High-Field EPR and ESEEM Investigation of the Nitrogen Quadrupole

J. Phys. Chem. B 2008, 112, 9079–9090

9079

High-Field EPR and ESEEM Investigation of the Nitrogen Quadrupole Interaction of Nitroxide Spin Labels in Disordered Solids: Toward Differentiation between Polarity and Proticity Matrix Effects on Protein Function A. Savitsky,† A. A. Dubinskii,‡ M. Plato,† Y. A. Grishin,§ H. Zimmermann,| and K. Mo¨bius*,† Department of Physics, Free UniVersity Berlin, Arnimallee 14, D-14195 Berlin, Germany, SemenoV Institute of Chemical Physics, Kosygina str. 4, 119991 Moscow, Russia, Institute of Chemical Kinetics and Combustion, Institutskaya str. 3, 630090 NoVosibirsk, Russia, and Max-Planck-Institute for Medical Research, Jahnstrasse 29, D-69120 Heidelberg, Germany ReceiVed: December 11, 2007; ReVised Manuscript ReceiVed: April 21, 2008

The combination of high-field electron paramagnetic resonance (EPR) with site-directed spin labeling (SDSL) techniques employing nitroxide radicals has turned out to be particularly powerful in revealing subtle changes of the polarity and proticity profiles in proteins enbedded in membranes. This information can be obtained by orientation-selective high-field EPR resolving principal components of the nitroxide Zeeman (g) and hyperfine (A) tensors of the spin labels attached to specific molecular sites. In contrast to the g- and A-tensors, the 14N (I ) 1) quadrupole interaction tensor of the nitroxide spin label has not been exploited in EPR for probing effects of the microenvironment of functional protein sites. In this work it is shown that the W-band (95 GHz) high-field electron spin echo envelope modulation (ESEEM) method is well suited for determining with high accuracy the 14N quadrupole tensor principal components of a nitroxide spin label in disordered frozen solution. By W-band ESEEM the quadrupole components of a five-ring pyrroline-type nitroxide radical in glassy ortho-terphenyl and glycerol solutions have been determined. This radical is the headgroup of the MTS spin label widely used in SDSL protein studies. By DFT calulations and W-band ESEEM experiments it is demonstrated that the Qyy value is especially sensitive to the proticity and polarity of the nitroxide environment in H-bonding and nonbonding situations. The quadrupole tensor is shown to be rather insensitive to structural variations of the nitroxide label itself. When using Qyy as a testing probe of the environment, its ruggedness toward temperature changes represents an important advantage over the gxx and Azz parameters which are usually employed for probing matrix effects on the spin labeled molecular site. Thus, beyond measurenments of gxx and Azz of spin labeled protein sites in disordered solids, W-band high-field ESEEM studies of 14N quadrupole interactions open a new avenue to reliably probe subtle environmental effects on the electronic structure. This is a significant step forward on the way to differentiate between effects from matrix polarity and hydrogen-bond formation. 1. Introduction In Nature, fine-tuning for optimum efficiency of biological processes, such as light-induced electron and proton transmembrane transfer with high quantum yield, often occurs Via weak cofactorprotein interactions employing electrostatic effects (matrix polarity) and/or the incorporation of hydrogen-bond networks (matrix proticity). Controlling effects of the protein matrix on structure and dynamics of reaction intermediates can favorably be probed by advanced multifrequency electron paramagnetic resonance (EPR) techniques, and instructive examples are found in the recent literature; for overviews see refs 1-7.EPR is, indeed, the method of choice for studying one-electron transfer processes like in primary photosynthesis, because paramagnetic (S ) 1/2) transient intermediates are formed. Their spin-interaction parameters, such as isotropic and anisotropic components of the g- and hyperfinetensors have been shown to be sensitive toward weak interactions with the matrix in which the reactants are embedded. 8,9 * Corresponding author: Tel: +49 (30) 83852770. Fax: +49 (30) 83856046. E-mail: [email protected]. † Free University Berlin. ‡ Semenov Institute of Chemical Physics. § Institute of Chemical Kinetics and Combustion. | Max-Planck-Institute for Medical Research.

For protein systems exhibiting solely diamagnetic states of their reactants, e.g., the intermediate states of the light-driven proton pump bacteriorhodopsin, EPR techniques can still serve for probing environmental effects on the process efficiency. This is possible by resorting to site-directed spin-labeling (SDSL) mutagenesis techniques, using specific nitroxide spin label side chains as reporter groups.10 SDSL has matured to an extremely important branch of bio-EPR spectroscopy, and nitroxide side chains can be introduced at almost any desired site in a protein. At this site, the amino acid is exchanged by a reactive cysteine residue and, subsequently, a sulfhydryl-selective nitroxide radical, such as the MTS [(1-oxyl-2,2,5,5-tetramethylpyrroline3-methyl) methanethiosulfonate] spin label, is used to mark the selected site. It has been shown11–19 that the isotropic and anisotropic components of the g- and hyperfine-tensors of the nitroxide spin label can be used to reveal the polarity and proticity properties of the immediate environment of the reporter group. Since single crystals of membrane proteins are often difficult to prepare, if at all, frozen-solution protein preparations, lacking long-range order, are commonly used for EPR studies of matrix effects. Nevertheless, spectral contributions from different molecular orientations can be differentiated in cases where

10.1021/jp711640p CCC: $40.75  2008 American Chemical Society Published on Web 07/02/2008

9080 J. Phys. Chem. B, Vol. 112, No. 30, 2008 dominating anisotropic spin interactions are present as, for instance, in many metalloproteins. For non-metalloproteins, however, such as nitroxide spin labeled molecules with rather small anisotropies of their spin interactions, the application of high-field EPR techniques with correspondingly high microwave frequencies is preferrable in comparison to standard X-band EPR techniques to ensure high orientational selectivity as well as high spectral and time resolution.5–7 The spectral and orientational resolution is increased with increasing magnetic field strength when, for a given g-tensor anisotropy, the anisotropic electron Zeeman interaction exceeds the inhomogeneous line width. Thus, molecules with different orientations with respect to the magnetic field axis contribute to separated regions in the EPR spectrum. Such a magnetoselection can be exploited further by using double-resonance techniques, e.g., electron nuclear double resonance (ENDOR), or specific electron spin echo (ESE) techniques, such as electron spin echo envelope modulation (ESEEM). They provide single-crystal like information from orientationally selected fractions of molecules in the disordered sample. It should be pointed out that the combination of high-field EPR with SDSL techniques is particularly powerful in revealing subtle changes of the polarity and proticity profiles along proton transfer pathways in proteins13,17 or along polypeptide and lipid chains14,20 in artificial and natural membranes. This information can be obtained by high-field EPR resolving the gxx and Azz components of the nitroxide interaction tensors of a series of molecules with the spin label attached to specific molecular sites. Thetheoreticallypredicted12,15,21–23 andexperimentallyestablished13,17 linear correlations gxx versus Azz allowed to differentiate between polar and nonpolar protein and membrane regions. Moreover, different slopes occasionally observed in the gxx versus Azz plots were assigned to either polarity or proticity effects on the magnetic parameters of the spin label from its local protein or membrane environment. So far, however, the scatter of the data has prevented the different slopes to become an established method to differentiate between polarity and proticity effects of the matrix. In contrast to the g- and nitrogen hyperfine-tensors, the 14N (I ) 1) quadrupole interaction tensor of the nitroxide spin label has not been exploited in EPR for probing effects of the microenvironment of functional protein sites. Moreover, there are only a several 14N quadrupole tensor X-band ENDOR investigations of nitroxides included in single crystals known up to date.24–27 From the nuclear quadrupole resonance (NQR) literature on 14N nuclei in diamagnetic molecular solids, we anticipate that the precise knowledge of the 14N quadrupole coupling constant e2qQ/h and the asymmetry parameter η of the electric field gradient (EFG) at the 14N nucleus in the nitroxide will enlarge the arsenal of sensitive probes for environmental effects on specific sites of the biomolecule. For example, it was shown28 that both e2qQ/h and η strongly depend on the molecular structure and the electric charge distribution within the molecule as well as on the intermolecular interactions. Furthermore, from inspecting the experimental NQR data and their quantum-chemical (DFT) interpretation29 it is obvious that hydrogen bonds can significantly modify the EFG. To measure directly the nuclear quadrupole interaction by EPR techniques, the nuclear transitions are driven by radiofrequency (rf) fields as in ENDOR. A more indirect alternative is offered by ESEEM, i.e., by applying solely a microwave (mw) pulse train and observing, under appropriate conditions, spin-echo modulations from hyperfine and quadrupole interactions. To obtain detectable modulations of the echo decays, it is required

