Gradient Pulse Lengths Research Articles

Response to Comment on "Following Molecular Mobility during Chemical Reactions: No Evidence for Active Propulsion" and "Molecular Diffusivity of Click Reaction Components: The Diffusion Enhancement Question".

In their Comment (DOI: 10.1021/jacs.2c02965) on two related publications by our groups (J. Am. Chem. Soc. 2021, 143, 20884-20890; DOI: 10.1021/jacs.1c09455) and another (J. Am. Chem. Soc. 2022, 144, 1380-1388; DOI: 10.1021/jacs.1c11754), Huang and Granick discuss the diffusion NMR measurements of molecules during a copper-catalyzed azide-alkyne cycloaddition (CuAAC) "click" reaction. Here we respond to these comments and maintain that no diffusion enhancement was observed for any species during the reaction. We show that the relaxation agent does not interfere with the CuAAC reaction kinetics nor the diffusion of the molecules involved. Similarly, the gradient pulse length and diffusion time do not affect the diffusion coefficients. Peak overlap was completely removed in our study with the use of hydrazine as the reducing agent. The steady-state assumption does not hold for these diffusion measurements that take several minutes, which is the reason monotonic gradient orders are not suitable. Finally, we discuss the other reactions where similar changes in diffusion have been claimed. Our conclusions are fully supported by the results represented in our original JACS Article and the corresponding Supporting Information.

Burial of the Polymorphic Residue 129 in Amyloid Fibrils of Prion Stop Mutants

Misfolding of the natively α-helical prion protein into a β-sheet rich isoform is related to various human diseases such as Creutzfeldt-Jakob disease and Gerstmann-Sträussler-Scheinker syndrome. In humans, the disease phenotype is modified by a methionine/valine polymorphism at codon 129 of the prion protein gene. Using a combination of hydrogen/deuterium exchange coupled to NMR spectroscopy, hydroxyl radical probing detected by mass spectrometry, and site-directed mutagenesis, we demonstrate that stop mutants of the human prion protein have a conserved amyloid core. The 129 residue is deeply buried in the amyloid core structure, and its mutation strongly impacts aggregation. Taken together the data support a critical role of the polymorphic residue 129 of the human prion protein in aggregation and disease.

Determination of the self-diffusion coefficient of intracellular water using PGSE NMR with variable gradient pulse length

A new pulsed-gradient spin-echo NMR protocol for assessing the local self-diffusion coefficient D 0 of water confined within living cells is proposed. Equations for the apparent mean-square displacement < Z 2> as a function of the effective diffusion time t d and the duration of the displacement-encoding gradient pulses δ are derived. The standard method of estimating D 0 – reducing t d until the influence of collisions between the water molecules and the plasma membrane can be neglected – often fails because of the small size of typical cells. As demonstrated here, the decrease of the apparent < Z 2> with increasing δ at constant t d can be utilized to measure D 0.

Extension of the double-wave-vector diffusion-weighting experiment to multiple concatenations

Experiments involving two diffusion-weightings in a single acquisition, so-called double- or two-wave-vector experiments, have recently been applied to measure the microscopic anisotropy in macroscopically isotropic samples or to estimate pore or compartment sizes. These informations are derived from the signal modulation observed when varying the wave vectors’ orientations. However, the modulation amplitude can be small and, for short mixing times between the two diffusion-weightings, decays with increased gradient pulse lengths which hampers its detectability on whole-body MR systems. Here, an approach is investigated that involves multiple concatenations of the two diffusion-weightings in a single experiment. The theoretical framework for double-wave-vector experiments of fully restricted diffusion is adapted and the corresponding tensor approach recently presented for short mixing times extended and compared to numerical simulations. It is shown that for short mixing times (i) the extended tensor approach well describes the signal behavior observed for multiple concatenations and (ii) the relative amplitude of the signal modulation increases with the number of concatenations. Thus, the presented extension of the double-wave-vector experiment may help to improve the detectability of the signal modulations observed for short mixing times, in particular on whole-body MR systems with their limited gradient amplitudes.

