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1.
New relaxation dispersion experiments are presented that probe millisecond time-scale dynamical processes in proteins. The experiments measure the relaxation of (1)H-(15)N multiple-quantum coherence as a function of the rate of application of either (1)H or (15)N refocusing pulses during a constant time relaxation interval. In contrast to the dispersion profiles generated from more conventional (15)N((1)H) single-quantum relaxation experiments that depend on changes in (15)N((1)H) chemical shifts between exchanging states, (1)H-(15)N multiple-quantum dispersions are sensitive to changes in the chemical environments of both (1)H and (15)N spins. The resulting multiple-quantum relaxation dispersion profiles can, therefore, be quite different from those generated by single-quantum experiments, so that an analysis of both single- and multiple-quantum profiles together provides a powerful approach for obtaining robust measures of exchange parameters. This is particularly the case in applications to protonated proteins where other methods for studying exchange involving amide proton spins are negatively influenced by contributions from neighboring protons. The methodology is demonstrated on protonated and perdeuterated samples of a G48M mutant of the Fyn SH3 domain that exchanges between folded and unfolded states in solution.  相似文献   

2.
A series of experiments are presented that provide an exchange-free measure of dipole-dipole (15)N transverse relaxation, R(dd), that can then be substituted for (15)N R(1rho) or R(2) rates in the study of internal protein dynamics. The method is predicated on the measurement of a series of relaxation rates involving (1)H-(15)N longitudinal order, anti-phase (1)H and (15)N single-quantum coherences, and (1)H-(15)N multiple quantum coherences; the relaxation rates of all coherences are measured under conditions of spin-locking. Results from detailed simulations and experiments on a number of protein systems establish that R(dd) values are independent of exchange and systematic errors from dipolar interactions with proximal protons are calculated to be less than 1-2%, on average, for applications to perdeuterated proteins. Simulations further indicate that the methodology is rather insensitive to the exact level of deuteration so long as proteins are reasonably highly deuterated (>50%). The utility of the methodology is demonstrated with applications involving protein L, ubiquitin, and a stabilized folding intermediate of apocytochrome b(562) that shows large contributions to (15)N R(1rho) relaxation from chemical exchange.  相似文献   

3.
An approach is presented that allows a detailed, quantitative characterization of conformational exchange processes in proteins on the micros-ms time scale. The approach relies on a combined analysis of NMR relaxation rates and chemical shift changes and requires that the chemical shift of the exchanging species can be determined independently of the relaxation rates. The applicability of the approach is demonstrated by a detailed analysis of the conformational exchange processes previously observed in the reduced form of the blue copper protein, plastocyanin from the cyanobacteria Anabaena variabilis (A.v. PCu) (Ma, L.; Hass, M. A. S.; Vierick, N.; Kristensen, S. M.; Ulstrup, J.; Led, J. J. Biochemistry 2003, 42, 320-330). The R1 and R2 relaxation rates of the backbone 15N nuclei were measured at a series of pH and temperatures on an 15N labeled sample of A.v. PCu, and the 15N chemical shifts were obtained from a series of HSQC spectra recorded in the pH range from 4 to 8. From the R1 and R2 relaxation rates, the contribution, Rex, to the transverse relaxation caused by the exchanges between the different allo-states of the protein were determined. Specifically, it is demonstrated that accurate Rex terms can be obtained from the R1 and R2 rates alone in the case of relatively rigid proteins with a small rotational anisotropy. The Rex terms belonging to the same exchange process were identified on the basis of their pH dependences. Subsequently the identifications were confirmed quantitatively by the correlation between the Rex terms and the corresponding chemical shift differences of the exchanging species. By this approach, the Rex terms of 15N nuclei belonging to contiguous regions in the protein could be assigned to the same exchange process. Furthermore, the analysis of the exchange terms shows that the observed micros-ms dynamics in A.v. PCu are caused primarily by the protonation/deprotonation of two histidine residues, His92 and His61, His92 being ligated to the Cu(I) ion. Also the exchange rate of the protonation/deprotonation process of His92 and its pH and temperature dependences were determined, revealing a reaction pathway that is more complex than a simple specific-acid/base catalysis. Finally, the approach allows a differentiation between two-site and multiple-site exchange processes, thus revealing that the protonation/deprotonation of His61 is at least a three-site exchange process. Overall, the approach makes it feasible to obtain exchange rates that are sufficiently accurate and versatile for studies of the kinetics and the mechanisms of local protein dynamics on the sub-millisecond time scale.  相似文献   

