The nuclear magnetic resonance relaxation data analysis in solids: general R1/R1(ρ) equations and the model-free approach

The advantage of the solid state NMR for studying molecular dynamics is the capability to study slow motions without limitations: in the liquid state, if orienting media are not used, all anisotropic magnetic interactions are averaged out by fast overall Brownian tumbling of a molecule and thus investigation of slow internal conformational motions (e.g., of proteins) in solution can be conducted using only isotropic interactions. One of the main tools for obtaining amplitudes and correlation times of molecular motions in the μs time scale is measuring relaxation rate R(1)(ρ). Yet, there have been a couple of unresolved problems in the quantitative analysis of the relaxation rates. First, when the resonance offset of the spin-lock pulse is used, the spin-lock field can be oriented under an arbitrary angle in respect to B(0). Second, the spin-lock frequency can be comparable or even less than the magic angle spinning rate. Up to now, there have been no equations for R(1)(ρ) that would be applicable for any values of the spin-lock frequency, magic angle spinning rate and resonance offset of the spin-lock pulse. In this work such equations were derived for two most important relaxation mechanisms: heteronuclear dipolar coupling and chemical shift anisotropy. The validity of the equations was checked by numerical simulation of the R(1)(ρ) experiment using SPINEVOLUTION program. In addition to that, the applicability of the well-known model-free approach to the solid state NMR relaxation data analysis was considered. For the wobbling in a cone at 30° and 90° cone angles and two-site jump models, it has been demonstrated that the auto-correlation functions G(0)(t), G(1)(t), G(2)(t), corresponding to different spherical harmonics, for isotropic samples (powders, polycrystals, etc.) are practically the same regardless of the correlation time of motion. This means that the model-free approach which is widely used in liquids can be equally applied, at least assuming these two motional models, to the analysis of the solid state NMR relaxation data.     

Characterization of micros-ms dynamics of proteins using a combined analysis of 15N NMR relaxation and chemical shift: conformational exchange in plastocyanin induced by histidine protonations

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.     

The trehalose coating effect on the internal protein dynamics

(15)N and (13)C NMR experiments were applied to conduct a comparative study of a cold shock protein (Csp) in two states-lyophilized powder and a protein embedded in a glassy trehalose matrix. Both samples were studied at various levels of rehydration. The experiments used (measuring relaxation rates R(1) and R(1ρ), motionally averaged dipolar couplings and solid state exchange method detecting reorientation of the chemical shift anisotropy tensor) allow obtaining abundant information on the protein structural features and internal motions in a range of correlation times from nanoseconds to seconds. The main results are: (a) the trehalose coating makes the protein structure more native in comparison with the dehydrated lyophilized powder, however, trehalose still cannot remove all non-native hydrogen bonds which are present in a dehydrated protein; (b) trehalose has an appreciable effect on the internal dynamics: the motion of the backbone N-H groups in the nanosecond and microsecond time scales becomes slower while the motional amplitude remains constant; (c) upon adding water to the Csp-trehalose mixture, water molecules accumulate around proteins forming a layer between the protein surface and the trehalose matrix. The protein dynamics become faster, however, not as fast as in the fully hydrated state; (d) the hydration response of dynamics of the NH and CH(CH(2)) groups in a protein is qualitatively different: upon increasing protein hydration, the correlation times of the N-H motions become shorter and the amplitude remains stable, and for CH(CH(2)) groups the motional amplitude increases and the correlation times do not change. This can be explained by a different ability of the NH and CH(CH(2)) groups to form hydrogen bonds.     

Biosynthetic 13C labeling of aromatic side chains in proteins for NMR relaxation measurements

Site-specific 13C labeling offers a desirable means of eliminating unwanted relaxation pathways and coherent magnetization transfer in NMR relaxation experiments. Here we use [1-13C]-glucose as the sole carbon source in the growth media for protein overexpression in Escherichia coli. The approach results in specific incorporation of 13C at isolated positions in the side chains of aromatic amino acids, which greatly simplifies the measurements and interpretation of 13C relaxation rates in these spin systems. The method is well suited for characterization of chemical exchange by CPMG or spin-lock relaxation methods. We validated the method by acquiring 13C rotating-frame relaxation dispersion data on the E140Q mutant of the C-terminal domain of calmodulin, which reveal conformational exchange dynamics with a time constant of 71 mus for Y138.     

