Complex methyl group and hydrogen-bonded proton motions in terms of the Arrhenius and Schrödinger equations

Equations for the temperature dependence of the spectral densities J(is)(m)(momega(I) +/-omega(T)), where m=1, 2, omega(I) and omega(T) are the resonance and tunnel splitting angular frequencies, in the presence of a complex motion, have been derived. The spin pairs of the protons or deuterons of the methyl group perform a complex motion consisting of three component motions. Two of them involve mass transportation over the barrier and through the barrier. They are characterized by k((H)) (Arrhenius) and k((T)) (Schr?dinger) rate constants, respectively. The third motion causes fluctuations of the frequencies (nomega(I)+/-omega(T)) and it is related to the lifetime of the methyl spin at the energy level influenced by the rotor-bath interactions. These interactions induce rapid transitions, changing the symmetry of the torsional sublevels either from A to E or from E(a) to E(b). The correlation function for this third motion (k((omega)) rate constant) has been proposed by Müller-Warmuth et al. The spectral densities of the methyl group hindered rotation (k((H)), k((T)) and k((omega)) rate constants) differ from the spectral densities of the proton transfer (k((H)) and k((T)) rate constants) because three compound motions contribute to the complex motion of the methyl group. The recently derived equation [Formula: see text] , where [Formula: see text] and [Formula: see text] are the fraction and energy of particles with energies from zero to E(H), is taken into account in the calculations of the spectral densities. This equation follows from Maxwell's distribution of thermal energy. The spectral densities derived are applied to analyse the experimental temperature dependencies of proton and deuteron spin-lattice relaxation rate in solids containing the methyl group. A wide range of temperatures from zero Kelvin up to the melting point is considered. It has been established that the motion characterized by k((omega)) influences the spin-lattice relaxation up to the temperature T(tun) only. This temperature is directly determined by the equation C(p)T=E(H) (thermal energy=activation energy), where C(p) is the molar heat capacity. Probably the cessation of the third motion is a result of the de Broglie wavelength related to this motion becoming too short. As shown recently, the potential barrier can be an obstacle for the de Broglie wave. The theoretical equations derived in this paper are compared to those known in the literature.     

Peptide internal motions on nanosecond time scale derived from direct fitting of (13)C and (15)N NMR spectral density functions

NMR relaxation-derived spectral densities provide information on molecular and internal motions occurring on the picosecond to nanosecond time scales. Using (13)C and (15)N NMR relaxation parameters [T(1), T(2), and NOE] acquired at four Larmor frequencies (for (13)C: 62.5, 125, 150, and 200 MHz), spectral densities J(0), J(omega(C)), J(omega(H)), J(omega(H) + omega(C)), J(omega(H) - omega(C)), J(omega(N)), J(omega(H) + omega(N)), and J(omega(H) - omega(N)) were derived as a function of frequency for (15)NH, (13)C(alpha)H, and (13)C(beta)H(3) groups of an alanine residue in an alpha-helix-forming peptide. This extensive relaxation data set has allowed derivation of highly defined (13)C and (15)N spectral density maps. Using Monte Carlo minimization, these maps were fit to a spectral density function of three Lorentzian terms having six motional parameters: tau(0), tau(1), tau(2), c(0), c(1), and c(2), where tau(0), tau(1) and tau(2) are correlation times for overall tumbling and for slower and faster internal motions, and c(0), c(1), and c(2) are their weighting coefficients. Analysis of the high-frequency portion of these maps was particularly informative, especially when deriving motional parameters of the side-chain methyl group for which the order parameter is very small and overall tumbling motions do not dominate the spectral density function. Overall correlation times, tau(0), are found to be in nanosecond range, consistent with values determined using the Lipari-Szabo model-free approach. Internal motional correlation times range from picoseconds for methyl group rotation to nanoseconds for backbone N-H, C(alpha)-H, and C(alpha)-C(beta) bond motions. General application of this approach will allow greater insight into the internal motions in peptides and proteins.     

