Conformational study of cyclolinopeptide A. A distance geometry and molecular dynamics approach

The conformation of cyclolinopeptide A, c(Pro-Pro-Phe-Phe-Leu-Ile-Ile-Leu-Val), a naturally occurring peptide with remarkable cytoprotective activity, has been investigated by means of distance geometry calculations and molecular dynamics simulations. The starting points for all the calculations were an X-ray structure and other structures obtained from distance geometry calculations based on NMR data. Restrained and unrestrained molecular dynamics simulations are reported in vacuo and in CCl4. Structural and dynamic properties are investigated and compared with those experimentally determined. The conformation obtained from the MD simulations which best reproduces the NMR parameters is at the same time one of the most stable ones and is also fairly similar to the crystal structure. An explanation for the occurrence of multiple conformations in solution at room temperature is given.     

Dimensional oscillation. A fast variation of energy embedding gives good results with the AMBER potential energy function.

The structure of the AMBER potential energy surface of the cyclic tetrapeptide cyclotetrasarcosyl is analyzed as a function of the dimensionality of coordinate space. It is found that the number of local energy minima decreases as the dimensionality of the space increases until some limit at which point equipotential subspaces appear. The applicability of energy embedding methods to finding global energy minima in this type of energy-conformation space is explored. Dimensional oscillation, a computationally fast variant of energy embedding is introduced and found to sample conformation space widely and to do a good job of finding global and near-global energy minima.     

Three-dimensional structure of potato carboxypeptidase inhibitor in solution. A study using nuclear magnetic resonance, distance geometry, and restrained molecular dynamics

The solution conformation of potato carboxypeptidase inhibitor (CPI) has been investigated by 1H NMR spectroscopy. The spectrum is assigned in a sequential manner by using two-dimensional NMR techniques to identify through-bond and through-space (less than 5 A) connectivities. A set of 309 approximate interproton distance restraints is derived from the two-dimensional nuclear Overhauser enhancement spectra and used as the basis of a three-dimensional structure determination by a combination of metric matrix distance geometry and restrained molecular dynamics calculations. A total of 11 converged distance geometry structures were computed and refined by using restrained molecular dynamics. The average atomic root mean square (rms) difference between the final 11 structures and the mean structure obtained by averaging their coordinates is 1.4 +/- 0.3 A for residues 2-39 and 0.9 +/- 0.2 A for residues 5-37. The corresponding values for all atoms are 1.9 +/- 0.3 and 1.4 +/- 0.2 A, respectively. The larger values for residues 2-38 relative to those for residues 5-37 arise from the fact that the positions of the N- (residues 1-4) and C- (residues 38-39) terminal tails are rather poorly determined, whereas those of the core of the protein (residues 5-37) are well determined by the experimental interproton distance data. The computed structures are very close to the X-ray structure of CPI in its complex with carboxypeptidase, and the backbone atomic rms difference between the mean of the computed structures and the X-ray structure is only 1.2 A. Nevertheless, there are some real differences present which are evidenced by significant deviations between the experimental upper interproton distance limits and the corresponding interproton distances derived from the X-ray structure. These principally occur in two regions, residues 18-20 and residues 28-30, the latter comprising part of the region of secondary contacts between CPI and carboxypeptidase in the X-ray structure.     

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.     

A polynomial-time algorithm for de novo protein backbone structure determination from nuclear magnetic resonance data.

We describe an efficient algorithm for protein backbone structure determination from solution Nuclear Magnetic Resonance (NMR) data. A key feature of our algorithm is that it finds the conformation and orientation of secondary structure elements as well as the global fold in polynomial time. This is the first polynomial-time algorithm for de novo high-resolution biomacromolecular structure determination using experimentally recorded data from either NMR spectroscopy or X-ray crystallography. Previous algorithmic formulations of this problem focused on using local distance restraints from NMR (e.g., nuclear Overhauser effect [NOE] restraints) to determine protein structure. This approach has been shown to be NP-hard, essentially due to the local nature of the constraints. In practice, approaches such as molecular dynamics and simulated annealing, which lack both combinatorial precision and guarantees on running time and solution quality, are used routinely for structure determination. We show that residual dipolar coupling (RDC) data, which gives global restraints on the orientation of internuclear bond vectors, can be used in conjunction with very sparse NOE data to obtain a polynomial-time algorithm for structure determination. Furthermore, an implementation of our algorithm has been applied to six different real biological NMR data sets recorded for three proteins. Our algorithm is combinatorially precise, polynomialtime, and uses much less NMR data to produce results that are as good or better than previous approaches in terms of accuracy of the computed structure as well as running time.     