Evaluation of two simplified 15N-NMR methods for determining micros-ms dynamics of proteins

Two methods for estimating the microsecond-millisecond dynamics in proteins from only two 15N relaxation parameters at one magnetic field strength are investigated. Thus, the chemical exchange contribution, R(ex), to the transversal relaxation rate, which contains the dynamics information, is evaluated by two methods: (i) one in which the R(ex) term is derived from the 15N R1 and R2 relaxation rates alone, and (ii) one in which it is obtained from the transversal dipole-chemical shift anisotropy (CSA) cross-correlation rate, eta(xy), and the R2 rate. Since the R1, R2, and eta(xy) experiments are fast and sensitive, both methods are attractive in studies where large amounts of dynamical information are required. However, both methods are liable to effects that can compromise the estimation of the R(ex) terms. In the R2/R1 method, internal ps-ns dynamics and rotational anisotropy can interfere with the determination of R(ex), while in the R2/eta(xy) method it can be affected by variations in the 15N chemical shift anisotropy. Here, the applicability of the two methods is investigated using plastocyanin from Anabaena variabilis as an example, and the quality of the obtained R(ex) terms is evaluated both theoretically and experimentally. It is found that the R2/R1 method gives reliable R(ex) terms if the protein is relatively rigid and tumbles fast and nearly isotropically in solution, as for instance plastocyanin, and is preferable in such cases. In contrast, the R2/eta(xy) method gives better results if the protein is flexible or highly non-spherical and can be used for such proteins, if the sequential variation in the 15N chemical shift anisotropy is negligible. For exchange terms <1 s(-1) neither method is reliable.     

A comprehensive analysis of multifield 15N relaxation parameters in proteins: determination of 15N chemical shift anisotropies.

This study deals with the exploitation of the three classical 15N relaxation parameters (the longitudinal relaxation rate, R1, the transverse relaxation rate, R2, and the 1H-15N cross-relaxation rate, sigmaNH) measured at several magnetic fields in uniformly 15N-labeled proteins. Spectral densities involved in R1, R2 and sigmaNH are analyzed according to the functional form A + B/(1 + omega(2) taus(2)), where taus is the correlation time associated with slow motions sensed by the NH vector at the level of the residue to which it belongs. The coefficient B provides a realistic view of the backbone dynamics, whereas A is associated with fast local motions. According to the "model free approach", B can be identified with 2tausS(2) where S is the generalized order parameter. The correlation time taus is determined from the field dependency of the relaxation parameters while A and B are determined through linear equations. This simple data processing is needed for obtaining realistic error bars based on a statistical approach. This proved to be the key point for validating an extended analysis aiming at the determination of nitrogen chemical shift anisotropy. The protein C12A-p8(MTCP1) has been chosen as a model for this study. It will be shown that all data (obtained at five magnetic field strengths corresponding to proton resonance of 400, 500, 600, 700, and 800 MHz) are very consistently fitted provided that a specific effective correlation time associated with slow motions is defined for each residue. This is assessed by small deviations between experimental and recalculated values, which, in all cases, remain within experimental uncertainty. This strategy makes needless elaborate approaches based on the combination of several slow motions or their possible anisotropy. Within the core of the protein taus fluctuates in a relatively narrow range (with a mean value of 6.15 ns and a root-mean-square deviation of 0.36 ns) while it is considerably reduced at the protein extremities (down to approximately 3 ns). To a certain extent, these fluctuations are correlated with the protein structure. A is not obtained with sufficient accuracy to be valuably discussed. Conversely, order parameters derived from B exhibit a significant correlation with the protein structure. Finally, the multi-field analysis of the evolution of longitudinal and transverse relaxation rates has been refined by allowing the 15N chemical shift anisotropy (csa) to vary residue by residue. Within uncertainties (derived here on a statistical basis) an almost constant value is obtained. This strongly indicates an absence of correlation between the experimental value of this parameter obtained for a given residue in the protein, the nature of this residue, and the possible involvement of this residue in a structured area of the protein.     

Quantitative analysis of conformational exchange contributions to 1H-15N multiple-quantum relaxation using field-dependent measurements. Time scale and structural characterization of exchange in a calmodulin C-terminal domain mutant

