Product operator analysis of the influence of chemical exchange on relaxation rates

Gas Uptake and Thermodynamics in Porous Liquids Elucidated by 129Xe NMR

We exploited 129Xe NMR to investigate xenon gas uptake and dynamics in a porous liquid formed by dissolving porous organic cages in a cavity-excluded solvent. Quantitative 129Xe NMR shows that when the amount of xenon added to the sample is lower than the amount of cages present (subsaturation), the porous liquid absorbs almost all xenon atoms from the gas phase, with 30% of the cages occupied with a Xe atom. A simple two-site exchange model enables an estimate of the chemical shift of 129Xe in the cages, which is in good agreement with the value provided by first-principles modeling. T2 relaxation times allow the determination of the exchange rate of Xe between the solvent and cage sites as well as the activation energies of the exchange. The 129Xe NMR analysis also enables determination of the free energy of confinement, and it shows that Xe binding is predominantly enthalpy-driven.

Inside information on xenon adsorption in porous organic cages by NMR

A solid porous molecular crystal formed from an organic cage, CC3, has unprecedented performance for the separation of rare gases. Here, xenon was used as an internal reporter providing extraordinarily versatile information about the gas adsorption phenomena in the cage and window cavities of the material. 129Xe NMR measurements combined with state-of-the-art quantum chemical calculations allowed the determination of the occupancies of the cavities, binding constants, thermodynamic parameters as well as the exchange rates of Xe between the cavities. Chemical exchange saturation transfer (CEST) experiments revealed a minor window cavity site with a significantly lower exchange rate than other sites. Diffusion measurements showed significantly reduced mobility of xenon with loading. 129Xe spectra also revealed that the cage cavity sites are preferred at lower loading levels, due to more favourable binding, whereas window sites come to dominate closer to saturation because of their greater prevalence.

Nonadiabatic exchange dynamics during adiabatic frequency sweeps

A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging.

Exchange-induced relaxation in the presence of a fictitious field

In the present study we derive a solution for two site fast exchange-induced relaxation in the presence of a fictitious magnetic field as generated by amplitude and frequency modulated RF pulses. This solution provides a means to analyze data obtained from relaxation experiments with the method called RAFFn (Relaxation Along a Fictitious Field of rank n), in which a fictitious field is created in a coordinate frame undergoing multi-fold rotation about n axes (rank n). The RAFF2 technique is relevant to MRI relaxation methods that provide good contrast enhancement for tumor detection. The relaxation equations for n=2 are derived for the fast exchange regime using density matrix formalism. The method of derivation can be further extended to obtain solutions for n>2.

MRI contrasts in high rank rotating frames

PURPOSE

MRI relaxation measurements are performed in the presence of a fictitious magnetic field in the recently described technique known as RAFF (Relaxation Along a Fictitious Field). This method operates in the 2(nd) rotating frame (rank n = 2) by using a nonadiabatic sweep of the radiofrequency effective field to generate the fictitious magnetic field. In the present study, the RAFF method is extended for generating MRI contrasts in rotating frames of ranks 1 ≤ n ≤ 5. The developed method is entitled RAFF in rotating frame of rank n (RAFFn).

THEORY AND METHODS

RAFFn pulses were designed to generate fictitious fields that allow locking of magnetization in rotating frames of rank n. Contrast generated with RAFFn was studied using Bloch-McConnell formalism together with experiments on human and rat brains.

RESULTS

Tolerance to B0 and B1 inhomogeneities and reduced specific absorption rate with increasing n in RAFFn were demonstrated. Simulations of exchange-induced relaxations revealed enhanced sensitivity of RAFFn to slow exchange. Consistent with such feature, an increased grey/white matter contrast was observed in human and rat brain as n increased.

CONCLUSION

RAFFn is a robust and safe rotating frame relaxation method to access slow molecular motions in vivo.

