Simulating electron spin resonance spectra of macromolecules labeled with two dipolar-coupled nitroxide spin labels from trajectories

An efficient method for simulating continuous-wave electron spin resonance spectra (ESR) of molecules labeled with two dipolar-coupled nitroxides from trajectories of the molecular motion is presented. Two approximate treatments of the dipolar spin evolution, resulting in significantly shorter simulation times, are examined in order to determine their range of applicability. The approach is illustrated in the context of a double-helical B-DNA. ESR spectra for DNA undergoing anisotropic global diffusion and internal stretching dynamics are calculated for three different labeling geometries with the spin labels bracketing, respectively, three, two and one base pairs. While multifrequency spectra of all three labeling schemes are very sensitive to DNA tumbling, the last one is found to be most informative about the local DNA dynamics.     

Using Markov models to simulate electron spin resonance spectra from molecular dynamics trajectories

Simulating electron spin resonance (ESR) spectra directly from molecular dynamics simulations of a spin-labeled protein necessitates a large number (hundreds or thousands) of relatively long (hundreds of nanoseconds) trajectories. To meet this challenge, we explore the possibility of constructing accurate stochastic models of the spin label dynamics from atomistic trajectories. A systematic, two-step procedure, based on the probabilistic framework of hidden Markov models, is developed to build a discrete-time Markov chain process that faithfully captures the internal spin label dynamics on time scales longer than about 150 ps. The constructed Markov model is used both to gain insight into the long-lived conformations of the spin label and to generate the stochastic trajectories required for the simulation of ESR spectra. The methodology is illustrated with an application to the case of a spin-labeled poly alanine alpha helix in explicit solvent.     

Parametrization, molecular dynamics simulation, and calculation of electron spin resonance spectra of a nitroxide spin label on a polyalanine alpha-helix

The nitroxide spin label 1-oxyl-2,2,5,5-tetramethylpyrroline-3-methyl-methanethiosulfonate (MTSSL), commonly used in site-directed spin labeling of proteins, is studied with molecular dynamics (MD) simulations. After developing force field parameters for the nitroxide moiety and the spin label linker, we simulate MTSSL attached to a polyalanine alpha-helix in explicit solvent to elucidate the factors affecting its conformational dynamics. Electron spin resonance spectra at 9 and 250 GHz are simulated in the time domain using the MD trajectories and including global rotational diffusion appropriate for the tumbling of T4 Lysozyme in solution. Analysis of the MD simulations reveals the presence of significant hydrophobic interactions of the spin label with the alanine side chains.     

Calculating slow-motional electron paramagnetic resonance spectra from molecular dynamics using a diffusion operator approach

A number of groups have utilized molecular dynamics (MD) to calculate slow-motional electron paramagnetic resonance (EPR) spectra of spin labels attached to biomolecules. Nearly all such calculations have been based on some variant of the trajectory method introduced by Robinson, Slutsky and Auteri (J. Chem. Phys. 1992,96, 2609-2616). Here we present an alternative approach that is specifically adapted to the diffusion operator-based stochastic Liouville equation (SLE) formalism that is also widely used to calculate slow-motional EPR line shapes. Specifically, the method utilizes MD trajectories to derive diffusion parameters such as the rotational diffusion tensor, diffusion tilt angles, and expansion coefficients of the orienting potential, which are then used as direct inputs to the SLE line shape program. This approach leads to a considerable improvement in computational efficiency over trajectory-based methods, particularly for high frequency, high field EPR. It also provides a basis for deconvoluting the effects of local spin label motion and overall motion of the labeled molecule or domain: once the local motion has been characterized by this approach, the label diffusion parameters may be used in conjunction with line shape analysis at lower EPR frequencies to characterize global motions. The method is validated by comparison of the MD predicted line shapes to experimental high frequency (250 GHz) EPR spectra.     