Savitsky et al.

Figure 1. (a) Molecular structure of the perdeuterated nitroxide radical R1. The conventional principal axes of the g-tensor are indicated; (b) ortho-terphenyl and (c) glycerol host for the diluted nitroxide glassy solution.

that forbidden transitions, flipping both the electron and nuclear spins, become partially allowed. This requires efficient mixing of the nuclear and electron spin eigenfunctions by the dipolar hyperfine interaction.30 Consequently, the strength of the external magnetic field has to be properly chosen to approximately balance the Zeeman splitting of the nuclear sublevels and the respective hyperfine splittings (“cancellation condition”).31 This means that an optimum Zeeman field value exists for each nucleus and hyperfine coupling, as has been demonstrated by multifrequency ESEEM experiments on S ) 1/2, I ) 1/2 as well as on S ) 1/2, I ) 1 systems.31–34 Pulsed ENDOR and ESEEM techniques are complementary to each other35,36 concerning their ability to reveal large or small nitrogen dipolar hyperfine interteractions (“geminate” or “distal” nitrogens), respectively. This has been exploited, for instance, to identify histidine ligands in metalloproteins.37,38 However, only a few high-field nitrogen ESEEM experiments on single-crystal37 and disordered samples33 have been reported in the past decade. Hence, it was the aim of this work to investigate, by means of high-field EPR and ESEEM methods in conjunction with DFT (density functional theory) calculations, the problem whether nitrogen quadrupole-tensor components can be determined with high accuracy from frozen-solution samples and what kind of information on the polarity and proticity of the nitroxide spin-label environment can be extracted from the interaction between the electric field gradient at the site of the 14N nitrogen nucleus and its quadrupole moment (Q). Specifically, we are addressing the question: Is the information on matrix effects from the 14N quadrupole-interaction tensor components of the nitroxide spin label similar or complementary to that obtained from the established spin-probe parameters, gxx and Azz? To find an answer, we are pursuing the following twostep approach. In the first step, we investigate the methodological prerequisites for determining the 14N quadrupole interaction of the nitroxide spin label as a reporter for matrix effects. Hence, we investigate the question to which experimental accuracy one can measure the 14N quadrupole coupling by high-field EPR methods, and what are the theoretically expected shifts of the EFG at the nitrogen nucleus of the spin label when changing the microenvironment? We focused on the spectroscopic and quantum-chemical aspects of measuring and calculating the quadrupole interaction parameters of the nitroxide radical R1 (Figure 1). The measurements were done by 95 GHz (W-band) EPR techniques, the molecular calculations by DFT methods. The calculations characterize the frequently used spin-label group MTS without and with considering perturbations from surrounding matrix molecules. The in-Vacuo situation was experimentally approximated by using ortho-terphenyl as nonpolar and aprotic solvent.39 The polar/protic case is modeled by using glycerol as solvent. The presented DFT calculation results include, beyond the in-Vacuo case, also different variations of the spin label microenvironment.

Nitrogen Quadrupole Interaction of Nitroxide Spin Labels

J. Phys. Chem. B, Vol. 112, No. 30, 2008 9081

Figure 2. W-band microwave pulse sequence for the stimulated high-field ESEEM experiment on the nitroxide radical R1. Top: The echodetected EPR spectrum of the R1-14N radical as well as the microwave excitation bandwidth for typical microwave pulse-length settings are shown for clarity. Typical settings of pulse sequence parameters are τ ) 40 ns, π/2-pulse length tp) 30 ns. The time T is stepped from T0 ) 100 ns in 5 ns steps. Bottom left: A representative example of a nuclear modulation echo decay trace at the indicated magnetic filed position is shown. Bottom right: The Fourier transformed spectrum of the ESEEM decay example is given, the cutoff frequency of the high-pass filter was set to 1.5 MHz.

In the second step, the microenvironment of the nitroxide spin label is systematically varied in terms of matrix polarity and proticity, and the changes of the spin-interaction parameters are measured by 95 GHz EPR techniques. The final step-2 results of this still ongoing work will be described in a forthcoming publication. 2. Experimental Section Materials. The molecular structure of the nitroxide spin label R1 (3-hydroxymethyl-2,2,5,5-tetramethylpyrrolin-1-oxyl40 is shown in Figure 1. The synthesis of 14N-perdeuterated R1 (R114N) was performed in the following way: Starting from acetoned6 and ND3, the 3-hydroxymethyl-2,2,5,5-tetramethylpyrrolin1-oxyl-d16 (R1) was prepared in seven reaction steps Via 2,2,6,6tetramethyl-4-oxopiperidin-d17 and 3,5-dibromo-2,2,6,6-tetramethyl-4-oxopiperidin hydrobromide to the deuterated tetramethylpyrrolin-3-carboxamide which was oxidized to the nitroxide radical. Cleavage to the corresponding 3-carboxy-2,2,5,5tetramethyl-3-pyrrolin-1-oxyl-d14 was accomplished by NaOD/ D2O followed by esterification with ethylchloroformate. The deuterated acylcarbonate was reduced to the labeled nitroxide R1 by NaBD4 in D2O. The 15N-perdeuterated nitroxide R1 (R115N) was analogously prepared by starting with acetone-d and 6 15ND . The 15N as well as the deuterium isotope enrichment 3 were checked by mass-spectrometry and found to be better than 98%. The nitroxides R1-14N and R1-15N were dissolved in benzene (Aldrich, puriss grade) to obtain a parent solution for all sample preparations. This solution was mixed with powdered orthoterphenyl (Fluka, puriss grade), and the benzene solvent was evaporated under air. The resulting powder solution containing 1 mM of nitroxide radical was heated to about 65 °C to become

