Electron‐spin relaxation and ordering in smectic and supercooled nematic liquid crystals

Mechanical ordering of pigment crystallites in oil binder: can electron paramagnetic resonance reveal the gesture of an artist?

Is it possible to reconstruct the gesture of an ancient artist applying a paint layer, considering that the orientation distribution of crystallites of an inorganic pigment remains definitively imprinted on the support after drying of the layer? If the pigment contains paramagnetic transition metal ions whose magnetic interactions are themselves anisotropic, then the shape of the electron paramagnetic resonance (EPR) spectrum should reflect the distribution of grain orientations. We have demonstrated this effect in the case of Egyptian blue CaCuSi4 O10 , a pigment used for at least 3 millennia in antiquity, by reconstructing the probability density of crystallite orientations under various modes of application, such as brush painting, dabbing and droplet deposition.

Theory and Least Squares Fitting of CW ESR Saturation Spectra Using the MOMD Model

CW saturation experiments are widely used in ESR studies of relaxation processes in proteins and lipids. We develop the theory of saturation in ESR spectra in terms of its close relation with that of 2D-ELDOR. Our treatment of saturation is then based on the microscopic order macroscopic disorder (MOMD) model and can be used to fit the full CW saturation spectrum, rather than fitting just the peak-peak amplitude as a function of microwave field B ₁ as is commonly done. This requires fewer experiments to yield effects on T ₁, as well as provides a more extensive dynamic structural picture, for example, for scanning experiments on different protein sites. The code is released as a publicly available software package in Python that can be used to fit CW saturation spectra from biological samples of interest.

Orientation Distribution of Molecules in a Smectic Liquid Crystal with a Distorted Director Geometry

Quantitative determination of the molecular orientation distribution function in samples of liquid crystals with a complex director geometry was performed using the numerical simulation of electron paramagnetic resonance (EPR) spectra of the spin probes in a liquid-crystalline medium. To achieve the quantitative agreement of experimental and simulated EPR spectra, the hierarchy of the orientation order was explicitly taken into account, namely, the local ordering of liquid crystal molecules by the mean-field potential of surrounding molecules, and the partial disordering of local directors within the sample. The samples under study are planar and twist LC cells with liquid crystal 8CB cooled from the nematic into the smectic A phase in the magnetic field. The presence of the magnetic field perpendicular to the cell director leads to distortion of the orientation of the liquid crystal in the cell. The spin probe technique was successfully employed for the reliable measurement of orientation distribution functions of the low nonorthorhombic symmetry. Orientation order parameters up to 12th rank were measured, including nonaxial and nonorthorhombic order parameters. It is shown that the presence of several contradicting aligning forces leads to the tilt of the preferential director toward the direction, which is a compromise between the orienting forces.

Microsecond dynamics in proteins by two-dimensional ESR. II. Addressing computational challenges

Two-dimensional electron-electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. In previous work, we provided simulations for the case of domain motions within proteins that are themselves slowly tumbling in a solution. In order to perform these simulations, it was found that the standard approach of solving the relevant stochastic Liouville equation using the efficient Lanczos algorithm for this case breaks down, so algorithms were employed that rely on the Arnoldi iteration. While they lead to accurate simulations, they are very time-consuming. In this work, we focus on a variant known as the rational Arnoldi algorithm. We show that this can achieve a significant reduction in computation time. The stochastic Liouville matrix, which is of very large dimension, N, is first reduced to a much smaller dimension, m, e.g., from N ∼ O(10⁴) to m ∼ 60, that spans the relevant Krylov subspace from which the spectrum is predicted. This requires the selection of the m frequency shifts to be utilized. A method of adaptive shift choice is introduced to optimize this selection. We also find that these procedures help in optimizing the pruning procedure that greatly reduces the dimension of the initial N dimensional stochastic Liouville matrix in such subsequent computations.

Microsecond dynamics in proteins by two-dimensional ESR: Predictions

Two-dimensional electron-electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. In this work, simulations are provided for the example of domain motions within proteins that are themselves slowly tumbling in solution. These show the nature of the exchange cross-peaks that are predicted to develop in real time from such domain motions. However, we find that the existing theoretical methods for computing 2D-ELDOR experiments over a wide motional range begin to fail seriously when applied to very slow motions characteristic of proteins in solution. One reason is the failure to obtain accurate eigenvectors and eigenvalues of the complex symmetric stochastic Liouville matrices describing the experiment when computed by the efficient Lanczos algorithm in the range of very slow motion. Another, perhaps more serious, issue is that these matrices are "non-normal," such that for the very slow motional range even rigorous diagonalization algorithms do not yield the correct eigenvalues and eigenvectors. We have employed algorithms that overcome both these issues and lead to valid 2D-ELDOR predictions even for motions approaching the rigid limit. They are utilized to describe the development of cross-peaks in 2D-ELDOR at 95 GHz for a particular case of domain motion.

