Effective rotational correlation times of proteins from NMR relaxation interference

Knowledge of the effective rotational correlation times, tauc, for the modulation of anisotropic spin-spin interactions in macromolecules subject to Brownian motion in solution is of key interest for the practice of NMR spectroscopy in structural biology. The value of tauc enables an estimate of the NMR spin relaxation rates, and indicates possible aggregation of the macromolecular species. This paper reports a novel NMR pulse scheme, [15N,1H]-TRACT, which is based on transverse relaxation-optimized spectroscopy and permits to determine tauc for 15N-1H bonds without interference from dipole-dipole coupling of the amide proton with remote protons. [15N,1H]-TRACT is highly efficient since only a series of one-dimensional NMR spectra need to be recorded. Its use is suggested for a quick estimate of the rotational correlation time, to monitor sample quality and to determine optimal parameters for complex multidimensional NMR experiments. Practical applications are illustrated with the 110 kDa 7,8-dihydroneopterin aldolase from Staphylococcus aureus, the uniformly 15N-labeled Escherichia coli outer membrane protein X (OmpX) in 60 kDa mixed OmpX/DHPC micelles with approximately 90 molecules of unlabeled 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC), and the 16 kDa pheromone-binding protein from Bombyx mori, which cover a wide range of correlation times.     

Measurements of the rotational relaxation times for absorption lines with Voigt profiles

A new method for determining the relaxation parameters T ₁ and T ₂ for the Voigt profile of an absorption line is presented. The method was tested on gaseous OCS with the use of a phase-switching spectrometer. The method is equally applicable for both pure gases and gas mixtures.     

Collisional transfer between rotational levels of OCS

Steady-state four-level microwave double-resonance experiments are described for pure OCS and OCS diluted with CH₃OH, H₂, and He. For pure OCS, interactions of higher order than first-order dipole-dipole dominate the behavior of some four-level systems, and the rates of ΔJ = 2 quadrupole-type collision-induced transitions are found to be greater than one-half of the ΔJ = 1 dipolar rates. For OCSCH₃OH mixtures, the dipolar rates are significantly enhanced with respect to the pure gas, but ΔJ = 2 transitions are still important. For the mixtures of astrophysical interest, OCSH₂ and OCSHe, all four-level systems show ΔJ = 2 collisional preferences. The ΔJ = 2 transition rates are comparable to those of ΔJ = 1 transitions, and there is evidence that ΔJ = 3 transition rates are substantial.     

Applications of DNP-NMR for the measurement of heteronuclear T1 relaxation times

Measurement of heteronuclear spin-lattice relaxation times is hampered by both low natural abundance and low detection sensitivity. Combined with typically long relaxation times, this results in extended acquisition times which often renders the experiment impractical. Recently a variant of dynamic nuclear polarisation has been demonstrated in which enhanced nuclear spin polarisation, generated in the cryo-solid state, is transferred to the liquid state for detection. Combining this approach with small flip angle pulse trains, similar to the FLASH-T(1) imaging sequence, allows the rapid determination of spin-lattice relaxation times. In this paper we explore this method and its application to the measurement of T(1) for both carbon-13 and nitrogen-15 at natural abundance. The effects of RF inhomogeneity and the influence of proton decoupling in the context of this experiment are also investigated.     

Methodology for the measurement and analysis of relaxation times in proton imaging

Measurements of proton T1 and T2 were performed on GdCl3 solutions (20 less than T2 less than 500 msec, 90 less than T1 less than 1000 msec) on large-bore NMR imaging systems operating at 1.0T and 1.5T. CPMG multi-echo (ME), multiple saturation recovery (MSR) and modified fast inversion recovery (MFIR) pulse sequences as well as a sequence that combines and interleaves T1 and T2 weighted data acquisition (which we call "multiple saturation-recovery multiple-echo" (MSRME) were used. The relaxation data are compared to those obtained on a small bore NMR spectrometer operated at 1.5T. T1 and T2 values for the solutions were found to be the same within 10% for the two fields. Reproducibility of measurements of T1, T2 and the unnormalized spin density of the solutions was better than 5%. Systematic errors, amenable to correction through calibration, are noted in the imager T1 and T2 values. T1 and T2 values for some typical neural tissues at 1.5T and body tissue at 1.0T for human volunteers were obtained and are tabulated.     