fluid and then transferred into the sample quartz capillary (i.d.) 0.6 mm). A glass-type solution was obtained by shock freezing the sample with liquid nitrogen. The cold sample was finally transferred into the precooled EPR cavity. The glycerol solution was handled in the same way. The solution was prepared by dissolving 1R-14N nitroxide in glycerol (Fluka, puriss grade, anhydrous). W-Band High-Field EPR and ESEEM Experiments. All EPR and ESEEM experiments were performed with a laboratory-built W-band spectrometer operating in both cw (continuous wave) and pulsed modes at an EPR frequency of 95 GHz and an external magnetic field of about 3.4 T, as described previously.6,11 For the measurements at 180 K, the temperature of the sample was controlled by a temperature stabilized nitrogen gas-flow cryostat in the probehead. For the experiments at 90 K, a liquid nitrogen injection mode of the cryostat was used. Cw EPR experiments were performed using a gold plated bronze TE011 cavity (loaded quality factor QL ) 2400 of the empty cavity, temperature independent in the range 80-290 K). Low mw power ( ) Tr(Sy · F^ SSE) ^

^

(5)

ˆ SSE in eq 3 is the product of consecutive The propagator matrix U propagators corresponding to the three-pulse echo scheme (Figure 2): ^

^

^

^

^

^

^

USSE ) Udet · Upls · Umix · Upls · Uprep · Upls

(6)

In the rotating frame, the DO evolution in the sequence of time occurs with time-independent spin Hamiltonians ^

^

^

^

^

Hprep ) Hmix ) Hdet ) H - νmw · Sz ^

^

^

^

Hpls ) H - νmw · Sz + ν1 · Sx

(7) (8)

where ν1 ) ω1/2π is the rotating-frame amplitude of the microwave magnetic field expressed in frequency units. Note that the pulse Hamiltonian (eq 8) differs from that of the nonselective pulses, Hˆpls ) ν1 · Sˆx, which acts uniformly on all electron spin transitions within the system. The static character of the Hamiltonians (eqs 7 and 8) allows the expression of the



propagators in eq 4 as matrix exponentials ^

Upls ) exp(-2π · i · Hpls · tp) ^

^

Uevol ) exp(-2π · i · Hevol · tevol) ^

(9) (10)

Here index “evol” stands for either “prep”, “mix”, or “det”. The pulse time tp satisfies the relation ν1 · tp ) 1/4 (the π/2-pulses applied to generate SSE), tprep) τ, and tmix) T. As for tdet, for nonselective pulses it also equals τ. Selective pulses, however, broaden and shift the echo peak time:36 tdet ) τ + δdet. Our test simulations of SSE transients (signals after the third pulse in dependence of tdet) allowed to estimate this shift and to adjust tdet to the echo peak position in ESEEM simulations. Echo amplitudes RSSE were evaluated as described above for every particular orientation of radicals with fixed parameters characterizing the static Hamiltonian of eq 1, the microwave irradiation (νmw, ν1), and the pulsing time diagram (tp, τ, δdet). Mixing time T and external magnetic field B0 were stepped in correspondence with the experimental settings. The 4-step phase cycling in the 3-pulse echo sequence was modeled as follows: four SSE responses were calculated with subsequent sign inversion of the ν1Sˆx term in the first and second pulse propagators, eq 8, thereafter they were summed with properly alternating signs. The echo amplitudes calculated for all orientational subensembles at particular T and B0 values were summed. The resulting data array, R(B0,T), is a computed analogue of the primary experimental ESEEM recordings. The primary output of an ESEEM experiment is a timedomain signal starting at some initial time. These signals can be analyzed by either direct fit in the time domain or by calculating and interpreting the spectrum in the frequency domain. In general, for powder-type samples it is preferable to perform the analysis in the frequency domain because it is difficult to distinguish effects due to more than two frequencies in the time domain. For the spectral analysis of the ESEEM data, the experimental and simulated time-domain data have to be converted into a “faithful” representation of the ESEEM spectrum. In this work, the following routine was applied to convert all ESEEM recordings to ESEEM spectra: (i) Every recording, R(B0,T), was padded along the T axis to double length with trailing zeros. (ii) Complex-Fourier transformation was applied to the padded arrays resulting in the frequency-domain images with complex amplitudes. (iii) The final spectral densities, S(B0,ν) were evaluated as modules of the complex amplitudes. Such conversion is rather common for ESEEM studies though it causes certain distortions in the resulting spectra, as will be discussed below. Density Functional Theory Computational Methods. Calculations of the local hyperfine- and quadrupole- tensors as well as of the global g-tensor of the radical R1 were performed on the density functional theory (DFT) level with the quantumchemical program package ORCA. This was developed by Frank Neese at the Max-Planck-Institute for Bioinorganic Chemistry in Mu¨lheim (Ruhr), Germany, starting 1995. Detailed information on the general features of ORCA is available through www.thch.uni-bonn.de/tc/orca. Publications related to the calculation of EPR parameters with ORCA are found in ref 44. All hyperfine-, quadrupole- and g-tensor calculations were preceded by an ORCA geometry optimization procedure to establish minimum energy molecular structures of R1. These calculations were performed for the in-Vacuo case and, additionally, for selected cases modeling matrix effects on the NO radical (see below). No geometrical restraints were introduced. The starting geometries were obtained by a Molecular Modeling

