Efficiency of simulated annealing for peptides with increasing geometrical restrictions

Simulated annealing (SA) is a popular global minimizer that can conveniently be applied to complex macromolecular systems. Thus, a molecular dynamics or a Monte Carlo simulation starts at high temperature, which is decreased gradually, and the system is expected to reach the low-energy region on the potential energy surface of the molecule. However, in many cases this process is not efficient. Alternatively, the low-energy region can be reached more effectively by minimizing the energy of selected molecular structures generated along the simulation pathway. The efficiency of SA to locate energy-minimized structures within 5 kcal/mol above the global energy minimum is studied as applied to three peptide models with increasing geometrical restrictions: (1) The linear pentapeptide Leu-enkephalin described by the ECEPP potential, (2) a cyclic hexapeptide described by the GROMOS force field energy E_GRO alone, and (3) the same cyclic peptide with E_GRO combined with a restraining potential based on 31 proton–proton restraints obtained from nuclear magnetic resonance (NMR) experiments. The efficiency of SA is compared to that of the Monte Carlo minimization (MCM) method of Li and Scheraga, and to our local torsional deformations (LTD) method for the conformational search of cyclic molecules. The results for the linear peptide show that SA provides a relatively weak guidance towards the most stable energy region; as expected, this guidance increases for the cyclic peptide and the cyclic peptide with NMR restraints. However, in general, MCM and LTD are significantly more efficient than SA as generators of low-energy minimized structures. This suggests that LTD might provide a better search tool than SA in structure determination of protein regions for which a relatively small number of restraints are provided by NMR. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1659–1670, 1999     

Conformation and absolute configuration of nocathiacin I determined by NMR spectroscopy and chiral capillary electrophoresis

Nocathiacin I (BMS-249524) is a highly cross-linked thiazolyl peptide that displays potent activity against Gram-positive bacteria, including a number of antibiotic-resistant strains. This natural product contains 10 chiral centers. NMR studies have been performed to characterize the solution structure of nocathiacin I. A uniformly 13C,15N-labeled sample was used to obtain NMR assignments. Restrained simulated annealing calculations were performed by using accurately determined NOE distance restraints. All of the chiral centers were allowed to float during the simulated annealing protocol. Two clusters of structures were obtained that satisfy the NOE restraints very well and that are reasonably consistent with vicinal J-coupling constants. Within each cluster, all 10 chiral centers are uniquely defined. The two clusters are effectively mirror images of each other: all chiral centers that have the R(S) configuration in one cluster have the S(R) configuration in the other. The single threonine residue in nocathiacin I was subsequently determined to be l-threonine by chiral capillary electrophoresis, allowing the absolute configurations of all 10 chiral centers to be defined.     

蒙特卡洛模拟退火与距离限制相结合的方法——在多肽溶液构象分析中的应用

Distance geometry and molecular dynamics are currently employed in determining molecular structures with interatomic distances from NMR NOESY experiment. Because of the flexibility of peptide, distances obtained from NMR are usually not sufficient to confine its structure. Both distance geometry and molecular dynamics will bias in the conformational space at this circumstance. Constraint Monte Carlo simulated annealing was established to solve this problem. Distance constraints were included into the ECEPP/2 force field by introducing a harmonic energy term. Conformational analysis of a pentapeptide with eight interatomic distances from NMR was carried out as a test. By comparison of the 100 conformers obtained from constraint simulated annealing and the 100 conformers from distance geometry calculation, it was found that constraint simulated annealing can cover the outcomes of distance geometry and at the same time give more con-formers fitting to the experimental data. The result shows that constraint Monte-Carlo simulated annealing is more valid in constructing peptide structures from NMR distances than currently employed methods when no sufficient distances from NMR are available.     

蒙特卡洛模拟退火与距离限制相结合的方法在多肽溶液构象分析中的应用

多维核磁共振技术的飞速发展议得其在生物大分子结构测定方面的应用已经达到可以与【射线晶体学并驾齐驱的地步．蛋白质结构堆积紧密，较适合于用核磁共振方法给出确定的结构．与蛋白质不同的是多肽的柔性较大，在溶液中可能存在多种构象，核磁共振实验给出的只是平均信息＊．利用核磁，（振数据构建分子结构模型常用的方法有距离几何、分子动力学等，在由核磁共振NOESZ得到的距离信息足够多时可以给出较好的结果问．由于多肽本身的特点：柔性较大，由核磁共振得到的距离信息较少等，利用距离几何、分子动力学方法进行构象搜索时容易陷入…     

