Exchange and dipolar spin-spin interaction and rotational diffusion in saturation transfer EPR spectroscopy

Saturation transfer EPR spectroscopy (STEPR) provides a means for investigating weak spin-spin interaction between spin-labelled molecules because the spectral intensity is proportional to the effective spin-lattice relaxation time,T ₁ ^eff. Rate equations for the spin population defferences yield equivalent results for the dependence ofT ₁ ^eff on the physical (or chemical) and Heisenberg spin exchange rates and show thatT ₁ ^eff depends on the extent of redistribution of saturation throughout the anisotropic spin label powder lineshape. This approach yields a particularly simple formulation for the dependence of the STEPR lineshape on slow rotational diffusion. The effects of spin exchange are readily distinguished from those of slow rotational diffusion because of the insensitivity of the STEPR lineshape in the former case. The characteristic dependence of the STEPR spectral intensity on spin concentration allows determination of the exchange rate and can be used for studying slow translational diffusion, e.g. of spin-labelled proteins. Dipolar relaxation induced by paramagnetic ions gives a linear dependence of the reciprocal spin label STEPR intensity on metal ion concentration. STEPR measurements with spin-labelled lipid molecules in gel phase membranes in the presence of Ni²⁺ ions yield reliable distance information and provide calibrations for use with other systems.     

Efficient and accurate determination of the overall rotational diffusion tensor of a molecule from (15)N relaxation data using computer program ROTDIF

We present a computer program ROTDIF for efficient determination of a complete rotational diffusion tensor of a molecule from NMR relaxation data. The derivation of the rotational diffusion tensor in the case of a fully anisotropic model is based on a six-dimensional search, which could be very time consuming, particularly if a grid search in the Euler angle space is involved. Here, we use an efficient Levenberg-Marquardt algorithm combined with Monte Carlo generation of initial guesses. The result is a dramatic, up to 50-fold improvement in the computational efficiency over the previous approaches. This method is demonstrated on a computer-generated and real protein systems. We also address the issue of sensitivity of the diffusion tensor determination from (15)N relaxation measurements to experimental errors in the relaxation rates and discuss possible artifacts from applying higher-symmetry tensor model and how to recognize them.     

Solid H2: Has the quadrupolar glass phase a well-defined transition?

We report measurements of the NMR lineshape, the second and fourth moments (M₂ and M₄), and of the longitudinal relaxation tine in H₂ single crystals. Although a sharp phase transition cannot be excluded, our results for ortho concentrations between 0.15 and 0.4 suggest rather a continuous freezing of rotational motion to a “glass state” as T decreases. In this regime; the NMR spectrum is found to be very nearly isotropic.     

Separation of anisotropy and exchange broadening using (15)N CSA-(15)N-(1)H dipole-dipole relaxation cross-correlation experiments

Based on the measurement of cross-correlation rates between (15)N CSA and (15)N-(1)H dipole-dipole relaxation we propose a procedure for separating exchange contributions to transverse relaxation rates (R(2) = 1/T(2)) from effects caused by anisotropic rotational diffusion of the protein molecule. This approach determines the influence of anisotropy and chemical exchange processes independently and therefore circumvents difficulties associated with the currently standard use of T(1)/T(2) ratios to determine the rotational diffusion tensor. We find from computer simulations that, in the presence of even small amounts of internal flexibility, fitting T(1)/T(2) ratios tends to underestimate the anisotropy of overall tumbling. An additional problem exists when the N-H bond vector directions are not distributed homogeneously over the surface of a unit sphere, such as in helix bundles or beta-sheets. Such a case was found in segment 4 of the gelation factor (ABP 120), an F-actin cross-linking protein, in which the diffusion tensor cannot be calculated from T(1)/T(2) ratios. The (15)N CSA tensor of the residues for this beta-sheet protein was found to vary even within secondary structure elements. The use of a common value for the whole protein molecule therefore might be an oversimplification. Using our approach it is immediately apparent that no exchange broadening exists for segment 4 although strongly reduced T(2) relaxation times for several residues could be mistaken as indications for exchange processes.     

Improvement of duty-cycle heating compensation in NMR spin relaxation experiments

To reliably measure NMR relaxation properties of macromolecules is a prerequisite for precise experiments that identify subtle variations in relaxation rates, as required for the determination of rotational diffusion anisotropy, CSA tensor determination, advanced motional modeling or entropy difference estimations. An underlying problem with current NMR relaxation measurement protocols is maintaining constant sample temperature throughout the execution of the relaxation series especially when rapid data acquisition is required. Here, it is proposed to use a combination of a heating compensation and a proton saturation sequence at the beginning of the NMR relaxation pulse scheme. This simple extension allows reproducible, robust and rapid acquisition of NMR spin relaxation data sets. The method is verified with (15)N spin relaxation measurements for human ubiquitin.     