4.
A method for quantifying millisecond time scale exchange in proteins is presented based on scaling the rate of chemical exchange using a 2D (15)N, (1)H(N) experiment in which (15)N dwell times are separated by short spin-echo pulse trains. Unlike the popular Carr-Purcell-Meiboom-Gill (CPMG) experiment where the effects of a radio frequency field on measured transverse relaxation rates are quantified, the new approach measures peak positions in spectra that shift as the effective exchange time regime is varied. The utility of the method is established through an analysis of data recorded on an exchanging protein-ligand system for which the exchange parameters have been accurately determined using alternative approaches. Computations establish that a combined analysis of CPMG and peak shift profiles extends the time scale that can be studied to include exchanging systems with highly skewed populations and exchange rates as slow as 20 s(-1).  相似文献   

5.
The three-site exchange folding reaction of an (15)N-labeled, highly deuterated Gly48Met mutant of the Fyn SH3 domain has been characterized at 25 degrees C using a suite of six CPMG-type relaxation dispersion experiments that measure exchange contributions to backbone (1)H and (15)N transverse relaxation rates in proteins. It is shown that this suite of experiments allows the extraction of all the parameters of this multisite exchange process in a robust manner, including chemical shift differences between exchanging states, from a data set recorded at only a single temperature. The populations of the exchanging folded, intermediate, and unfolded states that are fit are 94, 0.7, and 5%, respectively. Despite the small fraction of the intermediate, structural information is obtained for this state that is consistent with the picture of SH3 domain folding that has emerged from other studies. Taken together, the six dispersion experiments facilitate the complete reconstruction of (1)H-(15)N correlation spectra for the unfolded and intermediate states that are "invisible" in even the most sensitive of NMR experiments.  相似文献   

6.
In this paper, we present a series of heteronuclear NMR experiments for the direct observation and characterization of lysine NH3 groups in proteins. In the context of the HoxD9 homeodomain bound specifically to DNA we were able to directly observe three cross-peaks, arising from lysine NH3 groups, with 15N chemical shifts around approximately 33 ppm at pH 5.8 and 35 degrees C. Measurement of water-exchange rates and various types of 15N transverse relaxation rates for these NH3 groups, reveals that rapid water exchange dominates the 15N relaxation for antiphase coherence with respect to 1H through scalar relaxation of the second kind. As a consequence of this phenomenon, 15N line shapes of NH3 signals in a conventional 1H-15N heteronuclear single quantum coherence (HSQC) correlation experiment are much broader than those of backbone amide groups. A 2D 1H-15N correlation experiment that exclusively observes in-phase 15N transverse coherence (termed HISQC for heteronuclear in-phase single quantum coherence spectroscopy) is independent of scalar relaxation in the t(1) (15N) time domain and as a result exhibits strikingly sharper 15N line shapes and higher intensities for NH3 cross-peaks than either HSQC or heteronuclear multiple quantum coherence (HMQC) correlation experiments. Coherence transfer through the relatively small J-coupling between 15Nzeta and 13Cepsilon (4.7-5.0 Hz) can be achieved with high efficiency by maintaining in-phase 15N coherence owing to its slow relaxation. With the use of a suite of triple resonance experiments based on the same design principles as the HISQC, all the NH3 cross-peaks observed in the HISQC spectrum could be assigned to lysines that directly interact with DNA phosphate groups. Selective observation of functional NH3 groups is feasible because of hydrogen bonding or salt bridges that protect them from rapid water exchange. Finally, we consider the potential use of lysine NH3 groups as an alternative probe for larger systems as illustrated by data obtained on the 128-kDa enzyme I dimer.  相似文献   

