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.     

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.     

Determination of <Superscript>13</Superscript>C CSA Tensors: Extension of the Model-independent Approach to an RNA Kissing Complex Undergoing Anisotropic Rotational Diffusion in Solution

Chemical shift anisotropy (CSA) tensor parameters have been determined for the protonated carbons of the purine bases in an RNA kissing complex in solution by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109–7110]. A strategy for determining CSA tensor parameters of heteronuclei in isolated X–H two-spin systems (X = ¹³C or ¹⁵N) in molecules undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the ratio κ₂=R₂^auto/R₂^cross of the transverse auto- and cross-correlated relaxation rates involving the X CSA and the X–H dipolar interaction is independent of parameters related to molecular motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic κ₂ depends on the anisotropy D_||/D_⊥ of rotational diffusion. In this paper, the field dependence of both κ₂ and its longitudinal counterpart κ₁=R₁^auto/R₁^cross are determined. For anisotropic rotational diffusion, our calculations show that the average κ_av = 1/2 (κ₁+κ₂), of the ratios is largely independent of the anisotropy parameter D_||/D_⊥. The field dependence of the average ratio κ_av may thus be utilized to determine CSA tensor parameters by a generalized model-independent approach in the case of molecules with an overall motion described by an axially symmetric rotational diffusion tensor.     

Quasielastic light scattering from solutions of filamentous viruses. I. Experimental

Intensity fluctuations of laser light scattered from filamentous viruses Pf1 [length L (Å) × diameter d (Å) = 20,000 × 90], M13 (9000 × 90), potato virus X (5150 × 130), and tobacco mosaic virus (3000 × 180) in sucrose density gradients were measured with a photon correlation spectrometer over a range of scattering angles from 15° to 120°. The experimental data can be approximated by two exponential decays, “slow” and “fast.” The slow decay rate constant t corresponds to the translational diffusion D of the virus, i.e., t = K²D, where K is the magnitude of the scattering vector. The amplitude of the slow component, i.e., translational diffusion, remains greater than that of the fast component, even at high KL. The fast decay rate constant t is also proportional to K² for viruses such as Pf1, M13, and even potato virus X. In the companion paper, we shall attribute the amplitude enhancement of the translational diffusion to the coupling of its anisotropy to the rotational diffusion modes. In order to explain the excessive decay rates in the fast component, we need to consider the bending mode of rodlike viruses, especially in the longer viruses such as M13 and Pf1, in addition to the usually expected rotational diffusion modes.     

Molecular motion of small nonelectrolyte molecules in lecithin bilayers

Summary We have used magnetic resonance spectroscopy, both ESR and¹³C spin relaxation, to measure translational and rotational mobilities and partition coefficients of small nitroxide solutes in dipalmitoyl lecithin liposomes. Above the bilayer transition temperature,T _c, the bilayer interior is quite fluid, as determined from the solutes' rapid rotational and moderately rapid translational motion; the rotational and translational viscosities within the bilayer are _R <1cP and =6–10cP, respectively. and _R are independent of molecular size for all solutes studied, but all were small compared to the size of the phospholipids. , and probably _R , are relatively independent of temperature aboveT _c, but both increase very sharply as temperature is lowered belowT _c; at 32°C, _R increases to 6cP and is greater than 1000 cP. Anisotropy of rotational motion increases gradually as temperature is lowered toT _c, and changes little belowT _c; anisotropy of translational motion was not investigated.¹³C nuclear spin relaxation measurements indicate that translational motion of nitroxide solutes is more rapid in the center of the bilayer than near the polar interface. It takes at least 100 nsec for a solute molecule to cross the bilayer/water interface. We estimate a lower limit of 2 sec/cm for the interfacial resistance to solute diffusion; this result indicates that interfacial resistance dominates permeation across the membrane. The relative solubility, or partition coefficient, is a strong function of solute structure, and decreases abruptly on cooling through the transition temperature. From the partition coefficient and its temperature dependence we calculate the free energy, enthalpy, and entropy of partition. Effects of cholesterol on partition and diffusion coefficients are compatible with the interpretation that bilayers containing cholesterol consist of two phases.     

