Manifestation of chiral recognition of camphor enantiomers by alpha-cyclodextrin in longitudinal and transverse relaxation rates of the corresponding 1:2 complexes and determination of the orientation of the guest inside the host capsule

The 1:2 complexes of camphor enantiomers with alpha-cyclodextrin in (2)H(2)O manifest differences in longitudinal and transverse relaxation rates of camphor methyl protons owing to chiral recognition. The relaxation data obtained at two magnetic fields were quantitatively analyzed using the model of anisotropic overall tumbling with internal motion. In experimental conditions (guest-to-host ratio = 1:20, T = 300.6K), all camphor molecules are complexed. The complexes are not rigid but the rotational diffusion of camphor enantiomers embedded inside the capsules formed by two alpha-cyclodextrin hosts is well outside the extreme narrowing region. Both differences in the anisotropic overall tumbling and internal rotation of all methyl groups participate in enantiomeric differentiation of the relaxation rates. Anisotropic tumbling of camphor molecules provides information on the orientation of the guest in the host capsule that for the complex under study could not be obtained by other methods.     

How accurately can oligonucleotide structures be determined from the hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics approach?

The accuracy and precision of structures derived from a combined hybrid relaxation rate matrix/NOESY distance restrained molecular dynamics methodology were examined with simulations that included typical experimental errors. NOESY data were simulated for a DNA dodecamer duplex, d-(CGCGAATTCGCG)2, with added volume error of approximately 20% and low-level thermal noise. Distances derived from a hybrid relaxation matrix analysis of the NOE data were used as constraints in molecular dynamics driven structural refinements of several initial model geometries. The final structures were compared against results obtained from the traditional isolated two-spin approximation treatment of these NOESY volumes and also against refined structures that employed error-free data. Results show that the structures derived from the relaxation rate matrix analysis of the NOESY data are more accurate than those derived from a simple two-spin approximation analysis and it is possible to achieve refinement to the level of simulated experimental error. Results may be significantly improved with the use of either more accurately measured NOESY volumes or additional matrix-derived constraints. Many of the helical parameters and backbone torsional angles may be accurately reproduced by the hybrid matrix methodology.     

Sampling of protein dynamics in nanosecond time scale by 15N NMR relaxation and self-diffusion measurements.

This paper presents a procedure for detection of intermediate nanosecond internal dynamics in globular proteins. The procedure uses 1H-15N relaxation measurements at several spectrometer frequencies and hydrodynamic calculations based on experimental self-diffusion coefficients. New heteronuclear experiments, using pulse field gradients, are introduced for the measurement of translation diffusion coefficients of 15N labeled proteins. An advanced interpretation of recently published (Luginbühl et al., Biochemistry, 36, 7305-7312 (1997)) backbone amide 15N relaxation data, measured at two spectrometers (400 and 750 MHz for 1H) for N-terminal DNA-binding domain (1-63) of 434 repressor, is presented. Non-applicability of commonly used fast (picosecond) dynamics model (FD) was justified by (i) poor fit of relaxation data by the FD model-free spectral density function both for isotropic and anisotropic models of the overall molecular tumbling; (ii) specific dependence of the overall rotation correlation times calculated from T1/T2 ratio on the spectrometer frequency; (iii) mismatch of the ratio of longitudinal 15N relaxation times T1, measured at different spectrometer frequencies, in comparison with that anticipated for the FD model; (iv) significantly underestimated overall rotation correlation time provided by the FD model (5.50+/-0.15 and 5.80+/-0.15 ns for 750 and 400 MHz spectrometer frequency respectively) in comparison with correlation time obtained from hydrodynamics. On the other hand, all relaxation and hydrodynamics data are in good correspondence with the model of intermediate (nanoseconds) dynamics. Overall rotation correlation time of 7.5+/-0.7 ns was calculated from experimental translation self-diffusion rate using hydrodynamics formalism (Garcia de la Torre, J. and Bloomfield, V.A. Quart. Rev. Biophys., 14, 81-139 (1981)). The statistical analysis of 15N relaxation data along with the hydrodynamic consideration clearly revealed that most of the residues in 434(1-63) repressor are involved in the nanosecond internal dynamics characterized by the the mean order parameters of 0.59+/-0.06 and the correlation times of ca. 5 ns.     