7.
We demonstrate constraint of peptide backbone and side-chain conformation with 3D (1)H-(15)N-(13)C-(1)H dipolar chemical shift, magic-angle spinning NMR experiments. In these experiments, polarization is transferred from (15)N[i] by ramped SPECIFIC cross polarization to the (13)C(alpha)[i], (13)C(beta)[i], and (13)C(alpha)[i - 1] resonances and evolves coherently under the correlated (1)H-(15)N and (1)H-(13)C dipolar couplings. The resulting set of frequency-labeled (15)N(1)H-(13)C(1)H dipolar spectra depend strongly upon the molecular torsion angles phi[i], chi1[i], and psi[i - 1]. To interpret the data with high precision, we considered the effects of weakly coupled protons and differential relaxation of proton coherences via an average Liouvillian theory formalism for multispin clusters and employed average Hamiltonian theory to describe the transfer of (15)N polarization to three coupled (13)C spins ((13)C(alpha)[i], (13)C(beta)[i], and (13)C(alpha)[i - 1]). Degeneracies in the conformational solution space were minimized by combining data from multiple (15)N(1)H-(13)C(1)H line shapes and analogous data from other 3D (1)H-(13)C(alpha)-(13)C(beta)-(1)H (chi1), (15)N-(13)C(alpha)-(13)C'-(15)N (psi), and (1)H-(15)N[i]-(15)N[i + 1]-(1)H (phi, psi) experiments. The method is demonstrated here with studies of the uniformly (13)C,(15)N-labeled solid tripeptide N-formyl-Met-Leu-Phe-OH, where the combined data constrains a total of eight torsion angles (three phi, three chi1, and two psi): phi(Met) = -146 degrees, psi(Met) = 159 degrees, chi1(Met) = -85 degrees, phi(Leu) = -90 degrees, psi(Leu) = -40 degrees, chi1(Leu) = -59 degrees, phi(Phe) = -166 degrees, and chi1(Phe) = 56 degrees. The high sensitivity and dynamic range of the 3D experiments and the data analysis methods provided here will permit immediate application to larger peptides and proteins when sufficient resolution is available in the (15)N-(13)C chemical shift correlation spectra.  相似文献   

8.
TROSY-based NMR relaxation dispersion experiments that measure the decay of double- and zero-quantum (1)H-(15)N coherences as a function of applied (1)H and (15)N radio frequency (rf) fields are presented for studying millisecond dynamic processes in proteins. These experiments are complementary to existing approaches that measure dispersions of single-quantum (15)N and (1)H magnetization. When combined, data from all four coherences provide a more quantitative picture of dynamics, making it possible to distinguish, for example, between two-site and more complex exchange processes. In addition, a TROSY-based pulse scheme is described for measuring the relaxation of amide (1)H single-quantum magnetization, obtained by a simple modification of the multiple-quantum experiments. The new methodology is applied to a point mutant of the Fyn SH3 domain that exchanges between folded and unfolded states at 25 degrees C.  相似文献   

9.
Conformational changes occurring on the microsecond-millisecond time scale in basic pancreatic trypsin inhibitor (BPTI) are investigated using nuclear magnetic resonance spectroscopy. The rczz CPMG experiment (Wang, C.; Grey, M. J.; Palmer, A. G. J. Biomol. NMR 2001, 21, 361-366) is used to record (15)N spin relaxation dispersion data, R(ex)(1/tau(cp)), in which 1/tau(cp) is the pulsing rate in the CPMG sequence, at two static magnetic fields, 11.7 and 14.1 T, and three temperatures, 280, 290, and 300 K. These data are used to characterize the kinetics and mechanism of chemical exchange line broadening of the backbone (15)N spins of Cys 14, Lys 15, Cys 38, and Arg 39 in BPTI. Line broadening is found to result from two processes: the previously identified isomerization of the Cys 38 side chain between chi(1) rotamers (Otting, G.; Liepinsh, E.; Wüthrich, K. Biochemistry 1993, 32, 3571-3582) and a previously uncharacterized process on a faster time scale. At 300 K, both processes contribute significantly to the relaxation dispersion for Cys 14 and an analytical expression for a linear three-site exchange model is used to analyze the data. At 280 K, isomerization of the Cys 38 side chain is negligibly slow and the faster process dominates the relaxation dispersion for all four spins. Global analysis of the temperature and static field dependence of R(ex)(1/tau(cp)) for Cys 14 and Lys 15 is used to determine the activation parameters and chemical shift changes for the previously uncharacterized chemical exchange process. Through an analysis of a database of chemical shifts, (15)N chemical shift changes for Cys 14 and Lys 15 are interpreted to result from a chi(1) rotamer transition of Cys 14 that converts the Cys 14-Cys 38 disulfide bond between right- and left-handed conformations. At 290 K, isomerization of Cys 14 occurs with a forward and reverse rate constant of 35 s(-1) and 2500 s(-1), respectively, a time scale more than 30-fold faster than the Cys 38 chi(1) isomerization. A comparison of the kinetics and thermodynamics for the transitions between the two alternative Cys 14-Cys 38 conformations highlights the factors that affect the contribution of disulfide bonds to protein stability.  相似文献   