CABS‐NMR—De novo tool for rapid global fold determination from chemical shifts,residual dipolar couplings and sparse methyl‐methyl noes

Recent development of nuclear magnetic resonance (NMR) techniques provided new types of structural restraints that can be successfully used in fast and low‐cost global protein fold determination. Here, we present CABS‐NMR, an efficient protein modeling tool, which takes advantage of such structural restraints. The restraints are converted from original NMR data to fit the coarse grained protein representation of the C‐Alpha‐Beta‐Side‐group (CABS) algorithm. CABS is a Monte Carlo search algorithm that uses a knowledge‐based force field. Its versatile structure enables a variety of protein‐modeling protocols, including purely de novo folding, folding guided by restraints derived from template structures or, structure assembly based on experimental data. In particular, CABS‐NMR uses the distance and angular restraints set derived from various NMR experiments. This new modeling technique was successfully tested in structure determination of 10 globular proteins of size up to 216 residues, for which sparse NMR data were available. Additional detailed analysis was performed for a S100A1 protein. Namely, we successfully predicted Nuclear Overhauser Effect signals on the basis of low‐energy structures obtained from chemical shifts by CABS‐NMR. It has been observed that utility of chemical shifts and other types of experimental data (i.e. residual dipolar couplings and methyl‐methyl Nuclear Overhauser Effect signals) in the presented modeling pipeline depends mainly on size of a protein and complexity of its topology. In this work, we have provided tools for either post‐experiment processing of various kinds of NMR data or fast and low‐cost structural analysis in the still challenging field of new fold predictions. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Applications of simulated annealing to the conformational analysis of flexible molecules

We describe in this article our solution to the global minimum problem which uses the simulated annealing algorithm of Kirkpatrick. This method is a Metropolis (e-ΔE/kT) Monte Carlo sampling of conformation space with simultaneous constraint of the search by lowering the temperature T so that the search converges on the global minimum. The Anneal-Conformer program has been extensively tested with peptides and organic molecules using either the Amber or MM2 force fields. A history file of the simulated annealing process allows reconstruction of the random walk in conformation space for subsequent examination. Thus plots of distance and dihedral angle changes during the search for the global minimum can be examined to deduce molecular shape and flexibility. A separate program Conf-Gen reads the history file and extracts all low energy conformations visited during the run.     

Refinement of NMR structures using implicit solvent and advanced sampling techniques

NMR biomolecular structure calculations exploit simulated annealing methods for conformational sampling and require a relatively high level of redundancy in the experimental restraints to determine quality three-dimensional structures. Recent advances in generalized Born (GB) implicit solvent models should make it possible to combine information from both experimental measurements and accurate empirical force fields to improve the quality of NMR-derived structures. In this paper, we study the influence of implicit solvent on the refinement of protein NMR structures and identify an optimal protocol of utilizing these improved force fields. To do so, we carry out structure refinement experiments for model proteins with published NMR structures using full NMR restraints and subsets of them. We also investigate the application of advanced sampling techniques to NMR structure refinement. Similar to the observations of Xia et al. (J.Biomol. NMR 2002, 22, 317-331), we find that the impact of implicit solvent is rather small when there is a sufficient number of experimental restraints (such as in the final stage of NMR structure determination), whether implicit solvent is used throughout the calculation or only in the final refinement step. The application of advanced sampling techniques also seems to have minimal impact in this case. However, when the experimental data are limited, we demonstrate that refinement with implicit solvent can substantially improve the quality of the structures. In particular, when combined with an advanced sampling technique, the replica exchange (REX) method, near-native structures can be rapidly moved toward the native basin. The REX method provides both enhanced sampling and automatic selection of the most native-like (lowest energy) structures. An optimal protocol based on our studies first generates an ensemble of initial structures that maximally satisfy the available experimental data with conventional NMR software using a simplified force field and then refines these structures with implicit solvent using the REX method. We systematically examine the reliability and efficacy of this protocol using four proteins of various sizes ranging from the 56-residue B1 domain of Streptococcal protein G to the 370-residue Maltose-binding protein. Significant improvement in the structures was observed in all cases when refinement was based on low-redundancy restraint data. The proposed protocol is anticipated to be particularly useful in early stages of NMR structure determination where a reliable estimate of the native fold from limited data can significantly expedite the overall process. This refinement procedure is also expected to be useful when redundant experimental data are not readily available, such as for large multidomain biomolecules and in solid-state NMR structure determination.     