High-field EPR studies on polymer film formation from colloidal dispersions

High-field EPR on nitroxide spin probes is applied to characterize the dynamics of small additive molecules and surfactants in polymer films obtained from colloidal dispersions. Due to the increased width of the spectra and the smaller influence of hyperfine-dependent relaxation on the spectral lineshape at W band (94 GHz) compared to X band (9.6 GHz), it is possible to measure subnanosecond rotational correlation times for the isotropic motion of the unpolar spin probe TEMPO in the free volume of poly(acrylate) films. Likewise, the anisotropies of the rotational diffusion tensors of a surfactant and a small ionic additive molecule in poly(fluoroacrylate) films can be determined with better confidence at W band. From these anisotropies it is concluded that the surfactant aggregates exhibit low molecular order, whereas the ionic additives are strongly attached to immobilized ionic clusters. High-field EPR lineshapes at W band are also found to be more sensitive to slow motions on a microsecond time scale than X-band EPR lineshapes. The design of a Fabry-Pérot resonator for measurements on polymer films is discussed and its sensitivity is demonstrated on a wet polymer film with a thickness of 160 μm.     

Determination of the rotational diffusion tensor of macromolecules in solution from nmr relaxation data with a combination of exact and approximate methods--application to the determination of interdomain orientation in multidomain proteins

In this paper we present a method for determining the rotational diffusion tensor from NMR relaxation data using a combination of approximate and exact methods. The approximate method, which is computationally less intensive, computes values of the principal components of the diffusion tensor and estimates the Euler angles, which relate the principal axis frame of the diffusion tensor to the molecular frame. The approximate values of the principal components are then used as starting points for an exact calculation by a downhill simplex search for the principal components of the tensor over a grid of the space of Euler angles relating the diffusion tensor frame to the molecular frame. The search space of Euler angles is restricted using the tensor orientations calculated using the approximate method. The utility of this approach is demonstrated using both simulated and experimental relaxation data. A quality factor that determines the extent of the agreement between the measured and predicted relaxation data is provided. This approach is then used to estimate the relative orientation of SH3 and SH2 domains in the SH(32) dual-domain construct of Abelson kinase complexed with a consolidated ligand.     

HYDRONMR: prediction of NMR relaxation of globular proteins from atomic-level structures and hydrodynamic calculations

The heteronuclear NMR relaxation of globular proteins depends on the anisotropic rotational diffusion tensor. Using our previous developments for prediction of hydrodynamic properties of arbitrarily shaped particles, by means of bead models, we have constructed a computational procedure to calculate the rotational diffusion tensor and other properties of proteins from their detailed, atomic-level structure. From the atomic coordinates file used to build the bead model, the orientation of the pertinent dipoles can be extracted and combined with the hydrodynamic information to predict, for each residue in the protein, the relaxation times. All of these developments have been implemented in a computer program, HYDRONMR, which will be of public domain.     

Lineshape analysis of the J = 3 ← 2 and J = 5 ← 4 rotational transitions of room temperature CO broadened by N2, O2, CO2 and noble gases

Collisional relaxation has been considered for millimeter lines of carbon monoxide at room temperature. Accurate measurements of carbon dioxide- and rare gases-broadened widths have been performed on the J = 3 ← 2 rotational line of ¹²CO by using a video-type spectrometer. Measurements of nitrogen-, oxygen-, and xenon-broadened widths of the J = 5 ← 4 rotational line of ¹³CO were also carried by using a frequency-modulated spectrometer. A lineshape study performed on all the investigated binary systems provide confirmation that Voigt profile is not a suitable model to analyse experimental lines in the millimeter-waves region. On one hand, using this profile in the low pressure range, i.e. in the Doppler regime, the retrieved collisional linewidths do not follow a linear variation with the perturbing gas pressure. On the other hand, regardless of the pressure, lineshapes exhibit a narrowed profile. An accurate analysis of the pressure dependence of relaxation rates show that the Galatry profile is not appropriate and that experimental lineshapes are actually Speed Dependent Voigt profiles. Accurate broadening parameters were retrieved from this profile and compared to previous reported values and predictions calculated from the Robert-Bonamy formalism. Finally a variation of the ratio of relaxation speed dependence to broadening parameters versus relative masses of the collision partners is presented.     

Dynamic properties of P4O6S and P4O7:31P spin-echo and 31P MAS-NMR investigations.