Cross-term-compensated pulsed-gradient stimulated echo MR with asymmetric gradient pulse lengths

The magic asymmetric gradient stimulated echo (MAGSTE) sequence developed to compensate background-gradient cross-terms in the preparation and readout interval independently, assumes identical lengths for the two gradient pulses applied in each interval. However, this approach is rather inefficient if some extra delay time is present in one half of an interval, e.g. as required for special RF excitations or spatial encoding prior to the stimulated echo in MR imaging. Therefore, a generalized version of the sequence is presented that considers different gradient pulse lengths within an interval. It is shown theoretically that (i) for any pulse lengths a “magic” amplitude ratio exists which ensures the desired cross-term compensation in each interval and that (ii) prolonging one of the gradients can deliver a considerably higher diffusion weighting efficiency. These results are confirmed in MR imaging experiments on phantoms and in vivo in the human brain at 3 T using an echo-planar trajectory. In the examples shown, typically 10 times higher b values can be achieved or an echo time reduction with a 40% signal gain in brain white matter. Thus, in case of asymmetric timing requirements, the generalized MAGSTE sequence with different gradient pulse lengths may help to overcome signal-to-noise limitations in diffusion weighted MR.

Improved diffusion-weighting efficiency of pulsed gradient stimulated echo MR measurements with background gradient cross-term suppression

Accurate diffusion measurements with pulsed gradient NMR are hampered by cross-terms of the diffusion-weighting and background gradients. For experiments based on a stimulated echo pulse sequence, that is preferred for samples with a T2 short compared to the diffusion time, a diffusion-weighting scheme has been presented that avoids these cross-terms in each of the en- and decoding periods separately. However, this approach suffers from a reduced diffusion-weighting efficiency because the two gradients applied in each of the periods have effectively opposite polarities leading to a partial cancellation. An extension of this scheme is presented that involves an additional gradient pulse in each period and delivers an improved diffusion-weighting efficiency without sacrificing the cross-term compensation. Analytical expressions for the gradient pulse lengths and amplitudes are given for arbitrary timing parameters. MR measurements with artificial (switched) background gradients were performed to test the cross-term compensation capability of the proposed extension. The results show that considerably higher q and b values can be achieved with the extension without changing the timing parameters. The MR measurements yielded identical diffusion coefficients without, with the same, and with different background gradients in the en- and decoding periods demonstrating the cross-term compensation of the presented approach.

In situ pulsed-field gradient NMR determination of the size of oil bodies in vegetable seeds. Analysis of the effect of the gradient pulse length.

We report a pulsed-field gradient NMR study of the size of the oil bodies in lettuce seeds. The pulsed-field gradient spin-echo method (PFGSE) was applied to measure the self-diffusion coefficient of triacylglycerol molecules (TAG) inside the oil bodies. The confined nature of TAG diffusion is used to determine the size dispersion of the oil bodies. At long diffusion time, we measure a spin-echo attenuation that is related to the form factor of the confining volumes in the reciprocal q space, where q is proportional to the product of the gradient intensity and the length of the pulse gradient. Specific care was taken in analyzing the influence of the gradient pulse length delta on the shape of the PFGSE decay in order to construct the function corresponding to the short gradient pulse approximation (SGP). The SGP model gives an analytical framework for the PFGSE signal that enables the size distribution of the oil bodies to be determined. The SGP function was unambiguously obtained by varying the gradient pulse length delta in order to linearly extrapolate at delta = 0 the SGP limit. In this work, we also consider the Gaussian phase distribution (GPD) assumption that is often used to analyze confined diffusion experiments. Although the GPD assumption is known to be inaccurate in predicting the fine structure of the PFGSE function in q space, we point out that in the present case it can be used to take into account the finite value of delta. A log-normal distribution of the radius values was assumed in simulating the PFGNMR experiments since this type of distribution is observed in vegetable seeds by transmission electronic microscopy. From a practical and experimental standpoint, the NMR measurements reported here require no specific treatment of the seeds and the size of oil bodies is determined "in situ" on seeds poured into the NMR tube.

Mapping the intracellular fraction of water by varying the gradient pulse length in q-space diffusion MRI

Finite gradient pulse lengths are traditionally considered a nuisance in q-space diffusion NMR and MRI, since the simple Fourier relation between the acquired signal and the displacement probability is invalidated. Increasing the value of the pulse length leads to an apparently smaller value of the estimated compartment size. We propose that q-space data at different gradient pulse lengths, but with the same effective diffusion time, can be used to identify and quantify components with free or restricted diffusion from multiexponential echo decay curves obtained on cellular systems. The method is demonstrated with experiments on excised human brain white matter and a series of model systems with well-defined free, restricted, and combined free and restricted diffusion behavior. Time-resolved diffusion MRI experiments are used to map the spatial distribution of the intracellular fraction in a yeast cell suspension during sedimentation, and observe the disappearance of this fraction after a heat treatment.

Varying the gradient pulse length gives valuable information in NMR diffusometry

Varying the gradient pulse length gives valuable information in NMR diffusometry

Some “Reflections” on the Effects of Finite Gradient Pulse Lengths in PGSE NMR Experiments in Restricted Systems

AbstractFor Abstract see ChemInform Abstract in Full Text.