Lipid induced conformation of the tachykinin peptide Kassinin

Both the aqueous and lipid-induced structure of Kassinin, a dodecapeptide of amphibian origin, has been studied by two-dimensional proton nuclear magnetic resonance (2D 1H-NMR) spectroscopy and distance geometry calculations. Unambiguous NMR assignments of protons have been made with the aid of correlation spectroscopy (DQF-COSY and TOCSY) experiments and nuclear Overhauser effect spectroscopy (NOESY and ROESY) experiments. The distance constraints obtained from the NMR data have been utilized in a distance geometry algorithm to generate a family of structures, which have been refined using restrained energy minimization and dynamics. These data show that, while in water Kassinin prefers to be in an extended chain conformation, in the presence of perdeuterated dodecylphosphocholine (DPC) micelles, a membrane model system, helical conformation is induced in the central core and C-terminal region (K4-M12) of the peptide. N-terminus though less defined also displays some degree of order and a possible turn structure. The conformation adopted by Kassinin in the presence of DPC micelles is consistent with the structural motif typical of neurokinin-1 selective agonists and with that reported for Eledoisin in hydrophobic environment.     

蛋白质结构确定领域中的几种矩阵填充算法的对比评估

目的 目前,如何从核磁共振(nuclear magnetic resonance,NMR)光谱实验中准确地确定蛋白质的三维结构是生物物理学中的一个热门课题,因为蛋白质是生物体的重要组成成分,了解蛋白质的空间结构对研究其功能至关重要,然而由于实验数据的严重缺乏使其成为一个很大的挑战。方法 在本文中,通过恢复距离矩阵的矩阵填充(matrix completion,MC)算法来解决蛋白质结构确定问题。首先,初始距离矩阵模型被建立,由于实验数据的缺乏,此时的初始距离矩阵为不完整矩阵,随后通过MC算法恢复初始距离矩阵的缺失数据,从而获得整个蛋白质三维结构。为了进一步测试算法的性能,本文选取了4种不同拓扑结构的蛋白质和6种现有的MC算法进行了测试,探究了算法在不同的采样率以及不同程度噪声的情况下算法的恢复效果。结果 通过分析均方根偏差(root-mean-square deviation,RMSD)和计算时间这两个重要指标的平均值及标准差评估了算法的性能,结果显示当采样率和噪声因子控制在一定范围内时,RMSD值和标准差都能达到很小的值。另外本文更加具体地比较了不同算法的特点和优势,在精确采样情况下...     

Solution structures of proteins from NMR data and modeling: alternative folds for neutrophil peptide 5

The structure of neutrophil peptide 5 in solution has recently been reported (Pardi et al., 1988). The structure determination was accomplished by using a distance geometry algorithm and 107 interproton distance constraints obtained from 2D NMR data. In each of the eight independent solutions to the distance geometry equations, the overall fold of the polypeptide backbone was identical and the root mean square (rms) deviation between backbone atoms of the superimposed structures was small (approximately 2.4 A). In this paper we report additional NP-5 structures obtained by using a new structure generation algorithm: a Monte Carlo search in torsion angle space. These structures have a large rms backbone deviation from the distance geometry structures (approximately 5.0 A). The backbone topologies differ in significant respects from the distance geometry structures and from each other. Structures are found that are pseudo mirror images of part or all of the fold corresponding to that first obtained with the distance geometry procedure. For small proteins, the problem of distinguishing the correct structure among pseudo mirror images is likely to be greater than previously recognized. When a set of test distance constraints constructed from a novel Monte Carlo structure is used as input in the distance geometry algorithm, the fold of the resulting structure does not correspond to that of the target. The results also demonstrate that the previously accepted criteria (the magnitude of the rms deviation between multiple solutions of the distance geometry equations) for defining the accuracy and precision of a peptide structure generated from NMR data are inadequate. An energetic analysis of structures corresponding to the different folding topologies has been carried out. The molecular mechanics energies obtained by minimization and molecular dynamics refinement provide sufficient information to eliminate certain alternative structures. On the basis of a careful comparison of the different trial structures with the experimental data, it is concluded that the NP-5 peptide fold which was originally reported is most consistent with the data. An alternative fold corresponding to structures with low energies and small total distance violations is ruled out because for this fold predicted NOEs are not observed experimentally.     

