and with the increase in the number of minimizations. The minimized structures form an excellent decoy set for testing other energy functions because most structures are well-packed with minimum hard-core overlaps with correct hydrophobic/hydrophilic partitioning. They are available online at http://theory.med.buffalo.edu.     

Molecular mechanics analysis of inhibitor binding to HIV-1 protease.

Crystallographic structures of HIV protease with three different peptide-mimetic inhibitors were subjected to energy minimization using molecular mechanics, the minimized structures analyzed and the inhibitor binding energies calculated. Partial charge assignment for the hydrogen bonded catalytic aspartic acids, Asp25 and -25', was in good agreement with charge calculations using semi-empirical molecular orbital methods. Root mean square deviations on minimization were small and similar for both subunits in the protease dimer. The surface loops, which had the largest B factors, changed most on minimization; the hydrophobic core and the inhibitor binding site showed little change. The distance-dependent dielectric of D(r) = 4r was found to be preferable to D(r) = r. Distance restraints were applied for the intermolecular hydrogen bonds to maintain the conformation of the inhibitor binding site. Using the dielectric of D(r) = 4r, the calculated interaction energy of the three inhibitors with the protease ranged from -53 to -56 kcal/mol. The psi groups of the inhibitors were changed to add or remove a 'transition state analogue' hydroxyl group, and the loss in energy on the removal of this group was calculated to be 0.9-1.7 kcal/mol. This would represent 19-36% of the total measured difference in binding energy between the inhibitors JG365 and MVT-101.     

Molecular modeling of proteins: a strategy for energy minimization by molecular mechanics in the AMBER force field.

Energy minimization is an important step in molecular modeling of proteins. In this study, we sought to develop a minimization strategy which would give the best final structures with the shortest computer time in the AMBER force field. In the all-atom model, we performed energy minimization of the melittin (mostly alpha-helical) and cardiotoxin (mostly beta-sheet and beta-turns) crystal structures by both constrained and unconstrained pathways. In the constrained path, which has been recommended in the energy minimization of proteins, hydrogens were relaxed first, followed by the side chains of amino acid residues, and finally the whole molecule. Despite the logic of this approach, however, the structures minimized by the unconstrained path fit the experimental structures better than those minimized by constrained paths. Moreover, the unconstrained path saved considerable computer time. We also compared the effects of the steepest descents and conjugate gradients algorithms in energy minimization. Previously, steepest descents has been used in the initial stages of minimization and conjugate gradients in the final stages of minimization. We therefore studied the effect on the final structure of performing an initial minimization by steepest descents. The structures minimized by conjugate gradients alone resembled the structures minimized initially by the steepest descents and subsequently by the conjugate gradients algorithms. Thus an initial minimization using steepest descents is wasteful and unnecessary, especially when starting from the crystal structure. Based on these results, we propose the use of an unconstrained path and conjugate gradients for energy minimization of proteins. This procedure results in low energy structures closer to the experimental structures, and saves about 70-80% of computer time. This procedure was applied in building models of lysozyme mutants. The crystal structure of native T4 lysozyme was mutated to three different mutants and the structures were minimized. The minimized structures closely fit the crystal structures of the respective mutants (less than 0.3 A root-mean-square, RMS, deviation in the position of all heavy atoms). These results confirm the efficiency of the proposed minimization strategy in modeling closely related homologs. To determine the reliability of the united atom approximation, we also performed all of the above minimizations with united atom models. This approximation gave structures with similar but slightly higher RMS deviations than the all-atom model, but gave further savings of 60-70% in computer time. However, we feel further investigation is essential to determine the reliability of this approximation.(ABSTRACT TRUNCATED AT 400 WORDS)     

Predicting common foldings of homologous RNAs.

A new approach is proposed for determining common RNA secondary structures within a set of homologous RNAs. The approach is a combination of phylogenetic and thermodynamic methods which is based on the prediction of optimal and suboptimal secondary structures, topological similarity searches and phylogenetic comparative analysis. The optimal and suboptimal RNA secondary structures are predicted by energy minimization. Structural comparison of the predicted RNA secondary structures is used to find conserved structures that are topologically similar in all these homologous RNAs. The validity of the conserved structural elements found is then checked by phylogenetic comparison of the sequences. This procedure is used to predict common structures of ribonuclease P (RNAase P) RNAs.     

Can local energy minimization refine the PDB structures of different resolution universally?

