Algebraic expressions for Carr-Purcell-Meiboom-Gill relaxation dispersion for N-site chemical exchange.
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ABSTRACT:
SUBMITTER: Koss H
PROVIDER: S-EPMC8129722 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:The Carr-Purcell-Meiboom-Gill (CPMG) nuclear magnetic resonance experiment is widely used to characterize chemical exchange phenomena in biological macromolecules. Theoretical expressions for the nuclear spin relaxation rate constant for two-site chemical exchange during CPMG pulse trains valid for all time scales are well-known as are descriptions of N-site exchange in the fast limit. We have obtained theoretical expressions for N-site exchange outside of the fast limit by using approximations to an average Liouvillian describing the decay of magnetization during a CPMG pulse train. We obtain general expressions for CPMG experiments for any N-site scheme and all experimentally accessible time scales. For sufficiently slow chemical exchange, we obtain closed-form expressions for the relaxation rate constant and a general characteristic polynomial for arbitrary kinetic schemes. Furthermore, we highlight features that qualitatively characterize CPMG curves obtained for various N-site kinetic topologies, quantitatively characterize CPMG curves obtained from systems in various N-site exchange situations, and test distinguishability of kinetic models.
| S-EPMC6315113 | biostudies-literature
Project description:Chemical exchange saturation transfer (CEST) imaging is a novel MRI technique that is sensitive to biomolecules, local pH and temperature, and offers considerable advantages for in vivo applications. However, the magnitude of CEST effect for dilute CEST agents undergoing slow or intermediate chemical exchange is typically small, requiring the use of signal averaging to enhance its sensitivity. Given that T2 -induced signal loss can be normalized by asymmetry analysis, the magnitude of CEST effect is independent of echo time. Therefore, CEST MRI with multi-echo echo planar imaging (EPI) readout should yield the same CEST effect as conventional single echo acquisition. Importantly, CEST multi-echo (CESTme) EPI images can be averaged to enhance CEST MRI sensitivity. The goal of this study was to validate CESTme EPI using a creatine-agarose gel CEST phantom with similar T2 as biological tissue. Using least-squares optimization, we found that the sensitivity of CESTme sequence was significantly higher than that obtained by conventional single echo CEST-EPI acquisition. Specifically, signal-to-noise ratio and contrast-to-noise ratio from the proposed CESTme EPI were approximately equivalent to that obtained by doubling the number of signal averages of the standard single echo CEST MRI sequence. In summary, our results demonstrated CESTme EPI for sensitivity-enhanced CEST imaging.
| S-EPMC3957332 | biostudies-literature
Project description:To study microsecond processes by relaxation dispersion NMR spectroscopy, low power deposition and short pulses are crucial and encourage the development of experiments that employ (1)H Carr-Purcell-Meiboom-Gill (CPMG) pulse trains. Herein, a method is described for the comprehensive study of microsecond to millisecond time scale dynamics of methyl groups in proteins, exploiting their high abundance and favorable relaxation properties. In our approach, protein samples are produced using [(1)H, (13)C]-d-glucose in ?100% D(2)O, which yields CHD(2) methyl groups for alanine, valine, threonine, isoleucine, leucine, and methionine residues with high abundance, in an otherwise largely deuterated background. Methyl groups in such samples can be sequence-specifically assigned to near completion, using (13)C TOCSY NMR spectroscopy, as was recently demonstrated (Otten, R.; et al. J. Am. Chem. Soc. 2010, 132, 2952-2960). In this Article, NMR pulse schemes are presented to measure (1)H CPMG relaxation dispersion profiles for CHD(2) methyl groups, in a vein similar to that of backbone relaxation experiments. Because of the high deuteration level of methyl-bearing side chains, artifacts arising from proton scalar coupling during the CPMG pulse train are negligible, with the exception of Ile-?1 and Thr-?2 methyl groups, and a pulse scheme is described to remove the artifacts for those residues. Strong (13)C scalar coupling effects, observed for several leucine residues, are removed by alternative biochemical and NMR approaches. The methodology is applied to the transcriptional activator NtrC(r), for which an inactive/active state transition was previously measured and the motions in the microsecond time range were estimated through a combination of backbone (15)N CPMG dispersion NMR spectroscopy and a collection of experiments to determine the exchange-free component to the transverse relaxation rate. Exchange contributions to the (1)H line width were detected for 21 methyl groups, and these probes were found to collectively report on a local structural rearrangement around the phosphorylation site, with a rate constant of (15.5 ± 0.5) × 10(3) per second (i.e., ?(ex) = 64.7 ± 1.9 ?s). The affected methyl groups indicate that, already before phosphorylation, a substantial, transient rearrangement takes place between helices 3 and 4 and strands 4 and 5. This conformational equilibrium allows the protein to gain access to the active, signaling state in the absence of covalent modification through a shift in a pre-existing dynamic equilibrium. Moreover, the conformational switching maps exactly to the regions that differ between the solution NMR structures of the fully inactive and active states. These results demonstrate that a cost-effective and quantitative study of protein methyl group dynamics by (1)H CPMG relaxation dispersion NMR spectroscopy is possible and can be applied to study functional motions on the microsecond time scale that cannot be accessed by backbone (15)N relaxation dispersion NMR. The use of methyl groups as dynamics probes extends such applications also to larger proteins.