Refined structure of melittin bound to perdeuterated dodecylphosphocholine micelles as studied by 2D-NMR and distance geometry calculation

In our previous paper we reported the conformation of melittin bound to perdeuterated dodecylphosphocholine micelles as studied by 1H NMR experiment and distance geometry calculation. No hydrogen bonds were taken into consideration explicitly in the calculation. However, mostly alpha-helical conformations were obtained as results of the calculation even with no explicitly assumed hydrogen bonds. In the present paper we refined the distance geometry calculation by incorporating hydrogen bonds suggested by the previous calculation. As a result, we obtained the conformation of melittin, which was consistent with both NMR data and the additional hydrogen bonding data. The alpha-helical rod in the refined conformation also has a kink at Thr-11 and Gly-12, but its bent angle is now a bit narrowly distributed in 135 degrees +/- 15 degrees. In the present study another distortion at Trp-19 and IIe-20 becomes conspicuous. The average root-mean-square displacement of atoms is now much smaller and is 1.5 A for all backbone atoms. In the present paper side chain conformations are also analyzed.     

Integrating NOE and RDC using sum-of-squares relaxation for protein structure determination

We revisit the problem of protein structure determination from geometrical restraints from NMR, using convex optimization. It is well-known that the NP-hard distance geometry problem of determining atomic positions from pairwise distance restraints can be relaxed into a convex semidefinite program (SDP). However, often the NOE distance restraints are too imprecise and sparse for accurate structure determination. Residual dipolar coupling (RDC) measurements provide additional geometric information on the angles between atom-pair directions and axes of the principal-axis-frame. The optimization problem involving RDC is highly non-convex and requires a good initialization even within the simulated annealing framework. In this paper, we model the protein backbone as an articulated structure composed of rigid units. Determining the rotation of each rigid unit gives the full protein structure. We propose solving the non-convex optimization problems using the sum-of-squares (SOS) hierarchy, a hierarchy of convex relaxations with increasing complexity and approximation power. Unlike classical global optimization approaches, SOS optimization returns a certificate of optimality if the global optimum is found. Based on the SOS method, we proposed two algorithms—RDC-SOS and RDC–NOE-SOS, that have polynomial time complexity in the number of amino-acid residues and run efficiently on a standard desktop. In many instances, the proposed methods exactly recover the solution to the original non-convex optimization problem. To the best of our knowledge this is the first time SOS relaxation is introduced to solve non-convex optimization problems in structural biology. We further introduce a statistical tool, the Cramér–Rao bound (CRB), to provide an information theoretic bound on the highest resolution one can hope to achieve when determining protein structure from noisy measurements using any unbiased estimator. Our simulation results show that when the RDC measurements are corrupted by Gaussian noise of realistic variance, both SOS based algorithms attain the CRB. We successfully apply our method in a divide-and-conquer fashion to determine the structure of ubiquitin from experimental NOE and RDC measurements obtained in two alignment media, achieving more accurate and faster reconstructions compared to the current state of the art.     

Solution structures of human transforming growth factor alpha derived from 1H NMR data

The 600-MHz 1H NMR spectrum of the des-Val-Val mutant of human transforming growth factor alpha (TGF-alpha) was reassigned at pH = 6.3. The conformation space of des-Val-Val TGF-alpha was explored by distance geometry embedding followed by restrained molecular dynamics refinement using NOE distance constraints and some torsion angle constraints derived from J-couplings. Over 80 long-range NOE constraints were found by completely assigning all resolved cross-peaks in the NOESY spectra. Low NOE constraint violations were observed in structures obtained with the following three different refinement procedures: interactive annealing in DSPACE, AMBER 3.0 restrained molecular dynamics, and dynamic simulated annealing in XPLOR. The segment from Phe15 to Asp47 was found to be conformationally well-defined. Back-calculations of NOESY spectra were used to evaluate the quality of the structures. Our calculated structures resemble the ribbon diagram presentations that were recently reported by other groups. Several side-chain conformations appear to be well-defined as does the relative orientation of the C loop to the N-terminal half of the protein.     

Conformational analysis of human calcitonin in solution.