Toward understanding transverse relaxation in human brain through its field dependence

Apparent transverse-relaxation rate constants (R₂⁺ = 1/T₂⁺) were measured in various regions of the healthy human brain using a multiecho adiabatic spin-echo sequence at five different magnetic fields, 1.5, 1.9, 3, 4.7, and 7 T. The R₂⁺ values showed a clear dependence on magnetic field strength (B(0) ). The regional distribution of the R ₂⁺ was well explained by the sum of three components: (1) regional nonhemin iron concentration ([Fe]), (2) regional macromolecular mass fraction (f(M) ), and (3) a region-independent factor. Accordingly, R₂⁺ = α[Fe] + βf(M) + γ, where coefficients α, β, and γ were experimentally determined at each magnetic field by a least square fitting method using multiple regression analysis. Although the coefficient α linearly increased with B(0) , β showed a quadratic dependence on top of a field-independent component. The coefficient γ also increased slightly with B(0) on top of a field-independent component. The linear dependence of α on B(0) was consistent with that observed for the transverse-relaxation rate of water protons in ferritin solutions as found previously by others. The quadratic dependence of β on B(0) was accounted for by isochronous and anisochronous exchange mechanisms using intrinsic-relaxation parameters obtained from the literature.

Heteronuclear Adiabatic Relaxation Dispersion (HARD) for quantitative analysis of conformational dynamics in proteins

NMR relaxation methods probe biomolecular motions over a wide range of timescales. In particular, the rotating frame spin-lock R(1ρ) and Carr-Purcell-Meiboom-Gill (CPMG) R(2) experiments are commonly used to characterize μs to ms dynamics, which play a critical role in enzyme folding and catalysis. In an effort to complement these approaches, we introduced the Heteronuclear Adiabatic Relaxation Dispersion (HARD) method, where dispersion in rotating frame relaxation rate constants (longitudinal R(1ρ) and transverse R(2ρ)) is created by modulating the shape and duration of adiabatic full passage (AFP) pulses. Previously, we showed the ability of the HARD method to detect chemical exchange dynamics in the fast exchange regime (k(ex)∼10(4)-10(5) s(-1)). In this article, we show the sensitivity of the HARD method to slower exchange processes by measuring R(1ρ) and R(2ρ) relaxation rates for two soluble proteins (ubiquitin and 10C RNA ligase). One advantage of the HARD method is its nominal dependence on the applied radio frequency field, which can be leveraged to modulate the dispersion in the relaxation rate constants. In addition, we also include product operator simulations to define the dynamic range of adiabatic R(1ρ) and R(2ρ) that is valid under all exchange regimes. We conclude from both experimental observations and simulations that this method is complementary to CPMG-based and rotating frame spin-lock R(1ρ) experiments to probe conformational exchange dynamics for biomolecules. Finally, this approach is germane to several NMR-active nuclei, where relaxation rates are frequency-offset independent.

On-resonance low B1 pulses for imaging of the effects of PARACEST agents

Application of the exchange-sensitive, low-power RF pulses positioned on the bulk water resonance for imaging of the effects of PARACEST agents is proposed as an alternative to the standard CW off-resonance irradiation. Specifically, we applied a low-power WALTZ-16 RF train, with the 90 degrees pulse unit replaced by a pulse of the fixed length (WALTZ-16*). Using this sequence, the bulk water signal was found to be sensitive to exchange lifetimes with PARACEST complex bound protons, the transverse relaxation time of bulk water, and longitudinal relaxation time of bound protons. In this report, the concept of using WALTZ-16* to "activate" a PARACEST effect is introduced and some of the salient features of this technique with respect to experimental conditions and performance levels are discussed. Computational predictions are verified and explored by comparison with experimental spectroscopic and imaging data. It is shown that WALTZ-16* can be used to detect PARACEST agents with an RF intensity as low as 200 Hz for concentrations as low as a few tens of microM for lanthanide chelates having appropriate water-exchange rates (Tm,Dy).