Spin relaxation measurements using first-harmonic out-of-phase absorption EPR signals: rotational motion effects

A recent survey of nonlinear continuous-wave (CW) EPR methods revealed that the first-harmonic absorption EPR signal, detected 90 degrees out of phase with respect to the Zeeman modulation (V(1)(')-EPR), is the most appropriate for determining spin-lattice relaxation enhancements of spin labels (V. A. Livshits, T. Páli, and D. Marsh, 1998, J. Magn. Reson. 134, 113-123). The sensitivity of such V(1)(')-EPR spectra to molecular rotational motion is investigated here by spectral simulations for nitroxyl spin labels, over the entire range of rotational correlation times. Determination of the effective spin-lattice relaxation times is less dependent on rotational mobility than for other nonlinear CW EPR methods, especially at a Zeeman modulation frequency of 25 kHz which is particularly appropriate for spin labels. This relative insensitivity to molecular motion further enhances the usefulness of the V(1)(')-EPR method. Calibrations of the out-of-phase to in-phase spectral intensity (and amplitude) ratios are given as a function of spin-lattice relaxation time, for the full range of spin-label rotational correlation times. Experimental measurements on spin labels in the slow, intermediate, and fast motional regimes of molecular rotation are used to test and validate the method.     

Complex molecular dynamics of (CH3NH3)5Bi2Br11 (MAPBB) protons from NMR relaxation and second moment of NMR spectrum

Molecular dynamics of a polycrystalline sample of (CH(3)NH(3))(5)Bi(2)Br(11) (MAPBB) is studied on the basis of the proton T(1) (55.2 MHz) relaxation time and the proton second moment of NMR line. The T(1) (55.2 MHz) was measured for temperatures from 20K to 330 K, while the second moment M(2) for those from 40K to 330 K. The proton spin pairs of the methyl and ammonium groups perform a complex stochastic motion being a resultant of four components characterised by the correlation times τ(3)(T), τ(3)(H), τ(2), and τ(iso), referring to the tunnelling and over the barrier jumps in a triple potential, jumps between two equilibrium sites and isotropic rotation. The theoretical expressions for the spectral densities in the cases of the complex motion considered were derived. For τ(3)(H), τ(2), and τ(iso) the Arrhenius temperature dependence was assumed, while for τ(3)(T)-the Schr?dinger one. The correlation times τ(3)(H) for CH(3) and NH(3) groups differ, which indicates the uncorrelated motion of these groups. The stochastic tunnelling jumps are not present above the temperature T(tun) at which the thermal energy is higher than the activation energy of jumps over the barrier attributed to the hindered rotation of the CH(3) and NH(3) groups. The T(tun) temperature is 54.6 K for NH(3) group and 46.5 K for CH(3) group in MAPBB crystal. The tunnelling jumps of the methyl and ammonium protons are responsible for the flattening of T(1) temperature dependence at low temperatures. The isotropic tumbling is detectable only from the M(2) temperature dependence. The isotropic tumbling reduces the second moment to 4 G(2) which is the value of the intermolecular part of the second moment. The motion characterised by the correlation time τ(2) is well detectable from both T(1) and M(2) temperature dependences. This motion causes the appearance of T(1) minimum at 130 K and reduction of the second moment to the 7.7 G(2) value. The small tunnelling splitting ω(T) of the same value for the methyl and ammonium groups was estimated as 226 MHz from the Haupt equation or 80 MHz from the corrected by us Haupt equation. These frequencies correspond to 0.93 μeV and 0.34 μeV tunnel splitting energy.     

Sensitivity enhancement, assignment, and distance measurement in 13C solid-state NMR spectroscopy for paramagnetic systems under fast magic angle spinning