Influence of double scattering in determination of rotational diffusion coefficients by depolarized dynamic light scattering: Application to the bacteriophages T7 and T4B

Dynamic light scattering experiments were performed on solutions of the bacteriophages T7 and T4B in order to obtain the rotational diffusion coefficients of these phages. Correlation functions were determined from the depolarized intensity scattered in the forward direction. The apparatus used in this study is described in detail. Particular attention is paid to the minimalization of the depolarized intensity due to double scattering. If double scattering cannot be neglected, the correlation function of the depolarized field is the sum of the correlation functions resulting from single and double scattering. It is shown that by correcting for double scattering, it is then possible to obtain the rotational diffusion coefficient of the macromolecules. Although the optical anisotropy of both T4B (retracted fibers) and T7 is very small, the experimental conditions could be chosen in such a way that no depolarized scattering due to double scattering was observed. The measured rotational diffusion coefficients for T4B and T7 are D = 258 ± 12 and 4528 ± 100 sec^?1, respectively. These values compare very well with those obtained by electric birefringence experiments.     

Bounding fluid viscosity and translational diffusion in a fluid lipid bilayer

Fluorescence recovery after photobleaching was used to investigate the translational diffusion of a fluorescent derivative of a membrane-spanning lipid in L phase multibilayers of 1-palmitoyl-2-oleoylphosphatidylcholine prepared in water and in glycerol. The translational diffusion coefficient in hydrated bilayers (D _w) ranged between 2 and 5x10^–8 cm²/s and in glycerinated bilayers (D _g) the range was between 3 and 24×10^–10 cm²/s between 10° and 40°C. These results are discussed in terms of models for diffusion in membranes.     

The new program OPAL for molecular dynamics simulations and energy refinements of biological macromolecules

Summary A new program for molecular dynamics (MD) simulation and energy refinement of biological macromolecules, OPAL, is introduced. Combined with the supporting program TRAJEC for the analysis of MD trajectories, OPAL affords high efficiency and flexibility for work with diferent force fields, and offers a user-friendly interface and extensive trajectory analysis capabilities. Salient features are computational speeds of up to 1.5 GFlops on vector supercomputers such as the NEC SX-3, ellipsoidal boundaries to reduce the system size for studies in explicit solvents, and natural treatment of the hydrostatic pressure. Practical applications of OPAL are illustrated with MD simulations of pure water, energy minimization of the NMR structure of the mixed disulfide of a mutant E. coli glutaredoxin with glutathione in different solvent models, and MD simulations of a small protein, pheromone Er-2, using either instantaneous or time-averaged NMR restraints, or no restraints.Abbreviations D diffusion constant in cm²/s - Er-2 pheromone 2 from Euplotes raikovi - GFlop one billion floating point operations per second - Grx(C14S)-SG mixed disulfide between a mutant E. coli glutaredoxin, with Cys¹⁴ replaced by Ser, and glutathione - MD molecular dynamics - NOE nuclear Overhauser enhancement - rmsd root-mean-square deviation - density in g/cm³     

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.     

Biofilm thickness effect on the diffusion limitation in the bioprocess reaction: Biofloc critical diameter significance

A convenient physical model for biomass involves consideration of individual cells as active centers dispersed through a continuous region in which transport takes place by molecular diffusion. This paper investigates for steady state conditions the variation of apparent kinetic constant (K _m ) of bacteria in relation to biofloc diameter with solid and/or liquid-phase diffusion. When the biochemical reactions are limited only by liquid-phase diffusion, theK _m increases whenD increases. With solid-phase diffusion limitation only, theK _m increases linearly with the diameterD of the floc. When both solid and liquid-phase diffusion limitations are considered, the apparentK _m is affected by liquid-phase diffusion limitation with very smallD and by solid-phase diffusion limitation with higherD. The critical diameterD _c can be assumed to be theD at which solid-phase diffusion limitation becomes more significant than liquid-phase diffusion limitation.     

