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.     

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.     

Quasi-spin locking and simultaneous averaging of signal and baseline in dipolar solids

An alternating train of solid echoes and zero signals obtained by a 90° pulse sequence could be prolonged for a time of the order of T_1?. This quasi-spin locking effect enables one to average simultaneously the signal of the transverse magnetization and the baseline at a high data rate.     

Relation between effective couplings for asymptotically free models

For asymptotically free models with two independent couplings asymptotic expansions are constructed which express one effective coupling in terms of the other. The expansions involve powers (including fractional or irrational exponents) and logarithms. All orders of the-functions are taken into account. The expansions found are complete in the sense that they represent solutions (exact to any order) which generalize all the solutions obtained with the-functions approximated to second order. It is shown that higher orders are relevant since it is not possible in general to reparametrize the system such that the-functions become polynomials of the coupling parameters. The simplifications in case of supersymmetric models are discussed.     

Segmental mobility in short-chain grafted-PDMS by homo- and heteronuclear residual dipolar couplings

Different homo- ((1)H-(1)H) and heteronuclear ((1)H-(13)C) multiple quantum solid-state NMR experiments were applied to a series of short poly (dimethylsiloxane) (PDMS) chains grafted onto hydrophilic silica. The existence and clear separation of a strongly dipolar coupled region which is attributed to the silica-PDMS interface and a weakly dipolar coupled region attributed to the mobile chain portions outside the interface is evident in all experiments. In a sample series with different average chain lengths the residual dipolar couplings and with that the average order parameters are constant for the interface part and correlate for the mobile part linearly with the average chain length. Temperature dependent studies using (1)H double quantum experiments indicate the different stages of immobilization of the polymer chains. Solid-state NMR techniques therefore can give detailed information about the microscopic structure of this material and especially the effect of chain anchoring. It is also demonstrated that sample rotation influences the mobility of the mobile component and therefore the analysis of such materials should always be done under static conditions.     

2-D homonuclear correlation and separated local field experiments for solids with strong homonuclear dipolar couplings

An experiment for acquiring two-dimensional homonuclear correlation spectra of nuclei in solids in the presence of strong homonuclear dipolar couplings is described. The experiment utilizes a multiple-pulse homonuclear decoupling sequence with an effective precession axis parallel to the rotating frame z-axis during the evolution and detection periods. A multiple-pulse sequence that suppresses chemical shift and heteronuclear dipolar coupling evolution and scales the static homonuclear dipolar coupling is proposed for the mixing period. The evolution during the mixing period is analogous to the dynamics of the mixing period in solution-state TOCSY experiments, and can be interpreted as the oscillatory exchange of longitudinal magnetization between coupled spins. For nuclides with large gyromagnetic ratios, the static homonuclear dipolar interaction will be substantially larger than the mechanisms used to develop internuclear correlations in solution state 2-D experiments, which should make it possible to establish correlations over much longer distances and with significantly shorter mixing times. Extensions to separated local field experiments are discussed.     

Entropy of averaging for compressible two-pressure two-phase flow models

We propose here a new closure for compressible two-pressure two-phase flow models, which satisfies conservation requirements, boundary conditions at the edges of the mixing zone, hyperbolic stability (real eigenvalues for the characteristic version of the equations of motion) and an entropy inequality. Except for the latter, these properties are direct consequences of the proposed closures. The entropy, which is the main focus of this Letter, inequality (as opposed to entropy conservation for microphysically adiabatic processes) implies positivity for the entropy of averaging.     

Asymptotic behaviour and reduction of couplings for models including nonrenormalizable interactions

We study equivalence relations among parametrizations of models including nonrenormalizable polynomial interactions. The method of reduction of couplings allows for a classification of the parameter associated to the nonrenormalizable perturbations and stability considerations. The relation to effective models is briefly discussed.     

Anomalous specific heat of dipolar spin glasses and ferroelectrics

We show that for a random Ising model with 1/R³ interactions, the probability distribution of molecular field p(H) goes to zero as H tends to zero. We suggest that p(H) ～ H^{$\text{1}\text{2}$} for small H. Monte Carlo calculations of p(H) for the model are performed with results consistent with this suggestion. These results are used to explain the anomalous T^{$\text{3}\text{2}$} specific heat observed in alkali halides containing off-center ions, and in ferroelectrics.     

Nonuniform sampling and maximum entropy reconstruction applied to the accurate measurement of residual dipolar couplings

Residual dipolar couplings (RDC) provide important global restraints for accurate structure determination by NMR. We show that nonuniform sampling in combination with maximum entropy reconstruction (MaxEnt) is a promising strategy for accelerating and potentially enhancing the acquisition of RDC spectra. Using MaxEnt-processed spectra of nonuniformly sampled data sets that are reduced up to one fifth relative to uniform sampling, accurate 13C'-13Calpha RDCs can be obtained that agree with an RMS of 0.67 Hz with those derived from uniformly sampled, Fourier transformed spectra. While confirming that frequency errors in MaxEnt spectra are very slight, an unexpected class of systematic errors was found to occur in the 6th significant figure of 13C' chemical shifts of doublets obtained by MaxEnt reconstruction. We show that this error stems from slight line shape perturbations and predict it should be encountered in other nonlinear spectral estimation algorithms. In the case of MaxEnt reconstruction, the error can easily be rendered systematic by straightforward optimization of MaxEnt reconstruction parameters and self-cancels in obtaining RDCs from nonuniformly sampled, MaxEnt reconstructed spectra.     