Anisotropic rotational diffusion in model-free analysis for a ternary DHFR complex

Model-free analysis has been extensively used to extract information on motions in proteins over a wide range of timescales from NMR relaxation data. We present a detailed analysis of the effects of rotational anisotropy on the model-free analysis of a ternary complex for dihydrofolate reductase (DHFR). Our findings show that the small degree of anisotropy exhibited by DHFR (D_||/D=1.18) introduces erroneous motional models, mostly exchange terms, to over 50% of the NH spins analyzed when isotropic tumbling is assumed. Moreover, there is a systematic change in S², as large as 0.08 for some residues. The significant effects of anisotropic rotational diffusion on model-free motional parameters are in marked contrast to previous studies and are accentuated by lowering of the effective correlation time using isotropic tumbling methods. This is caused by the preponderance of NH vectors aligned perpendicular to the principal diffusion tensor axis and is readily detected because of the high quality of the relaxation data. A novel procedure, COPED (COmparison of Predicted and Experimental Diffusion tensors) is presented for distinguishing genuine motions from the effects of anisotropy by comparing experimental relaxation data and data predicted from hydrodynamic analyses. The procedure shows excellent agreement with the slow motions detected from the axially symmetric model-free analysis and represents an independent procedure for determining rotational diffusion and slow motions that can confirm or refute established procedures that rely on relaxation data. Our findings show that neglect of even small degrees of rotational diffusion anisotropy can introduce significant errors in model-free analysis when the data is of high quality. These errors can hinder our understanding of the role of internal motions in protein function.     

Analysis of fluorescence decay kinetics measured in the frequency domain using distributions of decay times

We describe the theoretical and practical aspects of analyzing complex fluorescence decay kinetics using continuous distributions of decay times. Our analysis uses frequency-domain data, provides for global analysis of multiple data sets and includes the possibility of excited-state processes. Simulated data were used to estimate the types of distributions which can be reasonably recovered from the measurements. Additionally, we describe a variety of distributions recovered from experimental data. For mixtures of one, two or three exponentially decaying fluorophores we recovered narrow lifetime distributions, which are essentially identical to a multiexponential decay. Similarly, a two-state excited-state reaction also yielded a narrow distribution with negative preexponential factors. The presence of time-dependent spectral relaxation of labeled lipids results in a wide distribution of decay times, which becomes narrower for faster relaxation rates at higher temperatures. Hence, the decay-time distributions appear to be sensitive to the dynamics of the environment surrounding the fluorophore. Additionally, distributions of decay times were observed to result from transient effects in collisional quenching, from energy transfer in the presence of a range of donor-to-acceptor distances, and for several single-tryptophan proteins.     

A graphical method for the analysis of anisotropic rotational diffusion in proteins

A graphical method for the analysis of relaxation data is presented. It allows a fast estimation of the range of values of the components of the axially symmetric rotational diffusion tensor that are compatible with the experimental relaxation data. The graphical method clearly shows the contribution of different experimental relaxation parameters to the measured anisotropy. In particular, for proteins with moderate anisotropy, data from at least two N-H bonds forming angles close to 0° and 90° with respect to the principal axis of the rotational diffusional tensor are needed. For very anisotropic systems, combination of different relaxation parameters from a single residue is enough to characterize the local anisotropy.     