The fidelity of response by 1-[4-(trimethylammonio)phenyl]-6-phenyl-1,3,5-hexatriene in time-resolved fluorescence anisotropy measurements on lipid vesicles

Time-resolved fluorescence anisotropy measurements on 1⁰-[4-(tri-methylammonio)phenyl]-6-phenyl-1,3,5-hexatriene (TMA-DPH) molecules in lipid vesicles of palmitoyloleoylphosphatidylcholine (POPC), PC extracted from egg yolk (EggPC), dioleoyl-PC (DOPC), dilinoleoyl-PC (DLPC), phosphatidylglycerol extracted from egg yolk (EggPG), dioleoyl-PG (DOPG), sulfoquinovosyldiacylglycerol (SQDG) and digalactosyl-DG (DGDG) with and without cholesterol are presented. The observed intensity decay curves are analyzed simultaneously in terms of the Brownian rotational diffusion model. The analysis thus yields the isotropic fluorescence decay, the initial anisotropy r (0), the order parameters P ₂ and P ₂ as well as the diffusion coefficient of the long molecular axis. It is shown that increasing unsaturation in the acyl chains of the PC lipids results in an increase in the rotational diffusion rates of the probes and a decrease in the order parameter P ₂. However, the value of P ₂ remains unchanged. The corresponding orientational distribution function of the probes is bimodal, with fractions lying preferentially parallel and perpendicular to the local vesicle surface. Surprisingly, the fraction of probe molecules lying with their long axes parallel to the bilayer surface increases with increasing unsaturation with a concomitant narrowing in the width of the distribution of the fraction lying perpendicular to it. As expected, cholesterol is found to increase the order parameters in all the systems and to suppress the tendency of the molecules to lie parallel to the bilayer surface. Furthermore, the rotational diffusion coefficients of the probes is found to increase in all the systems except for DLPC. Interestingly, the effects of unsaturation on the reorientational dynamics of TMA-DPH molecules in the vesicle systems are opposite to those found in the corresponding planar multibilayers (Deinum et al. 1988), whereas the same cholesterol effect is observed for the two systems. Nevertheless, the TMA-DPH molecules exhibit higher diffusion coefficients in the vesicle than in the planar multibilayer systems. In addition, a unimodal distribution of the probe molecules is found in the multibilayer systems. The differences between the two systems are ascribed to the differences in the radius of curvature and the hydration of the bilayers. Lastly we rationalize the bimodal distribution of the TMA-DPH molecules in the vesicles in terms of their observed partition between the lipid and aqueous phases.Abbreviations DPH 1,6-diphenyl-1,3,5-hexatriene - TMA-DPH 1-[4-(trimethylammonio)-phenyl]-6-phenyl-1,3,5-hexatriene - POPC palmitoyloleoylphosphatidylcholine - EggPC PC extracted from egg yolk - DOPC dioleoyl-PC - DLPC dilinoleoyl-PC - EggPG phosphatidylglycerol extracted from egg yolk - DOPG dioleoyl-PG - SQDG sulfoquinovosyldiacylglycerol - DGDG di-galactosyl-DG - HPTLC high performance thin layer chromatography     

Two dimensional diffusion of small molecules on protein surfaces: an EPR study of the restricted translational diffusion of protein-bound spin labels

Heisenberg spin exchange rates and dipole-dipole spin lattice relaxation rates for deuterated ¹⁴N- and ¹⁵N-spin labels bound selectively to the histidine His15 and to the lysines Lys13, 96, 97 of the lysozyme molecule have been determined with the aid of electron spin resonance spectroscopy. The results can be interpreted in terms of a two dimensional translational diffusion of the nitroxide tips of the spin labels along the protein surface within restricted surface areas. The spin labels are regarded as models for long amino acid side chains and as probes for the dynamics of protein and water in the vicinity of the protein surface. The translational diffusion coefficient DP_II is reduced by a factor of between six and thirty compared to the value of D found for the spin labels in bulk water, its value for T = 295 K is given by (1.3±0.6)·10^–10m²s^–1 D (2.4±0.3) 10^–11 m²s^–1. Offprint requests to: H.-J. Steinhoff     