software (HyperChem, Professional Version-Release 6, Hypercube, Inc.) on the semiempirical level. Special geometrical features of the ORCA optimized structure of R1 in Vacuo are near planarity of the five-membered ring (maximum twist angle 1°); bond length r(N-O) ) 1.262 Å; and small bending angle R ≈ 2° of the N-O bond with respect to the ring plane causing a slight pyramidal geometry around the N-atom. This will be a point of further discussion below. The ORCA input settings for the DFT calculations of the various tensors were chosen as follows: (i) A- and Q-tensors: spin unrestricted SCF; DFT functional B1LYP (one-parameter hybrid functional with Becke ’88 exchange and Lee-Yang-Parr correlation, 25% HF exchange (B1LYP); Kutzelnigg basis set IGLO-III for NMR and EPR calculations;45 integration grid “5” for high numerical accuracy in the nuclear regions. (ii) g-tensor: spin unrestricted SCF; LDS (local density) functional; Ahlrichs’ split-valence basis set with polarization (SVP) for non-hydrogens;46 resolution of the identity (RI) approximation; RI-SOMF(1X) treatment of the spin-orbit coupling operator; orbital window selection of -100 to +100 au. The ORCA output produces isotropic and/or anisotropic (traceless) contributions to all three tensors and gives the directions of principal axes in the chosen molecular axes system. In order to study the influence of external perturbations such as (i) hydrogen bonding (proticity), (ii) dielectric solvents as source of electric “reaction fields” (polarity), and (iii) electric fields from surrounding permanent dipoles and/or charges (polarity), we also present ORCA results from DFT calculations for the following model cases in addition to the in-Vacuo case: (i) Hydrogen Bonding. One water molecule was added to the R1 vacuum structure. Subsequent geometry optimization produced a linear O-H · · · O(N) hydrogen-bond geometry with r(H · · · O) ) 1.86 Å and r(O-O) ) 2.83 Å, thus revealing a weak electrostatic coupling case.47 (ii) SolWation. The perturbing influence of a surrounding dielectric solvent was taken into account by applying the conductor-like screening model developed by Klamt,48 which is implemented in the ORCA program package. In this model, the solvent is represented as a dielectric polarizable continuum (for a recent review, see ref 49). It is initially assumed to be a perfect conductor completely screening the charge density of the solute. The interactions are then scaled to a finite dielectric constant by the factor f(ε) ) (ε - 1)/(ε + x), where x is normally set to 0.5. The essential part of the calculation is the construction of a molecular surface embedding the solute molecule. This is modeled by assigning Van der Waals spheres to the individual atoms of the solute molecule. This is followed by an iterative process to determine self-consistent values of the screening charges and of the molecular density distribution. A similar approach has been taken by Barone50 in a numerical DFT-Hartree-Fock study based on the Block-Walker reaction-field theory,51 a modified version of the classical Onsager reaction-field model52 (for an alternative to this approach, see a recent publication of the Barone group23). (iii) Polarity. Polarity effects by distant point charges were simulated by an electric field Ex in the direction of the N-O bond (defining the molecular x-axis, see Figure 1). Analogous work has been performed previously on the NO spin label MTS to study matrix-induced gii- and Aii-shifts in the bacteriorhodopsin protein.12 For the maximum electric field strength expected in proteins, we set Ex ) 0.02 au (1 au ≈ 5 × 109 V · cm-1). This value follows from the maximum g-shift

9084 J. Phys. Chem. B, Vol. 112, No. 30, 2008

Figure 3. (a) Experimental W-band cw EPR spectra of 1 mM R1-15N (upper spectrum) and R1-14N (lower spectrum) nitroxide radicals in frozen solution of ortho-terphenyl taken at 180 K. They are overlaid with the corresponding best-fit spectra (dotted lines) obtained without taking the quadrupole interaction into account. For the derived magnetic parameters, see text. (b) Expanded view of gxx, gyy regions of the R114 N spectrum. The best-fit spectra calculated without quadrupole contributions and with the quadrupole couplings Qxx ) 1.1 MHz; Qyy ) 0.6 MHz are shown by black dotted and solid lines, respectively.

∆gxx(max) ≈ 1 × 10-3 observed for an NO spin label in a protein13,20 and from experimental and calculated values of the slope ∆gxx/Ex ≈ 1 × 10-11 V-1 · cm for various model nitroxides.12,22 Under ORCA, a sufficiently homogeneous electric field of this strength was created by placing appropriate electric point charges on the x-axis at large distances (>30 Å) from the N-O bond. 3. Results and Discussion Continuous Wave EPR Spectra. Figure 3 shows W-band cw EPR spectra of R1-14N and R1-15N nitroxide radicals measured at 180 K in frozen ortho-terphenyl solution. The spectra exhibit the typical powder pattern line shape expected for a dilute distribution of nitroxides. The spectra are clearly resolved into three separate regions corresponding to the principal values of the g-tensor, gxx, gyy, and gzz. Moreover, due to the reduction of the inhomogeneous line width by perdeuteration of the radicals the nitrogen hyperfine splitting (doublets for R1-15N, I ) 1/2, triplets for R1-14N, I ) 1) is clearly observed in all g-regions. The spectra were analyzed by numerical solution of the spin Hamiltonian, eq 2. At first the spectrum of R1-15N was analyzed. The best-fit spectrum of the R1-15N is shown in Figure 3a. Perfect agreement with the experimental spectrum is achieved by using the set of magnetic parameters, i.e., g-tensor, nitrogen hyperfine tensor, homogeneous EPR line width as well as orientation dependent EPR inhomogeneous linewidths, as listened in Table 1. In the next step, the spectrum of R1-14N was calculated using the parameters obtained from R1-15N, tentatively omitting quadrupole contributions and rescaling γN and A-values by the factor (1.4)-1 according to the ratio of nitrogen nuclear g-values gn(15N)/ gn(14N) ) 1.4. Although there is good agreement of the positions of the EPR lines in all g-regions (see Figure 3a), the EPR signal intensities agree only in the gzz spectral region. The disagreement of intensities in the gxx and gyy regions can not be improved by varying the corresponding linewidths. However, switching on

Savitsky et al. the quadrupole interaction in the spin Hamiltonian allows to reproduce the intensities of the experimental EPR spectrum, Figure 3b. From the simulation the values Qxx ) +1.1 MHz and Qyy ) +0.6 MHz were obtained. Thus, the quadrupole effects on the intensities in the EPR spectrum of 14N nitroxides are directly observed. This becomes possible because of a favorable disposition of the nitrogen nuclear Zeeman energy and the hyperfine interaction energies in the gxx, gyy regions of the R1-14N spectrum at W-band:25 the 14N-nuclear Zeeman frequency of 10.4 MHz at 3.38 T is comparable with the Axx (Ayy) hyperfine splitting of 13.7 MHz. Additionally, due to an EPR line width below 10 MHz the hyperfine structure is resolved in the gxx and gyy regions allowing to detect rather fine spectral distortions. Although the quadrupole effect is observed in the cw EPR spectra, the Qxx- and Qyy-values can be evaluated only with quite a large error because they are obtained by the multiparameter fit of the experimental cw EPR spectra. Thus, it will be generally preferable to perform the ESEEM measurement where the determination of the quadrupole interaction is straightforward. ESEEM Spectra. The stimulated ESE decays show distinct modulations for the R1-15N as well as for the R1-14N nitroxides. In the case of R1-15N nitroxides, the modulation is dominated by a single frequency around 22.1 MHz in the whole spectral region of nitroxide EPR absorption. This modulation is assigned to the nitroxide methyl deuterons, see Figure 1. Additional frequencies are detected in the gxx-gyy region. Figure 4a shows a contour plot representation of the R1-15N ESEEM spectrum derived by the conversion of the primary ESEEM recording from the time to the frequency domain. Beyond the ridge parallel to the magnetic field axis at 22.1 MHz mentioned above, two additional ridges are clearly distinguished in the spectrum. They are spread on the field axis in the gxx-gyy region, and terminated, i.e., confined, by the peaks at 5.05 and 24.2 MHz (low-field terminals in the gxx-region) and at 5.15 and 24.1 MHz (highfield terminals in the gyy-region). These structures are assigned to the 15N nuclear modulations. Indeed, when the direction of the external magnetic field becomes parallel to the principal xor y-axis (these orientations are selected for measurements performed at the x- and y-regions), the nuclear transition frequency approaches the values:

{ } { νx+(y)

νx-(y)

) 1.4 ·

νN + 1 ⁄ 2Axx(yy) νN - 1 ⁄ 2Axx(yy)

}

(11)

