## Abstract

The function of biomolecules is intrinsically linked to their structure and the complexes they form during function. Techniques for the determination of structures and dynamics of these nanometre assemblies are therefore important for an understanding on the molecular level. PELDOR (pulsed electron–electron double resonance) is a pulsed EPR method that can be used to reliably and precisely measure distances in the range 1.5–8 nm, to unravel orientations and to determine the number of monomers in complexes. In conjunction with site-directed spin labelling, it can be applied to biomolecules of all sizes in aqueous solutions or membranes. PELDOR is therefore complementary to the methods of X-ray crystallography, NMR and FRET (fluorescence resonance energy transfer) and is becoming a powerful method for structural determination of biomolecules. In the present review, the methods of PELDOR are discussed and examples where PELDOR has been used to obtain structural information on biomolecules are summarized.

- biomolecular complex
- double electron–electron resonance (DEER)
- electron paramagnetic resonance (EPR)
- pulsed electron–electron double resonance (PELDOR)
- spin labelling

## Introduction

The function of biomolecules is associated with their structure, the complexes that they form and the conformational changes that they undergo during function. For example, the eukaryotic TFIIH (transcription factor IIH) [1] and its analogue in archaea are multicomponent complexes that include also highly mechanical helicases. Since mutations in the proteins of the TFIIH complex lead to severe diseases [2], unravelling the structures and interactions of the individual components is an important step for a molecular understanding of these diseases and ultimately in the developments of new medicinal drugs [3]. Biophysical methods provide powerful tools to access these structures on length scale from angstrom (1 Å=0.1 nm) up to nanometre distances and their dynamics on timescales ranging from picoseconds to minutes. Of these methods, X-ray crystallography [4] and NMR [5] are capable of producing three-dimensional structures with resolution on the atomic scale. Yet obtaining good quality crystals and high-resolution structures can be arduous or even not possible. It should also be kept in mind that structures derived from X-ray crystallography represent a low-energy conformation of the biomolecule in the solid state, which can hamper the mechanistic understanding of dynamic systems. NMR can be performed on biomolecules in solution yielding atomistic structures and dynamics, but this becomes difficult for molecules exceeding ~50 kDa. EPR [6] has no such size restriction, can be applied to biomolecules in solution and yields atomistic resolution on a local scale, which makes it complementary to X-ray crystallography and NMR. In addition, it provides methods such as PELDOR (pulsed electron–electron double resonance) for long-range distance measurements of up to 8 nm and is thus also complementary to FRET (fluorescence resonance energy transfer) [7]. Whereas FRET can be applied on the single-molecule level and in liquid solution (giving access to real-time dynamics), PELDOR is applied in frozen solution and at micromolar concentrations. However, the distances obtained with PELDOR are precise within 1 Å, coupling mechanisms are easily separated, orientations are resolved in a two-dimensional version of PELDOR and dynamics/conformational states are accessible via ensemble distributions. PELDOR-based distance measurements rely on the measurement of the dipolar interaction between two paramagnetic centres. In biomolecules, these paramagnetic centres can either be metal ions [8,9], metal clusters [10,11], organic cofactors [12,13], amino acid radicals [14], or, if the biomolecule is intrinsically diamagnetic, artificially attached spin labels. With a set of long-range distance constraints, structures can be derived in conjunction with, e.g., molecular dynamics simulations [15–17], NMR methods [18–20] or X-ray crystallographic structures [8,21]. In particular, the combination of SDSL (site-directed spin labelling) with PELDOR emerged as a powerful strategy to obtain structures and dynamics of biomolecules. The present review briefly describes the dipolar coupling and the PELDOR method as such and then outlines how the different types of information can be gathered using biological systems as examples.