Effect of substituents on spin density in benzimidazole nitronyl nitroxide radicals studied by electron spin resonance

Several novel benzimidazole‐3‐oxide‐1‐oxyl radicals with substituents at 5 and/or 6 position were synthesized. The ESR analysis of nitrogen hyperfine coupling constants (hfccs) revealed that substituents at 5 and 6‐position affect the spin density to greater extent than substituents on the phenyl ring at 2‐position. Density functional theory calculations of nitrogen hfccs were performed using several different Pople type basis sets, as well as double and triple zeta quality individual gauge for localized orbital (IGLO‐II, IGLO‐III) and electron paramagnetic resonance (EPR‐II, EPR‐II) basis sets. Experimental and theoretical hfccs are compared. Copyright © 2009 John Wiley & Sons, Ltd.     

ESR molecular dynamics study at the oxidation sites of polypropylene with nitroxyl spin labels and spin probes

Novel methods suitable for the selective insertion of nitroxyl spin labels and spin probes at the oxidation sites of isotactic polypropylene have been developed based on reactions with the oxidation products, on spin trapping with nitroso and nitrone compounds and taking advantage of the spontaneous generation of nitroxyl radicals as intermediates in the stabilization mechanism by the HALS. The analysis of the esr spectra of the doxyl spin label and of the spin probes from the HALS, performed according to the stochastic Liouville theory, has allowed information to be obtained on the molecular mobility at the oxidation sites as a function of the temperature.     

Advantages of deuterium modification of nitroxide spin labels for biological epr studies

The spin label, perdeuterio-N-(1-oxy 1-2,2,6,6-tetramenthyl-4-piperidinyl)maleimide (DMSL) was synthesized and its EPR and saturation transfer EPR spectra were compared to those of the hydrogen analogue, HMSL- The labels were studied as freely tumbling entities and also bound to bovine serum albumin (BSA). Significant gains in spectral resolution and detectability were observed for DMSL relative to HMSL.     

Two-dimensional electron spin echoes: magnetization transfer and molecular dynamics

The utility of inversion recovery and stimulated echoes in studying slow motional dynamics is analyzed. A comparison between theory and experiment is provided for a nitroxide radical in viscous solvent. A new two-dimensional stimulated echo technique, suggested by the theory, is applied to study NO₂ physisorbed on vycor.     

Analysis of electron spin resonance spectra of irradiated gingers: Organic radical components derived from carbohydrates

Electron spin resonance (ESR) spectral characterizations of gingers irradiated with electron beam were studied. Complex asymmetrical spectra (near g=2.005) with major spectral components (line width=2.4 mT) and minor signals (at 6 mT apart) were observed in irradiated gingers. The spectral intensity decreased considerably 30 days after irradiation, and continued to decrease steadily thereafter. The spectra simulated on the basis of characteristics of free radical components derived from carbohydrates in gingers are in good agreement with the observed spectra. Analysis showed that shortly after irradiation the major radical components of gingers were composed of radical species derived from amylose and cellulose, and the amylose radicals subsequently decreased considerably. At 30 days after irradiation, the major radical components of gingers were composed of radical species derived from cellulose, glucose, fructose or sucrose.     

Analysis of electron spin resonance spectra of alkyl spin labels in excised guinea pig dorsal skin, its stratum corneum, delipidized skin and stratum corneum model lipid liposomes

The electron spin resonance (ESR) spectra of alkyl spin labels were observed in the excised guinea pig dorsal skin, its stratum corneum, delipidized skin and stratum corneum model lipid liposomes. The spectrum of 5-doxylstearic acid (5-NS) in the stratum corneum and order parameter obtained from the spectrum, indicated that the spin label was present in highly ordered lipid lamella. On the other hand, the spectrum of methyl ester of 5-NS (5-NMS) and its apparent rotational correlation time calculated from the spectrum, showed only a weakly immobilized component in the stratum corneum as well as in the whole excised skin. The ester spin label seemed to be scarcely present in the rigid lipid lamella, but mainly in the relatively fluid environment. On the other hand, cationic alkyl spin labels showed quite different spectra depending on their alkyl chain lengths. Long-chain 4-(N,N-dimethyl-N,-pentadecyl)ammonium-2,2,6,6-tetramethylpiperidine-1-oxyl (CAT-15) seemed to be present in the protein region of the stratum corneum as we recently reported, whereas hydrophilic quaternary ammonium spin label 4-trimethylammonium-2,2,6,6-tetramethylpiperidine-1-oxyl (CAT-1) seemed to be present in the bulk water of the skin, even in delipidized skin. These findings indicated that the different interaction and different localization of the alkyl spin labels depended on their electronic charge as well as their alkyl chain lengths.     