Here the factor 1.4 is introduced to rescale for the nucleus the Aii and νN values that were determined for 14N. The observed terminal peaks are positioned symmetrically about 14.63 MHz which is close to the 15N Zeeman frequency, 1.4 · νN)14.6 MHz at 3.38 T. The frequency differences of 19.15 and 18.95 MHz are in a good agreement with the hyperfine spitting constants 1.4 · Axx ) 19.2 ( 0.2 and 1.4 · Ayy ) 19.0 ( 0.2 MHz, as determined from the analysis of the cw EPR spectrum; see Table 1. However, the appearance of considerable ESEEM spectral densities close to the principal transition frequencies is, on the first sight, somewhat surprising: For radicals with S ) 1/2, I ) 1/2 and with an axial A-tensor (Azz ) A|, Axx ) Ayy ) A⊥), the ESEEM modulation-depth factor, k(θ), is equal to:53 15N

k(θ) )

(

B(θ) · νN νR(θ) · νβ(θ)

)

2

(12)

where νR,β(θ) ) [νN ( A(θ)/2)2 + B(θ)2/4]1/2 with A(θ) ) A| · cos2 θ + A⊥ · sin2 θ, B(θ) ) (A| - A⊥) sin θ cos θ. Here,



TABLE 1: The Magnetic Parameters of the R1-14N(15N) Nitroxides in Ortho-Terphenyl and R1-14N in Glycerol Obtained from the Combined Analysis of W-Band cw EPR Spectra and Nitrogen Nuclear ESEEM Patterns at 180 K ortho-terphenyl gii Aiia/MHz ∆B1/2b/MHz Qii/MHz

glycerol

xx

yy

zz

xx

yy

zz

2.00905(2) 13.60(15) 10.6 +1.26(3)

2.00617(2) 13.50(15) 6.2 +0.53(3)

2.00227(2) 93.20(15) 7.8 -1.79(4)

2.00841(2) 14.70(15) 21.6 +1.23(3)

2.00604(2) 14.70(15) 9.2 +0.36(3)

2.00223(2) 101.40(15) 10.5 -1.59(4)

a The measured 15N hyperfine values are a factor of 1.4 larger, which corresponds to the ratio of magnetic moments of 15N to 14N isotopes. The inhomogeneous (FWHM) line width due to unresolved internal 2H and external 1H hyperfine couplings (Gaussian distribution). The Lorentzian homogeneous line width of 3.9 MHz is orientation independent. b

Figure 4. (a) Frequency-field dependence of the experimental three-pulse stimulated ESEEM of 1 mM R1-15N/ortho-terphenyl glass at 180 K in the gxx, gyy regions. Beyond the gyy region no nuclear modulations due to 15N are observed. The contour lines are shown as isohypses from 0.05 to 0.4 of the maximum FT ESEEM intensity. (b) Contour plot of nitrogen W-band ESEEM intensities calculated for disordered R1-15N nitroxides using the parameters read out from panel a and cw EPR. The ESEEM contributions from the deuterons in R1 (νn(2H) in panel a) were omitted in the calculations. The contour lines are shown as isohypses from 0.05 to 1 of the maximum calculated FT ESEEM intensity. On top, the corresponding experimental (panel a) and calculated (panel b) cw EPR spectra are shown. For details, see text.

θ is the angle between the magnetic field direction and the z-axis of the A-tensor. Evidently, the nuclear modulation should vanish when orientations of the nitroxides approach the field-direction parallel to any principal axis of the A-tensor. The maximum modulation depth factor is expected at θ angles near the perpendicular orientation where the cancelation condition, i.e., νN ) A(θ)/2, is met. In the case of the 1R radical, this angle is approximately 82°. In order to understand this apparent contradiction to the observed ESEEM spectral densities, we performed a simplified simulation of the R1-15N ESEEM spectrum in a direct way, i.e., without calculating the time-domain responses and their further transformation to the frequency domain. In this simulation, resonance EPR fields and nuclear transition frequencies were calculated for a particular orientation of the radicals by solving the Hamiltonian in eq 2. Partial density contributions were evaluated being proportional to the statistical weight of the chosen orientation, and scaled by the ESEEM factor k(θ) given by eq 12. Such contributions were accumulated from all orientations. The resulting pattern was convoluted along the field axis with an EPR inhomogeneity function like in the cw-EPR simulations above. Indeed, this pattern does not give the sharp peak singularities observed in the experimental spectra of Figure 4a. Instead, slope singularities are observed there at the edges

of the inhomogeneous anisotropic lines. Thus, the “direct” calculation of the ESEEM spectrum also contradicts the experimental result. This discrepancy can be explained as follows. The nuclear modulations of the SSE envelope can be generally represented as the cosine-Fourier image of the frequency-domain spectrum of nuclear transitions

R(B0, t) )

∫0∞ S(B0, ν) · cos(2π · ν · t) dν

(13)

with t ) τ + T. Because experimental data of R(B0, t) at t < τ + T0 are not available, exact reconstruction of the spectrum S(B0, ν) by explicitly inverting the transformation in eq 13 is not possible. In our work, the composite routine was applied to convert simulated and experimentally measured ESEEM recordings to frequency spectra; see above. Such conversion procedure, when applied to reconstruct an inhomogeneous spectrum, specifically distorts the “true” spectral shape.54 During the dead time, amplitudes within the smooth spectral regions between canonical frequencies become damped much more than the canonical singularities. Importantly, the steep edge singularities are transformed to distinct peaks positioned at the edge slope. Hence, we calculated the cosine-Fourier image of the directly simulated ESEEM spectrum according to eq 13, truncated it


Savitsky et al.

Figure 5. (a) Frequency-field dependence of the experimental three-pulse stimulated ESEEM of 1 mM R1-14N/ortho-terphenyl glass at 180 K in the gxx, gyy regions. Above the gyy region no nuclear modulations due to 14N are observed. The contour lines are shown as isohypses from 0.05 to 1 of the maximum FT ESEEM intensity. (b) Contour plot of nitrogen W-band ESEEM intensities calculated for disordered R1-14N nitroxides using the parameters read out from panel a and cw EPR. The ESEEM contributions from the deuterons in R1 (νn(2H) in panel a) were omitted in the calculations. On top, the corresponding experimental (panel a) and calculated (panel b) cw EPR spectra are shown. For details, see text.

from t ) 0 to t ) τ + T0, and converted it back to the frequency domain by the same procedure employed for the ESEEM recordings. The resulting spectrum approaches the pattern at Figure 4a rather closely. The positions of nitrogen ridges and peaks become coincident; shape and relative amplitudes, however, are still not well reproduced. In order to get a more exact description the ESEEM spectra that accounts for the specific action of semiselective pulses in the echo experiments, numerical simulations were performed Via calculation of the time-domain ESEEM recordings (see Section 2) and their subsequent conversion to the frequencydomain spectra. Figure 4b shows the contour representation of the calculated ESEEM spectrum of R1-15N (2H contribution not included). This simulation is in perfect agreement with the experimental spectrum in Figure 4a. The terminal peaks in the calculated spectrum appear not only at exactly the same frequencies, but also at the same magnetic field positions as in the experiment. The experimental ESEEM spectrum of R1-14N at 180 K is shown in Figure 5a. The 22.1 MHz 2H ridge is observed with the same intensity as in the R1-15N spectrum. In contrast to the pattern of R1-15N in Figure 4a, this spectrum is dominated by the contribution from the 14N nuclear modulations. The observed nitrogen ESEEM pattern can be treated as follows. The two ridges at upper frequencies correspond to the upper ridge at Figure 4, which is shifted on the frequency axis by the downscaling factor 1.4, accounting for the reduced magnetic moment of 14N, and is split by the quadrupole interaction. The frequencies at the split terminal peaks are given by