## Spin labels and spin labelling

The site-specific incorporation of unpaired electrons into organic molecules in the form of spin labels is known as SDSL. Nitroxides, which are stable free organic radicals [22], are the most widely used spin labels. They are not only applicable to distance measurements with continuous-wave or pulsed EPR techniques, but also have EPR parameters that report on the dynamics of the spin-labelled biomolecule [23] and the polarity [24] and oxygen concentration [25] of the surroundings. Other examples of spin centres that have been used for labelling of biomolecules, are copper(II) [26], manganese(II) [9,27] and gadolinium(III) complexes [28–30]. For proteins, the most commonly used spin label is MTSSL [(1-oxyl-2,2,5,5-tetramethylpyrroline-3-methyl)-methanethiosulfonate] (Figure 1), which specifically reacts with the thiol group of cysteine residues, forming a disulfide bridge. By introducing cysteine residues to sites of interest via mutagenesis and subsequently allowing them to react with MTSSL, the nitroxide spin label can be positioned with high specificity and ease [31,32]. The resulting three-atom linker connecting the five-membered nitroxide ring with the protein backbone introduces some degree of flexibility independent of the biomolecule. This problem can be overcome by using spin-labelled amino acid analogues [33], which are rigid. Two examples for these are TOAC (2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid) [34] and POAC (2,2,5,5-tetramethylpirrolidine-1-oxyl-3-amino-4-carboxylic acid) [35] (Figure 1). However, these labels cannot be easily attached to a complete protein, but have to be incorporated into a peptide sequence during the synthesis of the peptide and the labelled peptide may then be fused on to the rest of the protein.

SDSL of nucleic acids has been performed with various nitroxide spin labels (Figure 2). Nitroxide spin labels have been covalently attached to the phosphate backbone [36,37] (spin label **1** in Figure 2), sugar moieties [38,39] (spin label **2** in Figure 2) or nucleobases [15,40–42] (spin labels **3**–**5** in Figure 2). The two leading methods of incorporating spin labels to nucleic acids are: (i) chemical synthesis of a spin-labelled nucleoside and incorporation of its phosphoramidite into the oligomer during chemical synthesis of the nucleic acid; and (ii) synthesis of nucleic acids with modified nucleotides and subsequent reaction of these with a complementary functionalized nitroxide. This method is known as post-synthetic spin labelling. Since DNAs and RNAs with modified nucleotides and most of the spin label reagents are commercially available, post-synthetic spin labelling is a more facile method. As in the case of MTSSL, the analysis of dynamics and distances between spin labels is complicated by any flexibility of the spin label independent of the nucleic acid [43,44]. With the invention of the rigid spin label **Ç** (spin label **6** in Figure 2), this problem has now also been solved for nucleic acids. This label is a modified cytidine fused with a nitroxide isoindol moiety, which forms a Watson–Crick base pair with an opposing guanine. Incorporation of **Ç** into nucleic acids yields a spin label with negligible flexibility [45,46]. To eliminate the laborious chemical synthesis steps of incorporating **Ç** into nucleic acids, the rigid spin label **ç** (spin label **7** in Figure 2) has been site-specifically incorporated into DNA abasic sites through non-covalent interactions. CW (continuous wave)-EPR measurements have shown complete binding of the **ç** spin label to abasic sites opposite guanine [47].

## Dipolar coupling

In the case of a biomolecule containing two unpaired electrons, their spin magnetic moments interact through space by means of the anisotropic electron spin dipole–dipole interaction [48–50]. The electron dipole–dipole coupling between a pair of unpaired electrons, A and B which are separated by the distance *r* is described by the Hamiltonian (eqn 1) [49]:
(1)
where Ŝ_{A} and Ŝ_{B} are the spin operators, and g_{A} and g_{B} are the g-values for spin A and B respectively. μ_{0} is the permeability of vacuum and ℏ is the reduced Planck constant. Expanding eqn (1) and expressing the orientation of the interspin tensor in spherical co-ordinates, the Hamiltonian for the dipole–dipole interaction between two unpaired electrons becomes eqn (2):
(2)
where

If the dipole–dipole coupling is small compared with the resonance difference between the two uncoupled spins A and B, ω_{dip}<<|ω_{A}−ω_{B}|, only the first term in eqn (2) needs to be considered. The frequency, ω_{dip}, of the dipole–dipole interaction is then described by eqn (3):
(3)
where θ is the angle between the vector that connects the two spin centres and the static magnetic field. Furthermore, it is assumed that the paramagnetic centres can be described by the point-dipole approximation [51] which assumes that the unpaired spin delocalization is small compared with the distance between the two spin centres. In cases where the spin density is delocalized over several centres, the point-dipole approximation is no longer valid and the dipole–dipole interaction tensor has to be calculated considering the interaction between each pair of spin-bearing atoms (eqn 4):
(4)
where δ* _{ij}* is the Kronecker delta,

*m*and

*n*are the atoms carrying spin density at the A and B spin centres respectively. ρ is the spin density,

*r*

_{mn}is the distance between the

*m*and

*n*atoms and

*r*

_{mni}and

*r*

_{mnj}are the

*i*and

*j*components of these interatomic distance vectors in the molecular frame of the A spins [52].