Despite success of previous studies, high-resolution solid-state NMR (SSNMR) of paramagnetic systems has been still largely unexplored because of limited sensitivity/resolution and difficulty in assignment due to large paramagnetic shifts. Recently, we demonstrated that an approach using very-fast magic angle spinning (VFMAS; spinning speed 20kHz) enhances resolution/sensitivity in (13)C SSNMR for paramagnetic complexes [Y. Ishii, S. Chimon, N.P. Wickramasinghe, A new approach in 1D and 2D (13)C high resolution solid-state NMR spectroscopy of paramagnetic organometallic complexes by very fast magic-angle spinning, J. Am. Chem. Soc. 125 (2003) 3438-3439]. In this study, we present a new strategy for sensitivity enhancement, signal assignment, and distance measurement in (13)C SSNMR under VFMAS for unlabeled paramagnetic complexes using recoupling-based polarization transfer. As a robust alternative of cross-polarization (CP), rapid application of recoupling-based polarization transfer under VFMAS is proposed. In the present approach, a dipolar-based analog of INEPT (dipolar INEPT) methods is used for polarization transfer and a (13)C signal is observed under VFMAS without (1)H decoupling. The resulting low duty factor permits rapid signal accumulation without probe arcing at recycle times ( approximately 3 ms/scan) matched to short (1)H T(1) values of small paramagnetic systems ( approximately 1 ms). Experiments on Cu(dl-Ala)(2) showed that the fast repetition approach under VFMAS provided sensitivity enhancement by a factor of 8-66 for a given sample, compared with the (13)C MAS spectrum under moderate MAS at 5kHz. The applicability of this approach was also demonstrated for a more challenging system, Mn(acac)(3), for which (13)C and (1)H paramagnetic shift dispersions reach 1500 and 700 ppm, respectively. It was shown that effective-evolution-time dependence of transferred signals in dipolar INEPT permitted one to distinguish (13)CH, (13)CH(2), (13)CH(3), (13)CO2- groups in 1D experiments for Cu(DL-Ala)(2) and Cu(Gly)(2). Applications of this technique to 2D (13)C/(1)H correlation NMR under VFMAS yielded reliable assignments of (1)H resonances as well as (13)C resonances for Cu(DL-Ala)(2) and Mn(acac)(3). Quantitative analysis of cross-peak intensities in 2D (13)C/(1)H correlation NMR spectra of Cu(DL-Ala)(2) provided distance information between non-bonded (13)C-(1)H pairs in the paramagnetic system.     

A new approach to visualizing spectral density functions and deriving motional correlation time distributions: applications to an alpha-helix-forming peptide and to a well-folded protein

A new approach to visualizing spectral densities and analyzing NMR relaxation data has been developed. By plotting the spectral density function, J(omega), as F(omega)=2 omega J(omega) on the log-log scale, the distribution of motional correlation times can be easily visualized. F(omega) is calculated from experimental data using a multi-Lorentzian expansion that is insensitive to the number of Lorentzians used and allows contributions from overall tumbling and internal motions to be separated without explicitly determining values for correlation times and their weighting coefficients. To demonstrate the approach, (15)N and (13)C NMR relaxation data have been analyzed for backbone NH and C(alpha)H groups in an alpha-helix-forming peptide 17mer and in a well-folded 138-residue protein, and the functions F(omega) have been calculated and deconvoluted for contributions from overall tumbling and internal motions. Overall tumbling correlation time distribution maxima yield essentially the same overall correlation times obtained using the Lipari-Szabo model and other standard NMR relaxation data analyses. Internal motional correlational times for NH and C(alpha)H bond motions fall in the range from 100 ps to about 1 ns. Slower overall molecular tumbling leads to better separation of internal motional correlation time distributions from those of overall tumbling. The usefulness of the approach rests in its ability to visualize spectral densities and to define and separate frequency distributions for molecular motions.     

Molecular dynamics of amide ions in potassium amide (KNH2) studied with orientation-dependent deuterium spin lattice relaxation

The reorientational molecular dynamics of the amide ions were investigated in three different phases of KND2 by means of 2H NMR line-shape analyses of solid-echo, T1Z as well as T1Q distorted spectra in a temperature range of 80-420 K. The correlation times of the amide dynamics cover roughly eight decades in this temperature range. Due to the nonzero asymmetry parameter (eta approximately 0.2) of the electric field gradient tensor the calculation of the orientation-dependent spectral densities Jm(theta, phi) required for the interpretation of the T1Z and T1Q distorted spectra cannot be simplified as in the case eta = 0 and a numerical approach was used for the calculation of Jm(theta, phi), which allows a maximum flexibility for simulating different models of motion. The amide ion dynamics in the low-temperature phase can be described as a superposition of a thermally activated large angle jump of the amide ions about their two-fold axes in an asymmetric four-well potential and strongly anisotropic molecular librations. The asymmetry of the potential surface of the jump process was found to be a function of temperature. Activation energy EA, attempt frequency tau0(-1) and DND bond angle epsilon were determined to 15.5(2) kJ/mol, 62(6) x 10(12) s(-1) and 104.7(3) degrees. In the middle- and high-temperature phases the amide ions perform 90 degrees jumps about the crystallographic four-fold axes. For the high-temperature modification the correlation times were observed to follow an Arrhenius law with EA = 6.3(2) kJ/mol and tau0(-1) = 32(3) x 10(12) s(-1).     

