Determining a helical protein structure using peptide pixels

The residual dipolar coupling-periodicity planarity correlation makes it possible to determine peptide plane orientations in regular periodic protein secondary structure elements. Each peptide plane orientation represents a "pixel" of protein structure, and is expressed in terms of three angles referred to as tilt, phase, and pitch angles. In this report, we present the novel "3P" (periodicity, planarity, and pixels) method that allows one to determine secondary and tertiary structure of alpha-helical proteins. We demonstrate the 3P method by determining the structure of domain 1 of the receptor-associated protein (RAP) to a backbone accuracy of 1.0 Angstrom using RDCs measured in a single alignment medium, together with a minimal number of NOE distance restraints, using a new Xplor-NIH module.     

Protein backbone dynamics from N-HN dipolar couplings in partially aligned systems: a comparison of motional models in the presence of structural noise

Residual dipolar couplings (RDCs) provide excellent probes for the exploration of dynamics in biomolecules on biologically relevant time-scales. Applying geometric motional models in combination with high-resolution structures to fit experimental RDCs allows the extraction of local dynamic amplitudes of peptide planes in proteins using only a limited number of data points. Here we compare the behaviour of three simple and intuitive dynamic modes: the Gaussian axial fluctuation model (1D-GAF), the two-site jump model, and a model supposing axially symmetric motion about a mean orientation. The requirement of a structural model makes this kind of methodology potentially very sensitive to structural imprecision. Numerical simulations of RDC dynamic averaging under different regimes show that the anisotropic motional models are more geometrically stringent than the axially symmetric model making it more difficult to alias structural noise as artificial dynamic amplitudes. Indeed, it appears that the model extracts accurate motional amplitudes even in the presence of significant structural error. We also show that a two-site jump model, also assuming the (alpha)C(i-1)-(alpha)C(i) as rotation axis, can only be distinguished from the previously developed GAF model beyond amplitude/jumps of around 40 degrees. The importance of appropriate estimation of the molecular alignment tensor for determination of local motional amplitudes is also illustrated here. We demonstrate a systematic scaling of extracted dynamic amplitudes if a static structure is assumed when determining the alignment tensor from dynamically averaged RDCs. As an example an artificial increase of 0.14 (0.85 compared to the expected 0.71) is observed in the extracted S2 if a pervasive 20 degrees GAF motion is present that is ignored in the tensor determination. Finally we apply a combined approach using the most appropriate motional model, to complete the analysis of dynamic motions from protein G.     

HACACO revisited: residual dipolar coupling measurements and resonance assignments in proteins

The revisited version of the HACACO experiment here presented, is more robust and straightforward to implement and continues to be, to a greater extent, a convenient tool for protein backbone resonance assignment. Additionally, it turns out to be a sensitive and accurate method to measure C(alpha)-H(alpha) residual dipolar couplings (RDCs). The performance of our new pulse scheme for measurement of RDCs was tested on two proteins with different secondary structures: one characterized by a high beta-sheet content, the second dominated by the presence of alpha-helices. In both examples the new method provided significantly more accurate data, compared to all previously published 3D techniques.     

Structural fitting of PISEMA spectra of aligned proteins

An algorithm for fitting protein structures to PISEMA spectra is described, and its application to helical proteins in aligned samples is demonstrated using both simulated and experimental results. The formulation of the algorithm in terms of rotation operators yields compact recursion relations that provide a fast and effective way of obtaining peptide plane orientations from chemical and torsion angle constraints. The algorithm in combination with experimental solid-state NMR data results in a method for determining the backbone structures of proteins, since it yields the orientation of a helix as a whole, including its tilt and twist angles, and describes kinks and curves with atomic resolution. Although the algorithm can be applied in an "assignment-free" manner to spectra of uniformly labeled proteins, the precision of the structural fitting is improved by the addition of assignment information, for example the identification of resonances by residue type from spectra of selectively labeled proteins.     

