Measuring Cu2+-Nitroxide Distances Using Double Electron–Electron Resonance and Saturation Recovery

Distance measurements were obtained between a bound Cu²⁺ and a spin label on two polypeptides of differing length using the double electron–electron resonance (DEER) and saturation recovery experiments. Distance distributions obtained from the DEER results resolved differences between the average distance and distribution of distances for each peptide. An average distance was also obtained for each peptide using the relaxation-based saturation recovery experiment. Predicted average distances for the relaxation-based method, <r_ESR>, were calculated using the distance distributions from the DEER experiment. The predicted <r_ESR> values were similar to those measured by saturation recovery; both were biased to shorter values compared with the DEER results. The breadth of the distance distributions had a significant effect on the average distance measured by saturation recovery. This work highlights the advantage of using DEER to measure metal-nitroxide distances in that the average distances measured are less biased than in relaxation-based techniques.     

Distance between a native cofactor and a spin label in the reaction centre of Rhodobacter sphaeroides by a two-frequency pulsed electron paramagnetic resonance method and molecular dynamics simulations

The distance between the paramagnetic state of a native cofactor and a spin label is measured in the photosynthetic reaction centre from the bacterium Rhodobacter sphaeroides R26. A two-frequency pulsed electron paramagnetic resonance method [double-electron-electron spin resonance (DEER)] is used. A distance of 3.05 nm between the semiquinone anion state of the primary acceptor (Q(A)) and the spin label at the native cysteine at position 156 in the H-subunit is found. Molecular-dynamics (MD) simulations are performed to interpret the distance. A 6 ns run comprising the entire RC protein yields a distance distribution that is close to the experimental one. The average distance found by the MD simulation is smaller than the distance obtained by DEER by at least 0.2 nm. To better represent the experiments performed at low temperature (60K), a MD method to mimic the freezing-in of the room-temperature conformations is introduced. Both MD methods yield similar distances, but the second method has a trend towards a wider distance distribution.     

High-field EPR and site-directed spin labeling reveal a periodical polarity profile: The sequence 88 to 94 of the phototransducer NpHtrII in complex with sensory rhodopsin, NpSRII

Taking advantage of the improved spectral resolution of high-field electron paramagnetic resonance (EPR) at 95 GHz/3.4 T as compared to conventional X-band EPR (9.5 GHz/0.34 T), detailed information on the polarity profile in a protein-protein interface is obtained. Nitroxide spin label side chains are introduced at positions 88 to 94 in the AS-1 sequence of the membrane adjacent HAMP domain of the transducer protein, NpHtrII, which is reconstituted in complex with sensory rhodopsin, NpSRII fromNatronobacterium pharaonis. Position-dependent variations of the values of the nitroxide magnetic tensor componentsg _xx andA _zz suggest that the spin label side chains at positions 88 to 93 of AS-1 are located between a hydrophobic and a hydrophilic microenvironment. The observed periodicity of the polarity properties of the respective spin label microenvironment agrees with an α-helical secondary structure of this part of AS-1 and validates a recently published molecular model which locates residues 88 and 91 in the interface between helices F and G of NpSRII and AS-1 of NpHtrII close to the cytoplasmic lipid-water interface.     

Data analysis procedures for pulse ELDOR measurements of broad distance distributions

The reliability of procedures for extracting the distance distribution between spins from the dipolar evolution function is studied with particular emphasis on broad distributions. A new numerically stable procedure for fitting distance distributions with polynomial interpolation between sampling points is introduced and compared to Tikhonov regularization in the dipolar frequency and distance domains and to approximate Pake transformation. Distance distribution with only narrow peaks are most reliably extracted by distance-domain Tikhonov regularization, while frequency-domain Tikhonov regularization is favorable for distributions with only broad peaks. For the quantification of distributions by their mean distance and variance, Hermite polynomial interpolation provides the best results. Distributions that contain both broad and narrow peaks are most difficult to analyze. In this case a high signal-to-noise ratio is strictly required and approximate Pake transformation should be applied. A procedure is given for renormalizing primary experimental data from protein preparations with slightly different degrees of spin labelling, so that they can be compared directly. Performance of all the data analysis procedures is demonstrated on experimental data for a shape-persistent biradical with a label-to-label distance of 5 nm, for a [2]catenane with a broad distance distribution, and for a doubly spin-labelled double mutant of plant light harvesting complex II     

