Deuterium spin probes of side-chain dynamics in proteins. 2. Spectral density mapping and identification of nanosecond time-scale side-chain motions

In the previous paper in this issue we have demonstrated that it is possible to measure the five different relaxation rates of a deuteron in (13)CH(2)D methyl groups of (13)C-labeled, fractionally deuterated proteins. The extensive set of data acquired in these experiments provides an opportunity to investigate side-chain dynamics in proteins at a level of detail that heretofore was not possible. The data, acquired on the B1 domain of peptostreptococcal protein L, include 16 (9) relaxation measurements at 4 (2) different magnetic field strengths, 25 degrees C (5 degrees C). These data are shown to be self-consistent and are analyzed using a spectral density mapping procedure which allows extraction of values of the spectral density function at a number of frequencies with no assumptions about the underlying dynamics. Dynamics data from 31 of 35 methyls in the protein for which data could be obtained were well-fitted using the two-parameter Lipari-Szabo model (Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 4546). The data from the remaining 4 methyls can be fitted using a three-parameter version of the Lipari-Szabo model that takes into account, in a simple manner, additional nanosecond time-scale local dynamics. This interpretation is supported by analysis of a molecular dynamics trajectory where spectral density profiles calculated for side-chain methyl sites reflect the influence of slower (nanosecond) time-scale motions involving jumps between rotameric wells. A discussion of the minimum number of relaxation measurements that are necessary to extract the full complement of dynamics information is presented along with an interpretation of the extracted dynamics parameters.     

Multiple-timescale dynamics of side-chain carboxyl and carbonyl groups in proteins by 13C nuclear spin relaxation

Side-chain carboxyl and carbonyl groups play a major role in protein interactions and enzyme catalysis. A series of (13)C relaxation experiments is introduced to study the dynamics of carboxyl and carbonyl groups in protein side chains on both fast (sub-ns) and slower (micros-ms) time scales. This approach is illustrated on the protein calbindin D(9k). Fast dynamics features correlate with hydrogen- and ion-binding patterns. We also identify chemical dynamics on micros time scales in solvent-exposed carboxyl groups, most probably due to exchange between the carboxylate and carboxylic acid forms.     

Quantifying millisecond exchange dynamics in proteins by CPMG relaxation dispersion NMR using side-chain 1H probes

A Carr-Purcell-Meiboom-Gill relaxation dispersion experiment is presented for quantifying millisecond time-scale chemical exchange at side-chain (1)H positions in proteins. Such experiments are not possible in a fully protonated molecule because of magnetization evolution from homonuclear scalar couplings that interferes with the extraction of accurate transverse relaxation rates. It is shown, however, that by using a labeling strategy whereby proteins are produced using {(13)C,(1)H}-glucose and D(2)O a significant number of 'isolated' side-chain (1)H spins are generated, eliminating such effects. It thus becomes possible to record (1)H dispersion profiles at the β positions of Asx, Cys, Ser, His, Phe, Tyr, and Trp as well as the γ positions of Glx, in addition to the methyl side-chain moieties. This brings the total of amino acid side-chain positions that can be simultaneously probed using a single (1)H dispersion experiment to 16. The utility of the approach is demonstrated with an application to the four-helix bundle colicin E7 immunity protein, Im7, which folds via a partially structured low populated intermediate that interconverts with the folded, ground state on the millisecond time-scale. The extracted (1)H chemical shift differences at side-chain positions provide valuable restraints in structural studies of invisible, excited states, complementing backbone chemical shifts that are available from existing relaxation dispersion experiments.     