Multiple-quantum spin relaxation is a sensitive probe for correlated conformational exchange dynamics on microsecond to millisecond time scales in biomolecules. We measured differential 1H-15N multiple-quantum relaxation rates for the backbone amide groups of the E140Q mutant of the C-terminal domain of calmodulin at three static magnetic field strengths. The differential multiple-quantum relaxation rates range between -88.7 and 92.7 s(-1), and the mean and standard deviation are 7.0 +/- 24 s(-1), at a static magnetic field strength of 14.1 T. Together with values of the 1H and 15N chemical shift anisotropies (CSA) determined separately, the field-dependent data enable separation of the different contributions from dipolar-dipolar, CSA-CSA, and conformational exchange cross-correlated relaxation mechanisms to the differential multiple-quantum relaxation rates. The procedure yields precise quantitative information on the dominant conformational exchange contributions observed in this protein. The field-dependent differences between double- and zero-quantum relaxation rates directly benchmark the rates of conformational exchange, showing that these are fast on the chemical shift time scale for the large majority of residues in the protein. Further analysis of the differential 1H-15N multiple-quantum relaxation rates using previously determined exchange rate constants and populations, obtained from 15N off-resonance rotating-frame relaxation data, enables extraction of the product of the chemical shift differences between the resonance frequencies of the 1H and 15N spins in the exchanging conformations, deltasigma(H)deltasigma(N). Thus, information on the 1H chemical shift differences is obtained, while circumventing complications associated with direct measurements of conformational exchange effects on 1H single-quantum coherences in nondeuterated proteins. The method significantly increases the information content available for structural interpretation of the conformational exchange process, partly because deltasigma(H)deltasigma(N) is a signed quantity, and partly because two chemical shifts are probed simultaneously. The present results support the hypothesis that the exchange in the calcium-loaded state of the E140Q mutant involves conformations similar to those of the wild-type apo (closed) and calcium-loaded (open) states.     

Analysis of one-dimensional pure-exchange NMR experiments for studying dynamics with broad distributions of correlation times

One-dimensional (1D) exchange NMR experiments can elucidate the geometry, time scale, memory, and heterogeneity of slow molecular motions (1 ms-1 s) in solids. The one-dimensional version of pure-exchange (PUREX) solid-state exchange NMR, which is applied to static samples and uses the chemical shift anisotropy as a probe for molecular motion, is particularly promising and convenient in applications where site resolution is not a problem, i.e., in systems with few chemical sites. In this work, some important aspects of the 1D PUREX experiment applied to systems with complex molecular motions are analyzed. The influence of intermediate-regime (10 micros-1 ms) motions and of the distribution of reorientation angles on the pure-exchange intensity are discussed, together with a simple method for estimating the activation energy of motions occurring with a single correlation time. In addition, it is demonstrated that detailed information on the motional geometry can be obtained from 1D PUREX spectral line shapes. Experiments on a molecular crystal, dimethyl sulfone, confirm the analysis quantitatively. In two amorphous polymers, atactic polypropylene (aPP) and polyisobutylene (PIB), which differ only by one methyl group in the repeat unit, the height of the normalized exchange intensity clearly reveals a striking difference in the width of the distribution of correlation times slightly above the glass transition. The aPP shows the broad distribution and Williams-Landel-Ferry temperature dependence of correlation times typical of polymers and other "fragile" glass formers. In contrast, the dynamics in PIB occur essentially with a single correlation time and exhibits Arrhenius behavior, which is more typical of "strong" glass formers; this is somewhat surprising given the weak intermolecular forces in PIB.     

Evidence for slow motion in proteins by multiple refocusing of heteronuclear nitrogen/proton multiple quantum coherences in NMR

A novel NMR method characterizes slow motions in proteins by multiple refocusing of double- and zero-quantum coherences of amide protons and nitrogen-15 nuclei. If both nuclei experience changes in their isotropic chemical shifts because of internal motions on slow time scales (mus - ms), this leads to a difference in the relaxation rates of double- and zero-quantum coherences. This is due to CSM/CSM (chemical shift modulation) cross-correlation effects that are related to the well-known chemical exchange contribution Rex to the decay rate R2 = 1/T2 of nitrogen-15 nuclei. The CSM/CSM contributions can be distinguished from other mechanisms through their dependence on the repetition rate of a Carr-Purcell-Meiboom-Gill (CPMG) multiple refocusing sequence. In ubiquitin, motional processes can be identified that could hitherto not be observed by conventional CPMG nitrogen-15 NMR.     

Hydrogen exchange rates in proteins from water (1)H transverse magnetic relaxation

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.     

New probes of ligand flexibility in drug design: transferred (13)C CSA-dipolar cross-correlated relaxation at natural abundance