The short-lived signaling state of the photoactive yellow protein photoreceptor revealed by combined structural probes

The signaling state of the photoactive yellow protein (PYP) photoreceptor is transiently developed via isomerization of its blue-light-absorbing chromophore. The associated structural rearrangements have large amplitude but, due to its transient nature and chemical exchange reactions that complicate NMR detection, its accurate three-dimensional structure in solution has been elusive. Here we report on direct structural observation of the transient signaling state by combining double electron electron resonance spectroscopy (DEER), NMR, and time-resolved pump-probe X-ray solution scattering (TR-SAXS/WAXS). Measurement of distance distributions for doubly spin-labeled photoreceptor constructs using DEER spectroscopy suggests that the signaling state is well ordered and shows that interspin-label distances change reversibly up to 19 ? upon illumination. The SAXS/WAXS difference signal for the signaling state relative to the ground state indicates the transient formation of an ordered and rearranged conformation, which has an increased radius of gyration, an increased maximum dimension, and a reduced excluded volume. Dynamical annealing calculations using the DEER derived long-range distance restraints in combination with short-range distance information from (1)H-(15)N HSQC perturbation spectroscopy give strong indication for a rearrangement that places part of the N-terminal domain in contact with the exposed chromophore binding cleft while the terminal residues extend away from the core. Time-resolved global structural information from pump-probe TR-SAXS/WAXS data supports this conformation and allows subsequent structural refinement that includes the combined energy terms from DEER, NMR, and SAXS/WAXS together. The resulting ensemble simultaneously satisfies all restraints, and the inclusion of TR-SAXS/WAXS effectively reduces the uncertainty arising from the possible spin-label orientations. The observations are essentially compatible with reduced folding of the I(2)' state (also referred to as the 'pB' state) that is widely reported, but indicates it to be relatively ordered and rearranged. Furthermore, there is direct evidence for the repositioning of the N-terminal region in the I(2)' state, which is structurally modeled by dynamical annealing and refinement calculations.     

Solution structure of a peptide nucleic acid duplex from NMR data: features and limitations

This paper describes the results of a 1D and 2D NMR spectroscopy study of a palindromic 8-base pair PNA duplex GGCATGCC in H2O and H2O-D2O solutions. The (1)H NMR peaks have been assigned for most of the protons of the six central base pairs, as well as for several amide protons of the backbone. The resulting 36 interbase and base-backbone distance restraints were used together with Watson-Crick restraints to generate the PNA duplex structure in the course of 10 independent simulated annealing runs followed by restrained molecular dynamics (MD) simulations in explicit water. The resulting PNA structures correspond to a P-type helix with helical parameters close to those observed in the crystal structures of PNA. Based on the current limited number of restraints obtained from NMR spectra, alternative structures obtained by MD from starting PNA models based on DNA cannot be ruled out and are also discussed.     

Structure and folding of glucagon-like peptide-1-(7–36)-amide in aqueous trifluoroethanol studied by NMR spectroscopy

The conformational changes of free, monomeric glucagon-like peptide-1-(7–36)-amide (GLP-1) in aqueous solution with increasing concentrations of 2,2,2-trifluoroethanol (TFE) were monitored by NMR spectroscopy. It was found that GLP-1 gradually assumes a stable, single-stranded helical structure in water solution when the TFE concentration is increased from 0 to 35% (v/v). No further structural changes were observed at higher TFE concentrations. The structure of GLP-1 in 35% TFE was determined from 292 distance restraints and 44 angle restraints by distance geometry, simulating annealing and restrained energy minimization. The helical structure extends from T7 to K28, with a less well-defined region around G16 and a disordered six-residue N-terminal domain. The folding process of GLP-1 from random coil (in water) to helix (in 35% TFE) is initiated by the formation of the C-terminal segment of the helix that is extended gradually towards the N-terminus of the peptide with increasing concentration of TFE. The exchange rates of the slow exchanging amide protons indicate that the C-terminal part of the helix is more stable than the N-terminal part. Copyright © 2001 John Wiley & Sons, Ltd.     

Three‐dimensional structure of cyclic antibiotic teicoplanin aglycone using NMR distance and dihedral angle restraints in a DMSO solvation model

The three‐dimensional solution conformation of teicoplanin aglycone was determined using NMR spectroscopy. A combination of NOE and dihedral angle restraints in a DMSO solvation model was used to calculate an ensemble of structures having a root mean square deviation of 0.17 Å. The structures were generated using systematic searches of conformational space for optimal satisfaction of distance and dihedral angle restraints. Comparison of the NMR‐derived structure of teicoplanin aglycone with the X‐ray structure of a teicoplanin aglycone analog revealed a common backbone conformation with deviation of two aromatic side chain substituents. Experimentally determined backbone ¹³C chemical shifts showed good agreement with those computed at the density functional level of theory, providing a cross validation of the backbone conformation. The flexible portion of the molecule was consistent with the region that changes conformation to accommodate protein binding. The results showed that a hydrogen‐bonded DMSO molecule in combination with NMR‐derived restraints together enabled calculation of structures that satisfied experimental data. Copyright © 2015 John Wiley & Sons, Ltd.     