Solid-state NMR studies of proteins immobilized on inorganic surfaces

Solid state NMR is the primary tool for studying the quantitative, site-specific structure, orientation, and dynamics of biomineralization proteins under biologically relevant conditions. Two calcium phosphate proteins, statherin (43 amino acids) and leucine rich amelogenin protein (LRAP; 59 amino acids), have been studied in depth and have different dynamic properties and 2D- and 3D-structural features. These differences make it difficult to extract design principles used in nature for building materials with properties such as high strength, unusual morphologies, or uncommon phases. Consequently, design principles needed for developing synthetic materials controlled by proteins are not clear. Many biomineralization proteins are much larger than statherin and LRAP, necessitating the study of larger biomineralization proteins. More recent studies of the significantly larger full-length amelogenin (180 residues) represent a significant step forward to ultimately investigate the full diversity of biomineralization proteins. Interactions of amino acids, a silaffin derived peptide, and the model LK peptide with silica are also being studied, along with qualitative studies of the organic matrices interacting with calcium carbonate. Dipolar recoupling techniques have formed the core of the quantitative studies, yet the need for isolated spin pairs makes this approach costly and time intensive. The use of multi-dimensional techniques to study biomineralization proteins is becoming more common, methodology which, despite its challenges with these difficult-to-study proteins, will continue to drive future advancements in this area.     

Dipolar Waves as NMR maps of helices in proteins

Dipolar Waves describe the periodic variation in the magnitudes of dipolar couplings in the backbone of a protein as a function of residue number. They provide a direct link between experimental measurements of dipolar couplings in aligned samples and the periodicity inherent in regular secondary structure elements. It is possible to identify the residues in a helix and the type of helix, deviations from ideality, and to orient the helices relative to an external axis in completely aligned samples and relative to each other in a common frame in weakly aligned samples with Dipolar Waves. They provide a tool for accurately describing helices and a step towards high throughput structure determination of proteins.     

Magnetic structure determined by nuclear orientation

Conclusion In conclusion we suggest that nuclear orientation is a useful technique for determining nuclear spin structures. For a known hyperfine interaction atomic magnetic structures may also be deduced. Measurements on antiferromagnets and the rare earth magnet holmium demonstrate the method, although in the latter case the turn angle cannot be determined because of the limitation of L2 radiation. These experiments show that nuclear orientation can at least complement neutron diffraction and at best furnish information about magnetic structure when the latter technique is not applicable. We intend to study other rare earth magnets and more complicated antiferromagnetic structures.     

Improvement and analysis of computational methods for prediction of residual dipolar couplings

We describe a new, computationally efficient method for computing the molecular alignment tensor based on the molecular shape. The increase in speed is achieved by re-expressing the problem as one of numerical integration, rather than a simple uniform sampling (as in the PALES method), and by using a convex hull rather than a detailed representation of the surface of a molecule. This method is applicable to bicelles, PEG/hexanol, and other alignment media that can be modeled by steric restrictions introduced by a planar barrier. This method is used to further explore and compare various representations of protein shape by an equivalent ellipsoid. We also examine the accuracy of the alignment tensor and residual dipolar couplings (RDC) prediction using various ab initio methods. We separately quantify the inaccuracy in RDC prediction caused by the inaccuracy in the orientation and in the magnitude of the alignment tensor, concluding that orientation accuracy is much more important in accurate prediction of RDCs.     

15N chemical shift anisotropy in protein structure refinement and comparison with NH residual dipolar couplings

Recent methods of aligning proteins which were developed in order to measure residual dipolar couplings (RDCs) in solution can also be used for additional applications such as measuring the 15N CSA in the form of chemical shift differences, Deltadelta. A new XPLOR-NIH module has been developed and implemented for NMR structure refinement using the 15N Deltadelta data as restraints. The results of this refinement are shown using the protein Bax. This method should be amenable to any protein which can be studied by NMR. An analysis comparing the structural information provided by NH RDCs and the 15N Deltadelta is included.     

The role of secondary structure in protein structure selection

The presence of highly regular secondary structure motifs in protein structure is a fascinating area of study. The secondary structures play important roles in protein structure and protein folding. We investigate the folding properties of protein by introducing the effect of secondary structure elements. We observed the emergence of several structures with both large average energy gap and high designability. The dynamic study indicates that these structures are more foldable than those without the effect of secondary structures.     