Understanding the impact of molecular flexibility remains an important outstanding problem in rational drug design. Toward this end, we present new NMR relaxation methods that describe ligand flexibility at the atomic level. Specifically, we measure natural abundance (13)C cross-correlated relaxation parameters for ligands in rapid exchange between the free and receptor-bound states. The rapid exchange transfers the bound state relaxation parameters to the free state, such that a comparison of relaxation rates in the absence and presence of protein receptor yields site-specific information concerning the bound ligand flexibility. We perform these measurements for aromatic carbons, which are highly prevalent in drug-like molecules and demonstrate significant cross-correlated relaxation between the (13)C-(1)H dipole-dipole (DD) and (13)C chemical shift anisotropy (CSA) relaxation mechanisms. Our use of natural abundance measurements addresses the practical difficulties of obtaining isotope-labeled ligands in pharmaceutical research settings. We demonstrate our methods on a small ligand of the 42 kDa kinase domain of the p38 MAP kinase. We show that exchange-transferred cross-correlated relaxation measurements are not only sensitive probes of bound ligand flexibility but also offer complementary advantages over standard R(1) = 1/T(1) and R(2) = 1/T(2) measurements. The ligand flexibility profiles obtained from the relaxation data can help assess the influence of dynamics on ligand potency or pharmacokinetic properties or both, and thereby include inherent molecular flexibility in drug design.     

Off-resonance R(1rho) NMR studies of exchange dynamics in proteins with low spin-lock fields: an application to a Fyn SH3 domain

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.     

Eta(z)/kappa: a transverse relaxation optimized spectroscopy NMR experiment measuring longitudinal relaxation interference

NMR spin relaxation experiments provide a powerful tool for the measurement of global and local biomolecular rotational dynamics at subnanosecond time scales. Technical limitations restrict most spin relaxation studies to biomolecules weighing less than 10 kDa, considerably smaller than the average protein molecular weight of 30 kDa. In particular, experiments measuring eta(z), the longitudinal (1)H(N)-(15)N dipole-dipole (DD)/(15)N chemical shift anisotropy (CSA) cross-correlated relaxation rate, are among those least suitable for use with larger biosystems. This is unfortunate because these experiments yield valuable insight into the variability of the (15)N CSA tensor over the polypeptide backbone, and this knowledge is critical to the correct interpretation of most (15)N-NMR backbone relaxation experiments, including R(2) and R(1). In order to remedy this situation, we present a new (1)H(N)-(15)N transverse relaxation optimized spectroscopy experiment measuring eta(z) suitable for applications with larger proteins (up to at least 30 kDa). The presented experiment also yields kappa, the site-specific rate of longitudinal (1)H(N)-(1)H(') DD cross relaxation. We describe the eta(z)/kappa experiment's performance in protonated human ubiquitin at 30.0 degrees C and in protonated calcium-saturated calmodulin/peptide complex at 20.0 degrees C, and demonstrate preliminary experimental results for a deuterated E. coli DnaK ATPase domain construct at 34 degrees C.     

High-resolution 31p field cycling NMR as a probe of phospholipid dynamics

We have used high-resolution field-cycling 31P NMR spectroscopy to measure spin-lattice relaxation rates (R1 = 1/T1) of multicomponent phospholipid vesicle and micelle samples over a large field range, from 0.1 to 11.7 T. The shape of the curve for R1 as a function of field and a model-free analysis were used to extract tauc, a correlation time for each type of phospholipid molecule in the bilayer that is likely to reflect rotation of the molecule about the axis perpendicular to the membrane surface; Sc2, a chemical shift anisotropy (CSA) order parameter; and tauhf, a time constant reflecting faster internal motion. This 31P technique was also used to monitor association of a peripheral membrane protein, Bacillus thuringiensis phosphatidylinositol-specific phospholipase C, with both phosphatidylcholine and phosphatidylmethanol bilayers. Differences in phospholipid dynamics induced by the protein shed light on how zwitterionic phosphatidylcholine, and not the anionic phosphatidylmethanol, activates the enzyme toward its substrate.     

Delineation of conformational and structural features of the amikacin-Cu(II) complex in water solution by 13C-NMR spectroscopy

The copper (II) complex of amikacin in water solution at pH 5.5 was investigated by 13C-NMR. The temperature dependence of spin-lattice relaxation rates was measured and fast exchange conditions were shown to apply. The motional correlation time of the complex was approximated by the pseudo-isotropic rotational correlation time of free amikacin in water solution (tau c = 0.17 ns at 300 K). Formation of a pseudo-tetrahedral 1:1 complex was demonstrated by relaxation rates analysis and also by UV-Vis spectrophotometry. Two amino nitrogens of amikacin, together with the amide nitrogen and the hydroxyl in the hydroxyl-aminopropyl carbonyl side chain, were assigned as the copper-binding sites and a model of the complex was built by using copper-carbon distances obtained by NMR analysis as input parameters.     