PulsedμSR and the measurement of Zeeman and Dipolar relaxation times

Pulsed muon sources are ideally suited to experiments which require a repetitive or periodic excitation of the sample. Various possibilities are discussed. Magnetic relaxation is considered in terms of the various thermodynamic reservoirs which make up a spin system, both for nuclear magnetism and for electronic paramagnetism.A synchronous pulse sequence is presented which, in a single experiment, allows the following distinct relaxation functions of the samples host spin system to be determined: that of its Zeeman energy, that of its secular dipolar components, and that of the total dipolar energy in zero field. The timescale of the high field measurements overlaps with and substantially extends the range accessible to NMR and ESR.     

Spin relaxation measurements using first-harmonic out-of-phase absorption EPR signals: rotational motion effects

A recent survey of nonlinear continuous-wave (CW) EPR methods revealed that the first-harmonic absorption EPR signal, detected 90 degrees out of phase with respect to the Zeeman modulation (V(1)(')-EPR), is the most appropriate for determining spin-lattice relaxation enhancements of spin labels (V. A. Livshits, T. Páli, and D. Marsh, 1998, J. Magn. Reson. 134, 113-123). The sensitivity of such V(1)(')-EPR spectra to molecular rotational motion is investigated here by spectral simulations for nitroxyl spin labels, over the entire range of rotational correlation times. Determination of the effective spin-lattice relaxation times is less dependent on rotational mobility than for other nonlinear CW EPR methods, especially at a Zeeman modulation frequency of 25 kHz which is particularly appropriate for spin labels. This relative insensitivity to molecular motion further enhances the usefulness of the V(1)(')-EPR method. Calibrations of the out-of-phase to in-phase spectral intensity (and amplitude) ratios are given as a function of spin-lattice relaxation time, for the full range of spin-label rotational correlation times. Experimental measurements on spin labels in the slow, intermediate, and fast motional regimes of molecular rotation are used to test and validate the method.     

Collisional broadening and shifting of OCS rotational spectrum lines

Broadening and shifting of carbonyl sulfide (OCS) rotational spectrum lines by pressure of N₂, O₂ and OCS were accurately studied in the frequency range 24–850 GHz at room temperature using a spectrometer with radio-acoustic detection of absorption. Rotational dependences of collisional widths of OCS spectrum lines were determined by a simple empirical polynomial fit of experimental data. Experimental uncertainties were analyzed. Results of supplementary test measurements of self-broadening of rotational OCS lines in the ν₂ excited vibrational state and carbon monoxide (CO) lines in the ground vibrational state are presented. Comparison of the obtained results with previously known measurements and theoretical calculations is given. The performed work allows for the first time development of accurate gaseous etalon of absorption for atmospheric applications and laboratory use, covering continuously the whole millimeter- and submillimeter-wave range.     

A longitudinally detected high-field ESR spectrometer for the measurement of spin-lattice relaxation times

We describe a high-field longitudinally detected electron spin resonance (LOD-ESR) spectrometer operating at 35 and 75 GHz. The lack of resonant microwave circuits facilitates operation at different microwave frequencies without changing the probehead. A very low noise radio frequency detection compensates partially the resulting low sensitivity. The major elements of the LOD-ESR spectrometer are commercially available and may be adapted to usual high frequency spectrometers. The instrument allows field and frequency dependent spin lattice relaxation time (T1) studies. T1 in the range of 2-80 ns can be determined from the phase sensitively detected LOD-ESR spectra. We demonstrate the performance of the apparatus by the measurement of T1 in the normal state of RbC60, an electrically conducting alkaline fulleride polymer.     