Modeling of motional EPR spectra using hindered Brownian rotational diffusion and the stochastic Liouville equation

Electron paramagnetic resonance (EPR) spectra of molecular spin centers undergoing reorientational motion are commonly simulated using the stochastic Liouville equation (SLE) with a rigid-body hindered Brownian diffusion model. Current SLE theory applies to specific spin systems such as nitroxides and to high-symmetry orientational potentials. In this work, we extend the SLE theory to arbitrary spin systems with any number of spins and any type of spin Hamiltonian interaction term, as well as to arbitrarily complex orientational potentials. We also examine the limited accuracy of the frequency-to-field conversion used to obtain field-swept EPR spectra and present a more accurate approach. The extensions allow for the simulation of EPR spectra of all types of spin labels (nitroxides, copper²⁺, and gadolinium³⁺) attached to proteins in low-symmetry environments.

Spin Probe Determination of Molecular Orientation Distribution and Rotational Mobility in Liquid Crystals: Model-Free Approach

A model-free approach for simulation of EPR spectra of nitroxide spin probes in liquid-crystalline materials was suggested and used to obtain parameters of molecular orientation and rotational mobility. The developed method is based on experimental recording and numerical simulation of the angular dependence of EPR spectra, which is shown to be much more informative in comparison with a single EPR spectrum. Quantitative spectral simulations considering both local orientational ordering and distribution of local directors in the sample were used for discrimination of models of rotational mobility and orientational alignment. The method was applied for detailed quantitative characterization of axial, orthorhombic, and low-symmetry non-orthorhombic molecular orientation distributions. It is shown that the ordinarily used model of rotational diffusion in a mean-field potential is suitable for the description of molecular mobility and orientational ordering only for relatively low sample temperatures and low-mobility probe molecules with large sizes. In cases of high molecular mobility, the more realistic jump mechanism of molecular moves can be approximately described as quasi-librations. For ordered liquid crystals it was found that mostly the order parameters up to rank 12-14 are essential and easily determined. When well-aligned materials are described, the order parameters up to 18th rank or even higher become meaningful. Both molecular and sample biaxiality is analyzed and quantitatively characterized. The local molecular ordering and sample orientational alignment are quantitatively characterized separately.

Local ordering and dynamics in anisotropic media by magnetic resonance: from liquid crystals to proteins

Magnetic resonance methods have been used extensively for over 50 years to elucidate molecular structure and dynamics of liquid crystals (LCs), providing information quite unique in its rigour and extent. The ESR- or NMR-active probe is often a solute molecule reporting on characteristics associated with the surrounding (LC) medium, which exerts the spatial restrictions on the probe. The theoretical approaches developed for LCs are applicable to anisotropic media in general. Of particular interest is the interior space of a globular protein labelled, e.g. with a nitroxide moiety or a ¹⁵N-¹H bond. The ESR or NMR label plays the role of the probe and the internal protein surroundings the role of the anisotropic medium. A general feature of the restricted motions is the local ordering, i.e. the nature, magnitude and symmetry of the spatial restraints exerted at the site of the moving probe. This property is the main theme of the present review article. We outline its treatment in our work from both the theoretical and the experimental points of view, highlighting the new physical insights gained. Our illustrations include studies on thermotropic (nematic and smectic) and lyotropic liquid crystals formed by phospholipids, in addition to studies of proteins.

Magnetic field effects in nematic and smectic liquid crystals probed by time resolved observation of orientation relaxation of the spin probe

The kinetics of reorientation of the liquid crystal HOPOOB in nematic and smectic phases in the magnetic field was studied by the spin probe technique.

Integrated Computational Approach to the Electron Paramagnetic Resonance Characterization of Rigid 310-Helical Peptides with TOAC Nitroxide Spin Labels

We address the interpretation, via an integrated computational approach, of the experimental continuous-wave electron paramagnetic resonance (cw-EPR) spectra of a complete set of conformationally highly restricted, stable 3₁₀-helical peptides from hexa- to nonamers, each bis-labeled with nitroxide radical-containing TOAC (4-amino-1-oxyl-2,2,6,6-tetramethylpiperidine-4-carboxylic acid) residues. The usefulness of TOAC for this type of analysis has been shown already to be due to its cyclic piperidine side chain, which is rigidly connected to the peptide backbone α-carbon. The TOAC α-amino acids are separated by two, three, four, and five intervening residues. This set of compounds has allowed us to modulate both the radical···radical distance and the relative orientation parameters. To further validate our conclusion, a comparative analysis has been carried out on three singly TOAC-labeled peptides of similar main-chain length.