| S-EPMC2991065 | biostudies-literature
Project description:PurposeDWI near metal implants has not been widely explored due to substantial challenges associated with through-slice and in-plane distortions, the increased encoding requirement of different spectral bins, and limited SNR. There is no widely adopted clinical protocol for DWI near metal since the commonly used EPI trajectory fails completely due to distortion from extreme off-resonance ranging from 2 to 20 kHz. We present a sequence that achieves DWI near metal with moderate b-values (400-500 s/mm2 ) and volumetric coverage in clinically feasible scan times.Theory and methodsMultispectral excitation with Cartesian sampling, view angle tilting, and kz phase encoding reduce in-plane and through-plane off-resonance artifacts, and Carr-Purcell-Meiboom-Gill (CPMG) spin-echo refocusing trains counteract T2* effects. The effect of random phase on the refocusing train is eliminated using a stimulated echo diffusion preparation. Root-flipped Shinnar-Le Roux refocusing pulses permits preparation of a high spectral bandwidth, which improves imaging times by reducing the number of excitations required to cover the desired spectral range. B1 sensitivity is reduced by using an excitation that satisfies the CPMG condition in the preparation. A method for ADC quantification insensitive to background gradients is presented.ResultsNon-linear phase refocusing pulses reduces the peak B1 by 46% which allows RF bandwidth to be doubled. Simulations and phantom experiments show that a non-linear phase CPMG pulse pair reduces B1 sensitivity. Application in vivo demonstrates complementary contrast to conventional multispectral acquisitions and improved visualization compared to DW-EPI.ConclusionVolumetric and multispectral DW imaging near metal can be achieved with a 3D encoded sequence.
| S-EPMC8979554 | biostudies-literature
Project description:Chemical exchange phenomena are ubiquitous in macromolecules, which undergo conformational change or ligand complexation. NMR relaxation dispersion (RD) spectroscopy based on a Carr-Purcell-Meiboom-Gill pulse sequence is widely applied to identify the exchange and measure the lifetime of intermediate states on the millisecond time scale. Advances in hyperpolarization methods improve the applicability of NMR spectroscopy when rapid acquisitions or low concentrations are required, through an increase in signal strength by several orders of magnitude. Here, we demonstrate the measurement of chemical exchange from a single aliquot of a ligand hyperpolarized by dissolution dynamic nuclear polarization (D-DNP). Transverse relaxation rates are measured simultaneously at different pulsing delays by dual-channel 19F NMR spectroscopy. This two-point measurement is shown to allow the determination of the exchange term in the relaxation rate expression. For the ligand 4-(trifluoromethyl)benzene-1-carboximidamide binding to the protein trypsin, the exchange term is found to be equal within error limits in neutral and acidic environments from D-DNP NMR spectroscopy, corresponding to a pre-equilibrium of trypsin deprotonation. This finding illustrates the capability for determination of binding mechanisms using D-DNP RD. Taking advantage of hyperpolarization, the ligand concentration in the exchange measurements can reach on the order of tens of ?M and protein concentration can be below 1 ?M, i.e., conditions typically accessible in drug discovery.
| S-EPMC6198795 | biostudies-literature
Project description:This review describes off-resonance R1ρ relaxation dispersion NMR methods for characterizing microsecond-to-millisecond chemical exchange in uniformly 13C/15N labeled nucleic acids in solution. The review opens with a historical account of key developments that formed the basis for modern R1ρ techniques used to study chemical exchange in biomolecules. A vector model is then used to describe the R1ρ relaxation dispersion experiment, and how the exchange contribution to relaxation varies with the amplitude and frequency offset of an applied spin-locking field, as well as the population, exchange rate, and differences in chemical shifts of two exchanging species. Mathematical treatment of chemical exchange based on the Bloch-McConnell equations is then presented and used to examine relaxation dispersion profiles for more complex exchange scenarios including three-state exchange. Pulse sequences that employ selective Hartmann-Hahn cross-polarization transfers to excite individual 13C or 15N spins are then described for measuring off-resonance R1ρ(13C) and R1ρ(15N) in uniformly 13C/15N labeled DNA and RNA samples prepared using commercially available 13C/15N labeled nucleotide triphosphates. Approaches for analyzing R1ρ data measured at a single static magnetic field to extract a full set of exchange parameters are then presented that rely on numerical integration of the Bloch-McConnell equations or the use of algebraic expressions. Methods for determining structures of nucleic acid excited states are then reviewed that rely on mutations and chemical modifications to bias conformational equilibria, as well as structure-based approaches to calculate chemical shifts. Applications of the methodology to the study of DNA and RNA conformational dynamics are reviewed and the biological significance of the exchange processes is briefly discussed.