{ }{ νx+,+ (y)

νx+,(y)

)

νN + 1/2Axx(yy) + 3/2Qxx(yy) νN + 1/2Axx(yy) - 3/2Qxx(yy)

}

(14)

The lower frequency ridge in Figure 5a represents only one of the two quadrupole-split components that is shifted upward; the downward shifted component falls too close to zero frequency where modulations are strongly damped. The Axx, and Ayy values of 13.6 and 13.5 MHz, as read out from the ESEEM spectrum, are in excellent agreement with the 13.60 ( 0.15 MHz and 13.50 ( 0.15 MHz values determined from cw EPR. The absolute values of the quadrupole couplings

[Qxx; Qyy] ) [1.26; 0.53] MHz are obtained from the positions of the high-frequency ESEEM peaks around 17 MHz. The Qzz value of -1.79 MHz is calculated from the traceless property of the quadrupole tensor. Figure 5b shows the calculated ESEEM spectrum of R1-14N with experimentally determined g-, A- and Q-values. Four trial calculations were performed with different signs of the Qxx, Qyy values and assuming Axx,yy > 0. The remarkably different ESEEM spectra allowed to determine the proper signs of the Q-values (for details see Supporting Information). The spectrum shown in Figure 5b, as calculated for [Qxx; Qyy; Qzz])[+1.26; +0.53; -1.79] MHz, perfectly fits the experimental pattern in Figure 5a. Moreover, an increased 14N modulation amplitude, compared to the 15N modulation, had resulted from our calculations. This increase is indicated by the enhanced spectral density of the nitrogen components with respect to the deuterium component, which can serve as an amplitude reference (compare Figures 4a and 5a). Thus, W-band ESEEM spectroscopy of 14N nitroxides allows for the accurate evaluation of the principal quadrupole-tensor values. In order to use the quadrupole interaction as a sensor for environmental properties of proteins, the accuracy of the measured Q-values as well as the limiting concentration for the nitroxide labeled samples have to be specified. The accuracy of the quadrupole splittings depends, to some extent, on the data evaluation procedure. A significant enhancement of frequency resolution and sensitivity could be obtained by improving the time-to-frequency domain conversion of the experimental data set. A special evaluation procedure was developed which includes construction of the data set from the multiple points across the spin-echo coordinate, baseline correction, application of a proper window function, and cross-term averaged Fourier transformation (for details, see Supporting Information). The resulting accuracy of the quadrupole frequencies was estimated to be ( 30 kHz. For a nitroxide concentration of 1 mM in the ortho-terphenyl sample the signal-to-noise ratio in the frequency domain ESEEM spectra was about 400. This means that concentrations around 100 µM of nitroxide spin-labeled protein solution will suffice for successful ESEEM measurements. A further improvement of the sensitivity is possible by lowering the sample temperature and increasing the measuring time.



TABLE 2: Theoretical Results for Q- and A-Tensorsa casea

Qxxb

Qyyb

Qzzb

η

Axxb

Ayyb

Azzb

Aisob

1 2 3 4 5 6

1.46 1.49 1.49 1.47 1.50 1.50

0.62 0.29 0.47 0.43 0.34 0.33

-2.08 -1.78 -1.96 -1.90 -1.84 -1.83

0.41 0.67 0.52 0.54 0.63 0.64

2.42 3.87 3.29 3.32 3.90 3.94

1.93 3.90 3.08 3.16 3.92 3.97

83.62 95.42 89.94 91.29 95.27 95.58

29.32 34.40 32.10 32.59 34.64 34.50

a Case 1: no H-bond, Vacuum, Ex ) 0. Case 2: no H-bond, Vacuum, Ex ) 0.02 au. Case 3: H-bond, Vacuum, Ex ) 0. Case 4. no H-bond, H2O, Ex ) 0. Case 5: H-bond, H2O, Ex ) 0. Case 6: H-bond, H2O, Ex ) 0.02 au. b The cases are explained in MHz.

TABLE 3: Theoretical Results for the g-Tensor casea

gxx

gyy

gzz

giso

1 2 3 4 5 6

2.008640 2.008170 2.008090 2.008360 2.007900 2.007900

2.006220 2.006000 2.005920 2.006090 2.005830 2.005830

2.002230 2.002240 2.002210 2.002230 2.002210 2.002210

2.005697 2.005470 2.005407 2.005560 2.005313 2.005313

a

The values are given in Table 2.

When probing matrix properties by quadrupole splittings, it is certainly necessary to clarify their temperature dependence. For this purpose, stimulated ESEEM experiments on R1-14N were performed not only at 180 K, but also at 90 K. Evaluation of the ESEEM spectrum yields the quadrupole couplings [+1.28; +0.51; -1.79] MHz and the hyperfine Axx and Ayy values of 12.1 and 12.2 MHz, respectively (13.60 and 13.50 MHz at 180 K). From the cw EPR spectrum an Azz value of 93.50 MHz (93.20 MHz at 180 K) is obtained. Apparently, for R1-14N the quadrupole values are largely temperature independent, whereas the hyperfine splittings show distinct variations with temperature. The hyperfine couplings have to be decomposed into isotropic (Aiso) and dipolar (D) contributions.36 When going from 180 to 90 K, the increase of D from 26.5 to 27.1 MHz is accompanied by the decrease of Aiso from 40.1 to 39.2 MHz. The temperature dependence of the dipolar hyperfine coupling can be explained by the model of fast librations of the nitroxide molecule.55,56 The large change of the isotropic hyperfine coupling with temperature, however, is not due to the overall motion of the nitroxide molecule in the host matrix. It probably stems from an intramolecular motion. In fact, earlier investigations of the isotropic 14N hyperfine couplings of radicals of similar structure in liquid solutions showed a positive temperature coefficient of Aiso.57,58 These observations were explained by out-of-plane vibration of the oxygen with respect to the planar nitrogen containing moiety. Moreover, ab initio and density functional calculations show that the angle between the NO bond and the plane of the attached five-membered ring is a very “soft” geometrical parameter, i.e., large changes in this angle lead only to small changes in the total energy.12,59,60 Our present calculations (see below), show a strong dependence of Aiso on this angle. An increased average squared angular deviation from the planar equilibrium geometry at the nitrogen atom with increasing temperature would explain the observed temperature behavior of Aiso. This distortion, however, does not influence the quadrupole values. DFT Calculations. The results of the ORCA DFT calculations of the hyperfine-, quadrupole- and g-tensor principal values are collected in Tables 2 and 3. The results are obtained for six different environmental cases characterized by combinations of (a) with or without H-bridge, (b) vacuum or water as solvent, and (c) with or without electric field Ex ) 0.02 au (see caption of Table 2).