A new Lanczos-based algorithm for simulating high-frequency two-dimensional electron spin resonance spectra

The Lanczos algorithm (LA) is a useful iterative method for the reduction of a large matrix to tridiagonal form. It is a storage efficient procedure requiring only the preceding two Lanczos vectors to compute the next. The quasi-minimal residual (QMR) method is a powerful method for the solution of linear equation systems, Ax = b. In this report we provide another application of the QMR method: we incorporate QMR into the LA to monitor the convergence of the Lanczos projections in the reduction of large sparse matrices. We demonstrate that the combined approach of the LA and QMR can be utilized efficiently for the orthogonal transformation of large, but sparse, complex, symmetric matrices, such as are encountered in the simulation of slow-motional 1D- and 2D-electron spin resonance (ESR) spectra. Especially in the 2D-ESR simulations, it is essential that we store all of the Lanczos vectors obtained in the course of the LA recursions and maintain their orthogonality. In the LA-QMR application, the QMR weight matrix mitigates the problem that the Lanczos vectors lose orthogonality after many LA projections. This enables substantially more Lanczos projections, as required to achieve convergence for the more challenging ESR simulations. It, therefore, provides better accuracy for the eigenvectors and the eigenvalues of the large sparse matrices originating in 2D-ESR simulations than does the previously employed method, which is a combined approach of the LA and the conjugate-gradient (CG) methods, as evidenced by the quality and convergence of the 2D-ESR simulations. Our results show that very slow-motional 2D-ESR spectra at W-band (95 GHz) can be reliably simulated using the LA-QMR method, whereas the LA-CG consistently fails. The improvements due to the LA-QMR are of critical importance in enabling the simulation of high-frequency 2D-ESR spectra, which are characterized by their very high resolution to molecular orientation.     

Triplet excitons in molecular pairs: Analytical investigation of electron spin resonance

For triplet excitons in pairs of differently oriented molecules ESR lineshape is investigated analytically using a microscopic model. The model hamilton takes into account the coherent tranfer of the exciton between the two molecules, the Zeeman and fine-structure energy and the interaction with phonons. The analytical expression for the line positions and linewidths are evaluated using values characteristic for triplet excitons in naphthalene pairs.     

Visualization and interpretation of attosecond electron dynamics in laser-driven hydrogen molecular ion using Bohmian trajectories

We analyze the attosecond electron dynamics in hydrogen molecular ion driven by an external intense laser field using the Bohmian trajectories. To this end, we employ a one-dimensional model of the molecular ion in which the motion of the protons is frozen. The Bohmian trajectories clearly visualize the electron transfer between the two protons in the field and, in particular, confirm the recently predicted attosecond transient localization of the electron at one of the protons and the related multiple bunches of the ionization current within a half cycle of the laser field. Further analysis based on the quantum trajectories shows that the electron dynamics in the molecular ion can be understood via the phase difference accumulated between the Coulomb wells at the two protons.     

Temperature dependence of ESR spectra of nitroxide spin probe in glassy polymers

Temperature dependencies of ESR spectra of nitroxide spin probes in glassy polymers near and below glass transition temperature were examined in detail. Three temperature ranges, each characterized by specific changes in spectral shape, were defined. (i) In the low temperature range, ESR spectra of nitroxide radical in glassy polymer matrix weakly depend on temperature and remain qualitatively the same. (ii) In the intermediate temperature range, significant changes in the shape of spectra are observed. (iii) A new phenomenon was revealed near and below glass transition temperature: narrowing of linewidths occurs while the ratio of amplitudes of different components varies insignificantly. Analysis of molecular rotational mobility was carried out by means of commonly used empirical approaches. It was shown that widely used formulas and empirical approaches are not applicable for characterization of molecular mobility in glassy polymers. Mechanisms of rotational molecular movements in glassy polymers are discussed. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 563–575, 2009     