The rotational dynamics of P₄O₆S and P₄O₇ in the solid state were studied by means of ³¹P NMR spectra of spinning and static powder samples in the temperature range of 153–295 K and 295–388 K, respectively. All spectra were simulated to confirm the type of the motion and to extract the time scales as a function of the temperature. Good agreement between experimental and theoretical data was obtained on the basis of a three-site jump model. For P₄O₆S, the activation energy and the pre-exponential factor derived from the lineshape simulations amount to 51(2) kJ/mol and 6(3)·10¹⁵ s⁻¹. For P₄O₇, the spectral analysis yields an activation energy of 67(1) kJ/mol and a pre-exponential factor of 6(2)·10¹⁴ s⁻¹. The dynamic behavior was checked independently by lineshape analyses under both MAS and static conditions. Activation energies are consistent within the errors for the lineshape analyses. Additionally, we have analyzed spin–lattice relaxation measurements, which show the correct trends for the activation energies.     

Rotating-Frame Proton Cross Relaxation in the Presence of Paramagnetic Metal Ions

Rotating-frame cross relaxation for a pair of protons rotating in a spherical molecule with external relaxation is examined theoretically. The results of this study allow us to model intensities in 1D ROE and 2D ROESY spectra of protons in the presence of a paramagnetic metal ion. External relaxation moves the threshold correlation time for spin diffusion to longer times. In contrast to the effect of external relaxation on longitudinal cross relaxation (NOESY), the range of observable transverse cross relaxation (ROESY) expands with increasing external relaxation. At the same time, external relaxation compresses the overall time scale for cross-peak evolution. The initial slopes of cross-peak evolution are unaffected by external relaxation, but are sensitive to the rotational correlation time of the proton pair. Very short mixing times are necessary for accurate estimation of the initial Slopes.     

Dynamical properties of ions confined within dense dispersions of charged anisotropic colloids : A <Superscript>23</Superscript>Na quadrupolar NMR study

We used ²³Na quadrupolar NMR spectroscopy and relaxation measurements to determine the mobility of the sodium counterions confined within dense aqueous dispersions of synthetic Laponite clays as a model of charged anisotropic nano-composite colloids. The lineshape analysis of the ²³Na spectra and the measurements of the Hahn echo attenuation are used to determine the critical clay concentration corresponding to the nematic organisation of the dispersion. As validated by numerical simulations of the ion diffusion within partially oriented nematic dispersion of the anisotropic colloids, the angular variation of the apparent relaxation rates is interpreted as an indice of degree of ordering of the dispersion.     

Nuclear spin relaxation in liquids due to interaction with paramagnetic ions having anisotropic g tensors

Analytical expressions are derived for spin-lattice and spin-spin relaxation times (T_1M and T_2M) of a nucleus arising from magnetic interactions (dipolar and contact) with a paramagnetic ion which has an anisotropic g tensor. The relaxation rates depend on the orientation of the ion-nucleus vector in the principal-axis system of the g tensor. The deviations caused by this angular dependence with reference to the corresponding relaxation rates for an isotropic g tensor are numerically illustrated by considering a case typical for Co (II) complexes.     

A phase cycle scheme that significantly suppresses offset-dependent artifacts in the R2-CPMG 15N relaxation experiment

R2-CPMG 15N relaxation experiments form the basis of NMR dynamics measurements, both for analysis of nano-pico second dynamics and milli-micro second dynamics (kinetics). It has been known for some time that in the practical limit of finite pulse widths, which becomes acute when using cryogenic probes, systematic errors in the apparent R2 relaxation behavior occur for spins far off-resonance from the RF carrier. Inaccurate measurement of R2 rates propagates into quantitative models such as model-free relaxation analysis, rotational diffusion tensor analysis, and relaxation dispersion. The root of the problem stems from evolution of the magnetization vectors out of the XY-plane, both during the pulses as well as between the pulses. These deviations vary as a function of pulse length, number of applied CPMG pulses, and CPMG inter-pulse delay. Herein, we analyze these effects in detail with experimentation, numerical simulations, and analytical equations. Our work suggests a surprisingly simple change in the phase progression of the CPMG pulses, which leads to a remarkable improvement in performance. First, the applicability range of the CPMG experiment is increased by a factor of two in spectral width; second, the dynamical/kinetic processes that can be assessed are significantly extended towards the slower time scale; finally, the robustness of the relaxation dispersion experiments is greatly improved.     