In comparing cases 1 and 2, the superposition of an electric field Ex ) 0.02 au (directed polarity) results in a strong decrease of Qyy and Qzz, whereas Qxx is only weakly affected. The asymmetry parameter η, defined by (Qyy - Qxx)/Qzz, increases from 0.41 to 0.67. Qualitatively, this behavior can be explained as follows. The 14N quadrupole-tensor components can be estimated according to Townes and Dailey by61

QiiTD/Qp ) (3ni - c) ⁄ 2

i ) x, y, z 2piN

(15)

where ni is the electron population on the atomic orbital, c ) Σi ni is the total charge on 14N and Qp ≈ -10 MHz is the quadrupole coupling for one 2pi electron. Values for ni were determined by the semiempirical method PM3, giving nx ) 0.937, ny ) 0.906, nz ) 1.403, c ) 3.246 for Ex ) 0 and nx ) 0.927, ny ) 0.945, nz ) 1.327, c ) 3.199 for Ex ) 0.02 au. Although these values give only a rather poor quantitative agreement of QiiTD with the ORCA results in Table 2 (the validity of eq 15 is restricted to almost uncharged atoms around the 14N atom; this is not fulfilled in the R1-14N radical where the large negative charge on the O atom contributes considerably to Qii of 14N), we deduce the following qualitative trends of electron redistribution under the influence of an electric field: The electron population nx and the sum c ) Σi ni are only weakly affected by the electric field. However, there is a strong charge depletion on 2pzN (accompanied by an increase of spin density) of about 0.07 unit charges. Because of the approximate charge preservation on N (c ≈ constant) a large part of this charge loss is compensated by a charge increase on 2pyN. This gives a smaller absolute value of 3ny - c and, therefore, also of Qyy. The relatively weak dependence of nx on Ex can be explained by the strong σ-bond interaction involving the orbital 2pxN between N and O. The addition of one water molecule forming an H-bond with the O-atom of the R1 NO bond has a similar, though weaker effect on Qii as the electric field with Ex ) 0.02 au. Its effect appears to be almost equivalent to that of Ex ) 0.01 au. The same can be stated for the behavior of Aii and gii (Tables 2 and 3). The dielectric properties of a surrounding aqueous solvent (ε ) 80) act similarly to the H-bond effect. As expected, corresponding shifts are amplified by the addition of the H-bond and by the superimposed electric field Ex.. The calculated values of Aii, Aiso and gii need no further discussion. Their dependence on H-bonding and on Ex is quite regular; it has already been discussed in a previous publication 12. Attention has to be given to the dependence of A , A , and xx yy gxx on special structural features of the NO spin label. These magnetic parameters depend rather strongly on the out-of-plane angle R of the NO-bond with respect to the adjacent fivemembered plane. This angle is a comparatively “soft” geometrical parameter, and out-of-plane vibrations have been found responsible for the temperature dependence of isotropic hyperfine coupling constants in liquid solution;57,58 see above. We


Savitsky et al.

Figure 6. (a) Comparison of the experimental W-band cw EPR spectra of 1 mM R1-14N nitroxide radicals in frozen solutions of ortho-terphenyl (lower trace) and glycerol (upper trace), taken at 180 K. The asterisk marks the nonpolar component in glycerol solution. (b) Frequency-field dependence of the experimental three-pulse stimulated ESEEM of 1 mM R1-14N/glycerol glass at 180 K in the gxx, gyy regions. Beyond the gyy region no nuclear modulations due to 14N are observed. The contour lines are shown as isohypses from 0.05 to 1 of the maximum FT ESEEM intensity.

have calculated the hyperfine-, quadrupole- and g-tensors as a function of the angle R in the range 0 E R E 20°. These calculations were of the same type as for the planar molecule and resulted in a considerable increase of Axx and Ayy up to 10 MHz and of gxx up to 4 × 10-4. This is in a good agreement with a recent theoretical study.60 Changes with the angle R in j and gj are smaller or even negliall other components of A j are below 50 gible. Changes in the Qxx, Qyy components of Q kHz. These results are consistent with our experimental observations in all details (Vide infra). For the strict planar case, R ) 0, the principal axes of all j , and Q j are clearly collinear for symmetry three tensors gj , A reasons (if neglecting the influence of the very remote side groups of the nitroxide central ring). This is confirmed by DFT calculations including all atoms. Even for values R up to ( 15° this collinearity is retained since the principal axes x and z of all three tensors follow the direction of the NO bond. Moreover, the joint analysis of experimental cw EPR and ESEEM spectra allow to estimate the maximum possible deviation from collinearity to be within 2°. Polar/Protic Environment. In order to prove the theoretical predictions, we have examined the R1-14N nitroxide in glassy glycerol solution which emulates the polar/protic protein environment. Figure 6a shows the comparison of cw EPR spectra of R1-14N in frozen solutions of ortho-terphenyl and glycerol, recorded at 180 K. As expected, the change from the nonpolar to a polar/protic environment produces clearly observable shifts in both gxx and Azz. The Azz value increases from 93.2 to 101.4 MHz by 8.2 MHz and the gxx value decreases from 2.00905 to 2.00841 by 6.4 × 10-4, which is in a good agreement with previous results.12 The analysis of the spectrum in glycerol shows slightly increased EPR linewidths in the y and z regions, see Table 1. However, the line width of the gxx component is practically doubled in the glycerol compared to the ortho-terphenyl solution. The increase of the gxx line width reflects the variation of the local polarity/proticity situations in glassy glycerol, which leads to a static distribution of the gxx values producing so-called g-strain. Moreover, a second gxx component with the overall weight of about 15% is present in glycerol solution, see the asterisk-marked region in Figure 6a.

The relative weight as well as the shape of this component was proven to be independent of the freezing protocol of the sample, i.e., slow cooling or shock freezing. The gxx value of this component is roughly equal to that in ortho-terphenyl showing that the nitroxide radicals are partially exposed to a nonpolar local environment in glycerol glass. Figure 6b shows the experimental ESEEM spectrum of 1R-14N in glycerol at 180 K. Similar to ortho-terphenyl solution, Figure 5a, the spectrum is dominated by the contribution from 14N nuclear modulations. However, the ratio of 2H to 14N lines increases in favor of the 2H modulations due to the increased of EPR line width, especially in the x spectral region. The Axx and Ayy values of 14.7 and 14.7 MHz are read out from the positions of the terminal peaks in the ESEEM spectrum. These values are higher compared to the ortho-terphenyl solution, which is in agreement with the theoretical prediction, see Table 2. The absolute values of the quadrupole couplings [Qxx; Qyy] ) [1.23; 0.36] MHz are obtained from the positions of the ESEEM peaks around 18 MHz. Thus, the Qxx value in polar/protic environment does not reveal a significant variation compared to the nonpolar case. The Qyy value, however, decreases by 0.17 MHz in agreement with DFT calculations; see Table 1 and 2. The analysis of the ESEEM spectrum recorded at 90 K yields the quadrupole couplings [Qxx; Qyy] ) [1.24; 0.37] MHz, thus revealing the temperature independence of the quadrupole parameters also in the polar/protic case. At 90 K the 14N hyperfine splittings of [Axx; Ayy; Azz] ) [13.4; 13.5; 101.7] MHz were obtained from the combined analysis of cw EPR and ESEEM spectra. Thus, when going from 180 to 90 K, the isotropic hyperfine contribution, Aiso, decreases from 43.6 to 42.9 MHz. The similar Aiso temperature variation in glycerol (0.7 MHz) and ortho-terphenyl (0.8 MHz) strongly supports the out-of-plane vibration mechanism to be responsible for these changes. 4. Conclusions Sensitivity of Q-Values to Environmental Effects. Our theoretical and experimental results (Table 1 and 2) show that Qyy has the strongest dependence on different environmental situations compared with Qxx and Qzz. This is essentially