Frequency-selective heteronuclear dephasing and selective carbonyl labeling to deconvolute crowded spectra of membrane proteins by magic angle spinning NMR

We present a new method that combines carbonyl-selective labeling with frequency-selective heteronuclear recoupling to resolve the spectral overlap of magic angle spinning (MAS) NMR spectra of membrane proteins in fluid lipid membranes with broad lines and high redundancy in the primary sequence. We implemented this approach in both heteronuclear (15)N-(13)C(α) and homonuclear (13)C-(13)C dipolar assisted rotational resonance (DARR) correlation experiments. We demonstrate its efficacy for the membrane protein phospholamban reconstituted in fluid PC/PE/PA lipid bilayers. The main advantage of this method is to discriminate overlapped (13)C(α) resonances by strategically labeling the preceding residue. This method is highly complementary to (13)C(i-1)(')-(15)N(i)-(13)C(i)(α) and (13)C(i-1)(α)-(15)N(i-1)-(13)C(i)(') experiments to distinguish inter-residue spin systems at a minimal cost to signal-to-noise.     

Internal dynamics of hydroxymethyl rotation from CH2 cross-correlated dipolar relaxation in methyl-beta-D-glucopyranoside

Conventional relaxation parameters (T1(-1), T2(-1), and NOE), obtained at different temperatures and magnetic fields, are reported for the hydroxymethyl (C6) carbon in methyl-beta-D-glucopyranoside in a D2O/DMSO cryosolvent. These data are interpreted with the Lipari-Szabo model. In addition, two-field measurements of longitudinal and spin-locked relaxation rates related to the cross-correlated carbon-proton dipole-dipole interactions for the same carbon are reported. The complete data set consisting the conventional and cross-correlated relaxation parameters is interpreted using a new "hybrid" approach, in which the Lipari-Szabo model for the auto-correlated spectral densities is combined with the two-site jump model for the cross-correlated spectral densities, with the global correlation time as a common parameter. The two-site jump rates thus obtained are in reasonable agreement with the ultrasonic relaxation measurements, and have reasonable temperature dependence.     

A field-cycling NMR investigation of resonant spin-lattice relaxation features arising from tunnelling methyl groups

(1)H nuclear spin-lattice relaxation has been investigated in sodium acetate trihydrate and sorbic acid using field-cycling NMR in the solid state. The relaxation is dominated by the reorientation of the methyl groups. Resonant features arising from coherent tunnelling are observed in both the magnetic field dependence of the spin lattice relaxation rate, T(1)(-1)(B(z)) and in the inverse temperature dependence, T(1)(-1)(1/T). The two systems have different barrier heights and tunnelling frequencies, providing different perspectives on the tunnel resonance phenomena. The magnetic field dependence enables different spectral density components to be separately investigated and in the carboxylic acid, sorbic acid, concerted proton transfer in the hydrogen bonds is also identified at low field and low temperature. The methyl hindering barriers and the correlation times characterising the reorientational dynamics has been accurately determined in both materials.     

Dephasing relaxation of the electron spin echo of the vibronic Cu(H(2)O)(6) complexes in Tutton salt crystals at low temperatures.

Two-pulse electron spin echo (ESE) measurements of the phase relaxation (phase memory time T(M)) were performed in a series of Tutton salt crystals M(I)(2)M(II)(SO(4))(2).6X(2)O (M(I)=NH(4), K, Cs; M(II)=Zn, Mg; X=H, D) weakly doped with Cu(2+) ions (c approximately equal to 10(18) ions/cm(3)) in temperature range 4-60 K where ESE signals were detectable. The ESE decay was strongly modulated with proton (or deuteron) frequencies and described by the decay function V(2tau)=V(0)exp(-btau-mtau(2)) with the mtau(2) term being temperature independent and negligible above 20 K. Various mechanisms leading to the tau- or tau(2)-type ESE decay are reviewed. The m and b coefficients for nuclear spectral diffusion (NSD), electron spectral diffusion (SD), and instantaneous diffusion (ID) were calculated in terms of existing theories and the resulting rigid lattice T(0)(M) times were found to be close one to another within the crystal family with average values: 17.5 micros (NSD protons), 200 micros (NSD deuterons), 8 micros (SD), and 5 micros (ID). The ID dominates but the calculated effective T(M)(0) is longer than the experimental T(M)(0)=2 micros. This is due to a nonuniform distribution of the Cu(2+) ions with a various degree of the disorder in the studied crystals. The acceleration of the dephasing rate 1/T(M) with temperature is due to the mechanisms producing exp(-btau) decay. They are reviewed and two of them were found to be operative in Tutton salt crystals: (a) Excitations to the vibronic levels of energy Delta leading to the temperature dependence 1/T(M)=B exp(-Delta/kT), with the vibronic levels produced by strong Jahn-Teller effect, and (b) spin-lattice relaxation processes being effective above 50 K. Based on the Delta values being on the order of 100 cm(-1), the scheme of vibronic levels in the Tutton salts is presented, and the independence of the Delta on temperature proves that the adiabatic potential surface shape of Jahn-Teller active Cu(H(2)O)(6) complexes is not affected by temperature below 65 K.     