10.
(15)N relaxation dispersion experiments were applied to the isolated N-terminal SH3 domain of the Drosophila protein drk (drkN SH3) to study microsecond to second time scale exchange processes. The drkN SH3 domain exists in equilibrium between folded (F(exch)) and unfolded (U(exch)) states under nondenaturing conditions in a ratio of 2:1 at 20 degrees C, with an average exchange rate constant, k(ex), of 2.2 s(-1) (slow exchange on the NMR chemical shift time scale). Consequently a discrete set of resonances is observed for each state in NMR spectra. Within the U(exch) ensemble there is a contiguous stretch of residues undergoing conformational exchange on a micros/ms time scale, likely due to local, non-native hydrophobic collapse. For these residues both the F(exch) <--> U(exch) conformational exchange process and the micros/ms exchange event within the U(exch) state contribute to the (15)N line width and can be analyzed using CPMG-based (15)N relaxation dispersion measurements. The contribution of both processes to the apparent relaxation rate can be deconvoluted numerically by combining the experimental (15)N relaxation dispersion data with results from an (15)N longitudinal relaxation experiment that accurately quantifies exchange rates in slow exchanging systems (Farrow, N. A.; Zhang, O.; Forman-Kay, J. D.; Kay, L. E. J. Biomol. NMR 1994, 4, 727-734). A simple, generally applicable analytical expression for the dependence of the effective transverse relaxation rate constant on the pulse spacing in CPMG experiments has been derived for a two-state exchange process in the slow exchange limit, which can be used to fit the experimental data on the global folding/unfolding transition. The results illustrate that relaxation dispersion experiments provide an extremely sensitive tool to probe conformational exchange processes in unfolded states and to obtain information on the free energy landscape of such systems.  相似文献   

11.
Analysis of the ratio of transverse and longitudinal relaxation rates (R2/R1) is an approach commonly used for estimation of overall correlation time and identification of chemical exchange in biological macromolecules. However, this analysis fails to distinguish between chemical exchange and motional anisotropy. We describe a simple method for identifying chemical exchange and motional anisotropy using the product, R1R2. In the slow tumbling regime, the R1R2 product results in a constant value that is independent of overall correlation time and motional anisotropy. This analysis provides a simple method for rapidly estimating and dissociating the effects of motional anisotropy and chemical exchange in NMR heteronuclear spin relaxation data. We demonstrate the utility of the method with 15N relaxation data collected on the proteins E. coli ribonuclease H and the trimeric E. coli membrane associated lipoprotein lpp.  相似文献   

12.
An (15)N NMR R(1rho) relaxation experiment is presented for the measurement of millisecond time scale exchange processes in proteins. On- and off-resonance R(1rho) relaxation profiles are recorded one residue at a time using a series of one-dimensional experiments in concert with selective Hartmann-Hahn polarization transfers. The experiment can be performed using low spin-lock field strengths (values as low as 25 Hz have been tested), with excellent alignment of magnetization along the effective field achieved. Additionally, suppression of the effects of cross-correlated relaxation between dipolar and chemical shift anisotropy interactions and (1)H-(15)N scalar coupled evolution is straightforward to implement, independent of the strength of the (15)N spin-locking field. The methodology is applied to study the folding of a G48M mutant of the Fyn SH3 domain that has been characterized previously by CPMG dispersion experiments. It is demonstrated through experiment that off-resonance R(1rho) data measured at a single magnetic field and one or more spin-lock field strengths, with amplitudes on the order of the rate of exchange, allow a complete characterization of a two-site exchange process. This is possible even in the case of slow exchange on the NMR time scale, where complementary approaches involving CPMG-based experiments fail. Advantages of this methodology in relation to other approaches are described.  相似文献   