Local energy minimization was statistically tested as the refinement strategy for PDB structure pairs of different resolution. The 13 pairs of structures with the only difference being the resolution were extracted from PDB and represented structures of 11 identical proteins obtained with different x-ray diffraction techniques. The rmsd distribution was calculated for these pairs before and after local energy minimization of each structure. MMFF94 was used for energy calculations and the quasi-Newtonian method was used for local energy minimization. By comparison of these two rmsd distributions, the local energy minimization was proved to statistically increase the structural differences in pairs, so it cannot be used for refinement purposes. To explore the prospects of complex refinement strategies based on energy minimization, randomized structures were obtained by moving the initial PDB structures as far as the minimized structures had been moved in the multidimensional space of atomic coordinates. For these randomized structures the rmsd distribution was calculated and compared with the one for minimized structures. The significant differences in their mean values proved the energy surface of the protein to have only few minima near the conformations of different resolution obtained by x-ray analysis for PDB. Some other results we obtained exploring the energy surface near these conformations are also presented. These results are expected to be useful for the development of new protein refinement strategies based on energy minimization.     

Calculation of protonation patterns in proteins with structural relaxation and molecular ensembles – application to the photosynthetic reaction center

The conventional method to determine protonation patterns of proteins was extended by explicit consideration of structural relaxation. The inclusion of structural relaxation was achieved by alternating energy minimization with the calculation of protonation pattern in an iterative manner until consistency of minimized structure and protonation pattern was reached. We applied this method to the bacterial photosynthetic reaction center (bRC) of Rps. viridis and could show that the relaxation procedure accounts for the nuclear polarization and therefore allows one to lower the dielectric constant for the protein from the typically chosen value of ɛ _p = 4 to a value of ɛ _p = 2 without fundamentally changing the results. Owing to the lower dielectric shielding at ɛ _p = 2, the charges of the titratable groups interact more strongly, which leads to sampling problems during Monte Carlo titration. We solved this problem by introducing triple moves in addition to the conventional single and double moves. We also present a new method that considers ensembles of protein conformations for the calculation of protonation patterns. Our method was successfully applied to calculate the redox potential differences of the quinones in the bRC using the relaxed structures for the different redox states of the quinones. Received: 30 October 1997 / Revised version: 2 March 1998 / Accepted: 7 March 1998     

Comparison of protein models minimized by the all-atom and united-atom models in the AMBER force field: correlation of RMS deviation with the crystallographic R factor and size.

We performed energy minimization of 25 protein structures, which vary significantly in their size, secondary structural content and crystallographic R factor, in the AMBER force field. We used an unconstrained path and the conjugate gradients algorithm. To determine the reliability of the united-atom approximation, we minimized all the proteins using both the all-atom and united-atom models. The RMS deviations of the minimized structures were plotted as a function of the crystallographic R factors of the initial structures. For the all-atom models, we found a strong linear relationship between the RMS deviations and the R factors (correlation coefficient of 0.78). The RMS deviations of protein structures minimized using united-atom models showed a wider range of distribution and had a correlation coefficient with the R factors of only 0.52. The RMS deviations decrease with an increase in the size of the protein, probably due to the decreased ratio of surface area to volume with increasing size of the protein. The surface atoms and residues showed higher RMS deviations than those in the interior of the protein. Even in these plots the united-atom models show a wide range of distribution of data points. From these results, we recommend the use of all-atom models for energy minimization of proteins in the AMBER force field.     

Using Molecular Dynamics Simulations on Crambin to Evaluate the Suitability of Different Continuum Dielectric and Hydrogen Atom Models for Protein Simulations

Abstract

Molecular dynamics simulations of enzymes with enough explicit waters of solvation to realistically account for solute-solvent interactions can burden the computational resources required to perform the simulation by more than two orders of magnitude. Since enzyme simulations even with an implicit solvation model can be imposing for a supercomputer, it is important to assess the suitability of different continuum dielectric models for protein simulations. A series of 100-picosecond molecular dynamics simulations were performed on the X-ray crystal structure of the protein crambin to examine how well computed structures, obtained using seven continuum dielectric and two hydrogen atom models, agreed with the X-ray structure. The best level of agreement between computed and experimental structures was obtained using a constant dielectric of 2 and the all-hydrogen model. Continuum dielectric models of 1,1^*r, and 2^*r also led to computed structures in reasonably good agreement with the X-ray structure. In all cases, the all-hydrogen model gave better agreement than the united atom model, although, in one case, the difference was not significant. Dielectric models of 4, 80, and 4^*r with either hydrogen model yielded significantly poorer fits. It is especially noteworthy that the observed trends did not semiquantitatively converge until about 50 picoseconds into the simulations, suggesting that validation studies for protein calculations based on energy minimizations or short simulations should be viewed with caution.     

Comparison of the solution and X-ray structures of barley serine proteinase inhibitor 2

A comparison of the solution n.m.r. structures of barley serine protease inhibitor 2 (BSPI-2) with the X-ray structures of both subtilisin complexed and native BSPI-2 is presented. It is shown that the n.m.r. and X-ray structures are very similar in terms of overall shape, size, polypeptide fold and secondary structure. The average atomic rms difference between the 11 restrained dynamics structures on the one hand and the two X-ray structures on the other is 1.9 +/- 0.2 A for the backbone atoms and 3.0 +/- 0.3 A for all atoms. The corresponding values for the restrained energy minimized mean dynamics structure are 1.5 and 2.4 A, respectively.     