Assessing potential bias in the determination of rotational correlation times of proteins by NMR relaxation

The various factors that influence the reliable and efficient determination of the correlation time describing molecular reorientation of proteins by NMR relaxation methods are examined. Nuclear Overhauser effects, spin-lattice, and spin-spin relaxation parameters of 15N NMR relaxation in ubiquitin have been determined at 17.6, 14.1, 11.7 and 9.4 Tesla. This unusually broad set of relaxation parameters has allowed the examination of the influence of chemical shift anisotropy, the functional form of the model-free spectral density, and the reliability of determined spin- spin relaxation parameters on the characterization of global tumbling of the protein. Treating the 15N chemical shift anisotropy (CSA) as an adjustable parameter, a consensus value of –170 ± 15ppm for the breadth of the chemical shift tensor and a global isotropic correlation time of 4.1ns are found when using the model-free spectral density to fit T1 and NOE data from all fields. The inclusion of T2 relaxation parameters in the determination of the global correlation time results in its increase to 4.6ns. This apparent inconsistency may explain a large portion of the discrepancy often found between NMR- and fluorescence-derived m values for proteins. The near identity of observed T2 and T1 values suggests that contributions from slow motions are not the origin of the apparent inconsistency with obtained T1 and NOE data. Various considerations suggest that the origin of this apparent discrepancy may reside in a contribution to the spectral density at zero frequency that is not represented by the simple model-free formalism in addition to the usual experimental difficulties associated with the measurement of these relaxation parameters. Finally, an axially symmetric diffusion tensor for ubiquitin is obtained using exclusively T1 and NOE data. A recommendation is reached on the types and combinations of relaxation data that can be used to reliably determine m values. It is also noted that the reliable determination of m values from 15N T1 and NOE relaxation parameters will become increasingly difficult as m increases.     

Efficient analysis of macromolecular rotational diffusion from heteronuclear relaxation data

A novel program has been developed for the interpretation of ¹⁵N relaxation rates in terms of macromolecular anisotropic rotational diffusion. The program is based on a highly efficient simulated annealing/minimization algorithm, designed specifically to search the parametric space described by the isotropic, axially symmetric and fully anisotropic rotational diffusion tensor models. The high efficiency of this algorithm allows extensive noise-based Monte Carlo error analysis. Relevant statistical tests are systematically applied to provide confidence limits for the proposed tensorial models. The program is illustrated here using the example of the cytochrome c from Rhodobacter capsulatus, a four-helix bundle heme protein, for which data at three different field strengths were independently analysed and compared.     

Characterization of the overall and local dynamics of a protein with intermediate rotational anisotropy: Differentiating between conformational exchange and anisotropic diffusion in the B3 domain of protein G

Because the overall tumbling provides a major contribution to protein spectral densities measured in solution, the choice of a proper model for this motion is critical for accurate analysis of protein dynamics. Here we study the overall and backbone dynamics of the B3 domain of protein G using ¹⁵N relaxation measurements and show that the picture of local motions is markedly dependent on the model of overall tumbling. The main difference is in the interpretation of the elevated R ₂ values in the -helix: the isotropic model results in conformational exchange throughout the entire helix, whereas no exchange is predicted by anisotropic models that place the longitudinal axis of diffusion tensor almost parallel to the helix axis. Due to small size (fast tumbling) of the protein, the T ₁ values have low sensitivity to NH bond orientation. The diffusion tensor derived from orientation dependence of R ₂/R ₁ is anisotropic (D _par/D _perp=1.4), with a small rhombic component. In order to distinguish the correct picture of motion, we apply model-independent methods that are sensitive to conformational exchange and do not require knowledge of protein structure or assumptions about its dynamics. A comparison of the CSA/dipolar cross-correlation rate constants with ¹⁵N relaxation rates and the estimation of R _ex terms from relaxation data at 9.4 and 14.1 T indicate no conformational exchange in the helix, in support of the anisotropic models. The experimentally derived diffusion tensor is in excellent agreement with theoretical predictions from hydrodynamic calculations; a detailed comparison with various hydrodynamic models revealed optimal parameters for hydrodynamic calculations.     