Non-linear van't Hoff behavior in pulmonary surfactant model membranes

Pulmonary surfactant exhibits phase coexistence over a wide range of surface pressure and temperature. Less is known about the effect of temperature on pulmonary surfactant models. Given the lack of studies on this issue, we used electron paramagnetic resonance (EPR) and nonlinear least-squares (NLLS) simulations to investigate the thermotropic phase behavior of the matrix that mimics the pulmonary surfactant lipid complex, i.e., the lipid mixture composed of dipalmitoyl phosphatidylcholine (DPPC), palmitoyl-oleoyl phosphatidylcholine (POPC) and palmitoyl-oleoyl phosphatidylglycerol (POPG). Irrespective of pH, the EPR spectra recorded from 5°C to 25°C in the DPPC/POPC/POPG (4:3:1) model membrane contain two spectral components corresponding to lipids in gel-like and fluid-like phases, indicating a coexistence of two domains in that range. The temperature dependence of the distribution of spin labels between the domains yielded nonlinear van't Hoff plots. The thermodynamic parameters evaluated were markedly different for DPPC and for the ternary DPPC/POPC/POPG (4:3:1) membranes and exhibited a dependence on chemical environment. While enthalpy and entropy changes for DPPC were always positive and presented a quadratic behavior with temperature, those of the ternary mixture were linearly dependent on temperature and changed from negative to positive values. Despite that, enthalpy-entropy compensation takes place in the two systems. The thermotropic process associated with the coexistence of the two domains is entropically-driven in DPPC and either entropically- or enthalpically-driven in the pulmonary surfactant membrane depending on the pH, ionic strength and temperature. The significance of these results to the structure and function of the pulmonary surfactant lipid matrix is discussed.

Local Ordering at Mobile Sites in Proteins from Nuclear Magnetic Resonance Relaxation: The Role of Site Symmetry

Restricted motions in proteins (e.g., N-H bond dynamics) are studied effectively with NMR. By analogy with restricted motions in liquid crystals (LC), the local ordering has in the past been primarily represented by potentials comprising the L = 2, |K| = 0, 2 spherical harmonics. However, probes dissolved in LCs experience nonpolar ordering, often referred to as alignment, while protein-anchored probes experience polar ordering, often referred to as orientation. In this study we investigate the role of local (site) symmetry in the context of the polarity of the local ordering. We find that potentials comprising the L = 1, |K| = 0, 1 spherical harmonics represent adequately polar ordering. It is useful to characterize potential symmetry in terms of the irreducible representations of D2h point group, which is already implicit in the definition of the rotational diffusion tensor. Thus, the relevant rhombic L = 1 potentials have B1u and B3u symmetry whereas the relevant rhombic L = 2 potentials have Ag symmetry. A comprehensive scheme where local potentials and corresponding probability density functions (PDFs) are represented in Cartesian and spherical coordinates clarifies how they are affected by polar and nonpolar ordering. The Cartesian coordinates are chosen so that the principal axis of polar axial PDF is pointing along the z-axis, whereas the principal axis of the nonpolar axial PDF is pointing along ±z. Two-term axial potentials with 1 ≤ L ≤ 3 exhibit substantial diversity; they are expected to be useful in NMR-relaxation-data-fitting. It is shown how potential coefficients are reflected in the experimental order parameters. The comprehensive scheme representing local potentials and PDFs is exemplified for the L = 2 case using experimental data from (15)N-labeled plexin-B1 and thioredoxin, (2)H-, and (13)C-labeled benzenehexa-n-alkanoates, and nitroxide-labeled T4 lysozyme. Future prospects for improved ordering analysis based on combined atomistic and mesoscopic approaches are delineated.

Focus: Two-dimensional electron-electron double resonance and molecular motions: The challenge of higher frequencies

The development, applications, and current challenges of the pulsed ESR technique of two-dimensional Electron-Electron Double Resonance (2D ELDOR) are described. This is a three-pulse technique akin to 2D Exchange Nuclear Magnetic Resonance, but involving electron spins, usually in the form of spin-probes or spin-labels. As a result, it required the extension to much higher frequencies, i.e., microwaves, and much faster time scales, with π/2 pulses in the 2-3 ns range. It has proven very useful for studying molecular dynamics in complex fluids, and spectral results can be explained by fitting theoretical models (also described) that provide a detailed analysis of the molecular dynamics and structure. We discuss concepts that also appear in other forms of 2D spectroscopy but emphasize the unique advantages and difficulties that are intrinsic to ESR. Advantages include the ability to tune the resonance frequency, in order to probe different motional ranges, while challenges include the high ratio of the detection dead time vs. the relaxation times. We review several important 2D ELDOR studies of molecular dynamics. (1) The results from a spin probe dissolved in a liquid crystal are followed throughout the isotropic → nematic → liquid-like smectic → solid-like smectic → crystalline phases as the temperature is reduced and are interpreted in terms of the slowly relaxing local structure model. Here, the labeled molecule is undergoing overall motion in the macroscopically aligned sample, as well as responding to local site fluctuations. (2) Several examples involving model phospholipid membranes are provided, including the dynamic structural characterization of the boundary lipid that coats a transmembrane peptide dimer. Additionally, subtle differences can be elicited for the phospholipid membrane phases: liquid disordered, liquid ordered, and gel, and the subtle effects upon the membrane, of antigen cross-linking of receptors on the surface of plasma membrane, vesicles can be observed. These 2D ELDOR experiments are performed as a function of mixing time, Tm, i.e., the time between the second and third π/2 pulses, which provides a third dimension. In fact, a fourth dimension may be added by varying the ESR frequency/magnetic field combination. Therefore, (3) it is shown how continuous-wave multifrequency ESR studies enable the decomposition of complex dynamics of, e.g., proteins by virtue of their respective time scales. These studies motivate our current efforts that are directed to extend 2D ELDOR to higher frequencies, 95 GHz in particular (from 9 and 17 GHz), in order to enable multi-frequency 2D ELDOR. This required the development of quasi-optical methods for performing the mm-wave experiments, which are summarized. We demonstrate state-of-the-art 95 GHz 2D ELDOR spectroscopy through its ability to resolve the two signals from a spin probe dissolved in both the lipid phase and the coexisting aqueous phase. As current 95 GHz experiments are restricted by limited spectral coverage of the π/2 pulse, as well as the very short T2 relaxation times of the electron spins, we discuss how these limitations are being addressed.