Refining Spin–Spin Distance Distributions in Complex Biological Systems Using Multi-Gaussian Monte Carlo Analysis

Pulse dipolar electron paramagnetic resonance spectroscopy provides means of distance measurements in the range of ~ 1.5–10 nm between two spin labels tethered to a biological system. However, the extraction of distance distribution between spin labels is an ill-posed mathematical problem. The most common approach for obtaining distance distribution employs Tikhonov regularization method, where a regularization parameter characterizing the smoothness of distribution is introduced. However, in case of multi-modal distance distributions with peaks of different widths, the use of a single regularization parameter might lead to certain distortions of actual distribution shapes. Recently, a multi-Gaussian Monte Carlo approach was proposed for eliminating this drawback and verified for model biradicals [1]. In the present work, we for the first time test this approach on complicated biological systems exhibiting multi-modal distance distributions. We apply multi-Gaussian analysis to pulsed electron–electron double resonance data of supramolecular ribosomal complexes, where the 11-mer oligoribonucleotide (MR) bearing two nitroxide labels at its termini is used as a reporter. Calculated distance distributions reveal the same conformations of MR as those obtained by Tikhonov regularization, but feature the peaks having different widths, which leads to a better resolution in several cases. The advantages, complications, and further perspectives of application of Monte-Carlo-based multi-Gaussian approach to real biological systems are discussed.     

Light induced radical pair intermediates in photosynthetic reaction centres in contact with an observer spin label: spin dynamics and effects on transient EPR spectra

A novel strategy is discussed using site directed spin labelling to study the electron transfer process in photosynthetic reaction centres. An algorithm is presented for numerical simulations of the time resolved EPR spectra of radical pair states in the presence of an observer spin label. This algorithm accounts for spin dynamics, charge recombination and relaxation processes. It is shown that satisfactory agreement between experimental and simulated EPR spectra of the first stabilized radical pair state in photosystem I is achieved for various microwave frequencies. Transient EPR spectra for the radical pair state P^?+Q^?- in photosystem I were simulated for various distances and positions of the observer spin label with respect to the acceptor quinone molecule. It is shown that distances up to more than 20 Å give rise to observable changes in the transient EPR spectra. Both the additional spin-spin coupling between the quinone radical and the label and the polarization transfer processes contribute to the changes. Furthermore, the shape and intensity of the EPR spectrum of the spin label is altered by the coupling with the radical pair spins for distances up to 25 Å. Experiments on site directed spin labelled photosystem I are thus expected to provide valuable information on the dynamics of electron transfer in photosystem I.     

A pulsed EPR method to determine distances between paramagnetic centers with strong spectral anisotropy and radicals: The dead-time free RIDME sequence

Methods to determine distances between paramagnetic metal centers and radicals are scarce. This is unfortunate because paramagnetic metal centers are frequent in biological systems and so far have not been employed much as distance markers. Successful pulse sequences that directly target the dipolar interactions cannot be applied to paramagnetic metal centers with fast relaxation rates and large g-anisotropy, if no echos can be detected and the excitation bandwidth is not sufficient to cover a sufficiently large part of the spectrum. The RIDME method Kulik et al. (2002) [20] circumvents this problem by making use of the T₁-induced spin-flip of the transition-metal ion. Designed to measure distance between such a fast relaxing metal center and a radical, it suffers from a dead time problem. We show that this is severe because the anisotropy of the metal center broadens the dipolar curves, which therefore, only can be analyzed if the full curve is known. Here, we introduce five-pulse RIDME (5p-RIDME) that is intrinsically dead-time free. Proper functioning of the sequence is demonstrated on a nitroxide biradical. The distance between a low-spin Fe(III) center and a spin label in spin-labeled cytochrome f shows the complete dipolar trace of a transition-metal ion center and a spin label, yielding the distance expected from the structure.     

