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.     

Water-filled MCM-41 characterized by double-quantum-filtered2H NMR spectral analysis

The dynamics of water molecules confined in adsorbed layers of siliceous MCM-41 with a pore diameter of 2.8 nm is investigated at 230 K by deuteron nuclear magnetic resonance (NMR) relaxation studies including line shapes of theT ₁ process and double quantum filtered (DQF) spectral analyses.²H DQF NMR is a particularly sensitive tool for the determination of the adsorbate dynamics resulting from residual quadrupolar interaction due to the local order. The amount of monolayer water is determined. The monolayer water is composed of two different water components characterized by water, with isotropic reorientational motions, exchanging with water displaying a solid-like spectrum with 4 kHz edge splitting. One may expect that the latter water is situated on surface sites in MCM-41. The restricted wobbling motion of the D-O bond is used to describe its dynamics which is one order of magnitude slower than the isotropic reorientational motion. The order parameter, the motional correlation time, and the exchange rate thus determined provide useful information on the structure and the adsorptive properties of the mesoporous system.     

Fitting of deuterium quadrupole echo spectra with multiple motional models

Dynamic information is generally extracted from deuterium quadrupole echo spectra by matching a spectrum calculated for a particular motional model to the experimental spectrum. In this work, a set of computer programs has been written to facilitate fitting of calculated spectra to experimental spectra that represent from one to five motional models. The fitting program requires pre-calculated libraries of spectra for the models of interest, and accomplishes the fitting either by a systematic method or by simulated annealing. The systematic method is convenient for fitting with one or two motional models, but the simulated annealing method is faster for two or more models, if the libraries are made up of hundreds of spectra. The parameter Q, with the standard deviation of the spectral points estimated as the standard deviation of the baseline noise, provides a stringent measure of goodness of fit. Acceptable fits of experimental data as judged by this criterion have not been found, even in the case of ring flip motion in phenylalanine-d(5) in which the fit may be judged acceptable by eye. An example of fitting with isotropic and methyl rotation motional models of alanine-d(3), which have distinct spectral patterns, shows that it is possible to obtain reasonably accurate estimates of the relative amounts of deuterium representing the different models, even from poorly fitted spectra.     

Detection of correlated dynamics on multiple timescales by measurement of the differential relaxation of zero- and double-quantum coherences involving sidechain methyl groups in proteins

Multiple effects may lead to significant differences between the relaxation rates of zero-quantum coherences (ZQC) and double-quantum coherences (DQC) generated between a pair of nuclei in solution. These include the interference between the anisotropic chemical shifts of the two nuclei participating in formation of the ZQC or DQC, the individual dipolar interactions of each of the two nuclei with the same proton, and the slow modulation of the isotropic chemical shifts of the two nuclei due to conformational exchange. Motional events that occur on a timescale much faster than the rotational correlation time (ps-ns) influence the first two effects, while the third results from processes that occur on a far slower timescale (mus-ms). An analysis of the differential relaxation of ZQC and DQC is thus informative about dynamics on the fast as well as the slow timescales. We present here an experiment that probes the differential relaxation of ZQC and DQC involving methyl groups in protein sidechains as an extension to our recently proposed experiments for the protein backbone. We have applied the methodology to (15)N, (13)C-labeled ubiquitin and used a detailed analysis of the measured relaxation rates using a simple single-axis diffusion model to probe the motional restriction of the C(next)H(next) bond vector where C(next) is the carbon that is directly bonded to a sidechain methyl carbon (C(methyl)). Comparison of the present results with the motional restriction of the C(next)C(methyl) bond (S(axis)(2)) reveals that the single-axis diffusion model, while valid in the fringes of the protein and for shorter chain amino acids, proves inadequate in the central protein core for long chain, asymmetrically branched amino acids where more complex motional models are necessary, as is the inclusion of the possibility of correlation between multiple motional modes. In addition, the present measurements report on the modulation of isotropic chemical shifts due to motion on the mus-ms timescale. Three Leu residues (8, 50, and 56) are found to display these effects. These residues lie in regions where chemical shift modulation had been detected previously both in the backbone and sidechain regions of ubiquitin.     