Goldstone fermion couplings and supersymmetry breaking in superstring models

We re-examine supersymmetry breaking in the observable sectors of superstring-inspired supergravity models by computing Goldstone fermion couplings at the one-loop level. We find that a single global U (1) phase invariance is sufficient to forbid masses for gauge non-singlet chiral scalar bosons, and that Heisenberg symmetry is not necessary.     

Determining the relative sign and size of scalar and residual dipolar couplings in homonuclear two-spin systems

Based on the sign and amplitude of TOCSY transfer functions, it is possible to determine the relative sign and size of scalar and residual dipolar couplings in homonuclear spin systems consisting of two spins 1/2. The efficiency of different mixing sequences and different transfer functions is examined both theoretically and experimentally.     

EPR spectra of the double triangular polyoxovanadates with exchange and electron transfer effects: Symmetry breaking and effective motional averaging

The interplay of isotropic exchange, antisymmetric (AS) exchange, and electron delocalization has been theoretically investigated for a system comprising two triangles, one with three localized d¹ spins, which gives rise to spin frustration effects, and the other with one d¹ center delocalized on the three sites. In the localized limit the AS exchange is partially reduced by the low symmetry components of an isotropic exchange (inter-triangle interaction) and splits the spin triplets only in the second order, contrary to what is found for a single triangular system where splitting of the spin doublet levels occurs in the first order. Zero-field splitting parameters depend on both AS exchange parameters and low symmetry components of the isotropic exchange. The EPR spectrum consists of intratriplet (Heisenberg type) and intertriplet (non-Heisenberg type) lines. AS exchange also induces singlet-triplet transitions. The EPR spectra of powder samples are generated for a domain of key parameters. Two different situations occur depending on the symmetry of the electronic states when the electron delocalization is taken into account. The orbital doublets of the localized system indicate a complete averaging of the exchange interactions, which results in effective enhancement of AS exchange. Unlike triplets, the orbital singlets are unaffected by a transfer process, developing only second-order AS exchange. Coexistence of localized and delocalized states is expected to be an intrinsic feature of exchange systems with partial delocalization. The relevance of these effects to the magnetic properties of exchange clusters is briefly discussed.     

Proton residual dipolar couplings by NMR magnetization exchange in cross-linked elastomers: determination and imaging.

Proton nuclear magnetic resonance (NMR) magnetization exchange is used to investigate residual dipolar couplings in a series of cross-linked poly(styrene-cobutadiene) elastomers. A new model for the dipolar unit is used for the evaluation of the signal decay in magnetization exchange experiments. It takes into account an extended residual dipolar coupling network along the polymer chain. It is shown that in the regime of short mixing times, information about the residual dipolar coupling between methine and methylene protons can be obtained which is not affected by other inter- and intramolecular dipolar couplings. The dynamic order parameter of methine-methylene protons is measured and correlated with cross-link density. This study certifies the quality of a filter for magnetization from residual dipolar couplings which exploit magnetization exchange. The filter can be used to generate contrast in NMR images of heterogeneous elastomers. The first proton NMR parameter image of a dynamic order parameter is presented for a phantom made from poly(styrene-cobutadiene) samples with different cross-link densities.     

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.     

Developments in quantum information processing by nuclear magnetic resonance: Use of quadrupolar and dipolar couplings

Use of dipolar and quadrupolar couplings for quantum information processing (QIP) by nuclear magnetic resonance (NMR) is described. In these cases, instead of the individual spins being qubits, the 2 ⁿ energy levels of the spin-system can be treated as an n-qubit system. It is demonstrated that QIP in such systems can be carried out using transition-selective pulses, in CH₃CN, ¹³CH₃CN, ⁷Li (I=3/2) and ¹³³Cs (I=7/2), oriented in liquid crystals yielding 2 and 3 qubit systems. Creation of pseudopure states, implementation of logic gates and arithmetic operations (half-adder and subtractor) have been carried out in these systems using transition-selective pulses.     

Efficiency of homonuclear Hartmann-Hahn and COSY-type mixing sequences in the presence of scalar and residual dipolar couplings

In the presence of scalar (J) and residual dipolar (D) couplings, the transfer efficiency of homonuclear Hartmann-Hahn and COSY-type mixing depends on the ratio D/J and on the mixing sequence. This dependence is analyzed theoretically and the results are confirmed experimentally. At least two different mixing sequences are required to yield good transfer efficiencies for all ratios D/J. In contrast to COSY-type experiments, homonuclear Hartmann-Hahn sequences can provide efficient transfer even if the sum of D and J is zero, i.e., if the coupling vanishes in the weak coupling limit.