Spin pair geometry revealed by high-field DEER in the presence of conformational distributions
Introduction
Magnetic resonance spectroscopy is one of only a few techniques that can reveal detailed structural information on matter that lacks long-range order. As many new materials and all functional biological systems belong to this class of samples, development of new approaches for such structure elucidation is an important and constantly evolving field. In particular, pulsed electron paramagnetic resonance [1] combined with site-directed spin labeling [2], [3], [4], [5], [6], [7], [8] is recently finding more and more applications in studies of structure and functionality of synthetic and biomacromolecules, as it nicely complements NMR and scattering techniques with respect to the distance range and requirements on the sample. Distances and distance distributions between fragments of the macromolecule carrying electron spins (nitroxide spin labels, transition metal ion etc.) can be studied with high precision applying double electron–electron resonance (DEER) [9], [10], [11] or double-quantum EPR experiments [12], [13], [14] if the distance between the spins falls within the 1.5–8 nm range. Application examples of DEER include soluble [15], [16], [17], [18] and membrane [19], [20], [21], [22] proteins, ribonucleic acids [23], and peptides [24] as well as nanostructured materials [25], [26], [27], [28], most of them spin-labeled.
Since the first steps made in early 1980s [9], [10] a fundamental theory of that method and sophisticated data analysis approaches have been elaborated [29], [30], [31], [32], [33], [34], [35], [36]. By now it is well understood how to select the pulse sequence and timing, the spin pair concentration, the type of the matrix, and the data analysis procedures to obtain structural information with the highest possible accuracy and reliability. These issues will be discussed in a forthcoming paper.
In the present work we consider the opportunities for obtaining geometric information on the structure of macromolecules beyond the distance distribution by making use of orientation selection [37], [38]—an approach which is strongly aided by performing the DEER experiments at high field [39]. We examine conditions under which such experiments can best be performed with commercial spectrometer hardware. To be applicable to spin-labeled macromolecules, which are almost invariably characterized by a conformational distribution of the nitroxide labels, the approach has to accommodate distributions of the geometric parameters. The modeling of such distributions and their use in the computation of orientation-selected DEER spectra is also discussed.
The paper is organized as follows. A detailed Materials and methods section introduces the model systems, on which the measurements were performed, the set-up of the DEER experiments at high field and the measurement strategy, as well as the basic procedures for structural modeling. The subsequent Theory section starts with a description for the case of an isolated spin pair with a fixed geometrical arrangement and proceeds with the introduction of an averaging procedure that can predict the DEER response for fully geometrically uncorrelated as well as correlated spin pairs and intermediate cases. The Theory section concludes with the presentation of an computationally efficient DEER simulation approach that provides two-dimensional spectra with a dipolar frequency and a magnetic field dimension that are averaged over the distribution of relative geometries of the two paramagnetic centers. Experimental results are presented and compared with theoretical predictions in the Results and Discussions section, and the paper concludes with considerations on the applicability of the approach to spin-labeled biomacromolecules.
Section snippets
Sample preparation
Two model systems with restricted conformational flexibility were used—a shape-persistent nitroxide spin-labeled biradical and a triradical (Fig. 1). Synthesis of the compounds is described in detail elsewhere [40]. Samples were prepared by dissolving approximately 0.1 mg of each compound in 100 mg of perdeuterated o-terphenyl. The deuterated matrix was used to increase the phase memory time Tm of the radicals [33]. Thus longer experimental dipolar evolution times can be achieved, and better
Isolated spin pair with full geometry correlation of the two spins
Theoretical treatment of DEER relies on the concept of the dipolar coupled spin pair. The entire sample is considered as an ensemble of such spin pairs in which individual pairs act together and contribute to the total sample response. DEER experiments at conventional m.w. frequencies (X-band) provide mainly information on the pair correlation function, i.e, on the interspin distance distribution information [31], [32], [35]. Furthermore, information on the spin concentration and possible
Results and Discussions
Characteristic orientation selection effects were clearly observed already by visual inspection of the raw data. Fig. 6A shows background corrected dipolar time domain signals for the biradical taken from the X, Y and Z regions of the nitroxide g-tensor. The dipolar frequency and the modulation depth undergo variations when the observer position is changed. Note that at a dipolar evolution time t as long as 4 μs the signal-to-noise ratio is still acceptable at all orientations, as becomes clear
Conclusions
Orientation selection in high-field DEER causes characteristic magnetic field dependencies of the dipolar frequencies and the modulation depth for compounds with limited but significant structural flexibility, namely a shape-persistent biradical and a shape-persistent triradical with conformationally flexible spin labels. Experimental dipolar data that were obtained for the first time with a commercial power-upgraded W-band spectrometer are in a good accord with simulations based on two
Acknowledgments
The authors thank Herbert Zimmermann for a generous gift of perdeuterated o-terphenyl and SFB 625 of Deutsche Forschungsgemeinschaft for financial support.
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