Molecules in a bicircular strong laser field

Strong-field ionization of nonlinear planar triatomic molecules by a bicircular laser field is analyzed within the improved molecular strong-field approximation. Our calculations include additional interaction between the liberated electrons and atomic or ionic centers of the parent molecular ion. The used bicircular field consists of two counterrotating circularly polarized fields having angular frequencies \(r \omega\) and \(s \omega\), with integer r and s. In the case when the laser-field-polarization plane is parallel to the plane of the considered molecule (example of ozone molecule is analyzed), the corresponding photoelectron spectra are not rotationally symmetric. On the other hand, when these planes are mutually perpendicular, for the \((r\omega ,s\omega )=(\omega ,3\omega )\) bicircular field, the electron spectra satisfy the corresponding rotational symmetries. Analyzing the obtained spectra and the corresponding symmetries, one can extract information about molecular orientation and structure. This technique may also be useful for more complex polyatomic molecules.     

REDCAT: a residual dipolar coupling analysis tool

Recent advancements in the utilization of residual dipolar couplings (RDCs) as a means of structure validation and elucidation have demonstrated the need for, not only a more user friendly, but also a more powerful RDC analysis tool. In this paper, we introduce a software package named REsidual Dipolar Coupling Analysis Tool (REDCAT) designed to address the above issues. REDCAT is a user-friendly program with its graphical-user-interface developed in Tcl/Tk, which is highly portable. Furthermore, the computational engine behind this GUI is written in C/C++ and its computational performance is therefore excellent. The modular implementation of REDCAT's algorithms, with separation of the computational engine from the graphical engine allows for flexible and easy command line interaction. This feature can be utilized for the design of automated data analysis sessions. Furthermore, this software package is portable to Linux clusters for high throughput applications. In addition to basic utilities to solve for order tensors and back calculate couplings from a given order tensor and proposed structure, a number of improved algorithms have been incorporated. These include the proper sampling of the Null-space (when the system of linear equations is under-determined), more sophisticated filters for invalid order-tensor identification, error analysis for the identification of the problematic measurements and simulation of the effects of dynamic averaging processes.     

Piezoelectric surface excitation and detection of GHz-sound waves using planar structures: Hertzian- and H-slot resonators

We report on experiments with two new kinds of microwave resonators for piezoelectric surface excitation of GHz-sound waves. These resonators consist of planar metal structures simply made by photolithography and especially suitable for the higher frequency range where the usual reentrant cavities can be applied no more due to mechanical fabrication difficulties. Moreover, by choosing an appropriate resonator geometry, an electric excitation field with preferred orientation can be generated which allows to enhance or to supress wanted sound modes simply by turning the crystal relative to the excitation structure into an optimum orientation.Supported by Deutsche Forschungsgemeinschaft     

Residual dipolar couplings and some specific models for motional averaging

The measurement of residual dipolar couplings (RDCs) from partially oriented molecules is now widely used to provide restraints for NMR structure determination. Bond vibrations, random angular fluctuations around bond vectors and conformational exchange all influence the magnitude of the experimental RDCs. The effect that angular fluctuations have upon the magnitude of RDCs is quantitatively compared using three new models (elliptic, uni-dimensional, and equally populated two site jump) and three established models (static, isotropic motion in a cone and free diffusion about a fixed symmetry axis: Woessner's model) for motional averaging in the limit that the amplitude of motion beta < or = (max)15-20 degrees. The influence of the different motional models on the value of R(obs) determined from the distribution of RDCs is explored. The consequences of the different types of angular motion for the accurate determination of bond vector orientation, with respect to the alignment tensor, A, is investigated. The extent to which motion influences the magnitude of RDCs is compared to some non-dynamic factors affecting RDC size.     

