On Neglecting Chemical Exchange Effects When Correcting in VivoP MRS Data for Partial Saturation

This article replies to Spencer et al. (J. Magn. Reson.149, 251–257, 2001) concerning the degree to which chemical exchange affects partial saturation corrections using saturation factors. Considering the important case of in vivo³¹P NMR, we employ differential analysis to demonstrate a broad range of experimental conditions over which chemical exchange minimally affects saturation factors, and near-optimum signal-to-noise ratio is preserved. The analysis contradicts Spencer et al.'s broad claim that chemical exchange results in a strong dependence of saturation factors upon M₀'s and T₁ and exchange parameters. For Spencer et al.'s example of a dynamic ³¹P NMR experiment in which phosphocreatine varies 20-fold, we show that our strategy of measuring saturation factors at the start and end of the study reduces errors in saturation corrections to 2% for the high-energy phosphates.     

Pitfalls in the measurement of metabolite concentrations using the one-pulse experiment in in Vivo NMR: commentary on "On neglecting chemical exchange effects when correcting in vivo (31)P MRS data for partial saturation"

In an article in a previous issue of the Journal of Magnetic Resonance, Ouwerkerk and Bottomley (J. Magn. Reson. 148, pp. 425--435, 2001) show that even in the presence of chemical exchange, the dependence of saturation factors on repetition time in the one-pulse experiment is approximately monoexponential. They conclude from this fact that the effect of chemical exchange on the use of saturation factors when correcting for partial saturation is negligible. We take issue with this conclusion and demonstrate that because saturation factors in the presence of chemical exchange are strongly dependent upon all of the chemical parameters of the system, that is, upon all T(1)'s and M(0)'s of resonances in the exchange network and upon the reaction rates themselves, it is problematic to apply saturation factor corrections in situations in which any of these parameters may change. The error criterion we establish reflects actual errors in quantitation, rather than departures from monoexponentiality.     

On neglecting chemical exchange effects when correcting in vivo (31)P MRS data for partial saturation

Signal acquisition in most MRS experiments requires a correction for partial saturation that is commonly based on a single exponential model for T(1) that ignores effects of chemical exchange. We evaluated the errors in (31)P MRS measurements introduced by this approximation in two-, three-, and four-site chemical exchange models under a range of flip-angles and pulse sequence repetition times (T(R)) that provide near-optimum signal-to-noise ratio (SNR). In two-site exchange, such as the creatine-kinase reaction involving phosphocreatine (PCr) and gamma-ATP in human skeletal and cardiac muscle, errors in saturation factors were determined for the progressive saturation method and the dual-angle method of measuring T(1). The analysis shows that these errors are negligible for the progressive saturation method if the observed T(1) is derived from a three-parameter fit of the data. When T(1) is measured with the dual-angle method, errors in saturation factors are less than 5% for all conceivable values of the chemical exchange rate and flip-angles that deliver useful SNR per unit time over the range T(1)/5 < or = T(R) < or = 2T(1). Errors are also less than 5% for three- and four-site exchange when T(R) > or = T(1)(*)/2, the so-called "intrinsic" T(1)'s of the metabolites. The effect of changing metabolite concentrations and chemical exchange rates on observed T(1)'s and saturation corrections was also examined with a three-site chemical exchange model involving ATP, PCr, and inorganic phosphate in skeletal muscle undergoing up to 95% PCr depletion. Although the observed T(1)'s were dependent on metabolite concentrations, errors in saturation corrections for T(R) = 2 s could be kept within 5% for all exchanging metabolites using a simple interpolation of two dual-angle T(1) measurements performed at the start and end of the experiment. Thus, the single-exponential model appears to be reasonably accurate for correcting (31)P MRS data for partial saturation in the presence of chemical exchange. Even in systems where metabolite concentrations change, accurate saturation corrections are possible without much loss in SNR.     