Docking of protein-protein complexes on the basis of highly ambiguous intermolecular distance restraints derived from 1H/15N chemical shift mapping and backbone 15N-1H residual dipolar couplings using conjoined rigid body/torsion angle dynamics

A simple and reliable method for docking protein-protein complexes using (1)H(N)/(15)N chemical shift mapping and backbone (15)N-(1)H residual dipolar couplings is presented and illustrated with three complexes (EIN-HPr, IIA(Glc)-HPr, and IIA(Mtl)-HPr) of known structure. The (1)H(N)/(15)N chemical shift mapping data are transformed into a set of highly ambiguous, intermolecular distance restraints (comprising between 400 and 3000 individual distances) with translational and some degree of orientational information content, while the dipolar couplings provide information on relative protein-protein orientation. The optimization protocol employs conjoined rigid body/torsion angle dynamics in simulated annealing calculations. The target function also comprises three nonbonded interactions terms: a van der Waals repulsion term to prevent atomic overlap, a radius of gyration term (E(rgyr)) to avoid expansion at the protein-protein interface, and a torsion angle database potential of mean force to bias interfacial side chain conformations toward physically allowed rotamers. For the EIN-HPr and IIA(Glc)-HPr complexes, all structures satisfying the experimental restraints (i.e., both the ambiguous intermolecular distance restraints and the dipolar couplings) converge to a single cluster with mean backbone coordinate accuracies of 0.7-1.5 A. For the IIA(Mtl)-HPr complex, twofold degeneracy remains, and the structures cluster into two distinct solutions differing by a 180 degrees rotation about the z axis of the alignment tensor. The correct and incorrect solutions which have mean backbone coordinate accuracies of approximately 0.5 and approximately 10.5 A, respectively, can readily be distinguished using a variety of criteria: (a) examination of the overall (1)H(N)/(15)N chemical shift perturbation map (because the incorrect cluster predicts the presence of residues at the interface that experience only minimal chemical shift perturbations; this information is readily incorporated into the calculations in the form of ambiguous intermolecular repulsion restraints); (b) back-calculation of dipolar couplings on the basis of molecular shape; or (c) the E(rgyr) distribution which, because of its global nature, directly reflects the interfacial packing quality. This methodology should be particularly useful for high throughput, NMR-based, structural proteomics.     

Completely automated, highly error-tolerant macromolecular structure determination from multidimensional nuclear overhauser enhancement spectra and chemical shift assignments

The major rate-limiting step in high-throughput NMR protein structure determination involves the calculation of a reliable initial fold, the elimination of incorrect nuclear Overhauser enhancement (NOE) assignments, and the resolution of NOE assignment ambiguities. We present a robust approach to automatically calculate structures with a backbone coordinate accuracy of 1.0-1.5 A from datasets in which as much as 80% of the long-range NOE information (i.e., between residues separated by more than five positions in the sequence) is incorrect. The current algorithm differs from previously published methods in that it has been expressly designed to ensure that the results from successive cycles are not biased by the global fold of structures generated in preceding cycles. Consequently, the method is highly error tolerant and is not easily funnelled down an incorrect path in either three-dimensional structure or NOE assignment space. The algorithm incorporates three main features: a linear energy function representation of the NOE restraints to allow maximization of the number of simultaneously satisfied restraints during the course of simulated annealing; a method for handling the presence of multiple possible assignments for each NOE cross-peak which avoids local minima by treating each possible assignment as if it were an independent restraint; and a probabilistic method to permit both inactivation and reactivation of all NOE restraints on the fly during the course of simulated annealing. NOE restraints are never removed permanently, thereby significantly reducing the likelihood of becoming trapped in a false minimum of NOE assignment space. The effectiveness of the algorithm is demonstrated using completely automatically peak-picked experimental NOE data from two proteins: interleukin-4 (136 residues) and cyanovirin-N (101 residues). The limits of the method are explored using simulated data on the 56-residue B1 domain of Streptococcal protein G.     