Anisotropic relaxation and motion of half-integer quadrupole nuclei studied by central transition nuclear magnetic resonance spectroscopy

An efficient theoretical formalism and advanced experimental methods are presented for studying the effects of anisotropic molecular motion and relaxation on solid-state central transition NMR spectra of half-integer quadrupole nuclei. The theoretical formalism is based on density operator algebra and involves the stochastic Liouville–von Neumann equation. In this approach the nuclear spin interactions are represented by the Hamiltonian while the motion is described by a discrete stochastic operator. The nuclear spin interactions fluctuate randomly in the presence of molecular motion. These fluctuations may stimulate the relaxation of the system and are represented by a discrete relaxation operator. This is derived from second-order perturbation theory and involves the spectral densities of the system. Although the relaxation operator is valid only for small time intervals it may be used recursively to obtain the density operator at any time. The spectral densities are allowed to be explicitly time dependent making the approach valid for all motional regimes. The formalism has been applied to simulate partially relaxed central transition ¹⁷O NMR spectra of representative model systems. The results have revealed that partially relaxed central transition lineshapes are defined not only by the nuclear spin interactions but also by anisotropic motion and relaxation. This has formed the basis for the development of central transition spin-echo and inversion-recovery NMR experiments for investigating molecular motion in solids. As an example we have acquired central transition spin-echo and inversion-recovery ¹⁷O NMR spectra of polycrystalline cristobalite (SiO₂) at temperatures both below and above the α–β phase transition. It is found that the oxygen atoms exhibit slow motion in α-cristobalite. This motion has no significant effects on the fully relaxed lineshapes but may be monitored by studying the partially relaxed spectra. The α–β phase transition is characterized by structural and motional changes involving a slight increase in the Si–O–Si bond angle and a substantial increase in the mobility of the oxygen atoms. The increase in the Si–O–Si angle is supported by the results of ¹⁷O and ²⁹Si NMR spectroscopy. The oxygen motion is shown to be orders of magnitude faster in β-cristobalite resulting in much faster relaxation and characteristic lineshapes. The measured oscillation frequencies are consistent with the rigid unit mode model. This shows that solid-state NMR and lattice dynamics simulations agree and may be used in combination to provide more detailed models of solid materials.     

Multiple-state ensemble structure determination from eNOE spectroscopy

The recent investigation of an ensemble-based structure calculation using mainly a large collection of exact nuclear Overhauser enhancements (eNOEs) revealed the presence of concerted motion within the protein GB3 (B. Vögeli, S. Kazemi, P. Güntert and R. Riek, Nat. Struct. Mol. Biol., in press). Here, we discuss the method used in this study in detail. Important steps include the NMR pulse sequence, the determination of the eNOEs corrected for spin diffusion, the conversion of eNOE rates into distances, the distance-restraint classification, the use of bundling restraints to generate a compact representation of the structure and the selection of the appropriate ensemble to represent the structure. It is further demonstrated that eNOEs can be obtained between most proton types in a macromolecule. These eNOEs are then used to calculate an ensemble-based structure using CYANA that is capable to reveal long-range concerted motion in the protein. The structure ensembles are cross-validated with jackknife tests applied to the eNOEs, RDCs, scalar couplings, cross-correlated relaxation rates, and with a high-resolution structure obtained independently from X-ray diffraction and refined with RDCs.     

Self-propelled particles with fluctuating speed and direction of motion in two dimensions

We study general aspects of active motion with fluctuations in the speed and the direction of motion in two dimensions. We consider the case in which fluctuations in the speed are not correlated to fluctuations in the direction of motion, and assume that both processes can be described by independent characteristic time scales. We show the occurrence of a complex transient that can exhibit a series of alternating regimes of motion, for two different angular dynamics which correspond to persistent and directed random walks. We also show additive corrections to the diffusion coefficient. The characteristic time scales are also exposed in the velocity autocorrelation, which is a sum of exponential forms.     