NMR analysis of carbohydrates with model-free spectral densities: the dispersion range revisited

Over the past decade molecular mechanics and molecular dynamics studies have demonstrated considerable flexibility for carbohydrates. In order to interpret the corresponding NMR parameters, which correspond to a time-averaged or 'virtual' conformer, it is necessary to simulate the experimental data using the averaged geometrical representation obtained with molecular modelling methods. This structural information can be transformed into theoretical NMR data using empirical Karplus-type equations for the scalar coupling constants and the appropriate formalism for the relaxation parameters. In the case of relaxation data, the 'model-free' spectral densities have been widely used in order to account for the internal motions in sugars. Several studies have been conducted with truncated model-free spectral densities based on the assumption that internal motion is very fast with respect to overall tumbling. In this report we present experimental and theoretical evidence that suggests that this approach is not justified. Indeed, recent results show that even in the case of moderate-sized carbohydrates internal motions are occurring on the same timescale as molecular reorientation. Simulations of relaxation parameters (NOESY volumes, proton cross-relaxation rates, carbon T1 and nOe values) in the dispersion range (0.1<Tc<5 ns) show that rates of internal motion can be fairly precisely defined with respect to overall tumbling. Experimental data for a variety of oligosaccharides clearly indicate similar timescales for internal and overall motion. This revised version was published online in August 2006 with corrections to the Cover Date.     

Comparison of (13)C(alpha)H and (15)NH backbone dynamics in protein GB1

This study presents a site-resolved experimental view of backbone C(alpha)H and NH internal motions in the 56-residue immunoglobulin-binding domain of streptococcal protein G, GB1. Using (13)C(alpha)H and (15)NH NMR relaxation data [T(1), T(2), and NOE] acquired at three resonance frequencies ((1)H frequencies of 500, 600, and 800 MHz), spectral density functions were calculated as F(omega) = 2omegaJ(omega) to provide a model-independent way to visualize and analyze internal motional correlation time distributions for backbone groups in GB1. Line broadening in F(omega) curves indicates the presence of nanosecond time scale internal motions (0.8 to 5 nsec) for all C(alpha)H and NH groups. Deconvolution of F(omega) curves effectively separates overall tumbling and internal motional correlation time distributions to yield more accurate order parameters than determined by using standard model free approaches. Compared to NH groups, C(alpha)H internal motions are more broadly distributed on the nanosecond time scale, and larger C(alpha)H order parameters are related to correlated bond rotations for C(alpha)H fluctuations. Motional parameters for NH groups are more structurally correlated, with NH order parameters, for example, being larger for residues in more structured regions of beta-sheet and helix and generally smaller for residues in the loop and turns. This is most likely related to the observation that NH order parameters are correlated to hydrogen bonding. This study contributes to the general understanding of protein dynamics and exemplifies an alternative and easier way to analyze NMR relaxation data.     

Repeat motions and backbone flexibility in designed proteins with different numbers of identical consensus tetratricopeptide repeats

The tetratricopeptide repeat (TPR) is a 34-residue helix-turn-helix motif that occurs as three or more tandem repeats in a wide variety of proteins. We have determined the repeat motions and backbone fluctuations of proteins containing two or three consensus TPR repeats (CTPR2 and CPTR3, respectively) using 15N NMR relaxation measurements. Rotational diffusion tensors calculated from these data for each repeat within each TPR protein indicate that there is a high degree of motional correlation between different repeats in the same protein. This is consistent with the prevailing view that repeat proteins, such as CTPR2 and CTPR3, behave as single cooperatively folded domains. The internal motions of backbone NH groups were determined using the Lipari-Szabo model-free formalism. For most residues, there was a clear separation between the influence of internal motion and the influence of global rotational tumbling on the observed magnetic relaxation. The local internal motions are highly restricted in most of the helical elements, with slightly greater flexibility in the linker elements. Comparisons between CTPR2 and CTPR3 indicate that an addition of a TPR repeat to the C-terminus (before the solvation helix) of CTPR2 slightly reduces the flexibility of the preceding helix.     