Polar Versus Non-polar Local Ordering at Mobile Sites in Proteins: Slowly Relaxing Local Structure Analysis of (15)N Relaxation in the Third Immunoglobulin-Binding Domain of Streptococcal Protein G

We developed recently the slowly relaxing local structure (SRLS) approach for studying restricted motions in proteins by NMR. The spatial restrictions have been described by potentials comprising the traditional L = 2, K = 0, 2 spherical harmonics. However, the latter are associated with non-polar ordering whereas protein-anchored probes experience polar ordering, described by odd-L spherical harmonics. Here we extend the SRLS potential to include the L = 1, K = 0, 1 spherical harmonics and analyze (15)N-(1)H relaxation from the third immunoglobulin-binding domain of streptococcal protein G (GB3) with the polar L = 1 potential (coefficients c0(1) and c1(1)) or the non-polar L = 2 potential (coefficients c0(2) and c2(2)). Strong potentials, with ⟨c0(1)⟩ ∼ 60 for L = 1 and ⟨c0(2)⟩ ∼ 20 for L = 2 (in units of kBT), are detected. In the α-helix of GB3 the coefficients of the rhombic terms are c1(1) ∼ c2(2) ∼ 0; in the preceding (following) chain segment they are ⟨c1(1)⟩ ∼ 6 for L = 1 and ⟨c2(2)⟩ ∼ 14 for L = 2 (⟨c1(1)⟩ ∼ 3 for L = 1 and ⟨c2(2)⟩ ∼ 7 for L = 2). The local diffusion rate, D2, lies in the 5 × 10(9)-1 × 10(11) s(-1) range; it is generally larger for L = 1. The main ordering axis deviates moderately from the N-H bond. Corresponding L = 1 and L = 2 potentials and probability density functions are illustrated for residues A26 of the α-helix, Y3 of the β1-strand, and L12 of the β1/β2 loop; they differ considerably. Polar/orientational ordering is shown to be associated with GB3 binding to its cognate Fab fragment. The polarity of the local ordering is clearly an important factor.

Orientation order and rotation mobility of nitroxide biradicals determined by quantitative simulation of EPR spectra

The biradical spin probe technique was used to obtain information on the molecular dynamics and structure of isotropic and anisotropic liquids.

Using spin-label W-band EPR to study membrane fluidity profiles in samples of small volume

Conventional and saturation-recovery (SR) EPR at W-band (94GHz) using phosphatidylcholine spin labels (labeled at the alkyl chain [n-PC] and headgroup [T-PC]) to obtain profiles of membrane fluidity has been demonstrated. Dimyristoylphosphatidylcholine (DMPC) membranes with and without 50 mol% cholesterol have been studied, and the results have been compared with similar studies at X-band (9.4 GHz) (L. Mainali, J.B. Feix, J.S. Hyde, W.K. Subczynski, J. Magn. Reson. 212 (2011) 418-425). Profiles of the spin-lattice relaxation rate (T(1)(-1)) obtained from SR EPR measurements for n-PCs and T-PC were used as a convenient quantitative measure of membrane fluidity. Additionally, spectral analysis using Freed's MOMD (microscopic-order macroscopic-disorder) model (E. Meirovitch, J.H. Freed J. Phys. Chem. 88 (1984) 4995-5004) provided rotational diffusion coefficients (R(perpendicular) and R(||)) and order parameters (S(0)). Spectral analysis at X-band provided one rotational diffusion coefficient, R(perpendicular). T(1)(-1), R(perpendicular), and R(||) profiles reflect local membrane dynamics of the lipid alkyl chain, while the order parameter shows only the amplitude of the wobbling motion of the lipid alkyl chain. Using these dynamic parameters, namely T(1)(-1), R(perpendicular), and R(||), one can discriminate the different effects of cholesterol at different depths, showing that cholesterol has a rigidifying effect on alkyl chains to the depth occupied by the rigid steroid ring structure and a fluidizing effect at deeper locations. The nondynamic parameter, S(0), shows that cholesterol has an ordering effect on alkyl chains at all depths. Conventional and SR EPR measurements with T-PC indicate that cholesterol has a fluidizing effect on phospholipid headgroups. EPR at W-band provides more detailed information about the depth-dependent dynamic organization of the membrane compared with information obtained at X-band. EPR at W-band has the potential to be a powerful tool for studying membrane fluidity in samples of small volume, ~30 nL, compared with a representative sample volume of ~3 μL at X-band.