The solution conformation of human calcitonin in a mixture of 60% water and 40% trifluoroethanol has been determined by the combined use of 1H NMR spectroscopy and distance geometry calculations with a distributed computing technique. 1H NMR spectroscopy provided 195 distance constraints and 13 hydrogen bond constraints. The 20 best converged structures exhibit atomic rmsd of 0.43 A for the backbone atoms from the averaged coordinate position in the region of Asn3-Phe22. The conformation is characterized by a nearly amphiphilic alpha-helix domain that extends from Leu4 in the cyclic region to His20. There are no significant differences observed among the overall structures of a series of calcitonins obtained from ultimobranchial bodies, including those that possess 20- to 50-fold greater activity. Three aromatic amino acid residues, Tyr12, Phe16 and Phe19, form a hydrophobic surface of human calcitonin. Bulky side chains on the surface could interfere with the ligand-receptor interaction thereby causing its low activity, relative to those of other species.     

Protein Folding: A Few Random Thoughts

Abstract

Both the aqueous and lipid-induced structure of Kassinin, a dodecapeptide of amphibian origin, has been studied by two-dimensional proton nuclear magnetic resonance (2D ¹H-NMR) spectroscopy and distance geometry calculations. Unambiguous NMR assignments of protons have been made with the aid of correlation spectroscopy (DQF-COSY and TOCSY) experiments and nuclear Overhauser effect spectroscopy (NOESY and ROESY) experiments. The distance constraints obtained from the NMR data have been utilized in a distance geometry algorithm to generate a family of structures, which have been refined using restrained energy minimization and dynamics. These data show that, while in water Kassinin prefers to be in an extended chain conformation, in the presence of perdeuterated dodecylphosphocholine (DPC) micelles, a membrane model system, helical conformation is induced in the central core and C-terminal region (K4-M12) of the peptide. N-terminus though less defined also displays some degree of order and a possible turn structure. The conformation adopted by Kassinin in the presence of DPC micelles is consistent with the structural motif typical of neurokinin-1 selective agonists and with that reported for Eledoisin in hydrophobic environment.     

A distance geometry program for determining the structures of small proteins and other macromolecules from nuclear magnetic resonance measurements of intramolecular1H−1H proximities in solution

DISGEO is a new implementation of a distance geometry algorithm which has been specialized for the calculation of macromolecular conformation from distance measurements obtained by two-dimensional nuclear Overhauser enhancement spectroscopy. The improvements include (1) a decomposition of the complete embedding process into two successive, more tractable calculations by the use of “substructures”, (2) a compact data structure for storing incomplete distance information on a structure, (3) a more efficient shortest-path algorithm for computing the triangle inequality limits on all distances from this information, (4) a new algorithm for selecting random metric spaces from within these limits, (5) the use of chirality constraints to obtain good covalent geometry without the use ofad hoc weights or excessive optimization. The utility of the resultant program with nuclear magnetic resonance data is demonstrated by embedding complete spatial structures for the protein basic pancreatic trypsin inhibitor vs all 508 intramolecular, interresidue proton-proton contacts shorter than 4.0 Å that were present in its crystal structure. The crystal structure could be reproduced from this data set to within 1.3 Å minimum root mean square coordinate difference between the backbone atoms. We conclude that the information potentially available from nuclear magnetic resonance experiments in solution is sufficient to define the spatial structure of small proteins.     

Solution conformation of endothelin determined by means of 1H-NMR spectroscopy and distance geometry calculations

The structure of endothelin-1 (ET-1), an endothelial cell-derived peptide with vasoconstricting activity, was determined in an aqueous solution by means of a combination of NMR and distance geometry calculations. The resulting structure is characterized by an alpha-helical conformation in the sequence region, Lys9-Cys15. Furthermore, an extended structure and a turn structure exist in the Cys1-Ser4 and Ser5-Asp8 regions respectively, and no preferred conformation was found for the C-terminal part of the peptide which was not uniquely constrained by the NMR data. These structural elements, the alpha-helical structure in the sequence portion, Cys-X-X-X-Cys, and the extended structure in Cys-X-Cys, are homologous to those found commonly in several neurotoxic peptides.     

Solution structure of endothelin-3 determined using NMR spectroscopy.

The aqueous solution structure of the 21-residue vasoactive peptide hormone endothelin-3 has been determined using high-resolution NMR spectroscopy. A total of 177 proton-proton distance measurements and 5 chi 1 dihedral angle constraints derived from NMR spectra were used to calculate the structure using a combination of distance geometry and dynamical simulated annealing calculations. The calculations reveal a highly ordered, compact conformation in which a helical region extending from K9 to C15 lies in close apposition with the C-terminal hexapeptide; this interaction seems to be largely driven by hydrophobic interactions. Structure-activity studies are interpreted in terms of the conformational features of the calculated endothelin-3 structure.     