The influence of nitrogen-15 proton-driven spin diffusion on the measurement of nitrogen-15 longitudinal relaxation times

The effect of nitrogen-15 proton-driven spin diffusion on quantitative (15)N T(1) measurements in solid proteins is investigated, and the impact on the measurement of dynamic parameters is assessed. A simple model of exchange between neighboring nitrogens is used to reproduce the evolution of (15)N spin systems whose longitudinal relaxation rates and exchange rates are compatible with experimental measurements. We show that the induced error in the measured T(1) and its effect on the determination of dynamics parameters is likely to be less than the current experimental error. The use of deuterated protein samples is shown to have a small but sometimes visible effect, and may also considerably slow down or even suppress the exchange of magnetization due to spin diffusion.     

Two-dimensional nutation exchange NQR spectroscopy: direct determination of rotational angles

A new method for the direct determination of rotational angles based on 2-dimensional nutation exchange NQR spectroscopy is proposed. The method involves the detection of exchange processes through NQR nutation spectra recorded after the mixing interval. The response is analysed of a system of spins I = 3/2 in zero applied field, experiencing electric quadrupole couplings, to the three-pulse sequence with incrementing pulse widths. The systems investigated here were hexachloroethane and tetrachloroethylene, which show threefold and twofold reorientational jumps about the carbon-carbon axis, respectively. It is shown that the 2D nutation exchange NQR spectrum exhibits characteristic ridges, which reveal the motional mechanism in a model-independent fashion. The angles through which the molecule rotates can be read directly from elliptical ridges in the 2D spectrum, which are also sensitive to the value of asymmetry parameter of the electric field gradient tensor.     

Decay of ESR nutation signals fromE′1 centers in quartz

Decay of time-dependent nutation signals from E′₁ centers in crystalline quartz is investigated at room temperature. ESR-nutation signals were excited in the single-photon mode and were shaped by Zeeman field pulses. It is found that the decay of this signal follows an exponential law with a rate Λ substantially smaller than 1/T₂ (T₂ being the transverse relaxation time) and increases with the amplitude of the acting ultrahigh-frequency field B₁. It is shown with the use of the Bloch equations that the intergral decay rate of nutations in an inhomogeneously broadened two-level system depends on the ratio of B₁ to the linewidth and increases nonlinearly with increasing B₁. The observed quantitative disagreement between the experimentally observed nutation decay with Bloch's theory is explained by the stochasticity of conditions of the resonant interaction of radiation with a system of spins. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 2, pp. 213–219, March–April, 1999.     

Determination of the rotational relaxation cross section of carbon dioxide from spectral measurements

The pressure-induced transformation of the spectrum of the Q branch of the ν₁ mode (1388 cm^?1) of CO₂ molecules is quantitatively interpreted. The contributions to the width of the spectrum from three relaxation mechanisms—vibrational dephasing, rotational relaxation, and the Doppler effect—are taken into account. From the fitting of the calculated and measured spectra of the Q branch, the effective cross section of the rotational energy relaxation is determined.     

The choice of optimal parameters for measurement of spin-lattice relaxation times. IV. Effects of nonideal pulses

Optimum pulse spacing times are determined for measurements of spin-lattice relaxation times, T,, when the radiofrequency pulses deviate from their ideal values of 90 and 180°. The performance of the fast inversion-recovery technique in the presence and absence of separate estimates of the values of the effective flip angles resulting from nonideal rf pulses are compared, using as the criterion the total experimental time required to achieve a specified precision in the estimate of T1. The important assumptions made are (1) that the cosine of the effective flip angles are either unknown or can be estimated in a separate experiment, (2) that M(∞) and T₁ are unknown, and (3) that an interval of uncertainty is known for the value of T₁.     

Calculation of spin-lattice relaxation times

A general expression is found for the probability for a direct (single-phonon) relaxation transition for arbitrary symmetry of the surroundings of a paramagnetic ion having an effective spin of S = 1/2. The expression is compared with experiment for the case of tetragonal symmetry. Since certain approximations frequently used in the calculations are not used here, a markedly improved agreement is found with the experimental relaxation times.Translated from Izvestiya VUZ. Fizika, No. 2, pp. 36–39, February, 1970.