Membrane fluidity profiles as deduced by saturation-recovery EPR measurements of spin-lattice relaxation times of spin labels

There are no easily obtainable EPR spectral parameters for lipid spin labels that describe profiles of membrane fluidity. The order parameter, which is most often used as a measure of membrane fluidity, describes the amplitude of wobbling motion of alkyl chains relative to the membrane normal and does not contain explicitly time or velocity. Thus, this parameter can be considered as nondynamic. The spin-lattice relaxation rate (T(1)(-1)) obtained from saturation-recovery EPR measurements of lipid spin labels in deoxygenated samples depends primarily on the rotational correlation time of the nitroxide moiety within the lipid bilayer. Thus, T(1)(-1) can be used as a convenient quantitative measure of membrane fluidity that reflects local membrane dynamics. T(1)(-1) profiles obtained for 1-palmitoyl-2-(n-doxylstearoyl)phosphatidylcholine (n-PC) spin labels in dimyristoylphosphatidylcholine (DMPC) membranes with and without 50 mol% cholesterol are presented in parallel with profiles of the rotational diffusion coefficient, R(⊥), obtained from simulation of EPR spectra using Freed's model. These profiles are compared with profiles of the order parameter obtained directly from EPR spectra and with profiles of the order parameter obtained from simulation of EPR spectra. It is shown that T(1)(-1) and R(⊥) profiles reveal changes in membrane fluidity that depend on the motional properties of the lipid alkyl chain. We find that cholesterol has a rigidifying effect only to the depth occupied by the rigid steroid ring structure and a fluidizing effect at deeper locations. These effects cannot be differentiated by profiles of the order parameter. All profiles in this study were obtained at X-band (9.5 GHz).

Two conserved residues are important for inducing highly ordered membrane domains by the transmembrane domain of influenza hemagglutinin

The interaction with lipids of a synthetic peptide corresponding to the transmembrane domain of influenza hemagglutinin was investigated by means of electron spin resonance. A detailed analysis of the electron spin resonance spectra from spin-labeled phospholipids revealed that the major effect of the peptide on the dynamic membrane structure is to induce highly ordered membrane domains that are associated with electrostatic interactions between the peptide and negatively charged lipids. Two highly conserved residues in the peptide were identified as being important for the membrane ordering effect. Aggregation of large unilamellar vesicles induced by the peptide was also found to be correlated with the membrane ordering effect of the peptide, indicating that an increase in membrane ordering, i.e., membrane dehydration, is important for vesicle aggregation. The possibility that hydrophobic interaction between the highly ordered membrane domains plays a role in vesicle aggregation and viral fusion is discussed.

Fusion peptide from influenza hemagglutinin increases membrane surface order: an electron-spin resonance study

A spin-labeling study of interactions of a fusion peptide from the hemagglutinin of the influenza virus, wt20, and a fusion-inactive mutant DeltaG1 with dimyristoylphosphatidylcholine (DMPC) and 1-palmitoyl-2-oleoyl-phosphatdylcholine bilayers was performed. We found that upon binding of wt20, the ordering of headgroups and the ordering of acyl chains near the headgroup increased significantly, in a manner consistent with a cooperative phenomenon. However, changes in the order at the end of the acyl chains were negligible. The ordering effect of wt20 on the headgroup was much stronger at pH 5 than at pH 7. No effect of DeltaG1 binding on the order of bilayers was evident. We also found that 1-palmitoyl-2-hydroxyl phosphatidylcholine, a membrane-fusion inhibitor, decreased the ordering of DMPC headgroups, whereas arachidonic acid, a membrane-fusion promoter, increased the ordering of DMPC headgroups. These results suggest that increases in headgroup ordering may be important for membrane fusion. We propose that upon binding of wt20, which is known to affect only the outer leaflet of the bilayer, this outer leaflet becomes more ordered, and thus more solid-like. Then the coupling between the hardened outer leaflet and the softer inner leaflet generates bending stresses in the bilayer, which tend to increase the negative curvature of the bilayer. We suggest that the increased ordering in the headgroup region enhances dipolar interactions and lowers electrostatic energy, which may provide an energy source for membrane fusion. Possible roles of bending stresses in promoting membrane fusion are discussed.