Accurate NMR structures through minimization of an extended hybrid energy

The use of generous distance bounds has been the hallmark of NMR structure determination. However, bounds necessitate the estimation of data quality before the calculation, reduce the information content, introduce human bias, and allow for major errors in the structures. Here, we propose a new rapid structure calculation scheme based on Bayesian analysis. The minimization of an extended energy function, including a new type of distance restraint and a term depending on the data quality, results in an estimation of the data quality in addition to coordinates. This allows for the determination of the optimal weight on the experimental information. The resulting structures are of better quality and closer to the X-ray crystal structure of the same molecule. With the new calculation approach, the analysis of discrepancies from the target distances becomes meaningful. The strategy may be useful in other applications-for example, in homology modeling.     

Three-dimensional structure of acyl carrier protein determined by NMR pseudoenergy and distance geometry calculations

Distance constraints from two-dimensional NMR cross-relaxation data are used to derive a three-dimensional structure for acyl carrier protein from Escherichia coli. Several approaches to structure determination are explored. The most successful proves to be an approach that combines the early stages of a distance geometry program with energy minimization in the presence of NMR constraints represented as pseudopotentials. Approximately 450 proton to proton distance constraints including 50 long-range constraints were included in these programs. Starting structures were generated at random by the distance geometry program and energies minimized by a molecular mechanics module to give final structures. Seven of the structures were deemed acceptable on the basis of agreement with experimentally determined distances. Root-mean-square deviations from the mean of these structures for backbone atoms range from 2 to 3 A. All structures show three roughly parallel helices with hydrophobic residues facing inward and hydrophilic residues facing outward. A hydrophobic cleft is recognizable and is identified as a likely site for acyl chain binding.     

Atomic resolution structure of prokaryotic phospholipase A2: analysis of internal motion and implication for a catalytic mechanism

We have found a secreted phospholipase A(2) (PLA(2), EC 3.1.1.4) from Streptomyces violaceoruber A-2688, which is the first PLA(2) identified in prokaryote, and determined its tertiary structure by NMR and X-ray analyses. In this study, we collected the X-ray diffraction data of the bacterial PLA(2) at room temperature (297 K) using conventional MoK(alpha) radiation and refined the structure at a 1.05 A resolution. The atomic resolution analysis led us to introduce disordered conformations and hydrogen atoms into a full anisotropic model. The molecular motion, which is expressed as the sum of rigid-body motion and internal motion of protein, is roughly estimated as the thermal motion when the X-ray diffraction data are collected at room temperature. In this study, we applied a TLS (rigid-body motion in terms of translation, libration, and screw motions) model to analyze the rigid-body motion of the bacterial PLA(2) and calculated the internal motion by subtracting the estimate of the rigid-body motion from the observed anisotropic temperature factor. We also subjected the TLS model to estimate the internal motion of the bovine pancreatic PLA(2) using the anisotropic temperature factor deposited in the Protein Data Bank. Both results indicate that the localization of regions exhibiting larger internal motion in the bacterial PLA(2) is almost the same as that in the bovine pancreatic PLA(2), suggesting that although the tertiary structure of the bacterial PLA(2) is strikingly different from that of the bovine pancreatic PLA(2), the internal motion, which is associated with the calcium(II) ion-binding, phospholipid-binding, and allosteric interfacial activation, is commonly observed in both PLA(2)s.     

Molecular simulation of the effects of alcohols on peptide structure

The effects of alcohols on local protein structure have been simulated using computational approaches and model peptides. Molecular simulations were carried out on a 7-residue peptide created in both an extended conformation and an alpha-helix to explore alcohol-induced changes in peptide structure. It was assumed that alcohols hydrogen bond at peptide carbonyl groups with an optimum geometry and compete with water molecules at these site. Energy minimization of the peptide/alcohol assemblies revealed that alcohols induced a twist in the peptide backbone as a function of (1) the methylene chain length, (2) the hydrogen-bond geometry, (3) halogenation of the molecule, (4) concentration, and (5) the dielectric constant. The rank ordering of the potencies of the alcohols was hexafluoroisopropanol > trifluoroethanol approximately pentanol > butanol > ethanol > methanol. Helix destabilization by cosolvent was measured by examining the hydrogen-bond lengths in peptide structures that resulted from a combination of energy minimization and molecular dynamics simulations. Destabilization was also found to be dependent upon the chemical nature of the alcohol and the hydrogen-bond geometry. The data suggest that alcohols at low concentrations affect protein structure mainly through a combination of hydrogen-bonding and hydrophobic interactions that are influenced by the properties of the solvent.