If the resonance difference between the two spins is less than the dipole–dipole coupling, ω_{dip}> >|ω_{A}−ω_{B}|, the first two terms in eqn (2) have to be included and eqn (3) becomes eqn (5):
(5)

For molecules in solution with a fast rotational correlation time compared with the inverse dipolar frequency between two paramagnetic centres, the dipole–dipole interaction (eqn 3) will be averaged to zero [6]. For this reason, aqueous samples have to be frozen into glass for PELDOR measurements.

The dipolar coupling leads to a splitting of the resonance lines of the two unpaired electrons. If the coupling is strong, the splitting can be observed in a CW-EPR experiment. However, if the coupling becomes smaller than the line width of the paramagnetic centre, it will not be resolved. For nitroxides and at conventional X-band frequencies, the upper limit is at ~2 nm [53–55]. For larger distances, the dipole–dipole splitting can no longer be resolved and pulsed EPR techniques that are able to recover the dipole–dipole interaction have to be used. A pulsed EPR technique that has successfully been applied to distance measurements on biomolecules is PELDOR.

## PELDOR

PELDOR, also known as DEER (double electron–electron resonance), is a pulsed EPR method that is capable of measuring distances in the range 1.5–8 nm [56,57]. The method separates the electron dipole–dipole interaction from hyperfine interactions and g-anisotropy. This is achieved by using two microwave sources with different frequencies and no phase correlation between them and by keeping the timings of the detection sequence fixed. Expanding the original three-pulse version of PELDOR [56,58] into the four-pulse PELDOR experiment [59,60] made PELDOR dead-time-free (Figure 3).

Microwave pulses applied at frequency ν_{A} are denoted as detection pulses, and the pulse applied at frequency ν_{B} is the inversion pulse. The first detection pulse (flip angle=π/2) at time *t*=0 flips a resonant spin packet (A spins) to the *xy* plane where the magnetic moments start to process around the *z*-axis in the *xy* plane with different angular frequencies. The second detection pulse at time *t*=τ_{1} (flip angle=π) reverses the dephasing of the magnetic moments and creates the spin echo at time *t*=2τ_{1}. The fourth pulse (flip angle=π) at time *t*=2τ_{1}+τ_{2} reverses the A spins to create a refocused echo at time *t*=2τ_{1}+2τ_{2}. The third pulse (flip angle=π), or the inversion pulse, at time *t*=*T* inverts the spin magnetic moments of a different resonant spin packet (B spins). The A spins that are coupled via dipolar interaction with the B spins will upon inversion of the B spins process with the opposite direction in the *xy* plane. The inversion of the coupled A spins during the time evolution of the A spins will affect the intensity of the refocused echo at time *t*=2τ_{1}+2τ_{2}. As the time position of the inversion pulse is incremented between the times *T*>τ_{1} to *T* <2τ_{1}+τ_{2}, the refocused echo is modulated by the dipole–dipole frequency and its intensity is expressed by eqn (6) [60]:
(6)

Recording the refocused echo as a function of *T*, a time trace is acquired that oscillates with the dipole–dipole frequency, ω_{dip}(*r*,θ). When the oscillation has damped, the refocused echo intensity is expressed by 1−Δ, where Δ is the modulation depth [61–63] (Figure 4a). Fourier-transforming the time trace yields a spectrum in frequency domain with sharp peaks at ± ω_{dip} and edges at ± 2ω_{dip}, which correspond to 90° and 0° respectively for the angle θ between the dipolar distance vector and the applied magnetic field (Figure 4b) [6,61].

Considering a single isolated pair of spins, the observed PELDOR signal *V*_{intra} is expressed by eqn (7) [52,64]:
(7)
where *V*_{0} is the PELDOR signal at *T*=0 and λ_{B} is the probability that the coupled B spin will be in resonance with the inversion pulse. If the two spins have angular correlations then λ_{B} will depend on the orientation of the interspin vector **r** relative to the magnetic field **B _{0}**.