Nuclear spin relaxation dynamics of 13CO2 sorbed in polyisobutene rubber

Recently we presented the dynamics of ¹³CO₂ molecules sorbed in silicone rubber (PDMS) ascertained from spin relaxation experiments. Results of a similar investigation for ¹³CO₂ sorbed in polyisobutene (PIB) are presented in this report. The spin-lattice and spin-spin relaxation times as well as nuclear Overhauser enhancements (NOE) were determined as a function of temperature and Larmor frequency. The relaxation mechanisms found to be important for ¹³CO₂/PIB system are intermolecular dipole-dipole relaxation and chemical shift anisotropy with a minor contribution from spin rotation relaxation. We have determined the parameters which characterize correlation times for ¹³CO₂ collisional motion, rotational motion, and translational motions in the PIB. The self-diffusion coefficient of 5.15 × 10^?8 cm²/s obtained from the nuclear magnetic resonance (NMR) data is close to the literature value of the mutual diffusion coefficient of CO₂ in PIB at 300 K obtained from permeability measurements. In contrast to the case of CO₂/PDMS in which a broad distribution (characterized by a fractional exponential correlation function of the Williams-Watts type with α = 0.58) is observed, a sharp distribution with a fractional exponent, α, of 0.99 is found for the CO₂/PIB system. Instead of assuming an Arrhenius type temperature dependence, we used a Williams-Landel-Ferry type temperature dependence and found it to be better suited to describe the behavior of this system. PIB is a densely packed “strong” chain polymer which responds gradually to the temperature variation and gas sorption. In contrast PDMS is a relatively loosely packed “fragile” polymer with a propensity to exhibit rapid dynamic responses to the temperature change and gas sorption. © 1993 John Wiley & Sons, Inc.     

Relaxation rates of degenerate 1H transitions in methyl groups of proteins as reporters of side-chain dynamics

Experiments for quantifying the amplitudes of motion of methyl-containing side chains are presented that exploit the rich network of cross-correlated spin relaxation interactions between intra-methyl dipoles in highly deuterated, selectively 13CH2D- or 13CH3-labeled proteins. In particular, the experiments measure spin relaxation rates of degenerate 1H transitions in methyl groups that, for high-molecular-weight proteins, are very simply related to methyl three-fold symmetry axis order parameters. The methodology presented is applied to studies of dynamics in a pair of systems, including the 7.5-kDa protein L and the 82-kDa enzyme malate synthase G. Good agreement between 1H- and 2H-derived measures of side-chain order are obtained on highly deuterated proteins with correlation times exceeding approximately 10 ns (correlation coefficients greater than 0.95). Although 2H- and 13C-derived measures of side-chain dynamics are still preferred, the present work underscores the potential of using 1H relaxation for semiquantitative estimates of methyl side-chain flexibility, while the high level of consistency between the different spin probes of motion establishes the reliability of the dynamics parameters.     

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.     

(13)C[(13)C] 2D NMR: a novel strategy for the study of paramagnetic proteins with slow electronic relaxation rates

Oxidized human [2Fe-2S] ferredoxin has a notably slow electronic relaxation rate, which precludes the observation of signals from nuclei near the iron-sulfur cluster by conventional 2D or 3D methods that utilize proton detection. We have demonstrated the utility of (13)C[(13)C]CT-COSY in identifying connectivity information from fast relaxing carbon nuclei near the paramagnetic center, including those from residues that ligate the metal center.     

Fractional viscosity dependence of relaxation rates and non-steady-state dynamics in barrierless reactions in solution

A finite decay model of barrierless electronic relaxation in solution is studied both analytically and numerically. The fractional viscosity (η) dependence of the rate (k∝η^−α with 1 > α> 0) is shown to be strongly correlated with non-steady-state dynamics on the reaction potential surface. We also find that the exponent α may depend strongly on the wavelength of the exciting light.     

C-13 magnetic relaxation rates and H-1 and C-13 paramagnetic shifts of Ni(II) complex of dopamine

The ¹H and ¹³C isotropic contact shifts and the ¹³C relaxation times of dopamine in aqueous solution have been measured in the presence of the Ni(II) ion. The pD dependence of the ¹H and ¹³C paramagnetic shifts was also investigated. From the analysis of the shifts at pD = 6.5 and from the INDO MO calculations on selected models of dopamine radicals, a dominant σ delocalization mechanism of the spin density is proposed. From the spin distribution on the ligand carbon atoms, the metal centered as well as the ligand centered dipolar contributions of the modified Solomon—Bloembergen equation were calculated and an estimate of the correlation time τ_c was given.     