Multifrequency ESR study of spin-labeled molecules in inclusion compounds with cyclodextrins

The molecular dynamics of spin-labeled compounds included into the solid phase of cyclodextrins (CDs) has been studied using conventional (X-band) ESR at 9 GHz and high-field high-frequency (HFHF) ESR at 240 and 170 GHz. The patterns of axial rotation at these higher frequencies are clear just by inspection of the spectrum, unlike the case for 9 GHz spectra. That is HFHF ESR is sensitive to molecular motion about the diffusion axis collinear with the X, Y or Z-direction of the magnetic g- and A-tensors of the nitroxide moiety (referred to, respectively, as X, Y or Z-rotation). For doxyl stearic acids (Z-rotation) and TEMPOyl caprylate (X-rotation) included in beta- and gamma-CDs we were able to determine the rate of molecular motion and the corresponding potential barriers. We emphasize that determining the rate of Z-rotation by ESR is feasible only using HFHF ESR. For the X-rotation case we suggest that the motion of the nitroxide moiety consists of fast small-angle librations about the magnetic X-axis superimposed by rotational diffusion about the same axis. The potential barrier of 1.7 Kcal mol(-1) for this rotational diffusion is unusually low. A fascinating feature of TEMPO derivatives included in beta-CD is the detectable molecular motion at temperatures below 77 K. For the other CD-spin probe systems, we used multifrequency analysis to assign the conformations of spin-labeled molecules. A dramatic spectral change for 16-sasl in beta- and gamma-CDs at approximately 260 K corresponds to a tilting of the position of the nitroxide moiety on the rotating molecule relative to the long diffusion axis, while for TEMPO derivatives in gamma-cyclodextrin below 200 K, we observe a rapid transition from fast to very slow rotational motion. More complex features are best studied by means of multifrequency ESR experiments. The visual clarity and the simplicity of analysis of the ESR spectra shown in this work should provide a benchmark for future studies of molecular motion by HFHF ESR.

Simulation of slow-motion CW EPR spectrum using stochastic Liouville equation for an electron spin coupled to two nuclei with arbitrary spins: matrix elements of the Liouville superoperator

An algorithm is developed that extends the well known nitroxide slow-motional continuous wave electron paramagnetic resonance (EPR) simulation technique developed originally by Meirovitch et al. [E. Meirovitch, D. Inger, E. Inger, G. Moro, J.H. Freed, J. Chem. Phys. 77 (1982) 3915-3938], and implemented by Schneider and Freed [D.J. Schneider, J.H. Freed, Calculating slow motional magnetic resonance spectra: a user's guide, in: Biological Magnetic Resonance, vol. 6, Plenum Publishing Corporation, 1989]. This paper deals with the more general case of coupling of one electron spin to two nuclear spins. A complete listing of the matrix elements of the Liouville superoperator for this extension has been included. This advance has been successfully tested by reproducing the observed spectral lineshapes of a solution of the novel radical Mes(*)(CH(3))P-PMes(*) [Mes(*)=2,4,6 (tBu)(3)C(2)H(2)] in tetrahydrofuran (THF), in which the radical is undergoing slow tumbling, with the coupling of one electron spin to two physically and magnetically inequivalent phosphorus ((31)P) nuclei.

Self-assembly of beta-cyclodextrin in water. 2. Electron spin resonance

The interaction of amphipilic spin labels with beta-cyclodextrin was investigated using conventional electron spin resonance (ESR) spectroscopy to explore the aggregation of cyclodextrins in water. Methyl 5-doxylstearate (5-DMS) and stearic acid spin probes (n-DSA), which contain a cyclic nitroxide moiety with unpaired electrons covalently linked to the aliphatic chain carbon in positions 5, 7, 12, and 16, show that different dynamic domains coexist in beta-CD water solutions above 3 mM. The results are consistent with the formation of beta-CD self-assembled structures in water above a critical aggregation concentration and confirm the previous findings that were reported in the part 1 article of this series.

Stochastic modeling of CW-ESR spectroscopy of [60]fulleropyrrolidine bisadducts with nitroxide probes

In this work, we address the interpretation of continuous wave electron spin resonance (CW-ESR) spectra of fulleropyrrolidine bisadducts with nitroxide addends. Our approach is based on a definition of the spin Hamiltonian which includes exchange and dipolar interactions and on a complete numerical solution of the resulting stochastic Liouville equation, with inclusion of diffusive rotational dynamics. CW-ESR spectra are simulated for a series of C60 bisadducts made up of four trans isomers and the equatorial isomer. A nonlinear least-squares fitting procedure allows extraction directly from the available experimental spectra of a wide range of parameters, namely interprobe relative distances, diffusion tensors, and values of the exchange parameter J. Results are in good agreement with previous, more phenomenological estimates, proving that the combination of sensitive ESR spectroscopy based on multiple spin labeling with nitroxide radicals and sophisticated modeling can be highly helpful in providing structural and dynamic information on molecular systems.