Time scales of slow motions in ubiquitin explored by heteronuclear double resonance

Understanding how proteins function at the atomic level relies in part on a detailed characterization of their dynamics. Ubiquitin, a small single-domain protein, displays rich dynamic properties over a wide range of time scales. In particular, several regions of ubiquitin show the signature of chemical exchange, including the hydrophobic patch and the β4-α2 loop, which are both involved in many interactions. Here, we use multiple-quantum relaxation techniques to identify the extent of chemical exchange in ubiquitin. We employ our recently developed heteronuclear double resonance method to determine the time scales of motions that give rise to chemical exchange. Dispersion profiles are obtained for the backbone NH(N) pairs of several residues in the hydrophobic patch and the β4-α2 loop, as well as the C-terminus of helix α1. We show that a single time scale (ca. 50 μs) can be used to fit the data for most residues. Potential mechanisms for the propagation of motions and the possible extent of correlation of these motions are discussed.     

Orientational relaxation dynamics in aqueous ionic solution: polarization-selective two-dimensional infrared study of angular jump-exchange dynamics in aqueous 6M NaClO4

The dynamics of hydrogen bond (H-bond) formation and dissociation depend intimately on the dynamics of water rotation. We have used polarization resolved ultrafast two-dimensional infrared (2DIR) spectroscopy to investigate the rotational dynamics of deuterated hydroxyl groups (OD) in a solution of 6M NaClO(4) dissolved in isotopically mixed water. Aqueous 6M NaClO(4) has two peaks in the OD stretching region, one associated with hydroxyl groups that donate a H-bond to another water molecule (OD(W)) and one associated with hydroxyl groups that donate a H-bond to a perchlorate anion (OD(P)). Two-dimensional IR spectroscopy temporally resolves the equilibrium inter conversion of these spectrally distinct H-bond configurations, while polarization-selective 2DIR allows us to access the orientational motions associated with this chemical exchange. We have developed a general jump-exchange kinetic theory to model angular jumps associated with chemical exchange events. We use this to model polarization-selective 2DIR spectra and pump-probe anisotropy measurements. We determine the H-bond exchange induced jump angle to be 49 ± 5° and the H-bond exchange rate to be 6 ± 1 ps. Additionally, the separation of the 2DIR signal into contributions that have or have not undergone H-bond exchange allows us to directly determine the orientational dynamics of the OD(W) and the OD(P) configurations without contributions from the exchanged population. This proves to be important because the orientational relaxation dynamics of the populations that have undergone a H-bond exchange differ significantly from the populations that remain in one H-bond configuration. We have determined the slow orientational relaxation time constant to be 6.0 ± 1 ps for the OD(W) configuration and 8.3 ± 1 ps for the OD(P) configuration. We conclude from these measurements that the orientational dynamics of hydroxyl groups in distinct H-bond configurations do differ, but not significantly.     

Structure and dynamics of the lincomycin-copper(II) complex in water solution by (1)H and (13)C NMR studies

The copper(II) complex of lincomycin in water solution at pH = 7.15 was characterized by (1)H and (13)C NMR and UV-vis spectroscopy. A 1:1 complex is formed in these conditions. The temperature dependence of spin-lattice relaxation rates was measured, showing that all protons behave in a similar fashion and slow exchange conditions prevail. The spin-lattice relaxation rate enhancements were interpreted by the Solomon-Bloembergen-Morgan theory. Reorientational dynamics of the complex was approximated by evaluating the motional correlation time of free lincomycin in water solution. The observed proton and carbon relaxation rate enhancements allowed us to calculate copper-proton and copper-carbon distances that were used for building a molecular model of the complex. The obtained data provide an interpretation of the relatively high stability constant.     

Dynamics of micellar oligomeric and monomeric sodium 10-undecenoate

Multifield carbon-13 NMR longitudinal relaxation time measurements were used to probe the dynamics and structure of monomeric and oligomeric sodium 10-undecenoate in micellar solutions. Longitudinal relaxation data were fit to a two-state model for the spectral density function which utilizes as adjustable parameters a fast correlation time and an order parameter for each carbon atom, and an overall slow correlation time for the entire aggregate. This model was needed to explain the relaxation phenomena because of the anisotropic reorientation of the amphiphiles. The monomeric fast correlation profile indicated a motional gradient increasing toward the micellar core. Comparison of the fast correlation time profiles for monomer and oligomer revealed that the motional gradient found in the monomer was not present in the oligomer. Slow correlation times extracted from the two-state model indicate that the radii of the oligomeric micelles, approximated from the Debye—Stokes—Einstein equation, are slightly larger than the monomeric micelles: 10.6 versus 9.4 Å, respectively. Radii calculated using self-diffusion coefficients also are larger for the oligomeric micelles: 13.4 Å for oligomeric micelles and 10.6 Å for the monomeric micelles. The values determined for the micellar radii are less than that for the extended monomeric chain, 14.7 Å.