A 2H NMR relaxation experiment for the measurement of the time scale of methyl side-chain dynamics in large proteins

An NMR experiment is presented for the measurement of the time scale of methyl side-chain dynamics in proteins that are labeled with methyl groups of the (13)CHD(2) variety. The measurement is accomplished by selecting a magnetization mode that to excellent approximation relaxes in a single-exponential manner with a T(1)-like rate. The combination of R(1)((13)CHD(2)) and R(2)((13)CHD(2)) (2)H relaxation rates facilitates the extraction of motional parameters from (13)CHD(2)-labeled proteins exclusively. The utility of the methodology is demonstrated with applications to proteins with tumbling times ranging from 2 ns (protein L, 7.5 kDa, 45 degrees C) to 54 ns (malate synthase G, 82 kDa, 37 degrees C); dynamics parameters are shown to be in excellent agreement with those obtained in (2)H NMR studies of other methyl isotopomers. A consistency relationship is found to exist between R(1)((13)CHD(2)) and the relaxation rates of pure longitudinal and quadrupolar order modes in (13)CH(2)D-labeled methyl groups, and experimental rates measured for a number of proteins are shown to be in excellent agreement with expectations based on theory. The present methodology extends the applicability of (2)H relaxation methods for the quantification of side-chain dynamics in high molecular weight proteins.     

(13)C-(1)H and (13)C-(13)C NMR J-couplings in (13)C-labeled N-acetyl-neuraminic acid: correlations with molecular structure

N-acetyl-neuraminic acid (Neu5Ac, 2) was prepared enzymatically containing single sites of (13)C-enrichment at C1, C2, and C3. Aqueous solutions of the three (13)C isotopomers were studied by (1)H and (13)C NMR spectroscopy at p(2)H 2 and pH 8 to obtain J(CH) and J(CC) values involving the labeled carbons. Experimental studies were complemented by DFT calculations of the same set of J-couplings in protonated and ionized structural mimics of 2 to determine how well theoretical predictions match the experimental findings in saccharides bearing ionizable functionality. Results show that: (a) (2)J(C2,H3ax/eq) values in 2 depend on anomeric configuration, thus complementing (3)J(C1,H3ax/eq) behavior, (b) J(CH) and J(CC) values involving C2 depend on anomeric configuration, the C1-C2 bond torsion, and solution pH, and (c) long-range (4)J(C2,H7) is sensitive to glycerol side-chain conformation. Intraring J(HH) and most (2)J(CH), (3)J(CH), (2)J(CC), and (3)J(CC) involving C1-C3 of 2 appear largely unaffected by the ionization state of the carboxyl group. In vacuo and solvated DFT calculations of geminal and vicinal J(CH) and J(CC) values are similar and reproduce the experimental data well, but better agreement with experiment was observed for (1)J(C1,C2) in the solvated calculations. The present work provides new information for future treatments of trans-glycoside couplings involving Neu5Ac residues by (a) providing new standard values of intraring J(CC) for coupling pathways that mimic those for trans-glycoside J(CC), (b) identifying potential effects of solution pH on trans-glycoside couplings inferred through the behavior of related intraring couplings, and (c) providing specific guidelines for more reliable DFT predictions of J(CH) and J(CC) values in ionizable saccharides.     