Rolling resistance moment of microspheres on surfaces

In the current work, for the first time, the existence of a rolling moment of resistance of an adhesion bond between a microsphere and flat surface subjected to external dynamic force has been experimentally demonstrated. The rotational motion of spherical particles deposited on a wafer is excited in the 0–3.5?MHz range using a piezoelectric transducer. The approach is based on (i) the observation that the contribution of the rotational (rocking) motion to the axial displacement of the particle are few orders of magnitude higher than those of the purely axial motion and (ii) the existence of a relationship between the rotational natural frequency of the adhesion bond and the work of adhesion. The natural frequency of the rotational (rocking) motion is extracted from the low frequency components of the transient response of the particle in the axial direction, which is measured by a laser interferometer. The existing theoretical adhesion models for rolling resistance moment are evaluated using the experimental results. Good agreement between the theoretical predictions and experimental values is found.     

On the impact of large amplitude pairing fluctuations on nuclear spectra

The influence of large amplitude pairing fluctuations is investigated in the framework of beyond mean field symmetry conserving configuration mixing calculations. In the numerical application the finite range density dependent Gogny force is used. We investigate the nucleus ⁵⁴Cr with particle number and angular momentum projected wave functions considering the axial quadrupole deformation and the pairing gap degree of freedom as generator coordinates. We find that the effects of the pairing fluctuations increase with the excitation energy and the angular momentum. The self-consistency in the determination of the basis states plays an important role.     

The role of (15)N CSA and CSA/dipole cross-correlation in (15)N relaxation in solid proteins

The influence of the (15)N CSA on (15)N longitudinal relaxation is investigated for an amide group in solid proteins in powder form under MAS. This contribution is determined to be typically 20-33% of the overall longitudinal relaxation rate, at 11.74 and 16.45 T, respectively. The improved treatment is used to analyze the internal dynamics in the protein Crh, in the frame of a motional model of diffusion in a cone, using the explicit average sum approach. Significant variations with respect to the determined dynamics parameters are observed when properly accounting for the contribution of (15)N CSA fluctuations. In general, the fit of experimental data including CSA led to the determination of diffusion times (tau(w)) which are longer than when considering only an (15)N-(1)H dipolar relaxation mechanism. CSA-Dipole cross-correlation is shown to play little or no role in protonated solids, in direct contrast to the liquid state case.     

On the anomalous large-scale flows in the Universe

Recent combined analyses of the CMB and galaxy cluster data reveal unexpectedly large and anisotropic peculiar velocity fields at large scales. We study cosmic models with included vorticity, acceleration and total angular momentum of the Universe in order to understand the phenomenon. The Zel’dovich model is used to mimic the low redshift evolution of the angular momentum. Solving coupled evolution equations of the second order for density contrast in corrected Ellis–Bruni covariant and gauge-invariant formalism one can properly normalize and evaluate integrated Sachs–Wolfe effect and peculiar velocity field. The theoretical results compared to the observations favor a much larger matter content of the Universe than that of the concordance model. Large-scale flows appear anisotropic with dominant components placed in the plane perpendicular to the axis of vorticity (rotation). The integrated Sachs–Wolfe term has a negative contribution to the CMB fluctuations for the negative cosmological constant and it can explain the observed small power of the CMB TT spectrum at large scales. The rate of the expansion of the Universe may be substantially affected by the angular momentum if its magnitude is large enough.     

A conformational study of N-acetyl glucosamine derivatives utilizing residual dipolar couplings

The conformational analyses of six non-rigid N-acetyl glucosamine (NAG) derivatives employing residual dipolar couplings (RDCs) and NOEs together with molecular dynamics (MD) simulations are presented. Due to internal dynamics we had to consider different conformer ratios existing in solution. The good quality of the correlation between theoretically and experimentally obtained RDCs show the correctness of the calculated conformers even if the ratios derived from the MD simulations do not exactly meet the experimental data. If possible, the results were compared to former published data and commented.     