Conformational Properties of the Spin-Labeled Tylopeptin B and Heptaibin Peptaibiotics Based on PELDOR Spectroscopy Data

X-Band pulsed electron–electron double resonance (PELDOR) spectroscopy was used to investigate for the first time the magnetic dipole–dipole interaction between spin labels for frozen glassy methanol solutions at 77 K of double spin-labeled, medium-length peptaibiotics, namely, tylopeptin B and heptaibin. This study was conducted on tylopeptin labeled at positions 3 and 13 (T313) and heptaibin labeled at positions 2 and 14 (H214). PELDOR data analysis was carried out using the theory developed for short inter-spin distances. The distance distribution functions between spin labels for T313 (maximum at 1.76 nm, half-width of 0.07 nm) and H214 (maximum at 2.30 nm, half-width of 0.065 nm) were determined. It is found that the distance distribution function for peptide T313 has the Gaussian shape. The main part of the distance spectrum for H214 has Gaussian shape and additional less intensive broad lines are shifted to high distances range 2.5–3.5 nm. The upper limit of distance spectrum in this case corresponds approximately to the length of extended peptide molecule and the number of such configurations is low. Intramolecular distances between the labels at maxima observed allowed us to assign α-helical conformation to T313 and 3₁₀-helical structure to H214 in methanol solution.     

The determination of pair distance distributions by pulsed ESR using Tikhonov regularization

Pulsed ESR techniques with the aid of site-directed spin labeling have proven useful in providing unique structural information about proteins. The determination of distance distributions in electron spin pairs directly from the dipolar time evolution of the pulsed ESR signals by means of the Tikhonov regularization method is reported. The difficulties connected with numerically inverting this ill-posed mathematical problem are clearly illustrated. The Tikhonov regularization with the regularization parameter determined by the L-curve criterion is then described and tested to confirm its accuracy and reliability. The method is applied to recent experimental results on doubly labeled proteins that have been studied using two pulsed ESR techniques, double quantum coherence (DQC) ESR and double electron-electron resonance (DEER). The extracted distance distributions are able to provide valuable information about the conformational constraints in various partially folded states of proteins. This study supplies a mathematically reliable method for extracting pair distributions from pulsed ESR experimental data and has extended the use of pulsed ESR to provide results of greater value for structural biology.     

Geometrical and dynamical state of the 252Cf nucleus at the scission point as determined from the experimental results of ternary fission

Resuits on the geometrical and dynamical states of fission fragments and α-particles are presented for the most probable mode of ternary fission, at the instant of release of the light particle. The distributions of the relevant physical quantities are obtained by means of a program calculating the trajectories of three point charges. A total of about 2 × 10⁵ combinations of the parameters, derived by subdividing the quantities into physically significant intervals, are used. The computed values are compared with experimental results and the distributions of the parameters are weighted by the spectrum of the α-parlicles. The dynamics of the system undergoing fission at scission point are characterized by the following quantities: (i) The total kinetic energy of fragments. (ii) The kinetic energy of the α-particle. (iii) The distance between the centres of charge of the fragments, (iv) The abscissa and Ordinate of the α-particle emission point, (v) The emission angle of the α-parlicle with respect to the line of flight of the light fragment. The distributions of above quantities are presented for the most probable model of spontaneous ternary fission of ²⁵²Cf The results obtained are discussed and relevant information on the dynamical properties of the last fission stage is presented.     