Nonadiabatic molecular dynamics simulations of correlated electrons in solution. 1. Full configuration interaction (CI) excited-state relaxation dynamics of hydrated dielectrons

The hydrated dielectron is composed of two excess electrons dissolved in liquid water that occupy a single cavity; in both its singlet and triplet spin states there is a significant exchange interaction so the two electrons cannot be considered to be independent. In this paper and the following paper,we present the results of mixed quantum/classical molecular dynamics simulations of the nonadiabatic relaxation dynamics of photoexcited hydrated dielectrons, where we use full configuration interaction (CI) to solve for the two-electron wave function at every simulation time step. To the best of our knowledge, this represents the first systematic treatment of excited-state solvation dynamics where the multiple-electron problem is solved exactly. The simulations show that the effects of exchange and correlation contribute significantly to the relaxation dynamics. For example, spin-singlet dielectrons relax to the ground state on a time scale similar to that of single electrons excited at the same energy, but spin-triplet dielectrons relax much faster. The difference in relaxation dynamics is caused by exchange and correlation: The Pauli exclusion principle imposes very different electronic structure when the electrons' spins are singlet paired than when they are triplet paired, altering the available nonadiabatic relaxation pathways. In addition, we monitor how electronic correlation changes dynamically during nonadiabatic relaxation and show that solvent dynamics cause electron correlation to evolve quite differently for singlet and triplet dielectrons. Despite such differences, our calculations show that both spin states are stable to excited-state dissociation, but that the excited-state stability has different origins for the two spin states. For singlet dielectrons, the stability depends on whether the solvent structure can rearrange to create a second cavity before the ground state is reached. For triplet dielectrons, in contrast, electronic correlation ensures that the two electrons do not dissociate, even if the dielectron is artificially kept from reaching the ground state. In addition, both singlet and triplet dielectrons change shape dramatically during relaxation, so that linear response fails to describe the solvation dynamics for either spin state. In the following paper (Larsen, R. E.; Schwartz, B. J. J. Phys. Chem. B 2006, 110, 9692), we use these simulations to calculate the pump-probe spectroscopic signal expected for photoexcited hydrated dielectrons and to predict an experiment to observe hydrated dielectrons directly.     

Enantioselective syntheses of (13)C-labeled (2R)- and (2S)-phytochromobilin dimethyl ester

(2R)- and (2S)-phytochromobilin dimethyl ester have been prepared in enantiomerically pure form, specifically (13)C-labeled at C(10) or C(15).     

An improved picture of methyl dynamics in proteins from slowly relaxing local structure analysis of 2H spin relaxation

Protein dynamics is intimately related to biological function. Core dynamics is usually studied with 2H spin relaxation of the 13CDH2 group, analyzed traditionally with the model-free (MF) approach. We showed recently that MF is oversimplified in several respects. This includes the assumption that the local motion of the dynamic probe and the global motion of the protein are decoupled, the local geometry is simple, and the local ordering is axially symmetric. Because of these simplifications MF has yielded a puzzling picture where the methyl rotation axis is moving rapidly with amplitudes ranging from nearly complete disorder to nearly complete order in tightly packed protein cores. Our conclusions emerged from applying to methyl dynamics in proteins the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Polimeno, A.; Freed, J. H. J. Phys. Chem. 1995, 99, 10995-11006.), which can be considered the generalization of MF, with all the simplifications mentioned above removed. The SRLS picture derived here for the B1 immunoglobulin binding domain of peptostreptococcal protein L, studied over the temperature range of 15-45 degrees C, is fundamentally different from the MF picture. Thus, methyl dynamics is characterized structurally by rhombic local potentials with varying symmetries and dynamically by tenfold slower rates of local motion. On average, potential rhombicity decreases, mode-coupling increases, and the rate of local motion increases with increasing temperature. The average activation energy for local motion is 2.0 +/- 0.2 kcal/mol. Mode-coupling affects the analysis even at 15 degrees C. The accuracy of the results is improved by including in the experimental data set relaxation rates associated with rank 2 coherences.     