Protein structures in solution by nuclear magnetic resonance and distance geometry. The polypeptide fold of the basic pancreatic trypsin inhibitor determined using two different algorithms, DISGEO and DISMAN

A set of conformational restraints derived from nuclear magnetic resonance (n.m.r.) measurements on solutions of the basic pancreatic trypsin inhibitor (BPTI) was used as input for distance geometry calculations with the programs DISGEO and DISMAN. Five structures obtained with each of these algorithms were systematically compared among themselves and with the crystal structure of BPTI. It is clear that the protein architecture observed in single crystals of BPTI is largely preserved in aqueous solution, with local structural differences mainly confined to the protein surface. The results confirm that protein conformations determined in solution by combined use of n.m.r. and distance geometry are a consequence of the experimental data and do not depend significantly on the algorithm used for the structure determination. The data obtained further provide an illustration that long intramolecular distances in proteins, which are comparable with the radius of gyration, are defined with high precision by relatively imprecise nuclear Overhauser enhancement measurements of a large number of much shorter distances.     

Solving a Generalized Distance Geometry Problem for Protein Structure Determination

We propose a new approach to the problem of determining an ensemble of protein structures with a set of interatomic distance bounds in NMR protein modeling. Similarly to X-ray crystallography, we assume that the protein has an equilibrium structure and the atoms fluctuate around their equilibrium positions. Then, the problem can be formulated as a generalized distance geometry problem, to find the equilibrium positions and maximal possible fluctuation radii for the atoms in the protein, subject to the condition that the fluctuations should be within the given distance bounds. We describe the scientific background of the work, the motivation of the new approach and the formulation of the problem. We develop a geometric buildup algorithm for an approximate solution to the problem and present some preliminary test results as a first step concept proofing. We also discuss related theoretical and computational issues and potential impacts of this work in NMR protein modeling.     

Distance geometry and related methods for protein structure determination from NMR data

Computational tools have been developed in the last few years, to allow a direct determination of protein structures from NMR data. Numerical calculations with simulated and experimental NMR constraints for distances and torsional angles show that data sets available with present NMR techniques carry enough information to determine reliably the global fold of a small protein. The maximum size of a protein for which the direct method can be applied is not limited by the computational tools but rather by the resolution of the two-dimensional spectra. A general estimate of the maximum size would be a molecular weight of about 10,000 (Markley et al. 1984), but parts of larger proteins might be accessible with the method. Effort for improvement of the NMR structures should be concentrated more on the local conformation rather than the global features. The r.m.s. D values for variations of the polypeptide backbone fold are on the order of 1.5-2 A for several of the studied proteins, indicating that the global structure is well determined by the present NMR data and their interpretation. The local structures are sometimes rather poor, with standard deviations for the backbone torsion angles of about 50 degrees. Possible improvements would be stereospecific resonance assignments of individual methylene protons and individual assignments of the methyl groups of the branched side-chains. Accurate estimates of the short-range NOE distance constraints by calibrating the distance constraints, including segmental flexibility effects, and combined use of distance geometry, energy minimization and molecular dynamics calculations, are further tools for improving the structures.     

1H nuclear magnetic resonance determination of the membrane-bound conformation of senktide,a highly selective neurokinin B agonist

Summary Senktide is a highly specific and potent analog of neurokinin B, the natural ligand of the tachykinin receptor NK-3. The membrane-bound conformation of senktide, interacting with negatively charged membrane vesicles composed of perdeuterated phosphatidylcholine and phosphatidylglycerol (70:30), has been investigated using two-dimensional transferred nuclear Overhauser effect spectroscopy (TRNOESY). The occurrence of an N-methylated phenylalanine in the peptide's sequence induces a cis-trans-isomerisation of the corresponding peptide bond which is slow on the chemical-shift scale. NMR data indicate a much stronger membrane affinity of the trans isomer, allowing the determination of a highly resolved membrane-bound conformation using distance geometry and energy minimization. The membrane-bound backbone conformation of several residues is found to be close to a left-handed helix, certainly due to the presence of nonnatural residues (succinylated N-terminal, N-methyl-phenylalanine) as well as a glycine. The results are discussed in the context of a possible biological relevance of the membrane-bound conformation, in terms of the affinity and specificity of this neuropeptide.