固体NMR 研究PMMA 纳米复合材料结构与受限链运动

聚合物/无机纳米复合材料的微观结构和动力学决定了其宏观性能,阐明无机纳米材料对复合材料结构和动力学的影响,对认识材料结构-性能关系及设计新材料都具有重要意义．该文通过乳液聚合方法合成了聚甲基丙烯酸甲酯/锂藻土(PMMA/Laponite)纳米复合材料,采用1H MAS 和¹³C CPMAS、弛豫时间及¹³C 化学位移各向异性谱(SUPER)等多种固体NMR 技术,详细研究了无机纳米材料的界面改性及其对纳米复合材料的微观结构和动力学的影响．¹H MAS 和¹³C CPMAS 实验表明,有机改性剂与锂藻土形成强的有机-无机界面相互作用,¹³C 纵向弛豫时间实验表明,PMMA 及其锂藻土纳米复合物均含有刚性和柔性两个组分,而纳米复合物中的聚合物链运动相对较低,特别是其中PMMA 的酯基分子运动明显受限．进一步的¹³C SUPER 实验表明,PMMA 酯基的化学位移各向异性在加入锂藻土后发生变化,预示酯基与锂藻土表面的羟基可能存在氢键作用而导致聚合物的链段运动进一步受限,上述纳米尺度受限效应提高了复合材料的玻璃化转变温度．     

Phosphorus-31 spin-lattice NMR relaxation in bone apatite and its mineral standards

Phosphorus-31 spin-lattice relaxation, both in the laboratory (B(0)=4.7 T) and rotating frame (B(1)=2.2 mT), was studied in the following samples: mineral of whole human bone (samples B1-B6), apatite prepared from bone (BHA), natural brushite (BRU), synthetic hydroxyapatite hydrated (HAh) and calcined (HAc), and synthetic carbonatoapatite of type B (CHA-B) with 9 wt% of CO(3)(2-). The T(1)(P) relaxation time was determined directly using the saturation recovery technique, while the T(1 rho)(P) relaxation time was measured via (1)H-->(31)P CP by incrementing the (31)P spin-lock. In order to avoid an effect of magic-angle spinning (MAS) on CP and relaxation, the experiments were carried out on static samples. The (31)P spin-lattice relaxation was discussed for trabecular and cortical bone tissue from adult subjects in comparison to the synthetic mineral standards. None of the reference materials has matched accurately the relaxation behaviour of the bone mineral. The most striking differences between the examined substances were observed for T(1)(P), which for human bone was sample dependent and appeared in the range 55-100 s, while for HAh, HAc, and CHA-B was 7.2, 10.0, and 25.8 s, respectively. Possible reasons of so large relaxation diversity were discussed. It has been suggested that T(1)(P) of apatites is to some extent dependent on the concentration of the structural hydroxyl groups, and this in turn is controlled by the material crystallinity. It was also found that T(1)(P) decreased on hydration by ca. 30%. For T(1rho)(P), both its magnitude and dependence on the CP contact time gave useful structural information. The dehydrated samples (HAc and BHA) had long T(1 rho)(P) over 250 ms. Those, which contained water, either structural (BRU) or adsorbed on the crystal surface (HAh, CHA-B, and B1-B6), had shorter T(1 rho)(P) below 120 ms. It was concluded that the effect of water on T(1 rho)(P) is much more pronounced than on T(1)(P). The interpretation has involved P-OH groups and adsorbed water, which cover the apatite crystal surface.     