Spin probe mobility in relation to free volume and relaxation dynamics of glass‐formers: A series of spin probes in poly(isobutylene)

We present the dynamics of a series of three paramagnetic molecules of different volume, mass, and shape in amorphous glass‐forming polymer poly(isobutylene) (PIB) as investigated by means of electron spin resonance (ESR) technique. The reorientation behavior of spin probes is related to the ortho‐positronium (o‐Ps) annihilation in PIB from positron annihilation lifetime spectroscopy (PALS) and the extracted free volume information. It is also related to the dynamic data of PIB from broadband dielectric spectroscopy (BDS), neutron scattering (NS), and nuclear magnetic resonance (NMR) spectroscopy from literature. In the case of the smallest spin probe, 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO), a discontinuous course of the spectral parameter 2A_zz′ versus T dependence was observed and the subsequent phenomenological model‐free analyses of the spectral parameter, 2A_zz′ versus T, as well as of the correlation time, τ_c, versus 1/T plots provided the characteristic ESR temperatures ( , T_50G, ) and (T, T, T). These characteristic ESR temperatures were found to be consistent with the characteristic PALS temperatures: T, T = T from temperature dependences of the mean o‐Ps lifetime, τ₃, or the width of o‐Ps lifetime distribution, σ₃, respectively. In addition, the relationships between the spin probe size, V, and the free volume hole size distributions g_n(V_h) at the characteristic ESR temperatures indicate the significant influence of the free volume fluctuation at the crossover from slow to rapid regime as well as within the rapid motional regime. On the other hand, the two larger spin probes exhibit a rather continuous 2A_zz′–T plots with the respective T_50G's lying in the vicinity of T independently of their volume, mass and shape, suggesting the common origin of underlying process controlling this T_50G transition. Finally, these mutual PALS and ESR findings were compared with the known dynamic behavior of PIB which suggest that the dynamics of the TEMPO and the larger spin probes are related to free volume fluctuation associated with primary α ‐ and secondary β processes, respectively. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1058–1068, 2009     

13C CPMAS spectroscopy of deuterated proteins: CP dynamics, line shapes, and T1 relaxation

(13)C CPMAS NMR has been investigated in application to protein samples with a variety of deuteration patterns. Samples were prepared with protons in either all hydrogen positions, only in the exchangeable sites, or in the exchangeable sites plus select methyl groups. CP dynamics, T(1) relaxation times, and (13)C line widths have been compared. Using ubiquitin as a model system, reasonable (1)H-(13)C CP transfer is observed for the extensively deuterated samples. In the absence of deuterium decoupling, the (13)C line widths observed for the deuterated samples are identical to those observed for the perprotio samples with a MAS rate of 20 kHz. Extensive deuteration has little effect on the T(1) of the exchangeable protons. On the basis of these observations, it is clear that there are no substantive compromises accompanying the use of extensive deuteration in the design of (1)H, (15)N, or (13)C solid-state NMR methods.     

Non-Kramers' behavior of the chain local dynamics of PVC in dilute solution. Carbon-13 NMR relaxation study

Carbon-13 spin-lattice, spin-spin relaxation times, and NOE values were measured as a function of temperature at two magnetic fields for poly(vinyl chloride) (PVC) in three solvents: chloroform, dioxane, and dimethyl sulfoxide. The relaxation data were interpreted in terms of chain local motions by using the bimodal time-correlation function of the Dejean-Laupretre-Monnerie (DLM) model. Using this model, the correlation times obtained in this study, as well as those from an earlier study in dibutyl phthalate and 1,1,2,2-tetrachloroethane did not follow a linear relationship with solvent viscosity. Instead, the chain local dynamics showed a 0.60 power dependence on solvent viscosity, indicating that PVC deviates from the hydrodynamic Kramers' theory. © 1997 John Wiley & Sons, Inc.     

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.     

Carbon-13 NMR relaxation study of 1,8-bis(dimethylamino)naphthalene in isotropic solution

Carbon-13 nuclear spin relaxation in 1,8-bis(dimethylamino)naphthalene (DMAN) was investigated in a dimethylformamide- d 7 solution. In addition, the chemical shielding tensors were measured in the crystalline powder. Detailed analysis of (13)C longitudinal relaxation in this molecule yielded its rotational diffusion tensor. Comparison to the protonated form of DMAN, DMANH(+), leads to conclusions concerning interaction of the latter with its counterion.