13.
NMR relaxation data on disordered proteins can provide insight into both structural and dynamic properties of these molecules. Because of chemical shift degeneracy in correlation spectra, detailed site-specific analyses of side chain dynamics have not been possible. Here, we present new experiments for the measurement of side chain dynamics in methyl-containing residues in unfolded protein states. The pulse schemes are similar to recently proposed methods for measuring deuterium spin relaxation rates in (13)CH(2)D methyl groups in folded proteins.(1) However, because resolution in (1)H-(13)C correlation maps of unfolded proteins is limiting, relaxation data are recorded as a series of (1)H-(15)N spectra. The methodology is illustrated with an application to the study of side chain dynamics in delta131delta, a large disordered fragment of staphylococcal nuclease containing residues 1-3 and 13-140 of the wide-type protein. A good correlation between the order parameters of the symmetry axes of the methyl groups and the backbone (1)H-(15)N bond vectors of the same residue is observed. Simulations establish that such a correlation is only possible if the unfolded state is comprised of an ensemble of structures which are not equiprobable. A motional model, which combines wobbling-in-a-cone and Gaussian axial fluctuations, is proposed to estimate chi(1) torsion angle fluctuations, sigma(chi)()1, of Val and Thr residues on the basis of the backbone and side chain order parameters. Values of sigma(chi)()1 are approximately 10 degrees larger than what has previously been observed in folded proteins. Of interest, the value of sigma(chi)()1 for Val 104 is considerably smaller than for other Val or Thr residues, suggesting that it may be part of a hydrophobic cluster. Notably large (15)N transverse relaxation rates are observed in this region. To our knowledge, this is the first time that side chain dynamics in an unfolded state have been studied in detail by NMR.  相似文献   

14.
Solid-state 31P NMR spectroscopy was applied to measure the isotropic chemical shifts, chemical shift anisotropies and asymmetry parameters of three phosphorylated amino acids, O-phospho-L-serine, O-phospho-L-threonine and O-phospho-L-tyrosine. The cross-polarization buildup rates and longitudinal relaxation times of 31P and 1H were-determined and compared with the values measured for a triphosphate (GppCH2p) bound to a crystalline protein (Ras). It is shown that the phosphorylated amino acids are well-suited model compounds, e.g. for the optimization of experiments on crystalline proteins. Two-dimensional exchange experiments on O-phospho-L-tyrosine indicate the existence of an exchange between the two different conformations of the molecule.  相似文献   

15.
The acid-activated proton channel formed by the influenza M2 protein is important for the life cycle of the virus. A single histidine, His37, in the M2 transmembrane domain (M2TM) is responsible for pH activation and proton selectivity of the channel. Recent studies suggested three models for how His37 mediates proton transport: a shuttle mechanism involving His37 protonation and deprotonation, a H-bonded imidazole-imidazolium dimer model, and a transporter model involving large protein conformational changes in synchrony with proton conduction. Using magic-angle-spinning (MAS) solid-state NMR spectroscopy, we examined the proton exchange and backbone conformational dynamics of M2TM in a virus-envelope-mimetic membrane. At physiological temperature and pH, (15)N NMR spectra show fast exchange of the imidazole (15)N between protonated and unprotonated states. To quantify the proton exchange rates, we measured the (15)N T(2) relaxation times and simulated them for chemical-shift exchange and fluctuating N-H dipolar fields under (1)H decoupling and MAS. The exchange rate is 4.5 × 10(5) s(-1) for Nδ1 and 1.0 × 10(5) s(-1) for Nε2, which are approximately synchronized with the recently reported imidazole reorientation. Binding of the antiviral drug amantadine suppressed both proton exchange and ring motion, thus interfering with the proton transfer mechanism. By measuring the relative concentrations of neutral and cationic His as a function of pH, we determined the four pK(a) values of the His37 tetrad in the viral membrane. Fitting the proton current curve using the charge-state populations from these pK(a)'s, we obtained the relative conductance of the five charge states, which showed that the +3 channel has the highest time-averaged unitary conductance. At physiologically relevant pH, 2D correlation spectra indicated that the neutral and cationic histidines do not have close contacts, ruling out the H-bonded dimer model. Moreover, a narrowly distributed nonideal helical structure coexists with a broadly distributed ideal helical conformation without interchange on the sub-10 ms time scale, thus excluding the transporter model in the viral membrane. These data support the shuttle mechanism of proton conduction, whose essential steps involve His-water proton exchange facilitated by imidazole ring reorientations.  相似文献   