High resolution off-magic-angle spinning NMR for cholesteric liquid crystals

High resolution NMR of cholesteric liquid crystals is realized by off-magic-angle spinning (OMAS). Using the average potential theory, it is shown that the pitch axes of a cholesteric liquid crystal with a positive (negative) magnetic susceptibility anisotropy are aligned along the spinning axis with an OMAS angle larger (smaller) than the magic angle without any distortion of the helical structure, which is untwisted or distorted by the static magnetic field in some static samples. Hence, the line broadening due to the anisotropies of chemical shifts and/or quadrupole couplings is removed, while information of the anisotropies in cholesteric alignments can be obtained from the line positions. A detailed theoretical analysis of effects of spinning frequency and molecular diffusion along the pitch axis on the linewidth is given, predicting that the resolution is improved greatly at a spinning frequency much higher than the rotational diffusion coefficient. These theoretical results are verified by ¹³C OMAS experiments on a cholesteric liquid crystal of p-ethoxybenzyl-p-[(S)-2- methylbutyl]aniline (EBMBA) and cholesteric mixtures of p-methoxybenzylidene-p-n-butylaniline (MBBA) and cholesteryl chloride (CC).     

有机磷化合物的NMR研究——Ⅱ0,0-二烷基膦酸酯的1H、13C和31PNMR谱

本文报道了21个0,0一二烷基膦酸酯类化合物的¹H、¹³C和³¹P NMR参数。研究和讨论了不等价的二烷基¹H、¹³C化学位移和磷碳偶合常数与立体化学的关系。测定了(CH₃CH₂O)₂P(O)CH(CH₂NO₂)(p-OCH₃C₆H₄)的¹³C自旋一晶格弛豫时间T₁,二乙基¹³C T₁间的差别,说明在类似化合物中,含有化学位移各向异性对弛豫的贡献。     

DNA Duplex Dynamics: NMR Relaxation Studies of a Decamer with UniformlyC-Labeled Purine Nucleotides

Dynamics in a DNA decamer duplex,d(CATTTGCATC) ·d(GATGCAAATG), were investigated via a detailed¹³C NMR relaxation study. Every 2′-deoxyadenosine and 2′-deoxyguanidine was chemically enriched with 15%¹³C and 98%¹⁵N isotopes. Six nuclear relaxation parameters [R(¹³C_z),R(¹H_z),R(2¹H_z¹³C_z),R(¹³C_x),R(2¹H_z¹³C_x) and steady-state¹³C{¹H} NOE] were measured at 600 MHz and three were measured at 500 MHz (¹H frequency) for the CH spin systems of sugar 1′, 3′, and 4′ as well as base 8 and 2 positions. A dependence of relaxation parameter values on chemical position was clearly observed; however, no sequence-specific variation was readily evident within our experimental error of ∼5–10%, except for 3′ and 5′ termini. It was demonstrated that the random 15%¹³C enrichment effectively suppressed both scalar and dipolar contributions of the neighboring carbons and protons on the relaxation parameters. To analyze dynamics via all observed relaxation parameters, full spectral density mapping (1992, J. W. Peng and G. Wagner,J. Magn. Reson.98, 308) and the “model-free” approach (1982, Lipari and Szabo,J. Am. Chem. Soc.104, 4546) were applied complementarily. A linear correlation between three spectral density values,J(ω_C),J(ω_H− ω_C), andJ(ω_H+ ω_C) was observed in plots containing all measured values, but not for the other spectral density terms includingJ(0). These linear correlations reflect the effect of overall motion and similar internal motions for each CH vector in the decamer. The correlations yielded two correlation times, 3–4 ns and 10–200 ps. One value, 3–4 ns, corresponds to the value of 3.3 ns obtained for the overall isotropic tumbling correlation time determined from analysis of¹³C T1/T2 ratios. The possibility of overall anisotropic tumbling was examined, but statistical analysis showed no advantage over the assumption of simple isotropic tumbling. Lack of correlations entailingJ(0) implies that a relatively slow chemical exchange contributes to yielding of effectiveJ_eff(0) values. Based on spectral density mapping and the T1/T2 ratio analysis, three basic assumptions were initially employed (and subsequently justified) for the model-free calculation: isotropic overall tumbling, one internal motion, and the presence of chemical exchange terms. Except for terminal residues, the order parameterS²and the corresponding fast internal motion correlation time were determined to be about 0.8 ± 0.1 and 20 ± 20 ps, respectively, for the various CH vectors. Only a few differences were observed between or within sugars and bases. The internal motion is very fast (ps–ns time scale) and its amplitude restricted; e.g., assuming a simple wobble-in-a-cone model, the internal motion is restricted to an angular amplitude of ±22.5° for each of the 1′, 3′, 4′, 2, and 8 positions in the purine nucleotides in the entire duplex.     