On the predictability of the positions of the convergence zones in the ocean

The disagreement between the experimental and calculated positions of the first convergence zone are known from many publications. The most probable cause for such a disagreement, namely, the incorrect specification of the input data for the calculations, is considered. The lack of simultaneity between the hydrological surveys of the region and the acoustic experiments is emphasized. The experimental data obtained by the author in five ocean regions are presented. These data characterize the diurnal variability of the distance from the source to the nearest boundary of the convergence zone. The relations proposed by different researchers for calculating the sound speed from the temperature, salinity, and hydrostatic pressure are analyzed. It is shown that these relations lead to a substantial difference in the estimated depth dependence of the hydrostatic gradient of the sound speed. The position of the first convergence zone is calculated for the propagation conditions determined by vertical temperature and salinity profiles with the subsequent recalculation of these profiles into sound speed profiles by using eight different formulas known from the literature. It is shown that different formulas lead to different values of the distance to the first zone; this difference is substantially greater than that between the calculations and experiment. The necessity of improving the recalculation relations in view of the experimental data on sound propagation in natural oceanic waveguides, including the data on the actual positions of the convergence zones, is emphasized.     

Double Quantum Coherence EPR Reveals the Structure–Function Relationships of the Cardiac Troponin C–Troponin I Complex Regulated by Ca<Superscript>2+</Superscript> Ions and a Phosphomimetic

Troponin (Tn) is a protein that consists of three subunits, troponin C (TnC), troponin I (TnI), and troponin T (TnT), and Tn controls cardiac muscle contraction by calcium ion binding and phosphorylation. The Ca²⁺-binding site is the E–F hand motif (C helix–loop–D helix) in the N-terminal domain of TnC, and the structural transition induced by Ca²⁺ is the opening of these helices and the interaction with TnI, probably at the A and B helices. In this paper, we studied structural changes in the TnC–TnI binary complex on Ca²⁺ binding by double quantum coherence (DQC) distance measurements. We used a binary complex of the cardiac troponin C and I (cTnC and cTnI) complexes, chose four positions of nitroxide spin label at helices A, B, C, and D in the N-terminal domain and chose the E helix in the C-terminal domain as the reference position to study the structural changes on Ca²⁺ addition. The label positions were (A22C/S98C), (M47C/S98C), (Q58C/S98C), and (C84/S98C) for the A, B, C, and D helices, respectively. The effects of phosphorylation of the cardiac-specific N-terminal region of cTnI were studied using a phosphomimetic cTnI mutant. Analysis of the modulation of the DQC echo signals provided the distribution of the spin–spin distance. The distances averaged over the distribution showed that the labels on the A, B, and C helices decreased, i.e., moved to the E helix, on Ca²⁺ binding, while the distance of the label on the D helix showed almost no change. Shoulders and/or small separate peaks were observed in the shape of the distribution and were analyzed as the sum of a few Gaussian functions. The Gaussian functions were grouped into two components, components 1 and 2, at the longer and shorter distances, respectively, separated by 0.7–1.5 nm. The fractions of component 2 were ca. 0.1–0.2 in the Ca²⁺-free state and increased by 0.2–0.3 on Ca²⁺ addition, suggesting that the increase in component 2 is related to physiological control of cardiac muscle contraction. The phosphomimetic-modification effects on the Ca²⁺-induced changes of the fraction of components and the distances of the C- and D-helix labels are small. On the other hand, in the A and B helices, there are significant effects on the Ca²⁺-induced changes in the distances of the components. The different behaviors of A/B and C/D helices support the current model of the phosphorylation effects in which both N-terminal region and regulatory domain of cTnI interact with the A and B helices of cTnC.     

An NMR Investigation of the Conformational Effect of Nitroxide Spin Labels on Ala-Rich Helical Peptides

Nitroxide spin labels, in conjunction with electron spin resonance (ESR) experiments, are extensively employed to probe the structure and dynamics of biomolecules. One of the most ubiquitous spin labeling reagents is the methanethiosulfonate spin label which attaches a spin label selectively to Cys residues via a disulfide bond (Cys-SL). However, the actual effect of the nitroxide spin label upon the conformation of the peptide or protein cannot be unambiguously determined by ESR. In this study, a series of 16-residue Ala-rich helical peptides was characterized by nuclear magnetic resonance techniques. The C_αH chemical shift analysis, NOEs, and³J_NHαcoupling constants for peptides with no Cys, free Cys, and Cys-SL (with the N–O group reduced) were compared. These results indicate that while replacement of an Ala with a Cys residue causes a loss of overall helical structure, the Cys-SL residue is helix supporting, as would be expected for a non-β-branched aliphatic amino acid. Thus, the Cys-SL residue does not perturb helical structure and, instead, exhibits helix-stabilizing characteristics similar to that found for Ala, Met, and Leu.     

