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 peptide rotational diffusion by homonuclear NMR

The analysis of the rotational diffusion of a molecule using homonuclear NMR is investigated. The homonuclear longitudinal and transverse cross-relaxation rates, which can be quantitatively measured using off-Resonance Rotating frame nuclear Overhauser Effect Spectroscopy (ROESY), are used to build a distribution, which exhibits a solid-state-like pattern characteristic of the diffusion tensor. The distributions of the antimicrobial peptide ranalexin in water and in 30% of trifluoracetic acid (TFE) are compared, and the peptide rotational diffusion is shown to be more isotropic in water than in 30% TFE. This difference is further supported by the analysis of NMR ranalexin conformers in 30% TFE, and by the analysis of a molecular dynamics simulation of peptide in water.     

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.     

Solution structure determination of the two DNA-binding domains in the Schizosaccharomyces pombe Abp1 protein by a combination of dipolar coupling and diffusion anisotropy restraints

We have solved the solution structure of the N-terminal region of the fission yeast centromere protein, Abp1, bound to a 21-base pair DNA fragment bearing its recognition site (Mw = 30 kDa). Although the two DNA-binding domains in the Abp1 protein were defined well by a conventional NOE-based NMR methodology, the overall structure of the Abp1 protein was poorly defined, due to the lack of interdomain distance restraints. Therefore, we additionally used residual dipolar couplings measured in a weakly aligned state, and rotational diffusion anisotropies. Neither the NH residual dipolar couplings nor the backbone ¹⁵N T ₁/T ₂ data were sufficient to determine the overall structure of the Abp1 protein, due to spectral overlap. We used a combination of these two orientational restraints (residual dipolar coupling and rotational diffusion anisotropy), which significantly improved the convergence of the overall structures. The range of the observed T ₁/T ₂ ratios was wider (20–50 for the secondary structure regions of Abp1) than the previously reported data for several globular proteins, indicating that the overall shape of the Abp1DNA complex is ellipsoid. This extended form would facilitate the recognition of the two separate sites in the relatively long DNA sequence by the DNA-binding domains of Apb1.     

Optimisation of NMR dynamic models II. A new methodology for the dual optimisation of the model-free parameters and the Brownian rotational diffusion tensor

Finding the dynamics of an entire macromolecule is a complex problem as the model-free parameter values are intricately linked to the Brownian rotational diffusion of the molecule, mathematically through the autocorrelation function of the motion and statistically through model selection. The solution to this problem was formulated using set theory as an element of the universal set —the union of all model-free spaces (d’Auvergne EJ and Gooley PR (2007) Mol BioSyst 3(7), 483–494). The current procedure commonly used to find the universal solution is to initially estimate the diffusion tensor parameters, to optimise the model-free parameters of numerous models, and then to choose the best model via model selection. The global model is then optimised and the procedure repeated until convergence. In this paper a new methodology is presented which takes a different approach to this diffusion seeded model-free paradigm. Rather than starting with the diffusion tensor this iterative protocol begins by optimising the model-free parameters in the absence of any global model parameters, selecting between all the model-free models, and finally optimising the diffusion tensor. The new model-free optimisation protocol will be validated using synthetic data from Schurr JM et al. (1994) J Magn Reson B 105(3), 211–224 and the relaxation data of the bacteriorhodopsin (1–36)BR fragment from Orekhov VY (1999) J Biomol NMR 14(4), 345–356. To demonstrate the importance of this new procedure the NMR relaxation data of the Olfactory Marker Protein (OMP) of Gitti R et al. (2005) Biochem 44(28), 9673–9679 is reanalysed. The result is that the dynamics for certain secondary structural elements is very different from those originally reported. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Rotational diffusion tensor of nucleic acids from 13C NMR relaxation

Rotational diffusion properties have been derived for the DNA dodecamer d(CGCGAATTCGCG)₂ from ¹³C R₁ and R₁ measurements on the C₁, C₃, and C₄ carbons in samples uniformly enriched in ¹³C. The narrow range of C-H bond vector orientations relative to the DNA axis make the analysis particularly sensitive to small structural deviations. As a result, the R₁/R₁ ratios are found to fit poorly to the crystal structures of this dodecamer, but well to a recent solution NMR structure, determined in liquid crystalline media, even though globally the structures are quite similar. A fit of the R₁/R₁ ratios to the solution structure is optimal for an axially symmetric rotational diffusion model, with a diffusion anisotropy, D_||/D, of 2.1±0.4, and an overall rotational correlation time, (2D_||+4D)^–1, of 3.35 ns at 35 °C in D₂O, in excellent agreement with values obtained from hydrodynamic modeling.     

The shape of a membrane protein derived from rotational diffusion

Membrane proteins are modelled as cylinders with an elliptic cross-section in the plane of the membrane. The coefficient for rotational diffusion about the cylinder axis is calculated as a function of the axial ratio of the elliptic cross-section.     

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.     

Interpretation of 15N NMR relaxation data of globular proteins using hydrodynamic calculations with HYDRONMR

HYDRONMR is an implementation of state of the art hydrodynamic modeling to calculate the spectral density functions for NH or C-H vectors in a rigid protein structure starting from an atomic level representation. Thus HYDRONMR can be used to predict NMR relaxation times from a rigid model and to compare them with the experimental results. HYDRONMR contains a single adjustable parameter, the atomic element radius. A protocol to determine the value that gives the best agreement between calculated and experimental T₁/T₂values is described. For most proteins, the value of the atomic element radius ranges between 2.8 Å and 3.8 Å with a distribution centered at 3.3 Å. Deviations from the usual range towards larger values are associated to aggregation in several proteins. Deviations to lower values may be related to large-scale motions or inappropriate model structures.If the average structure is correct, deviations between experimental T₁/T₂values and those calculated with HYDRONMR can be used to distinguish residues affected by anisotropic motion from those that are involved in chemical exchange.     