Pitfalls in the Measurement of Metabolite Concentrations Using the One-Pulse Experiment in in Vivo NMR: Commentary on “On Neglecting Chemical Exchange Effects When Correcting in VivoP MRS Data for Partial Saturation”

In an article in a previous issue of the Journal of Magnetic Resonance, Ouwerkerk and Bottomley (J. Magn. Reson.148, pp. 425–435, 2001) show that even in the presence of chemical exchange, the dependence of saturation factors on repetition time in the one-pulse experiment is approximately monoexponential. They conclude from this fact that the effect of chemical exchange on the use of saturation factors when correcting for partial saturation is negligible. We take issue with this conclusion and demonstrate that because saturation factors in the presence of chemical exchange are strongly dependent upon all of the chemical parameters of the system, that is, upon all T₁'s and M₀'s of resonances in the exchange network and upon the reaction rates themselves, it is problematic to apply saturation factor corrections in situations in which any of these parameters may change. The error criterion we establish reflects actual errors in quantitation, rather than departures from monoexponentiality.     

Experimental demonstration of quantitation errors in MR spectroscopy resulting from saturation corrections under changing conditions

Metabolite concentration measurements in in vivo NMR are generally performed under partially saturated conditions, with correction for partial saturation performed after data collection using a measured saturation factor. Here, we present an experimental test of the hypothesis that quantitation errors can occur due to application of such saturation factor corrections in changing systems. Thus, this extends our previous theoretical work on quantitation errors due to varying saturation factors. We obtained results for two systems frequently studied by 31P NMR, the ischemic rat heart and the electrically stimulated rat gastrocnemius muscle. The results are interpreted in light of previous theoretical work which defined the degree of saturation occurring in a one-pulse experiment for a system with given spin-lattice relaxation times, T(1)s, equilibrium magnetizations, M(0)s, and reaction rates. We found that (i) the assumption of constancy of saturation factors leads to quantitation errors on the order of 40% in inorganic phosphate; (ii) the dominant contributor to the quantitation errors in inorganic phosphate is most likely changes in T(1); (iii) T(1) and M(0) changes between control and intervention periods, and chemical exchange contribute to different extents to quantitation errors in phosphocreatine and gamma-ATP; (iv) relatively small increases in interpulse delay substantially decreased quantitation errors for metabolites in ischemic rat hearts; (v) random error due to finite SNR led to approximately 4% error in quantitation, and hence was a substantially smaller contributor than were changes in saturation factors.     

Measurement of spin-lattice relaxation times and concentrations in systems with chemical exchange using the one-pulse sequence: breakdown of the Ernst model for partial saturation in nuclear magnetic resonance spectroscopy

A fundamental problem in Fourier transform NMR spectroscopy is the calculation of observed resonance amplitudes for a repetitively pulsed sample, as first analyzed by Ernst and Anderson in 1966. Applications include determination of spin-lattice relaxation times (T(1)'s) by progressive saturation and correction for partial saturation in order to determine the concentrations of the chemical constituents of a spectrum. Accordingly, the Ernst and Anderson formalism has been used in innumerable studies of chemical and, more recently, physiological systems. However, that formalism implicitly assumes that no chemical exchange occurs. Here, we present an analysis of N sites in an arbitrary chemical exchange network, explicitly focusing on the intermediate exchange rate regime in which the spin-lattice relaxation rates and the chemical exchange rates are comparable in magnitude. As a special case of particular importance, detailed results are provided for a system with three sites undergoing mutual exchange. Specific properties of the N-site network are then detailed. We find that (i) the Ernst and Anderson analysis describing the response of a system to repetitive pulsing is inapplicable to systems with chemical exchange and can result in large errors in T(1) and concentration measurements; (ii) T(1)'s for systems with arbitrary exchange networks may still be correctly determined from a one-pulse experiment using the Ernst formula, provided that a short interpulse delay time and a large flip angle are used; (iii) chemical concentrations for exchanging systems may be correctly determined from a one-pulse experiment either by using a short interpulse delay time with a large flip angle, as for measuring T(1)'s, and correcting for partial saturation by use of the Ernst formula, or directly by using a long interpulse delay time to avoid saturation; (iv) there is a significant signal-to-noise penalty for performing one-pulse experiments under conditions which permit accurate measurements of T(1)'s and chemical concentrations. The present results are analogous to but are much more general than those that we have previously derived for systems with two exchanging sites. These considerations have implications for the design and interpretation of one-pulse experiments for all systems exhibiting chemical exchange in the intermediate exchange regime, including virtually all physiologic samples.     