Improved measurement of (3)J(H(alpha)(i),N(i+1)) coupling constants in H(2)O dissolved proteins.

A modification to the recently proposed alpha/beta-HN(CO)CA-J TROSY pulse sequence (P. Permi et al., J. Magn. Reson. 146, 255-259 (2000)) makes it possible to determine (3)J(H(alpha)(i), N(i+1)) coupling constants from a single E.COSY-type cross-peak pattern rather than from two (1)H(alpha) spin-state-edited subspectra. Advantages are increased (15)N resolution, critical to extracting accurate (1)H(alpha)-(15)N coupling constants, and minimized differential relaxation due to nested (13)C(alpha) and (15)N evolution periods. Application of the improved pulse sequence to Desulfovibrio vulgaris flavodoxin results in (3)J(H(alpha)(i), N(i+1)) values being systematically larger than those obtained with the original scheme. Parametrization of the coupling dependence on the protein backbone torsion angle psi yields the Karplus relation (3)J(H(alpha)(i), N(i+1))=-1.00 cos(2)(psi-120 degrees )+0.65 cos(psi-120 degrees )-0.15 Hz, with a residual root-mean-square difference of 0.13 Hz between measured and back-calculated coupling constants. The curve compares with data derived from ubiquitin (A. C. Wang and A. Bax, J. Am. Chem. Soc. 117, 1810-1813 (1995)), although spanning a slightly larger range of J values in flavodoxin. The orientation of the Ala39/Ser40 peptide link, forming a type-II beta-turn in flavodoxin, is twisted against X-ray-derived torsions by approximately 10 degrees in the NMR structure as evident from the analysis of straight phi- and psi-related (3)J coupling constants. The remaining deviation of some experimental values from the prediction is likely to be due to strong hydrogen bonding, substituent effects, or the additional dependence on the adjacent torsions straight phi.     

Effect of the frequency of intramolecular motions on the NMR relaxation in liquid state temperature regime

Equations for the spectral densities of complex motion of a spin pair undergoing internal motion and isotropic/anisotropic overall rotation have been considered. The fluctuations of the interproton distances, caused by internal motion, have been taken into account in the theoretical equations. A method allowing a distinction between the isotropic and the anisotropic overall rotation of molecules has been proposed. The effect of the activation parameters of internal motions (known from the solid state study) on the measured T ₁ relaxation of the ¹³C and ¹H–¹H cross-relaxation rates has been analysed for methyl-β-D-galactopyranoside in DMSO-d6 solution. The conformational trans-gauche jumps of the methylene group are not fast enough to affect the T ₁ value of carbon C6 in the liquid state temperatures regime. Only the methyl group rotation is a very fast internal motion. This motion influences the carbon C7 relaxation and methyl protons–anomeric proton cross-relaxation. The values of interatomic distances between anomeric H(C1) and H(C5) as well as the three methyl protons H(C7) have been calculated from the cross-relaxation rates. The distance H(C1)–H(C7) fluctuates due to the rotation of methyl group. The application of the ‘model-free approach’ to study molecular dynamics in solutions is discussed.     

13C/14N heteronuclear multiple-quantum correlation with rotary resonance and REDOR dipolar recoupling

A two-dimensional (13)C/(14)N heteronuclear multiple quantum correlation (HMQC) experiment using dipolar recoupling under magic-angle spinning (MAS) is described. The experiment is an extension of the recent indirect (13)C detection scheme for measuring (14)N quadrupolar coupling under MAS. The recoupling allows the direct use of the much larger dipolar interaction instead of the small J and residual dipolar couplings for establishing (13)C/(14)N correlations. Two recoupling methods are incorporated into the HMQC sequence, both applying rf only to the observed (13)C spin. The first one uses the REDOR sequence with two pi-pulses per rotor cycle. The second one uses a cw rf field matching the spinning frequency, known as rotary resonance. The effects of CSA, T(2)(') signal loss, MAS frequency and stability and t(1)-noise are compared and discussed.