NMR diffusometry and the short gradient pulse limit approximation

In NMR diffusometry, one often uses the short gradient pulse (SGP) limit approximation in the interpretation of data from systems with restricted diffusion. The SGP limit approximation means that the gradient pulse length, δ, is so short that the spins do not diffuse during the pulse duration, but this condition is rarely met. If the length scale of the pores corresponds to the molecular mean square displacement during the gradient pulse, the measured echo intensities become a function of the gradient pulse length. Here, we have studied highly concentrated emulsions to show how the length of the gradient pulse influences NMR diffusion experiments. We have focused on molecules confined to one pore and molecules that can migrate through the porous system. For the former the echo decays give smaller pores than the actual case and for the latter we show large changes in echo decay depending on the gradient pulse length, everything else being equal.

Some “Reflections” on the Effects of Finite Gradient Pulse Lengths in PGSE NMR Experiments in Restricted Systems

AbstractIt is generally difficult to analytically derive models describing the echo attenuation in pulsed gradient spin‐echo (PGSE) experiments for even the simplest porous systems that are commonly studied—especially when the gradient pulse (δ) is of finite length compared to the timescale of the diffusion measurement (Δ). Consequently, various levels of approximation are used to evaluate PGSE experiments. In the present paper, a conceptual view ofq‐space is given and two of the most common approximations, the short gradient pulse (SGP) and Gaussian phase distribution (GPD) approximations, are compared in detail with a recent matrix method, which provides “analytically” exact results giving a visual representation of the limitations of these approximations. The simulations are performed for diffusion between a pair of reflecting planes separated by a distancea.A modification that is sometimes applied to the short gradient pulse approximation in attempting to extend it to finite gradient pulses is also compared. The simulations reveal that, except when the experimental conditions closely match the requirements of the SGP and GPD simulations, the matrix method must be used in order to correctly interpret the data.

NMR spectral selectivity by radio-frequency field gradients

It is shown that a train of radio-frequency field ( B 1) gradient pulses, separated by appropriate precession intervals, enables the selection of a given frequency zone, that is the refocusing of magnetizations whose resonance frequencies belong within this zone whereas complete defocusing occurs outside. The B 1 gradient pulse length must be adjusted to produce a 180° flip angle at the center of the sample (in practice, a mean 180° pulse); more reliable results are obtained if the pulse train is applied to transverse magnetization rather than to longitudinal magnetization.

Pure-phase heteronuclear multiple-quantum spectroscopy using field gradient selection

The fundamental advantages of using pulsed field gradients to improve multidimensional NMR experiments are now well established. Unwanted resonances, such as that of water in spectra of biomolecules, can easily be eliminated ( I ) , and coherences belonging to groups of nuclei of particular interest can be efficiently selected (2). Many experiments also inherently provide quadrature detection in the indirectly detected dimension because of the selection of a single coherence pathway (+2wr -P ~2) as opposed to a linear combination of pathways that results in amplitude modulation of a single quadrature channel (3). Less frequently addressed are problems associated with maintaining optimum resolution of cross peaks in 2D plots (4). Straightforward implementation of quadrature detection in the indirect dimension often produces phase-twisted peaks. This results because of the direct correlation of phases of coherence in one dimension with phases of magnetization in the other dimension (phase modulation of signal by t, evolution). For non-gradient-enhanced versions of 2D and 3D experiments these problems have traditionally been addressed using hypercomplex data acquisition in a manner such as that described by States et al. (5)) or time-proportional phase incrementation in a manner such as that described by Marion and Wtithrich (6). Neither of these procedures is directly applicable to gradient-enhanced spectroscopy because of selection of a single coherence pathway. Here we take a lead from a recent paper by Hurd et al. ( 7) that employs changes in the sign of gradient pulses to retrieve both positive and negative coherence pathways in a single experiment. The procedure described in that paper places high demands on gradient pulse length and may not, at this stage of hardware development, be generally applicable. However, a procedure using gradient changes in alternate t, points provides a simple alternative. Here, we acquire hypercomplex data for a heteronuclear multiple-quantum-coherence (HMQC) experiment. The data show pure amplitude modulation in both channels and transform to give pure-absorption signals. Moderate efficiency of acquisition is retained as illustrated with a 13C‘H natural-abundance HMQC data set on the trisaccharide Lewisx glucal (galactosyl-& ( 1,4) [ CX( 1,3 )-fucosyl] ghtcal). These data required just 36 min on 10 mg of the trisaccharide. Suppression of 12C lines is complete with just two pulses per t, point.