Choice of Force Field for Proteins Containing Structured and Intrinsically Disordered Regions

Biomolecular force fields optimized for globular proteins fail to properly reproduce properties of intrinsically disordered proteins. In particular, parameters of the water model need to be modified to improve applicability of the force fields to both ordered and disordered proteins. Here, we compared performance of force fields recommended for intrinsically disordered proteins in molecular dynamics simulations of three proteins differing in the content of ordered and disordered regions (two proteins consisting of a well-structured domain and of a disordered region with and without a transient helical motif and one disordered protein containing a region of increased helical propensity). The obtained molecular dynamics trajectories were used to predict measurable parameters, including radii of gyration of the proteins and chemical shifts, residual dipolar couplings, paramagnetic relaxation enhancement, and NMR relaxation data of their individual residues. The predicted quantities were compared with experimental data obtained within this study or published previously. The results showed that the NMR relaxation parameters, rarely used for benchmarking, are particularly sensitive to the choice of force-field parameters, especially those defining the water model. Interestingly, the TIP3P water model, leading to an artificial structural collapse, also resulted in unrealistic relaxation properties. The TIP4P-D water model, combined with three biomolecular force-field parameters for the protein part, significantly improved reliability of the simulations. Additional analysis revealed only one particular force field capable of retaining the transient helical motif observed in NMR experiments. The benchmarking protocol used in our study, being more sensitive to imperfections than the commonly used tests, is well suited to evaluate the performance of newly developed force fields.     

Relationships between protein structure and dynamics from a database of NMR-derived backbone order parameters

The amplitude of protein backbone NH group motions on a time-scale faster than molecular tumbling may be determined by analysis of (15)N NMR relaxation data according to the Lipari-Szabo model free formalism. An internet-accessible database has been compiled containing 1855 order parameters from 20 independent NMR relaxation studies on proteins whose three-dimensional structures are known. A series of statistical analyses has been performed to identify relationships between the structural features and backbone dynamics of these proteins. Comparison of average order parameters for different amino acid types indicates that amino acids with small side-chains tend to have greater backbone flexibility than those with large side-chains. In addition, the motions of a given NH group are also related to the sizes of the neighboring amino acids in the primary sequence. The secondary structural environment appears to influence backbone dynamics relatively weakly, with only subtle differences between the order parameter distributions of loop structures and regular hydrogen bonded secondary structure elements. However, NH groups near helix termini are more mobile on average than those in the central regions of helices. Tertiary structure influences are also relatively weak but in the expected direction, with more exposed residues being more flexible on average than residues that are relatively inaccessible to solvent.     

New approaches to the dynamic interpretation and prediction of NMR relaxation data from proteins

NMR relaxation experiments of isotopically labeled proteins provide a wealth of information on reorientational global and local dynamics on nanosecond and subnanosecond timescales for folded and nonfolded proteins in solution. Recent methodological advances in the interpretation of relaxation data have led to a better understanding of the overall tumbling behavior, the separability of internal and overall motions, and the presence of correlated dynamics between different nuclear sites, as well as to new insights into the relationship between reorientational dynamics and primary and tertiary protein structure. Some of the new methods are particularly useful when dealing with nonfolded protein states.     

Assessment of protein reorientational diffusion in solution by 13C off-resonance rotating frame spin-lattice relaxation: effect of anisotropic tumbling

The 13C off-resonance rotating frame spin-lattice relaxation technique is applicable to the study of protein rotational diffusion behavior in a variety of experimental situations. The original formalism of James and co-workers (1978) (J. Amer. Chem. Soc. 100, 3590-3594) was constrained by the assumption of random isotropic reorientational motion. Here we include in the formalism anisotropic tumbling, and present the results of computer simulations illustrating the differences between anisotropic and isotropic reorientational motion for the off-resonance rotating frame spin-lattice relaxation experiment. In addition, we have included chemical shift anisotropy of the peptide carbonyl carbon as an additional relaxation mechanism contribution, to permit high-field nmr protein rotational diffusion measurements.