Unraveling Solvent-Driven Equilibria between α- and 310-Helices through an Integrated Spin Labeling and Computational Approach

In this work we present an effective and flexible computational approach, which is the result of an ongoing development in our groups, allowing the complete a priori simulation of the ESR spectra of complex systems in solution. The usefulness and reliability of the method are demonstrated on the very demanding playground represented by the tuning of the equilibrium between 3(10)- and alpha-helices of polypeptides by different solvents. The starting point is the good agreement between computed and X-ray diffraction structures for the 3(10)-helix adopted by the double spin-labelled heptapeptide Fmoc-(Aib-Aib-TOAC)2-Aib-OMe. Next, density functional computations, including dispersion interactions and bulk solvent effects, suggest another energy minimum corresponding to an alpha-helix in polar solvents, which, eventually, becomes the most stable structure. Computation of magnetic and diffusion tensors provides the basic ingredients for the building of complete spectra by methods rooted in the Stochastic Liouville Equation (SLE). The remarkable agreement between computed and experimental spectra at different temperatures allowed us to identify helical structures in the various solvents. The generality of the computational strategy and its implementation in effective and user-friendly computer codes pave the route toward systematic applications in the field of biomolecules and other complex systems.

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.

Depth Dependence of Stratum Corneum Lipid Ordering: A Slow-Tumbling Simulation for Electron Paramagnetic Resonance

We investigated the structural ordering of stratum corneum (SC) lipid by means of electron paramagnetic resonance (EPR) slow-tumbling simulation in conjunction with spin probe studies. The SC of human mid-volar forearm was stripped consecutively from three to six times. The EPR probe method detected a characteristic peak of sebaceous matter in the first SC stripping. The order parameter values obtained by the slow-tumbling simulation (S(0)) showed significant differences between each layer compared with those indicated by the conventional order parameter (S) using hyperfine couplings. Although the conventional S values were in the range of 0.56 (outermost layer) to 0.61 (bottom layer), the S(0) values by the simulation changed from 0.22 to 0.96. The present results suggest that the structural ordering of the outermost SC layer is less tight, whereas the structure of inner layers becomes more rigid. Therefore, we concluded that the EPR probe method recognizes sebaceous matters, whereas EPR in conjunction with the simulation allows quantitative evaluation of SC lipid ordering in relation to skin depth.

Ab Initio Modeling of CW-ESR Spectra of the Double Spin Labeled Peptide Fmoc-(Aib-Aib-TOAC)2-Aib-OMe in Acetonitrile

In this work we address the interpretation, via an ab initio integrated computational approach, of the CW-ESR spectra of the double spin labeled, 310-helical, peptide Fmoc-(Aib-Aib-TOAC)2-Aib-OMe dissolved in acetonitrile. Our approach is based on the determination of geometric and local magnetic parameters of the heptapeptide by quantum mechanical density functional calculations taking into account solvent and, when needed, vibrational averaging contributions. The system is then described by a stochastic Liouville equation for the two electron spins interacting with each other and with two 14N nuclear spins, in the presence of diffusive rotational dynamics. Parametrization of the diffusion rotational tensor is provided by a hydrodynamic model. CW-ESR spectra are simulated with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing 3D structural and dynamic information on molecular systems.

Modeling the effects of structure and dynamics of the nitroxide side chain on the ESR spectra of spin-labeled proteins

In the companion paper (J. Phys. Chem. B 2006, 110, jp0629487), a study of the conformational dynamics of methanethiosulfonate spin probes linked at a surface-exposed alpha-helix has been presented. Here, on the basis of this analysis, X-band ESR spectra of these spin labels are simulated within the framework of the Stochastic Liouville equation (SLE) methodology. Slow reorientations of the whole protein are superimposed on fast chain motions, which have been identified with conformational jumps and fluctuations in the minima of the chain torsional potential. Fast chain motions are introduced in the SLE for the protein reorientations through partially averaged magnetic tensors and relaxation times calculated according to the motional narrowing theory. The 72R1 and 72R2 mutants of T4 lysozyme, which bear the spin label at a solvent-exposed helix site, have been taken as test systems. For the side chain of the R2 spin label, only a few noninterconverting conformers are possible, whose mobility is limited to torsional fluctuations, yielding almost identical spectra, typical of slightly mobile nitroxides. In the case of R1, more complex spectra result from the simultaneous presence of constrained and mobile chain conformers, with relative weights that can depend on the local environment. The model provides an explanation for the experimentally observed dependence of the spectral line shapes on temperature, solvent, and pattern of substituents in the pyrroline ring. The relatively simple methodology presented here allows the introduction of realistic features of the spin probe dynamics into the simulation of ESR spectra of spin-labeled proteins; moreover, it provides suggestions for a proper account of such dynamics in more sophisticated approaches.

Development and Validation of an Integrated Computational Approach for the Modeling of cw-ESR Spectra of Free Radicals in Solution: p-(Methylthio)phenyl Nitronylnitroxide in Toluene as a Case Study

In this work we address the interpretation, via an ab initio integrated computational approach, of continuous wave electron spin resonance (cw-ESR) spectra of p-(methylthio)phenyl nitronylnitroxide (MTPNN) dissolved in toluene. Our approach is based on the determination of the spin Hamiltonian, averaged with respect to fast vibrational motions, with magnetic tensor parameters (Zeeman and hyperfine tensors) characterized by quantum mechanical density functional calculations. The system is then described by a stochastic Liouville equation, with inclusion of diffusive rotational dynamics. Parametrization of diffusion rotational tensor is provided by a hydrodynamic model. Cw-ESR spectra of MTPNN are simulated for a wide range of temperatures (155-292 K) with minimal resorting to fitting procedures, proving that the combination of sensitive ESR spectroscopy and sophisticated modeling can be highly helpful in providing structural and dynamic information on molecular systems.