2D 1H-31P solid-state NMR studies of the dependence of inter-bilayer water dynamics on lipid headgroup structure and membrane peptides

The dynamics of hydration-water in several phospholipid membranes of different compositions is studied by 2D (1)H-(31)P heteronuclear correlation NMR under magic-angle spinning. By using a (1)H T(2) filter before and a (1)H mixing-time after the evolution period and (31)P detection, inter-bilayer water is selectively detected without resonance overlap from bulk water outside the multilamellar vesicles. Moreover the (1)H T(2) relaxation time of the inter-bilayer water is measured. Lipid membranes with labile protons either in the lipid headgroup or in sterols exhibit water-(31)P correlation peaks while membranes free of exchangeable protons do not, indicating that the mechanism for water-lipid correlation is chemical exchange followed by relayed magnetization transfer to (31)P. In the absence of membrane proteins, the inter-bilayer water (1)H T(2)'s are several tens of milliseconds. Incorporation of charged membrane peptides shortened this inter-bilayer water T(2) significantly. This T(2) reduction is attributed to the peptides' exchangeable protons, molecular motion and intermolecular hydrogen bonding, which affect the water dynamics and the chemically relayed magnetization transfer process.     

Chemical exchange magnetic resonance imaging (CHEMI)

Systems investigated with NMR spectroscopy are sometimes heterogeneous with respect to chemical composition, rates of chemical exchange, and other properties influencing magnetic resonance parameters. A method was developed to spatially encode reaction kinetic information and produce NMR images sensitive to chemical exchange. A modified spin-echo pulse sequence was used to allow chemical shift-selective imaging and chemical exchange encoding. 1H and 31P images with microscopic resolution were obtained which yielded chemical exchange as a function of position. Chemical exchange images of the base-catalyzed proton exchange of acetylacetone and of the enzyme-catalyzed 31P transfer between PCr and ATP were obtained at 8.4 T in phantoms at 360 and 146 MHz, respectively. These images demonstrate a means of investigating kinetic heterogeneity and compartmentalization of reactions that are important in the study of both living and non-living systems.     

The enhancement of three-party simultaneous quantum secure direct communication scheme with EPR pairs

Recently, Wang et al. proposed a three-party simultaneous quantum secure direct communication (3P-SQSDC) scheme with EPR pairs, which enables three involved parties to exchange their secret messages simultaneously by using an EPR pair. This work proposed an enhancement on Wang et al.'s scheme. With the enhancement, the communications in the improved 3P-SQSDC can be paralleled and thus improves the protocol efficiency.     

Probing proteins in solution by (129)Xe NMR spectroscopy

The interaction of xenon with different proteins in aqueous solution is investigated by (129)Xe NMR spectroscopy. Chemical shifts are measured in horse metmyoglobin, hen egg white lysozyme, and horse cytochrome c solutions as a function of xenon concentration. In these systems, xenon is in fast exchange between all possible environments. The results suggest that nonspecific interactions exist between xenon and the protein exteriors and the data are analyzed in term of parameters which characterize the protein surfaces. The experimental data for horse metmyoglobin are interpreted using a model in which xenon forms a 1:1 complex with the protein and the chemical shift of the complexed xenon is reported (Locci et al., Keystone Symposia "Frontiers of NMR in Molecular Biology VI", Jan. 9--15, 1999, Breckenridge, CO, Abstract E216, p. 53; Locci et al., XeMAT 2000 "Optical Polarization and Xenon NMR of Materials", June 28--30, 2000, Sestri Levante, Italy, p. 46).     