Nitrogen Quadrupole Interaction of Nitroxide Spin Labels different to the behavior of the g- and A-tensors, where changes dominate along the other two axes, x and z, respectively. This difference, for which a qualitative explanation has been given in the preceding paragraph, introduces some interesting new aspects for probing environmental effects The dependence of Qyy on environmental effects is at least as strong as for Azz. For example, if looking at the relative changes of Qyy by a superimposed electric field Ex as polarity parameter, we obtain

dQyy ⁄ Qyy ≈ 0.37 ⁄ 0.01 au dEx The corresponding quantity for Azz amounts only to 0.06 for 0.01 au (an electric field of 0.02 atomic units corresponds to 0.5 V/Å; in proteins typically E ≈ 0.01 au12), thus being less favored in sensitivity by a factor of 6. On the other hand, the polarity detection limit Emin, defined by the minimum detectable electric field Ex, is less favorable for Qyy than for Azz. In fact, taking ∆νQ ) 30 kHz and ∆νA ) 200 kHz as resolution limits, from

Emin(P) )

dEx · ∆νp dP

(P ) Qyy, Azz)

we get Emin (Qyy) ) 0.002 au, and Emin(Azz) ) 0.0004 au. Dependence of Q-Values on Changes of the Out-of-Plane Angle r. As is known from earlier publications57–60 and as will be treated in more detail in our forthcoming paper, quantumchemical molecular orbital methods at different levels generally predict a significant dependence of the 14N isotropic hyperfine coupling constant Aiso on the out-of-plane or “tilt”-angle R of the NO bond. In NO spin labels of the pyrroline-type studied here, the reference plane is meant to be the plane of the adjacent five-membered ring. This tilt angle R is a very “soft” structural parameter, requiring only very weak external disturbing forces to produce large angles of up to 15° (the required energy is 0.84 kcal/mol ) 2 · kT at 200 K). The consequences for Azz, which is given by the sum of the Fermi contact contribution Aiso and classical dipolar contributions, can be quite dramatic. In the presently studied spin label R1, DFT methods predict a change of 4 MHz for R ) 15°. Since R can be affected by thermally excited vibrations, spatial crowding effects and hydrogen bonding to the oxygen atom (e.g., inside a locally rigid hydrogen-bond network), Azz can become temperature dependent as well as dependent on environmental effects in an unpredictable way. Such structural ambiguities can, in special situations, question the reliability of the NO spin label as a polarity probe. The same holds true for the value of gxx although there the dependence on R is not quite as pronounced as for Azz. In contrast to Azz and gxx, the value of Qyy is predicted, and experimentally verified, to be practically independent of R, varying by at most 0.04 MHz between R ) 0° and R ) 15°. This variation is close to the measuring error of 30 kHz. The other two components Qxx and Qzz show a similarly weak dependence on R. More details on these results will be given in a subsequent paper. It should be pointed out that even for the larger values of R (e15°) the A- and g-tensors remain collinear since their principal axes follow the direction of the NO bond. The same holds true for the Q-tensor. Thus, measurement of Qyy can already, in itself, provide very important contributions to the study of environmental effects or, additionally, serve as a consistency check for polarity and/

J. Phys. Chem. B, Vol. 112, No. 30, 2008 9089 or proticity results obtained from the often employed gxx versus Azz correlation. Differentiation between Polarity and Proticity Effects. Polarity effects from intermolecular electric fields have been widely investigated by observing shifts of Azz and/or gxx on NO spin labels in various environments. Whereas Azz reacts to polarity changes in nonbonding as well as H-bonding situations predominantly through changes in the spin density distribution of the NO bond (as a consequence of charge displacements between N and O), gxx is also significantly affected by additional perturbations of the n-π energy gap of the O-atom 12 in H-bonding situations. Thus, the observation of gxx shifts may be desirable for the detection of H-bond formation (proticity), but can also lead to ambiguous results in trying to separate proticity from pure polarity effects quantitatively. If measurement of Azz alone does not safely yield the desired information on polarity changes, because of reasons given above, measurement of Qyy is therefore the appropriate choice. Qualitatively, Qyy has the same probing properties as Azz in detecting polarity and proticity effects. However, apart from its relative insensitivity to structural and temperature variations, this parameter is exclusively dependent on the electronic charge distribution of the NO bond and, therefore, particularly qualified for polarity studies in nonbonding as well as H-bonding situations. A theoretical manifestation of this behavior can be deduced from Table 2. Two by plotting Qyy against Azz for the cases 1 (in Vacuo), 2 (with electric field), and 3 (with H-bond). This plot yields a straight line inspite of the inclusion of the H-bond. This linear relation between Qyy and Azz is a consequence of the linear relation (to first order) between charge and spin densities and of the fact that direct energetic contributions from changes in the n-π excitation energy (Vide supra) are absent. Finally, collecting all above arguments, it appears justified to state that in NO spin-label studies of the microenvironment of reactants in proteins the measurement of Qyy can provide important additional information on polarity effects. This information is complimentary to that obtained by measurements of gxx and Azz. This statement is supported by our preliminary results on R1-14N nitroxide in different glassy solutions. The polarity and proticity sensitivity of the quadrupole parameters is not only in good agreement with theoretical predictions described here, but certainly will allow to distinguish and characterize a multiple heterogeneous local environment of a nitroxide radical in glassy alcohol solutions.17,62 Acknowledgment. We gratefully acknowledge financial support by the Deutsche Forschungsgemeinschaft in the frame of the Priority Program SPP 1051 (“High-field EPR in Biology, Chemistry and Physics”), the Collaborative Research Center SFB 498 (“Protein-Cofactor Interactions in Biological Processes”) and the Group Project MO 132/19-2 (“Protein Action Observed by Advanced EPR”). Y.A.G. is thankful for financial support by Russian Foundation for Basic Reaseach, Grant 0603-040020-HHIO, and A.A.D thanks the Program 1-OHNM of the Russian Academy of Sciences. Supporting Information Available: Conversion procedure of the time domain data to the frequency domain; estimation of experimental accuracy; results of optimization of the 3-pulse ESEEM experimental settings; determination of the sign of the quadrupole values. This material is available free of charge Via the Internet at http://pubs.acs.org.

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JP711640P

High-Field EPR and ESEEM Investigation of the Nitrogen Quadrupole

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