Nonlinear-least-squares analysis of slow motional regime EPR spectra

A comparison between the full Newton-type optimization NL2SNO, the Levenberg-Marquardt method with the model-trust region modification, and the simplex algorithm is made in the context of the iterative fitting of EPR spectra. EPR lineshape simulations are based on the stochastic Liouville equation (SLE), with an anisotropic diffusion tensor and an anisotropic restraining potential describing the motional amplitude of the spin label. The simplex algorithm was found to be the most reliable, and an approach-incorporating both NL2SNO as well as the downhill simplex methods-is proposed as a strategy-of-choice.

High-field ESR on aligned membranes: a simple method to record spectra from different membrane orientations in the magnetic field

A combination of isopotential spin-dry ultracentrifugation (ISDU) and microtome techniques was used to facilitate the collection of high field/high frequency (170 GHz) ESR spectra corresponding to different orientations of the membrane normal relative to the magnetic field. This technique is particularly valuable for aligned biological samples in vitro. At 170 GHz, conventional sample preparation techniques based solely on ISDU constrained the sample to be oriented so that the membrane normal was parallel to the applied magnetic field due to the geometry and the millimeter wave field distribution of the Fabry-Pérot resonator used in these experiments. This orientational constraint limited the information that could be obtained from aligned membranes at high field. The combined ISDU/microtome technique overcame this limitation. Spectra from spin-labeled Gramicidin A and the spin label cholestane in aligned DPPC membranes provide a demonstration of the technique. We also discuss some virtues of high field/high frequency ESR on aligned membranes compared to X-band.

Chain ordering of Stratum corneum lipids investigated by EPR slow-tumbling simulation

We investigated the chain ordering of the lipid bilayer of Stratum corneum (SC) using an electron paramagnetic resonance (EPR) spin probe method in conjunction with slow-tumbling simulation. The ordering of SC lipids was evaluated by analysis of the signals of 5-doxylstearic acid (5-DSA) spin probe incorporated into the lamellar lipids. The result obtained with the conventional method of calculating the order parameter using hyperfine values was 0.80. The value of the order parameter obtained by spectral simulation was 0.73. It was found that the conventional method of calculating the chain ordering using hyperfine values could not differentiate subtle EPR spectral changes. However, EPR slow-tumbling simulation can differentiate such subtle spectral changes. Thus, the present EPR investigation suggests that simulation provides more detail about the structure of the lipid bilayer than the conventional method.

Toward an integrated computational approach to CW-ESR spectra of free radicals

Interpretation of structural properties and dynamic behaviour of molecules in solution is of fundamental importance to understand their stability, chemical reactivity and catalytic action. Information can be gained, in principle, by a variety of spectroscopic techniques, magnetic as well as optical. In particular, continuous wave electron spin resonance (CW-ESR) measurements are highly informative. However, the wealth of structural and dynamic information which can be extracted from ESR spectroscopy is, at present, limited by the necessity of employing computationally efficient models, which are increasingly complex as they need to take into account diverse relaxation processes affecting the spectrum. In this paper, we address the basic theoretical tools needed to predict, essentially ab initio, CW-ESR spectra observables according to the stochastic Liouville equation (SLE) approach, combined with quantum mechanical and hybrid methods for the accurate and efficient computation of structural, spectroscopic and magnetic properties of molecular systems. We shall discuss, on one hand, the quantum mechanical calculation of magnetic observables, via density functional theory (DFT), time-dependent DFT (TD-DFT) and application of the polarizable continuum model (PCM) for the description of environmental effects, including anisotropic environments and systems where different regions are characterized by different dielectric constants. One the other hand, the explicit evaluation of dynamical effects will be discussed based on the numerically exact treatment of the SLE in the presence of several relaxation processes, which has been proven to be a challenging task.

ESR as a valuable tool for the investigation of the dynamics of EPC and EPC/cholesterol liposomes containing a carboranyl-nucleoside intended for BNCT

Electron Spin Resonance (ESR) spectroscopy of long-chain nitroxides (5-, 7-, and 16-doxyl stearic acid) has been used to evaluate the perturbations induced by beta-5-o-carboranyl-2'-deoxyuridine (CDU) on the structure and dynamics of egg phosphatidylcholine (EPC) and EPC/cholesterol liposomes. Loaded liposomes are intended for the use in Boron Neutron Capture Therapy (BNCT). From a detailed analysis of the motional and order parameters determining the ESR line shape as a function of temperature and of CDU content in liposomes, an increased order and a hindered motion of the phospholipid membranes resulted in the presence of increasing CDU concentration. This occurred particularly at the liposome surface level. Both higher ordering and increased rigidity of the membrane lipids were the result of the constraints exerted by the embedded carboranyl-nucleoside.