Phosphorus-31 NMR studies of stabilized phosphorus ylids in the solid state.

Phosphorus-31 powder NMR spectra and high-resolution MAS spectra have been obtained for a number of stabilized phosphorus ylids under conditions of high-power proton decoupling and cross-polarization. The 31P CP/MAS spectra are compared to those obtained from isotropic solutions. The variation of chemical shift anisotropy and of the principal components of the 31P chemical shift tensor determined from 31P powder NMR line shapes are discussed in terms of the relative importance of accepted valence bond resonance structures. The results indicate that the invariance of the isotropic chemical shift, delta iso, observed in previous 31P NMR investigations of phosphorus ylids in solution is due to fortuitous cancellation of opposing changes in the principal components, delta 11 and delta 33, of the 31P chemical shift tensor. The 31P dipolar NMR powder spectrum of a typical stabilized ylid, (C6H5)3(31)P-13CHC(O)OCH2CH3, is analyzed in order to obtain the orientation of the 31P chemical shift tensor with respect to the 31P-13C alpha dipolar vector.     

Complete relaxation and conformational exchange matrix (CORCEMA) analysis of intermolecular saturation transfer effects in reversibly forming ligand-receptor complexes

A couple of recent applications of intermolecular NOE (INOE) experiments as applied to biomolecular systems involve the (i) saturation transfer difference NMR (STD-NMR) method and (ii) the intermolecular cross-saturation NMR (ICS-NMR) experiment. STD-NMR is a promising tool for rapid screening of a large library of compounds to identify bioactive ligands binding to a target protein. Additionally, it is also useful in mapping the binding epitopes presented by a bioactive ligand to its target protein. In this latter application, the STD-NMR technique is essentially similar to the ICS-NMR experiment, which is used to map protein-protein or protein-nucleic acid contact surfaces in complexes. In this work, we present a complete relaxation and conformational exchange matrix (CORCEMA) theory (H. N. B. Moseley et al., J. Magn. Reson. B 108, 243-261 (1995)) applicable for these two closely related experiments. As in our previous work, we show that when exchange is fast on the relaxation rate scale, a simplified CORCEMA theory can be formulated using a generalized average relaxation rate matrix. Its range of validity is established by comparing its predictions with those of the exact CORCEMA theory which is valid for all exchange rates. Using some ideal model systems we have analyzed the factors that influence the ligand proton intensity changes when the resonances from some protons on the receptor protein are saturated. The results show that the intensity changes in the ligand signals in an intermolecular NOE experiment are very much dependent upon: (1) the saturation time, (2) the location of the saturated receptor protons with respect to the ligand protons, (3) the conformation of the ligand-receptor interface, (4) the rotational correlation times for the molecular species, (5) the kinetics of the reversibly forming complex, and (6) the ligand/receptor ratio. As an example of a typical application of the STD-NMR experiment we have also simulated the STD effects for a hypothetical trisaccharide bound to a protein. The CORCEMA theory for INOE and the associated algorithm are useful in a quantitative interpretation of the intensity changes in the ligand in both the STD-NMR and ICS-NMR, provided the identity of the receptor protons experiencing direct RF saturation is known. The formalism presented here is likely to be useful in the design of bioactive ligands to a specific target protein and in the quantitative mapping of binding epitopes and interfaces between molecules in complexes.     

Bose fluids above T(c): incompressible vortex fluids and "supersolidity"

This Letter emphasizes that nonlinear rotational or diamagnetic susceptibility is characteristic of Bose fluids above their superfluid T(C)'s. For sufficiently slow rotation or, for superconductors, weak B fields, this amounts to an incompressible response to vorticity. The cause is that there are terms missing in the conventionally accepted model Hamiltonian for quantized vortices in the Bose fluid. The resulting susceptibility can account for recent observations of Chan et al. [Nature (London) 427, 225 (2004); Science 305, 1941 (2004)] on solid He and Ong et al. [Europhys. Lett. 72, 451 (2005) on cuprate superconductors.     