16.
Cross-correlated nuclear spin relaxation between 1H chemical shift anisotropy (CSA) and 1H-1H dipolar relaxation mechanisms in ribonucleosides in solution phase are observed and used to identify their anomeric configuration. Only alpha-ribonucleosides showed the presence of cross-correlated spin relaxation through differential spin-lattice relaxation (T1) of the H1' doublet. Dependence of the magnitude and the orientation of the H1' CSA tensor values on the glycosidic torsion angle and the fast time-scale internal motions present in the ribose moiety play a significant role in the characterization of the anomeric configuration of the nucleosides via cross-correlated relaxation.  相似文献   

17.
High-frequency pulsed EPR and ENDOR have been employed to characterize the tyrosyl radical (Y*)-diiron cofactor in the Y2-containing R2 subunit of ribonucleotide reductase (RNR) from yeast. The present work represents the first use of 140-GHz time domain EPR and ENDOR to examine this system and demonstrates the capabilities of the method to elucidate the electronic structure and the chemical environment of protein radicals. Low-temperature spin-echo-detected EPR spectra of yeast Y* reveal an EPR line shape typical of a tyrosyl radical; however, when compared with the EPR spectra of Y* from E. coli RNR, a substantial upfield shift of the g(1)-value is observed. The origin of the shift in g(1) was investigated by 140-GHz (1)H and (2)H pulsed ENDOR experiments of the Y2-containing subunit in protonated and D(2)O-exchanged buffer. (2)H ENDOR spectra and simulations provide unambiguous evidence for one strongly coupled (2)H arising from a bond between the radical and an exchangeable proton of an adjacent residue or a water molecule. Orientation-selective 140-GHz ENDOR spectra indicate the direction of the hydrogen bond with respect to the molecular symmetry axes and the bond length (1.81 A). Finally, we have performed saturation recovery experiments and observed enhanced spin lattice relaxation rates of the Y* above 10 K. At temperatures higher than 20 K, the relaxation rates are isotropic across the EPR line, a phenomenon that we attribute to isotropic exchange interaction between Y* and the first excited paramagnetic state of the diiron cluster adjacent to it. From the activation energy of the rates, we determine the exchange interaction between the two irons of the cluster, J(exc) = -85 cm(-)(1). The relaxation mechanism and the presence of the hydrogen bond are discussed in terms of the differences in the structure of the Y*-diiron cofactor in yeast Y2 and other class I R2s.  相似文献   

18.
Access to the fast exchange kinetics of labile protein hydrogens in solution is provided by exchange broadening of the water 1H NMR line. We analyzed the chemical shift modulation contribution of labile hydrogens in bovine pancreatic trypsin inhibitor (BPTI) to the transverse 1H spin relaxation rate, R2, of the bulk solvent. Both the experimental pH dependence and the CPMG dispersion of R2 could be quantitatively accounted for on the basis of known chemical shifts, exchange rates, and ionization constants for BPTI. This analysis provided, for the first time, the hydrogen exchange rate constants for Lys and Arg side chains in a protein and pointed to an internal catalysis of the N-terminal amino protons in BPTI by a salt bridge. The method can be used for mapping the hydrogen exchange rates in protein solutions and biomaterials, which may be important for the control of relaxation-weighted contrast in biological MRI.  相似文献   

19.
对辛伐他汀的红外(IR)、紫外(UV)、质谱(MS)、氢-氢相关谱(^1H-^1HCOSY)、碳谱(^13C NMR,DEPT)、碳氢相关谱(HMQC)、碳氢远程相关谱(HMBC)予以解析并进行了报道,对所有的^1H NMR和^13C NMR谱信号进行了归属;讨论了红外特征吸收峰所对应的官能团的振动形式,并且对样品进行热差和热重分析,显示该样品为单一晶型,不含结晶水。  相似文献   

20.
Pimonidazole is one of a series of nitroimidazole compounds that is widely used as a marker for qualitative and quantitative assessment of tumour hypoxia. We have observed a novel dynamic conformational exchange process in this molecule in aqueous solution. By a combination of 1H, 13C, two-dimensional 1H-1H EXchange SpectroscopY (EXSY) and spectral simulation, we unambiguously attribute the conformational exchange process to flipping of the six-membered heterocyclic ring.  相似文献   

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