Rotational spectroscopy of the first excited state of the acetylenic C-H stretch of 3-fluoropropyne performed by infrared-Fourier transform microwave-microwave triple-resonance spectroscopy

The rotational spectra of 3-fluoropropyne in the ground and first excited acetylenic C-H stretch vibrational state have been measured. The pure rotational spectrum of the normal species and the ¹³C isotopomers were measured using FTMW-cwMW double-resonance spectroscopy based on the Autler-Townes (AC Stark) effect. The lineshape properties of this measurement make it possible to determine the transition strength, ΔJ-selection rules, and the relative energy ordering of the quantum states. The frequency accuracy of this technique is tested against a previous pure rotational study of 3-fluoropropyne. The rotational spectrum of vibrationally excited state was obtained through IR-FTMW-cwMW methods. In this technique a single-longitudinal-mode pulsed infrared laser source vibrationally excites the acetylenic C-H stretch with J-selectivity. The rotational spectrum of the excited state is then obtained by FTMW and FTMW-cwMW double-resonance methods. The excited-state measurements have a signal-to-noise ratio comparable to the pure rotational spectrum. The residuals in the excited-state fit are larger than those obtained in the ground-state fit. This greater deviation from a standard asymmetric top spectrum is most likely due to weak perturbations to the acetylenic C-H spectrum.     

Slow motion lineshapes

A slow motion expansion about the characteristic features of the powder spectrum is presented. Analytic expressions for the lineshape function, modulated by slow rotational diffusion, are derived. It is shown that the slow motion limit is characterized by harmonic oscillator equations of motion, and the resulting spectrum is determined by harmonic oscillator eigenvalues. The essential features of the lineshape show up naturally, and in particular the axial lineshape diverges like τ^1/4 while there is only a weak motional correction to the logarithmic divergence of the non-axial lineshape. The dynamic frequency shifts converge to their static limits like τ^-1/2 for all cases.     

Dynamic properties of P4O6S and P4O7: P spin–echo and P MAS–NMR investigations

The rotational dynamics of P₄O₆S and P₄O₇ in the solid state were studied by means of ³¹P NMR spectra of spinning and static powder samples in the temperature range of 153–295 K and 295–388 K, respectively. All spectra were simulated to confirm the type of the motion and to extract the time scales as a function of the temperature. Good agreement between experimental and theoretical data was obtained on the basis of a three-site jump model. For P₄O₆S, the activation energy and the pre-exponential factor derived from the lineshape simulations amount to 51(2) kJ/mol and 6(3)·10¹⁵ s⁻¹. For P₄O₇, the spectral analysis yields an activation energy of 67(1) kJ/mol and a pre-exponential factor of 6(2)·10¹⁴ s⁻¹. The dynamic behavior was checked independently by lineshape analyses under both MAS and static conditions. Activation energies are consistent within the errors for the lineshape analyses. Additionally, we have analyzed spin–lattice relaxation measurements, which show the correct trends for the activation energies.     

Magnetic resonance lineshape in the presence of slow motion

The effect on the magnetic resonance lineshape of slow molecular motion is considered. The molecules are assumed to undergo diffusive jumps of angle ε described by the distribution function W(ε)=(N/τ) exp (λ cos ε), where τ is the mean lifetime between jumps and λ a parameter describing the width of the distribution. As λ is varied from zero to infinity this distribution describes diffusion models that change continuously from the strong collision limit to Brownian rotational diffusion. Magnetic resonance lineshapes are calculated by Freed's method using the asymptotic expansion technique, and results are presented for an axially symmetric (secular) Zeeman hamiltonian.

An exact expression for the magnetic resonance lineshape is derived in the strong collision limit for any secular hamiltonian and a few examples are presented. It is also shown how this technique can be used as a basis for lineshape calculations in the presence of moderately large jumps.     

Nonstationary rotational diffusion in room temperature liquids measured by femtosecond three-pulse transient anisotropy

A femtosecond three-pulse chi((5)) polarization anisotropy experiment is used to examine the time dependence of the rotational diffusion of coumarin 153 in polar liquids. By probing the polarization anisotropy decay at various points during the molecule's excited state lifetime, a time-dependent diffusion coefficient is found in several solvents. This anomalous behavior is consistent with the relaxation of the solvent friction to accommodate the solute's excited state charge distribution. Rotational diffusion times measured immediately after photoexcitation by two-pulse chi((3)) experiments may reflect a nonstationary bath dynamics, rather than the equilibrium friction of the solvent.     

Investigation of the rotational diffusion of the Rose Bengal fluorescent nanomarker in human serum albumin solutions

The polarized fluorescence of the Rose Bengal fluorescent nanomarker in HSA solutions was investigated and parameters of its rotational diffusion were calculated. The increase in the degree of fluorescence polarization, rotational relaxation time, and the effective hydrodynamic radius of Rose Bengal, as well as the decrease of the rotational diffusion coefficient in HSA solutions, were found. The effects of the electronegativity of atoms in the structure of the nanomarker on the parameters of its rotational diffusion were established based on comparison of Rose Bengal with other nanomarkers of the homologous family.