| S-EPMC6727989 | biostudies-literature
Project description:PurposeTo investigate the effect of Carr-Purcell (CP) pulse trains on transverse relaxation times, T2, of tissue water and metabolites (both noncoupled and J-coupled spins) in the rat brain at 9.4 Tesla (T) using LASER, CP-LASER, and T2ρ-LASER sequences.MethodsProton NMR spectra were measured in rat brain in vivo at 9.4T. Spectra were acquired at multiple echo times ranging from 18 to 402 ms. All spectra were analyzed using LCModel with simulated basis sets. Signals of metabolites as a function of echo time were fitted using a mono-exponential function to determine their T2 relaxation times.ResultsMeasured T2 s for tissue water and all metabolites were significantly longer with CP-LASER and T2ρ-LASER compared with LASER. The T2 increased by a factor of ∼ 1.3 for noncoupled and weakly coupled spins (e.g., N-acetylaspartate and total creatine) and by a factor of ∼ 2 (e.g., glutamine and taurine) to ∼ 4 (e.g., glutamate and myo-inositol) for strongly coupled spins.ConclusionApplication of a CP pulse train results in a larger increase in T2 relaxation times for strongly coupled spins than for noncoupled (singlet) and weakly coupled spins. This needs to be taken into account when correcting for T2 relaxation in CP-like sequences such as LASER.
| S-EPMC4101080 | biostudies-literature
Project description:A number of NMR methods possess the capability of probing chemical exchange dynamics in solution. However, certain drawbacks limit the applications of these NMR approaches, particularly, to a complex system. Here, we propose a procedure that integrates the regularized nonnegative least squares (NNLS) analysis of multiexponential T2 relaxation into Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments to probe chemical exchange in a multicompartmental system. The proposed procedure was validated through analysis of (19)F T2 relaxation data of 6-fluoro-DL-tryptophan in a two-compartment solution with and without bovine serum albumin. Given the regularized NNLS analysis of a T2 relaxation curve acquired, for example, at the CPMG frequency ? CPMG = 125, the nature of two distinct peaks in the associated T2 distribution spectrum indicated 6-fluoro-DL-tryptophan either retaining the free state, with geometric mean */multiplicative standard deviation (MSD) = 1851.2 ms */1.51, or undergoing free/albumin-bound interconversion, with geometric mean */MSD = 236.8 ms */1.54, in the two-compartment system. Quantities of the individual tryptophan species were accurately reflected by the associated T2 peak areas, with an interconversion state-to-free state ratio of 0.45 ± 0.11. Furthermore, the CPMG relaxation dispersion analysis estimated the exchange rate between the free and albumin-bound states in this fluorinated tryptophan analog and the corresponding dissociation constant of the fluorinated tryptophan-albumin complex in the chemical-exchanging, two-compartment system.
| S-EPMC4452398 | biostudies-literature
Project description:PurposeIn clinical studies, compartmental average chemical exchange saturation transfer (CEST) measurements rather than voxel-by-voxel CEST images may suffice for evaluating its diagnostic value. A recently developed method-spectroscopy with linear algebraic modeling, or SLAM-could directly provide compartmental measures with dramatically reduced scan time and optimal signal-to-noise ratios. Here, we test whether SLAM can be adapted to significantly accelerate CEST acquisitions.Theory and methodsConventional anatomical images and raw CEST image k-space data were acquired from seven brain tumor patients. SLAM was applied to the CEST data using acceleration factors of R = 1-45, after segmenting compartments from co-registered images. SLAM-CEST measures were compared with average values from the identical compartments obtained by conventional Fourier transform (FT) CEST.ResultsSLAM generated compartmental average CEST z-spectra that were indistinguishable from conventional FT-CEST for R ≤ 45. SLAM-CEST z-spectra at ±3.5 ppm were highly correlated with FT-CEST measures (r(2) ≥ 0.98 for R ≤ 9; r ≥ 0.995 for R ≤ 45). The average error of SLAM-CEST versus FT-CEST measures was ≤10% for R ≤ 45, in acquisitions requiring as few as a single k-space phase-encoding step.ConclusionApplied to patients with brain tumors, SLAM-CEST can yield results that are quantitatively equivalent to conventional CEST up to 45 times faster, which could prove enabling in clinical settings where scan time is limiting. Magn Reson Med 76:136-144, 2016. © 2015 Wiley Periodicals, Inc.
| S-EPMC4548835 | biostudies-literature
Project description:NMR relaxation dispersion experiments have been widely applied to probe important conformational exchange of macro-molecules in many biological systems. The current improvements in computational techniques as well as the theoretical breakthroughs make the quantitative data analysis of complex exchange models possible. However, the topology of a given exchange model is also one of the main factors affecting the solution of Bloch-McConnell equation. The lack of a theoretical analysis of the exchange topologies at n-site exchange hinders further progress of such data analysis. Here, using graph theory, we reveal the topological complexity of n-site exchange and present all exchange models when n is less than 6. Furthermore, we introduce an alternative way, using machine learning, to select an exchange model based on a set of relaxation dispersion data without fitting them with every individual exchange model.
| S-EPMC8205974 | biostudies-literature