On the possible manifestation of harmonic-anharmonic dynamical transition in glassy media in electron paramagnetic resonance of nitroxide spin probes

Continuous wave (cw) electron paramagnetic resonance (EPR) and echo-detected (ED) EPR were applied to study molecular motions of nitroxide spin probes in glassy glycerol and o-terphenyl. A linear decrease with increasing temperature of the total splitting in the cw EPR line shape was observed at low temperatures in both solvents. Above some temperature points the temperature dependencies become sharper. Within the model of molecular librations, this behavior is in qualitative and quantitative agreement with the numerical data on neutron scattering and Mossbauer absorption for molecular glasses and biomolecules, where temperature dependence of the mean-squared amplitude of the vibrational motion was obtained. In analogy with these data the departure from linear temperature dependence in cw EPR may be ascribed to the transition from harmonic to anharmonic motion (this transition is called dynamical transition). ED EPR spectra were found to change drastically above 195 K in glycerol and above 245 K in o-terphenyl, indicating the appearance of anisotropic transverse spin relaxation. This appearance may also be attributed to the dynamical transition as an estimation shows the anisotropic relaxation rates for harmonic and anharmonic librational motions and because these temperature points correspond well to those known from neutron scattering for these solvents. The low sensitivity of ED EPR to harmonic motion and its high sensitivity to the anharmonic one suggests that ED EPR may serve as a sensitive tool to detect dynamical transition in glasses and biomolecules.     

The electron spin resonance spectra and structures of some aluminium derivatives of 3,6-di-t-butyl-1,2-benzoquinone

ESR spectra are reported for the aluminium derivatives of the semiquinones which are formed when the compounds Et_nAlCl_3-n (n = 0, 1, or 3) react with 3,6-di-t-butyl-1,2-benzoquinone. The conditions (solvent and other ligands about the metal) are identified under which three different types of spectra can be observed, which are assigned to monodentate non-fluxional, monodentate fluxional, and bidentate structures respectively.     

On the interpretation of continuous wave electron spin resonance spectra of tempo-palmitate in 5-cyanobiphenyl

Electron spin resonance (ESR) measurements are highly informative on the dynamic behavior of molecules, which is of fundamental importance to understand their stability, biological functions and activities, and catalytic action. The wealth of dynamic information which can be extracted from a continuous wave electron spin resonance (cw-ESR) spectrum can be inferred by a basic theoretical approach defined within the stochastic Liouville equation formalism, i.e., the direct inclusion of motional dynamics in the form of stochastic (Fokker-Planck/diffusive) operators in the super Hamiltonian H governing the time evolution of the system. Modeling requires the characterization of magnetic parameters (e.g., hyperfine and Zeeman tensors) and the calculation of ESR observables in terms of spectral densities. The magnetic observables can be pursued by the employment of density functional theory which is apt, provided that hybrid functionals are employed, for the accurate computation of structural properties of molecular systems. Recently, an ab initio integrated computational approach to the in silico interpretation of cw-ESR spectra of multilabeled systems in isotropic fluids has been discussed. In this work we present the extension to the case of nematic liquid crystalline environments by performing simulations of the ESR spectra of the prototypical nitroxide probe 4-(hexadecanoyloxy)-2,2,6,6-tetramethylpiperidine-1-oxy in isotropic and nematic phases of 5-cyanobiphenyl. We first discuss the basic ingredients of the integrated approach, i.e., (1) determination of geometric and local magnetic parameters by quantum-mechanical calculations, taking into account the solvent and, when needed, the vibrational averaging contributions; (2) numerical solution of a stochastic Liouville equation in the presence of diffusive rotational dynamics, based on (3) parameterization of diffusion rotational tensor provided by a hydrodynamic model. Next we present simulated spectra with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing three-dimensional structural and dynamic information on molecular systems in anisotropic environments.