Decreased rotational diffusion of band 3 in melanesian ovalocytes from Papua,New Guinea

Summary Melanesian ovalocytes from Papua New Guinea have an N-terminal extension of the band 3 polypeptide (Jones, G.L., Edmunson. H.M., Wesche, D., Saul, A. 1990.Biochim. Biophys. Acta 1096:33–40). The ovalocytes showed a threefold increase in shear elastic modulus as determined by micropipette aspiration measurements of membrane rigidity. Time-resolved phosphorescence anisotropy has been used to study the rotational freedom of band 3 in membranes prepared from ovalocytes. The ovalocytic polymorphism was found to be associated with a marked decrease in the rotational mobility of band 3. This may indicate participation of band 3 in large homoaggregates or in complexes with other proteins at the cytoplasmic surface. There was no morphological clustering of band 3 detectable by immunofluorescence microscopy.     

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.     

Measurement of 15N relaxation in the detergent-solubilized tetrameric KcsA potassium channel

A set of TROSY-HNCO (tHNCO)-based 3D experiments is presented for measuring ¹⁵N relaxation parameters in large, membrane-associated proteins, characterized by slow tumbling times and significant spectral overlap. Measurement of backbone ¹⁵N R ₁, R _1ρ, ¹⁵N–{¹H} NOE, and ¹⁵N CSA/dipolar cross correlation is demonstrated and applied to study the dynamic behavior of the homotetrameric KcsA potassium channel in SDS micelles under conditions where this channel is in the closed state. The micelle-encapsulated transmembrane domain, KcsA^TM, exhibits a high degree of order, tumbling as an oblate ellipsoid with a global rotational correlation time, τ_c = 38 ± 2.5 ns, at 50 °C and a diffusion anisotropy, , corresponding to an aspect ratio a/b ≥ 1.4. The N- and C-terminal intracellular segments of KcsA exhibit considerable internal dynamics (S ² values in the 0.2–0.45 range), but are distinctly more ordered than what has been observed for unstructured random coils. Relaxation behavior in these domains confirms the position of the C-terminal helix, and indicates that in SDS micelles, this amphiphilic helix does not associate into a stable homotetrameric helical bundle. The relaxation data indicate the absence of elevated backbone dynamics on the ps–ns time scale for the 5-residue selectivity filter, which selects K⁺ ions to enter the channel. Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at . An erratum to this article can be found at     

A new approach to graphical analysis of feeding strategy from stomach contents data—modification of the Costello (1990) method

A modification of the graphical Costello method is proposed for the analysis of stomach contents data. The new method allows prey importance, feeding strategy and the interand intra-individual components of niche width to be explored using graphical presentation. The analysis is based on a two-dimensional representation of prey-specific abundance and frequency of occurrence of the different prey types in the diet. The paper describes the new method and the parameters therein, and also present some examples of the utilization of the method. The method may be particularly well-suited for the examination of predictions made from optimal foraging, competition and niche theories.     

A simple method for estimating cytoplasmic diffusion coefficients

The diffusion coefficients of radioactively labelled substances in cytoplasm or other fluids are determined in vitro. The fluid containing the labelled substance is filled into a cylinder with one open end, through which the labelled substance diffuses out into a stirred outer medium. The diffusion coefficient is calculated by a one-dimensional diffusion equation from the rate of loss from the cylinder, and the length of the cylinder. The diffusion coefficients of tritiated water in several fluids have been determined. The results are in good agreement with those obtained by other methods.     

A graphical method for analyzing distance restraints using residual dipolar couplings for structure determination of symmetric protein homo-oligomers

High-resolution structure determination of homo-oligomeric protein complexes remains a daunting task for NMR spectroscopists. Although isotope-filtered experiments allow separation of intermolecular NOEs from intramolecular NOEs and determination of the structure of each subunit within the oligomeric state, degenerate chemical shifts of equivalent nuclei from different subunits make it difficult to assign intermolecular NOEs to nuclei from specific pairs of subunits with certainty, hindering structural analysis of the oligomeric state. Here, we introduce a graphical method, DISCO, for the analysis of intermolecular distance restraints and structure determination of symmetric homo-oligomers using residual dipolar couplings. Based on knowledge that the symmetry axis of an oligomeric complex must be parallel to an eigenvector of the alignment tensor of residual dipolar couplings, we can represent distance restraints as annuli in a plane encoding the parameters of the symmetry axis. Oligomeric protein structures with the best restraint satisfaction correspond to regions of this plane with the greatest number of overlapping annuli. This graphical analysis yields a technique to characterize the complete set of oligomeric structures satisfying the distance restraints and to quantitatively evaluate the contribution of each distance restraint. We demonstrate our method for the trimeric E. coli diacylglycerol kinase, addressing the challenges in obtaining subunit assignments for distance restraints. We also demonstrate our method on a dimeric mutant of the immunoglobulin-binding domain B1 of streptococcal protein G to show the resilience of our method to ambiguous atom assignments. In both studies, DISCO computed oligomer structures with high accuracy despite using ambiguously assigned distance restraints.     

E-type delayed fluorescence depolarization, technique to probe rotational motion in the microsecond range.

E (eosin)-type delayed fluorescence depolarization studies extend the time range for the measurement of rotational diffusion to microseconds and ms, thereby allowing investigation of slow rotational movement of macromolecules like membrane proteins. An apparatus is described for the determination of time-dependent anisotropy in this interesting time range. The method has been tested on eosin-labelled cytochrome P-450 incorporated into phospholipid membrane vesicles.