In a sample of randomly oriented molecules with two paramagnetic centres, one has to take into account contributions from dipole–dipole interactions between spin centres on the same molecule (intramolecular) and between spin centres on different molecules (intermolecular). The PELDOR signal is therefore expressed by a product of these two interactions, *V*(*T*)=*V*_{intra}(*T*)*V*_{inter}(*T*) [64].

The intermolecular part of the PELDOR signal, *V*_{inter}(*T*), can be derived considering dipolar coupling between randomly distributed spin centres (eqn 8):
(8)

The index *i* refers to the B spins and the <…> represent averaging over all dipolar angles θ and distances between spin centres. γ is the electron gyromagnetic ratio and *C* is the spin concentration in mol·m^{−3}. The broad distribution of interspin distances and hence dipole–dipole couplings results in a spin echo signal that decays exponentially (eqn 8) [57,64]. Thus the intermolecular contribution can be separated by dividing the PELDOR signal by a monoexponential decay fitted to the last part of the PELDOR time trace where all intramolecular modulation is damped.

Considering a sample of randomly oriented biradicals, where correlation between the orientation of the spin centres and the interspin orientation can be neglected, the orientations of the interspin vector will be random and the field orientation-dependence of the modulation depth parameter λ_{B} will be averaged. The intramolecular PELDOR signal *V*_{intra} for a disordered biradical powder sample can then be obtained by integrating eqn (7) over the angle θ (eqn 9):
(9)

For systems with one well-defined distance, Fourier transformation of the resulting *V*_{intra} yields a dipolar spectrum where the interspin distance can be read from the peaks at ± ω_{dip} (Figure 4b). If there is a distribution in the distance between spin centres, the distance distribution can be determined by fitting the PELDOR time trace using mathematical algorithms that are numerically stable [65]. If no correlation exists between the orientations of the spin centres relative to the interspin vector **r**, *V*_{intra} is expressed by eqn (10):
(10)
where *P*(*r*) is a distance distribution, and *K*(*T*,*r*) is the kernel function given by eqn (11) [65]:
(11)

An algorithm that reliably solves *P*(*r*) from eqn (10) by fitting the experimental dipolar time evolution function is Tikhonov regularization, which is implemented into the software package DeerAnalysis [66].

Numerous applications of PELDOR to measure distances on biomolecules can be found in the literature. One of the early examples is the development of a PELDOR-based nanometer oligonucleotide distance ruler [15,17] (Figure 5). A series of six duplex DNAs and RNAs were doubly spin-labelled with TPA (2,2,5,5-tetramethylpyrrolin-1-oxyl-3-acetylene), spin label **3** in Figure 2, and the distance between the nitroxide spin labels was measured with four-pulse PELDOR. The distances measured were in good agreement with distances obtained from molecular dynamics simulations. Comparison of the distances obtained from RNA showed that the A- and B-forms of the duplexes can be distinguished.

Sicoli et al. [67] followed recently the interconversion of two complementary RNA hairpins into an extended duplex in dependence of the ratio of the two hairpins. They found complete conversion into the duplex at a hairpin ratio of 1:1.5 [67].

Beyond mere duplexes, PELDOR has been used to probe the conformational rearrangement of the neomycin-responsive riboswitch upon binding of neomycin B [68]. From the distance measurements, it was concluded that the riboswitch binds to the ligand without considerable global rearrangements. On the protein side, the folding mechanism of the integral membrane protein LHCII (light-harvesting complex II) has been monitored by site-specifically spin labelling recombinant LHCII (Figure 6) and measuring the distance between different domains with PELDOR. Using rapid freeze–quench, the folding of LHCII was determined to occur in two steps: the first within less than 1 min and the second over several minutes [69].

With the ETF (electron-transfer flavoprotein) from *Paracoccus denitrificans*, it has been shown that one can also use an intrinsic organic cofactor for PELDOR measurements. In the case of ETF, reduced FAD has been used. The distance distribution obtained from PELDOR measurement between the native FAD and the single spin label MTSSL showed two peaks: a major peak at 4.2 nm, which agreed with the inferred distance obtained from a crystal structure of ETF in the closed form and a smaller peak at 5.1 nm, which was proposed to represent an intermediate conformation between substrate-free and substrate-bound ETF [70].