Estimation of relative order tensors, and reconstruction of vectors in space using unassigned RDC data and its application

Advances in NMR instrumentation and pulse sequence design have resulted in easier acquisition of Residual Dipolar Coupling (RDC) data. However, computational and theoretical analysis of this type of data has continued to challenge the international community of investigators because of their complexity and rich information content. Contemporary use of RDC data has required a-priori assignment, which significantly increases the overall cost of structural analysis. This article introduces a novel algorithm that utilizes unassigned RDC data acquired from multiple alignment media (nD-RDC, n  3) for simultaneous extraction of the relative order tensor matrices and reconstruction of the interacting vectors in space.Estimation of the relative order tensors and reconstruction of the interacting vectors can be invaluable in a number of endeavors. An example application has been presented where the reconstructed vectors have been used to quantify the fitness of a template protein structure to the unknown protein structure. This work has other important direct applications such as verification of the novelty of an unknown protein and validation of the accuracy of an available protein structure model in drug design. More importantly, the presented work has the potential to bridge the gap between experimental and computational methods of structure determination.     

DNA and PNA as templates for building nanoassemblies via electrostatic complexation with gold nanoparticles

Organisation of nanoparticles on structurally well-defined templates is a first step towards creating nanomachines. In this respect, nucleic acids are ideal structural templates and a variety of secondary structures realizable from DNA/RNA––e.g., duplexes, hairpins, triplexes, cruciforms, tetraplexes can be exploited to engineer nanoparticle organization at will. We have used oligonucleotides and their analogues such as phosphorothioates and peptide nucleic acids to electrostatically encapsulate cationic-capped gold nanoparticles. This article describes synthesis and characterization of DNA/PNA-gold nanoparticle composites using TEM and UV-T_m techniques. These types of assemblies may have potential for creating nanowires and lithographic circuits.     

Solid state NMR analysis of the dipolar couplings within and between distant CF3-groups in a membrane-bound peptide

Dipolar couplings contain information on internuclear distances as well as orientational constraints. To characterize the structure of the antimicrobial peptide gramicidin S when bound to model membranes, two rigid 4-CF3-phenylglycine labels were attached to the cyclic backbone such that they reflect the behavior of the entire peptide. By solid state 19F NMR we measured the homonuclear dipolar couplings of the two trifluoromethyl-groups in oriented membrane samples. Using the CPMG experiment, both the strong couplings within each CF3-group as well as the weak coupling between the two CF3-groups could be detected. An intra-CF3-group dipolar coupling of 86 Hz and a weak inter-group coupling of 20 Hz were obtained by lineshape simulation of the complex dipolar spectrum. It is thus possible to explore the large distance range provided by 19F-labels and to resolve weak dipolar couplings even in the presence of strong intra-CF3 couplings. We applied this approach to distinguish and assign two epimers of the labeled gramicidin S peptide on the basis of their distinct 19F dipolar coupling patterns.     

The new method of topological charge determination of optical vortices in the interference field of the optical vortex interferometer

In this paper, the new method of determination of the topological charge of vortex points in the interference field obtained by three plane waves interference is presented. Such optical fields are used in the optical vortex interferometer (OVI) and the determination of vortex points’ topological charge allows of unique determination of the relative phase between interfering waves (phase unwrapping problem). The new method uses additional plane wave, which produce a characteristic fork-like fringe structure in the neighbourhood of vortex points. By analysing the orientation of these fork-like patterns one can read the sign of the topological charge of the given vortex point. The method is simple and can be used for OVI calibration performed before the measurements.     

Assessment of protein alignment using 1H-1H residual dipolar coupling measurements

A quick and accurate method is described for assessing protein alignment from residual dipolar coupling (RDC) measurements. In contrast to observing D(2)O resonance splitting, which reflects the orientational order of the alignment medium, the degree of alignment of a protein of interest can be estimated directly from (1)H-(1)H RDCs. In this study, RDCs between aromatic protons in unlabeled Cp-rubredoxin were measured from proton homonuclear J-resolved experiments with high sensitivity, and the alignment was assessed without the need of extensive resonance assignment. Since labeled proteins are not needed, this method provides an efficient way for screening alignment media. In situations where the protein structure is known, as in the case of Cp-rubredoxin, a full set of order tensor parameters can be determined, allowing further studies, such as those of ligand alignment relative to a target protein.