NMR Solution Structure of the Duplex Formed by Self‐Pairing of α‐L‐Arabinopyranosyl‐(4′2′)‐(CGAATTCG)

The solution structure of the duplex formed by α‐L ‐arabinopyranosyl‐(4′→2′)‐(CGAATTCG) was studied by NMR. The resonances of all H‐, P‐ and most C‐atoms could be assigned. Dihedral angles and distance estimates derived from coupling constants and NOESY spectra were used as restraints in a simulated annealing calculation, which generated a well‐defined bundle of structures for the six innermost nucleotide pairs. The essential features of the resulting structures are an antiparallel, Watson Crick‐paired duplex with a strong backbone inclination of ca. −50° and, therefore, predominant interstrand base stacking. The very similar inclination and rise parameters of arabinopyranosyl‐(4′→2′)‐oligonucleotides and p‐RNA explain why these two pentapyranosyl isomers are able to cross‐pair.     

Automated protein structure determination from NMR spectra

Fully automated structure determination of proteins in solution (FLYA) yields, without human intervention, three-dimensional protein structures starting from a set of multidimensional NMR spectra. Integrating existing and new software, automated peak picking over all spectra is followed by peak list filtering, the generation of an ensemble of initial chemical shift assignments, the determination of consensus chemical shift assignments for all (1)H, (13)C, and (15)N nuclei, the assignment of NOESY cross-peaks, the generation of distance restraints, and the calculation of the three-dimensional structure by torsion angle dynamics. The resulting, preliminary structure serves as additional input to the second stage of the procedure, in which a new ensemble of chemical shift assignments and a refined structure are calculated. The three-dimensional structures of three 12-16 kDa proteins computed with the FLYA algorithm coincided closely with the conventionally determined structures. Deviations were below 0.95 A for the backbone atom positions, excluding the flexible chain termini. 96-97% of all backbone and side-chain chemical shifts in the structured regions were assigned to the correct residues. The purely computational FLYA method is suitable for substituting all manual spectra analysis and thus overcomes a main efficiency limitation of the NMR method for protein structure determination.     

Protein structure prediction: combining de novo modeling with sparse experimental data

Routine structure prediction of new folds is still a challenging task for computational biology. The challenge is not only in the proper determination of overall fold but also in building models of acceptable resolution, useful for modeling the drug interactions and protein-protein complexes. In this work we propose and test a comprehensive approach to protein structure modeling supported by sparse, and relatively easy to obtain, experimental data. We focus on chemical shift-based restraints from NMR, although other sparse restraints could be easily included. In particular, we demonstrate that combining the typical NMR software with artificial intelligence-based prediction of secondary structure enhances significantly the accuracy of the restraints for molecular modeling. The computational procedure is based on the reduced representation approach implemented in the CABS modeling software, which proved to be a versatile tool for protein structure prediction during the CASP (CASP stands for critical assessment of techniques for protein structure prediction) experiments (see http://predictioncenter/CASP6/org). The method is successfully tested on a small set of representative globular proteins of different size and topology, including the two CASP6 targets, for which the required NMR data already exist. The method is implemented in a semi-automated pipeline applicable to a large scale structural annotation of genomic data. Here, we limit the computations to relatively small set. This enabled, without a loss of generality, a detailed discussion of various factors determining accuracy of the proposed approach to the protein structure prediction.     

NMR solution structure of dsDNA containing a bicyclic D-arabino-configured nucleotide fixed in an O4'-endo sugar conformation

[3.2.0]bcANA is a D-arabino-configured bicyclic nucleotide with a 2'-O,3'-C-methylene bridge. We here present the high-resolution NMR structure of a [3.2.0]bcANA modified dsDNA nonamer with one modified nucleotide incorporated. NOE restraints were obtained by analysis of NOESY cross peak intensities using a full relaxation matrix approach, and subsequently these restraints were incorporated into a simulated annealing scheme for the structure determination. In addition, the furanose ring puckers of the deoxyribose moieties were determined by analysis of COSY cross peaks. The modified duplex adopts a B-like geometry with Watson-Crick base pairing in all base pairs and all glycosidic angles in the anti range. The stacking arrangement of the nucleobases appears to be unperturbed relative to the normal B-like arrangement. The 2'-O,3'-C-methylene bridge of the modified nucleotide is located at the brim of the major groove where it fits well into the B-type duplex framework. The sugar pucker of the [3.2.0]bcANA nucleotide is O4'-endo and this sugar conformation causes a change in the delta backbone angle relative to the C2'-endo deoxyribose sugar pucker. This change is absorbed locally by slight changes in the epsilon and zeta angles of the modified nucleotide. Overall, the [3.2.0]bcANA modifications fits very well into a B-like duplex framework and only small and local perturbations are observed relative to the unmodified dsDNA of identical base sequence.