### Orientation selectivity

In the case of angular correlations between the spin centres, λ_{B} will depend on the relative orientation of the spin centres. The dipolar angles θ contributing to the PELDOR signal will depend on the excitation of spins A and B and hence the positions of the microwave pulses. The equation for the intramolecular PELDOR signal for this case becomes more complex and is expressed by eqn (12) [71]:
(12)

Since the extraction of reliable distances and distance distributions from the dipolar evolution function via the Deer Analysis program is not valid for spin centres with angular correlations, the experimental PELDOR time traces have to be simulated. Generating spin-pair conformations from a geometric model and calculating the dipolar contribution for each pair using eqn (7), the PELDOR dipolar evolution function can be simulated. Fitting the simulation to the experimental time trace distances, distance distributions and the mutual orientation of spin centres can be determined.

SDSL of DNA duplexes using the rigid spin label **Ç** permitted the determination of both distances and relative orientations of the spin labels by PELDOR measurements at X-band frequencies [72] (Figure 7).

PELDOR measurements on the tetrameric K^{+} ion channel KcsA demonstrated angular correlations between nitroxide spin labels and allowed the separation of distance and orientation from the time traces (Figure 8). It was observed that the positions and orientation of spin labels remained identical in both detergent and membrane-reconstituted proteins [73].

One of the first PELDOR measurements used to resolve orientations were performed on the ribonucleotide reductase from *Escherichia coli* and mouse (Figure 9). The measurements were performed at 180 GHz and enabled the determination of the orientation of the two tyrosyl radicals. Analysis of the orientational selective PELDOR time traces showed the structure of the homodimeric protein in solution and crystal to be nearly identical and the tyrosyl biradical to be almost symmetrical [14,74].

### Exchange coupling

For a pair of paramagnetic centres in a molecule, there is the possibility of exchange interaction between the unpaired electrons either through bonds or overlap of the electron wave functions. In the case of exchange coupling, the interaction between two unpaired electrons is given by the Hamiltonian *Ĥ*_{AB}=**S**_{A}DS_{B}+**S**_{A}**S**_{B}J, where D and J are the anisotropic dipole–dipole coupling tensor and the isotropic electron–electron exchange constant respectively [50]. The interaction between two unpaired electrons A and B is then described by eqn (13):
(13)

PELDOR has been used successfully to separate the contribution of exchange coupling from the dipole–dipole coupling and determine the sign and magnitude of the exchange-coupling constant in biradical model systems with conjugated bonds between spin centres [50,75].

To date, there are no examples in the literature where a contribution from an exchange-coupling constant had to be taken into account for the analysis of PELDOR data from a biomolecule because the distances are too large and the paramagnetic centres are not connected via conjugated bridges. However, exchange coupling can occur in biological systems, as shown recently for two stacked Cu(II)–salen complexes inside a DNA double helix (Figure 10). Temperature-dependent CW-EPR measurements of the exchange coupling between the two paramagnetic centres inside the DNA helix revealed an antiferromagnetic exchange coupling constant, J_{average}, of −11.2 ± 1.0 cm^{−1}, in agreement with theoretical predictions [76].

A second example is the CW-EPR study of the secondary structure of hexameric β-peptide foldamers using POAC as the spin label (Figure 11). The strength of the exchange coupling and the distances between spin labels confirmed the β-peptides to adopt a 12-helix conformation [35].

### Counting the number of interacting spins

For molecules containing *n* identical spin centres with no mutual angular correlation, the intensity of the intramolecular PELDOR signal is given by eqn (14) [63]:
(14)

It can be derived from eqn (14) that, when all modulation is damped, *V*_{intra} will reach a constant value of *V*_{λ}, which can be expressed by eqn (15):
(15)

Rearranging eqn (15) into eqn (16):
(16)
shows that by determining *V*_{λ} from a PELDOR experiment one can derive the number (*n*) of interacting spins in a cluster if one knows λ_{B}, and λ_{B} can be experimentally determined from a model biradical system. If the sample contains a mixture of oligomers with different number of interacting spins, the resulting PELDOR signal is the weighted sum of *V*_{λ} values from each oligomer. The limiting value of *V*_{intra} is then given by eqn (17):
(17)
where *s*_{i} is a scaling factor that accounts for differing transversal relaxation in oligomers *i*, and *x _{i}* is the fraction of oligomer

*i*in the mixture [61]. The method of PELDOR can therefore be used to determine the number of spins on a molecule and the fraction of clusters with different numbers of spin centres in a mixture [61]. The following examples demonstrate the use of PELDOR and spin-counting on biological samples. Using SDSL and PELDOR, the structure of the octameric outer-membrane protein Wza from

*E. coli*was assessed. Not only did measured distances between monomers agree well with distances deduced from crystal structure, but also the octameric state of the proteins was confirmed [21].