The simulation of 31P NMR line shapes of lipid bilayers using an analytically soluble model

Van Faassen's method for obtaining an explicit solution to a first order stochastic differential equation is applied to the simulation of 31P NMR line shapes of unoriented phospholipid bilayers in the Lalpha phase and of oriented bilayers in both the Lalpha and Lbeta' phases. The effects of the two slowest motions on the density matrix are described by the stochastic Liouville equation (SLE) which is solved analytically using the method of van Faassen. These two slowest motions are assumed to be a rotational re-orientation about the long molecular axis and a uniform wobble of this axis within a conical volume with re-orientation rates characterised by correlation times tau(parallel) and tau(perpendicular) respectively. In the present work the Hamiltonian contains the intramolecular dipole-dipole interaction between the phosphorous nucleus and the four closest methylene protons of the choline headgroup, as well as the anisotropic chemical shielding interaction. Hence the contribution to relaxation from cross correlation between the dipole-dipole and anisotropic chemical shielding interactions is included. The reorientation of the headgroup is assumed to be a rotation sufficiently fast to lead to complete axially symmetric averaging of the Hamiltonian about the rotational axis (the P-O11 bond axis). Evaluation of the line shape in the present work involves only numerical integration and is therefore less computationally demanding than the large matrix inversions involved in the approaches of Campbell, Freed et al. The present theory also uses fewer parameters than that of Dufourc et al. but nevertheless results in good agreement with these authors' measurements on DMPC bilayers, using a fixed value of 10 for the ratio tau(perpendicular)/tau(parallel) in the case of the Lalpha phase. However, in contrast to Dufourc et al., we find that these correlation times are equal for the Lbeta' phase. Finally, we have simulated the decoupled powder line shapes obtained from the Lbeta' phase of DPPC by Campbell and Meirovitch. Again, we get good agreement providing tau(perpendicular)=tau(parallel).     

系列Mo-Cu(Ag,Au)-Se簇合物的95Mo和31P NMR研究

报道了含硬币金属和四硒代钼酸盐的异金属硒簇合物的⁹⁵Mo NMR研究结果和含膦配体Mo(W)-Cu(Ag,Au)-Se配合物的³¹P NMR谱学性能。发现不同硬币金属对⁹⁵Mo核的化学屏蔽效应顺序为Au > Cu > Ag;对系列Mo-Cu-Se化合物的⁹⁵Mo NMR研究结果表明:⁹⁵Mo NMR的化学位移和线宽不仅与配位的Cu原子数目有关,而且对结构的变化特别敏感;[MoSe₄]^2-离子的相对四个方向被Cu⁺配位后,其Mo核的屏蔽基本饱和;外围配体对⁹⁵Mo NMR数据影响甚微。同时还用动态⁹⁵Mo NMR谱技术跟踪配体的取代反应和从MoCu₄到MoCu₁₀核的簇骼转变过程。此外,还讨论了这些化合物在不同构型之间,同一构型不同金属中心和不同配体基团的³¹P NMR化学位移的变化特征。     

Meson exchange corrections and properties of nuclear matter and neutron matter

A calculation of meson exchange corrections to the binding energy as function of the density is presented for nuclear matter and neutron matter. The framework is the application of non-covariant perturbation theory to a field theoretical Hamiltonian. Within a Brueckner-type approximation we restrict ourselves to the calculation of those meson exchange corrections which are due to one meson exchange and which produce no mass renormalization corrections. The results are reported in detail and the structure of the results is revealed. As a net effect, we find that our meson exchange corrections give a repulsion in nuclear matter yielding about 5 MeV less binding at the saturation point. For neutron matter, the effects are very small.     