Most probable transition paths in eutrophicated lake ecosystem under Gaussian white noise and periodic force

The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored. Unlike the existing work in detecting early warning signals, this paper presents the most probable transition paths to characterize the regime shifts. The most probable transition paths are obtained by minimizing the Freidlin-Wentzell (FW) action functional and Onsager-Machlup (OM) action functional, respectively. The most probable path shows the movement trend of the lake eutrophication system under noise excitation, and describes the global transition behavior of the system. Under the excitation of Gaussian noise, the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths. Under the excitation of Gaussian white noise and periodic force, we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.     

Exchange and dipolar spin-spin interaction and rotational diffusion in saturation transfer EPR spectroscopy

Saturation transfer EPR spectroscopy (STEPR) provides a means for investigating weak spin-spin interaction between spin-labelled molecules because the spectral intensity is proportional to the effective spin-lattice relaxation time,T ₁ ^eff. Rate equations for the spin population defferences yield equivalent results for the dependence ofT ₁ ^eff on the physical (or chemical) and Heisenberg spin exchange rates and show thatT ₁ ^eff depends on the extent of redistribution of saturation throughout the anisotropic spin label powder lineshape. This approach yields a particularly simple formulation for the dependence of the STEPR lineshape on slow rotational diffusion. The effects of spin exchange are readily distinguished from those of slow rotational diffusion because of the insensitivity of the STEPR lineshape in the former case. The characteristic dependence of the STEPR spectral intensity on spin concentration allows determination of the exchange rate and can be used for studying slow translational diffusion, e.g. of spin-labelled proteins. Dipolar relaxation induced by paramagnetic ions gives a linear dependence of the reciprocal spin label STEPR intensity on metal ion concentration. STEPR measurements with spin-labelled lipid molecules in gel phase membranes in the presence of Ni²⁺ ions yield reliable distance information and provide calibrations for use with other systems.     

A short note on orientation selection in the DEER experiments on a native cofactor and a spin label in the reaction center ofRhodobacter sphaeroides

The analysis of the two-frequency pulsed electron paramagnetic resonance (EPR) (double electron-electron spin resonance, DEER) investigation on the coupling between the semiquinone anion state of the primary acceptor (Q_A) and the spin label at the cysteine 156 in the H-subunit in the photosynthetic reaction center (RC) fromRhodobacter sphaerodes (R26) (I. V. Borovykh, S. Ceola, P. Gajula, P. Gast, H. J. Steinhoff, M. Huber: J. Magn. Reson. 180, 178–185, 2006) is reinvestigated to include orientation selection. The combination of the EPR properties of the two radicals and the pump and observer frequencies suggests that such an effect could play a role even at the X-band (9 GHz) EPR fields and frequencies employed. The magnitude of the effect is estimated from the structures obtained from the molecular-dynamics (MD) simulations from the previous study: the distance change is small (around 2%) and the distance of 3.05 nm obtained then is possibly underestimated by 0.06 nm. Thus, the difference of at least 0.2 nm between the measured distance and the average distance of 2.8 nm found by the MD simulation remains, suggesting a significant difference between the measurement and the X-ray structure of the RC, as discussed previously.     