Determination of protein rotational correlation time from NMR relaxation data at various solvent viscosities

An accurate determination of the overall rotation of a protein plays a crucial role in the investigation of its internal motions by NMR. In the present work, an innovative approach to the determination of the protein rotational correlation time _R from the heteronuclear relaxation data is proposed. The approach is based on a joint fit of relaxation data acquired at several viscosities of a protein solution. The method has been tested on computer simulated relaxation data as compared to the traditional _R determination method from T₁/T₂ ratio. The approach has been applied to ribonuclease barnase from Bacillus amyloliquefaciens dissolved in an aqueous solution and deuterated glycerol as a viscous component. The resulting rotational correlation time of 5.56 ± 0.01 ns and other rotational diffusion tensor parameters are in good agreement with those determined from T₁/T₂ ratio.     

Residual motion of hemoglobin-bound spin labels and protein dynamics: viscosity dependence of the rotational correlation times

The residual motion of spin labels bound to cysteine 93 and to lysines of methemoglobin has been studied by electron paramagnetic resonance spectroscopy. To separate the influences of the solvent and the protein environment of the label fluctuations, the correlation times, , were analyzed as a function of temperature for fixed solvent viscosities, . Results show that over a wide range of viscosity the dependence of on may be empirically described by a power law ^k . The exponent k depends strongly on the location of the label on the protein surface. If one regards the spin labels as artificial amino acid side chains, characteristic values of correlation times and amplitudes of the rotational motion at the surface can be given. For =1 cP and T=297 K the correlation time of the labels bound to lysines is found to be =9 · 10^–10 s and the rotational diffusion is nearly isotropic. The spin label bound to cysteine 93 occupies a protein pocket, its rotational motion is therefore restricted. The correlation time of the label motion within a limited motion cone of semi angle =30° ± 3° is found to be =1.3 · 10^–9 s for =1 cP and T=297 K.     

Molecular modeling of the complexes between Saccharomyces cerevisiae phosphoenolpyruvate carboxykinase and the ATP analogs pyridoxal 5'-diphosphoadenosine and pyridoxal 5'-triphosphoadenosine. Specific labeling of lysine 290

Molecular mechanics calculations have been employed to obtain models of the complexes between Saccharomyces cerevisiae phosphoenolpyruvate (PEP) kinase and the ATP analogs pyridoxal 5-diphosphoadenosine (PLP-AMP) and pyridoxal 5-triphosphoadenosine (PLP-ADP), using the crystalline coordinates of the ATP-pyruvate-Mn²⁺-Mg²⁺ complex of Escherichia coli PEP carboxykinase [Tari et al. (1997), Nature Struct. Biol. 4, 990–994]. In these models, the preferred conformation of the pyridoxyl moiety of PLP-ADP and PLP-AMP was established through rotational barrier and simulated annealing procedures. Distances from the carbonyl-C of each analog to -N of active-site lysyl residues were calculated for the most stable enzyme-analog complex conformation, and it was found that the closest -N is that from Lys²⁹⁰, thus predicting Schiff base formation between the corresponding carbonyl and amino groups. This prediction was experimentally verified through chemical modification of S. cerevisiae PEP carboxykinase with PLP-ADP and PLP-AMP. The results here described demonstrate the use of molecular modeling procedures when planning chemical modification of enzyme-active sites.     

Dynamic light scattering from collagen solutions. II. Photon correlation study of the depolarized light.

The depolarized forward-scattered light from solutions of rat tail collagen has been studied by photon correlation spectroscopy. The measured autocorrelation function is seen to decay on two widely different time scales. The decay time for the fast component is consistent with the rotational diffusion of rodlike collagen monomers. The slowly decaying autocorrelation component is attributed to large nonspecific aggregates of collagen. A substantial fraction of the collagen is in this aggregated form. Extrapolation of the faster decay times to zero concentration yields a value of θ = 1082 ± 30 sec^?1 for the rotational diffusion coefficient of the collagen monomer.     