Relayed magnetization transfer from nuclear Overhauser effect and chemical exchange observed by in vivo ³¹P MRS in rat brain

The ³¹P magnetization transfer effects among nuclear magnetic resonances (NMRs) of phosphocreatine (PCr), γ-adenosine-5'-triphosphate (γ-ATP) and inorganic phosphate (Pi) have been attributed to the chemical exchange reactions among PCr, ATP and Pi catalyzed by creatine kinase (CK) and ATPase enzymes and, therefore, are commonly applied in situ to measure chemical exchange fluxes involving two chemically coupled CK and ATPase reactions (i.e., PCr↔ATP↔Pi) by selectively saturating γ-ATP resonance. Besides the expected reductions in the Pi and PCr NMR signals upon saturating γ-ATP resonance, one particularly interesting phenomenon showing decreases in α-ATP and β-ATP signals was also observed. The underlying mechanism was investigated and identified via saturating NMR of β-ATP in the present study. The unique relayed magnetization transfer effects through spin diffusion were observed in the rat brain using in vivo ³¹P magnetic resonance spectroscopy.     

Information leakage in three-party simultaneous quantum secure direct communication with EPR pairs

In 2007, Wang et al. [M. Y. Wang and F. L. Yan, Chin. Phys. Lett. 24 (2007) 2486] proposed a three-party simultaneous quantum secure direct communication (3P-SQSDC) scheme with EPR pairs. Recently, Chong et al. [S. K. Chong and T. Hwang, Opt. Commun. OPTICS-15438 (2010(online))] proposed an enhancement on Wang et al.'s scheme. The communications in Chong et al.'s 3P-SQSDC can be paralleled and thus their scheme has higher efficiency. However, we find that both of the schemes have the information leakage, because the legitimate parties' secret messages have a strong correlation. This kind of security loophole leads to the consequence that any eavesdropper (Eve) can directly conjecture some information about the secrets without any active attack.     

Magic-angle-spinning NMR on solid biological systems. Analysis Of the origin of the spectral linewidths

Magic-angle-spinning (MAS) high-power ¹H-decoupled ¹³C and ³¹P NMR has been applied to solid biological materials to obtain information about the mechanisms that determine the spectral linewidths. The line broadening in MAS ³¹P NMR spectra of solid tobacco mosaic virus (TMV) has been investigated by selective saturation and T₂ measurements. About 90 Hz stems from homogeneous effects, whereas the inhomogeneous contribution is approximately 100 Hz. The inhomogeneous line broadening is assigned to macroscopic inhomogeneities in the sample and not to variations in the nucleotide bases along the RNA strand in TMV. It is concluded that sample preparation is of vital importance for obtaining well-resolved spectra. Under optimal preparation techniques the isotropic values of the chemical shift of the different ³¹P sites have been determined to obtain information about the secondary structure of the viral RNA. The chemical shift anisotropy has been determined from the relative intensities of the spinning side bands in the spectra. The chemical shift information is used to make a tentative assignment of the resonance in terms of the three structurally distinguishable phosphate groups in TMV. The origin of the linewidths in MAS NMR has been examined further by ¹³C NMR of approximately 10% ¹³C-enriched coat protein of cowpea chlorotic mottle virus, using selective excitation and saturation techniques, as well as measurements of the relaxation times T_1γ and T₂. The CO resonance in the spectrum is composed of an inhomogeneous and homogeneous part with a total linewidth of 700 Hz. The homogeneous linewidth, contributing with 200 Hz, is found to arise from slow molecular motions in the solid on a millisecond timescale.     

Correcting for incomplete saturation and off-resonance effects in multiple-site saturation-transfer kinetic measurements

The effects of incomplete saturation and off-resonance irradiation on nuclear magnetic resonance saturation-transfer measurements of three-site chemical-exchange rates are discussed. A new method that uses double-saturation measurements is compared with two published methods, one that uses single-saturation measurements and one that uses a single-saturation measurement and a double-saturation measurement. Several formulas are compared for measuring the exchange rate constant k(DE) for exchange from a detected spin D to an exchanging spin E in the presence of exchange from spin D to a competing spin C. For each method, formulas are derived with corrections for incomplete saturation or off-resonance effects, with both corrections, and with neither correction. Exact formulas are available for three exchanging sites with incomplete saturation if there are no off-resonance effects. Off-resonance corrections are imperfect even with complete saturation.