Rotational resonance NMR: separation of dipolar coupling and zero quantum relaxation

The solid state NMR technique of rotational resonance (R2) has been used extensively to measure distances approaching 5-6 A between 13C nuclei in a variety of compounds including amyloidogenic peptides and membrane proteins. The accuracy of the distance information extracted from the time-dependent spin dynamics at R2 is often limited by the accuracy with which the relevant zero-quantum lineshape parameters are estimated. Here we demonstrate that measurement of spinning frequency dependent magnetization exchange dynamics provides data from which both distance and zero-quantum relaxation parameters can be extracted independently. In addition to providing more accurate distance information, this technique allows examination of the zero-quantum lineshape, which can indicate the presence of correlated relaxation or chemical shift distributions between dipolar-coupled sites. With this approach we have separated the contribution of dipolar couplings and zero quantum relaxation to R2 exchange curves. Thus, we have significantly improved the accuracy of the measurement of the intramolecular, internuclear distances between a pair of 13C's in two model compounds (N-acetyl-D,L-valine and glycylglycine.HCl) that lie in the distance range 4.6-4.7 A.     

Maltose Binding Protein Is Partially Structured in Its Molten Globule State

Seven double cysteine mutants of maltose binding protein (MBP) were generated with one each in the active cleft at position 298 and the second cysteine distributed over both domains of the protein. These cysteines were spin labeled and distances between the labels in biradical pairs determined by pulsed double electron–electron resonance (DEER) measurements. The values were compared with theoretical predictions of distances between the labels in biradicals constructed by molecular modeling from the crystal structure of MBP without maltose and were found to be in excellent agreement. MBP is in a molten globule state at pH 3.3 and is known to still bind its substrate maltose. The nitroxide spin label was sufficiently stable under these conditions. In preliminary experiments, DEER measurements were carried out with one of the mutants yielding a broad distance distribution as was to be expected if there is no explicit tertiary structure and the individual helices pointing into all possible directions.     

ESEEM Measurements of Local Water Concentration in D<Subscript>2</Subscript>O-Containing Spin-Labeled Systems

To calibrate electron spin echo envelope modulation (ESEEM) amplitudes with respect to the deuterium water content in spin-labeled biological systems, ESEEM of nitroxide TEMPO has been studied in frozen glassy D₂O-dimethylsulfoxide mixtures of different composition. The interaction between the unpaired electron of nitroxide and the deuterium nuclei manifests itself in a cosine Fourier transform spectrum as the sum of a narrow line with the doublet quadrupole splitting and of a broad one. The narrow line arises from interaction with distant deuterium nuclei, the broad one arises from interaction with nearby nuclei belonging to nitroxide-water molecule complexes. The dependence on water concentration was found to be nonlinear for the intensity of the narrow line and close to linear for the intensity of the quadrupole doublet. Therefore, the intensity of the quadrupole doublet is suggested as a measure of concentration of free water around a spin label in biological objects. Fourier transform line shape was theoretically simulated for different model distributions of water molecules around the spin label. Simulations confirm the linear dependence of the quadrupole doublet intensity on water concentration seen in the experiment. The suggested approach was applied to analyze data for spin-labeled dipalmitoylphosphatidylcholine (DPPC) and DPPC-cholesterol D₂O-hydrated model membranes. The concentration of free water near the spin-labeled fourth carbon atom along the lipid chain was estimated as 5.2 and 7.2 M for DPPC and DPPC-cholesterol membranes, respectively. Authors’ address: Sergei Dzuba, Institute of Chemical Kinetics and Combustion, Russian Academy of Sciences, Institutskaya 3, 630090 Novosibirsk, Russian Federation     

The T 1 and T 2 Relaxation Times Distribution for the 35Cl and 14N NQR in Micro-composites and in Porous Materials

The paper describes the results of an experimental study of the ³⁵Cl and ¹⁴N nuclear quadrupole resonance in composite and porous materials, the influence of the environment and the crystallite size of powder on the nuclear quadrupole resonance line widths, as well as on the spin–spin and spin–lattice relaxation times. It is established that the spin–lattice relaxation time has a unimodal distribution, and the spin–spin relaxation time—bimodal distributions for all the investigated samples. The idealized distribution function of the relaxation times is obtained on the assumption that the concentration of inhomogeneities and relaxativity decreases with an increasing distance from the surface into the interior of the crystallite exponentially. It is shown that the model with the spin diffusion explains the shortening of the decay signal with decreasing grain size, but this is not confirmed by the experimental distribution of relaxation times obtained by means of the inverse Laplace transformation.