The modulation depth in PELDOR experiments has also been used to determine the fractions of monomers and dimers of human and rat monoamine oxidases both in outer mitochondrial membranes and octyl β-D-glucopyranoside micelles. The study showed that both monoamine oxidases form nearly 100% dimers in the membrane, but a 1:1 ratio of monomers and dimers in micelles [77].

Also the pH-dependent dimerization of the membrane protein NhaA Na^{+}/H^{+} antiporter of *E. coli* has been derived from the modulation depth of PELDOR time traces. It was verified that the singly spin-labelled mutant of NhaA H255R1 existed in a monomer/dimer equilibrium, with the fraction of dimers increasing from 0.6 to 1 as the pH increased from 5.8 to 8 [78].

### Metal centres

In addition to free organic radicals, paramagnetic metal centres have been used as spin probes for PELDOR measurements. Usually, these centres have short relaxation times, broad spectral widths and show delocalization of spin density. Yet, PELDOR experiments can still be performed and the data successfully analysed. One of the metal centres studied thoroughly is copper(II). Despite the fact that co-ordinated copper(II) has a large g-anisotropy and delocalized spin density, distance measurements not only on copper–nitroxide model systems [52,79,80], but also between two copper centres in biomolecules [81,82], have been performed successfully. Other examples of intrinsic metal centres in biomolecules that have been used as spin probes in PELDOR experiments are Fe–S clusters and nickel [10,83]. Currently, the application of co-ordinated Gd^{3+} ions as spin labels are being explored. The Gd^{3+} ion is a high-spin system (*S*=7/2) for which the Δ*m*_{3}=±1/2 transition can be selected at higher frequencies, e.g. 95 GHz [29]. Distance measurements between Gd^{3+} ions, attached to proteins and model systems have shown that Gd^{3+} can function as a spin label that is complementary to nitroxides [28,30]. Advantage of the gadolinium system is the localized spin density, the single line spectrum and the high-sensitivity.

## Conclusions

During the last decade, PELDOR evolved as a powerful tool to determine structures in complex biomolecules and its precession made it a suitable tool to follow even small conformational changes. Recently, a new EPR spectrometer has been developed that operates at high fields/high frequencies and with high microwave powers which allowed to reduce the sample concentration for PELDOR experiments down to 1 μM or even lower [84]. This opens up new areas for PELDOR measurements on biomolecular complexes not accessible before.

## Funding

This work was supported by the Biotechnology and Biological Sciences Research Council [grant numbers BB/H017917/1 and F004583/1]. O.S. thanks the Research Councils UK for a fellowship and G.W.R. thanks the School of Biology, University of St Andrews for a SORS (Scottish Overseas Research Students) Scholarship.

## Footnotes

Molecular Biology of Archaea II: A Biochemical Society Focused Meeting held at Robinson College, Cambridge, U.K., 16–18 August 2010. Organized and Edited by Stephen Bell (Oxford, U.K.) and Finn Werner (University College London, U.K.).

**Abbreviations:**
CW, continuous wave;
ETF, electron-transfer flavoprotein;
FRET, fluorescence resonance energy transfer;
LHCII, light-harvesting complex II;
MTSSL, (1-oxyl-2,2,5,5-tetramethylpyrroline-3-methyl)methanethiosulfonate;
PELDOR, pulsed electron–electron double resonance;
POAC, 2,2,5,5-tetramethylpirrolidine-1-oxyl-3-amino-4-carboxylic acid;
SDSL, site-directed spin labelling;
TFIIH, transcription factor IIH;
TOAC, 2,2,6,6-tetramethylpiperidine-1-oxyl-4-amino-4-carboxylic acid

- © The Authors Journal compilation © 2011 Biochemical Society