Precipitation of protein by ultracentrifuge with angle rotor

Precipitation of a protein by ultracentrifuge with an angle rotor was simulated by a model for sedimentation process. Assuming that the concentration of solute in an inclined ultracentrifugal tube is given by averaging the concentration in the imaginary horizontal tube, the governing equation describing the concentration in the rectangular-shaped tube with a uniform field of ultracentrifugal force for an inclined tube in an angle rotor was derived. The exact solution to this governing equation was obtained under the condition that the diffusion is absent or present. The dimensionless concentration which is reduced by the initial concentration can be expressed as the function of a dimensionless ultracentrifugal times ² t in case that the diffusion is absent, and as the function of dimensionless parameters andt ^*in case that the diffusion is present. From our first approximated model it is found that the precipitation of a protein by ultracentrifuge with an angle rotor proceeds more rapidly than that with a swing rotor whether diffusion is absent or present.List of Symbols c kg/m³ concentration of solute - c ⁰ kg/m³ initial concentration of solute - c ^A kg/m³ concentration of solute for angle rotor - c ^s kg/m³ concentration of solute for swing rotor - D cm²/s diffusion coefficient - d cm diameter of ultracentrifugal tube - k ₁ dimensionless constant - k ² dimensionless constant - r cm radial coordinate - r ₁ cm minimum radius of ultracentrifugal tube - r ₂ cm maximum radius of ultracentrifugal tube - r _m cm mean radius of ultracentrifugal tube - r _s cm radius from which sedimentation starts - s s sedimentation constant - t s time - z cm vertical coordinate - dimensionless parameter - ^m dimensionless parameter - deg inclination of ultracentrifugal tube - s^–1 angular velocity of rotation     

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 relative orientation of the fibronectin 6F11F2 module pair: A 15N NMR relaxation study

The structure of a pair of modules (⁶F1¹F2), that forms part of the collagen-binding region of fibronectin, is refined using heteronuclear relaxation data. A structure of the pair was previously derived from ¹H-¹H NOE and ³ J _HHN data [Bocquier et al. (1999) Structure, 7, 1451–1460] and a weak module–module interface, comprising Leu19 and Leu28, in ⁶F1, and Tyr68 in ²F1, was identified. In this study, the definition of the average relative orientation of the two modules is improved using the dependence of ¹⁵N relaxation on rotational diffusion anisotropy. This structure refinement is based on the selection of a subset of structures from sets calculated with NOE and ³ J _HHN data alone, using the quality of the fits to the relaxation data as the selection criterion. This simple approach is compared to a refinement strategy where ¹⁵N relaxation data are included in the force field as additional restraints [Tjandra et al. (1997) Nat. Struct. Biol., 4, 443–449].     

Modeling 2hJiso(N, N) in nucleic acid base pairs: Ab initio characterization of the 2hJ(N, N) tensor in the methyleneimine dimer as a function of hydrogen bond geometry

The observation of ^2h J _iso(N, N) coupling has prompted considerable interest in this phenomenon from experimentalists and theoreticians due to the potential these couplings hold for the determination of secondary and tertiary structure in biologically important molecules. Here, we present an ab initio (MCSCF) study of the complete ^2h J(N, N) tensor for a model methyleneimine dimer system as a function of (i) the N-N separation, r _NN, and (ii) the hydrogen bond angle, . This simple system models the ^2h J(N, N) tensor of nucleic acid base pairs. Results indicate that although the Fermi-contact mechanism dominates ^2h J _iso(N, N), the coupling tensor is anisotropic due to contributions from the Fermi-contact spin-dipolar cross term. The variation in ^2h J _iso(N, N) as a function of r _NN is fit to an exponential decay. The influence of on the coupling constant is less pronounced but must be considered if experimental coupling constants are to be used for quantitative structure determination. Our results for this simple model system demonstrate that ^2h J _iso(N, N) is a valuable probe of hydrogen bonding in nucleic acid base pairs.