The Nonreciprocal Errors in Fiber Optic Current Sensors

Nonreciprocal errors in fiber-optic current sensors, which are induced by environment fluctuations such as temperature and linear and angular vibrations, are specified. These errors in three current sensor configurations are evaluated and compared theoretically. The comparison indicates that the in-line sensor with strip waveguide modulator has the best resistance to the mentioned three environment fluctuations. Methods that may be used to suppress the nonreciprocal errors in different sensor configurations are suggested.     

Periodicity, planarity, residual dipolar coupling, and structures

The periodic behavior of residual dipolar couplings (RDCs) arising from nucleic acid and protein secondary structures is shown to be more complex and information-rich than previously believed. We have developed a theoretical framework which allows the bond vector orientation of nucleic acids and the peptide plane orientations of protein secondary structures to be extracted from their Dipolar waves. In this article, we focus on utilizing "Dipolar waves" of peptides to extract structure information, and describe in more detail the fundamental principles of the relationship between the periodicities in structure and RDCs, the practical procedure to extract peptide plane orientation information from RDC data, and assessment of errors using Monte-Carlo simulations. We demonstrate the utility of our method for two model alpha-helices, one kinked and one curved, and as well as an irregular beta-strand.     

Rosette motion and string scattering of 20 MeV electrons in MgO single crystals

Analytical estimates and computer simulations were undertaken to perceive the motion of negative particles through a lattice structure, the interaction being classical binary scattering. Three distinct modes of particle motion along atomic strings were found depending on the magnitude of the transverse energy and the angular momentum L of the particle with regard to the string axis. At small and large L increased scattering on the strings as compared with random penetration dominates. At medium L and negative transverse energy (bound state particles in the attractive potential) a rosette motion along the string occurs. In this case small impact parameters to the string atoms are avoided and thus an increased penetrability of the negative particles results. The influence of thermal lattice vibrations on these motions was studied.

Experimentally, the negative particle motion modes manifested themselves in the penetration profiles of 20 MeV electrons through an 8 μm MgO single crystal.     

Biased motion about the long molecular axis in ‘ordered’ smectic phases as studied by deuterium NMR relaxation

Spectral densities of motion were determined by deuteron NMR relaxation measurements in the ‘ordered’ smectic-B and -G phases of 4-n-pentyloxybenzylidene-d ₁-4′-heptylaniline and 4-n-pentyloxybenzylidene-4′-heptylaniline-2,3,5,6-d ₄ at two different Larmor frequencies. Different forms of motional behaviour are involved in these phases in comparison with those in the high temperature ‘disordered’ phases. Specifically, internal ring rotation and direction fluctuation are not effective in the ordered smectic phases. In addition, the fast rotation of the molecule about its long molecular axis is now strongly hindered to give a libration motion of angular amplitudes of about 100°. The third-rate model is again used to describe the molecular reorientation, taking the restricted γ motion into account. The effects of phase biaxiality on spin relaxation in the smectic-G phase are also discussed.     

Some effects of partial averaging of signal fluctuations in a random medium

The concept of partial averaging of signal fluctuations in a stretched turbulent medium is considered. Such uncontrollable averaging over time, frequency, or space arises from the mutual influence of signals scattered by irregularities of different scales (or different scattering layers) on fluctuations of the received signal intensity. The scintillation index of a partially averaged field is defined for the averaging action of a radiation source of finite angular dimensions. The proposed concept and obtained results may be useful in many applications as a development of the statistical theory of wave propagation in random media.Scientific-Research Institute of Radiophysics. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 6, pp. 754–762, June, 1994.     

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.     

空气/水界面水分子的取向和运动

对四种不同的实验构型下空气／水界面自由O-H键在3700cm~(-1)的和频振动光谱的分析表明,水分子在空气／水界面的取向运动只可能是在平衡位置附近有限角度之内的受限转动。界面水分子的自由O-H键取向距界面法线约33°,而取向分布或运动的宽度不超过15°。这一图像显著地不同于Wei等人(Phys. Rev. Lett.86,4799(2001))只通过单一的SFG实验构型所得出结论,即：空气／水界面的水分子在超快的振动弛豫时间内在很大的角度范围内运动。