The Functional Structure of Human Serum Albumin

Abstract

Human serum albumin (HSA) is a versatile transport protein for various endogenous compounds and drugs. This study focuses on its highly relevant transport function for fatty acids in the circulatory system. While extensive crystallographic data on HSA–fatty acid binding exist, a new spectroscopic approach is used to gain information on the functional structure of HSA in solution. Using spin-labeled stearic acid and applying double electron–electron resonance (DEER) spectroscopy, the functional protein structure is accessed for the first time from the ligands’ point of view.

Human serum albumin (HSA) is a versatile transport protein for various endogenous compounds and drugs. This study focuses on its highly relevant transport function for fatty acids in the circulatory system. While extensive crystallographic data on HSA–fatty acid binding exist, a new spectroscopic approach is used to gain information on the functional structure of HSA in solution. Using spin-labeled stearic acid and applying double electron–electron resonance (DEER) spectroscopy, the functional protein structure is accessed for the first time from the ligands’ point of view. Spatial distributions of the anchoring groups and entry points of the fatty acid binding sites are obtained studying fatty acids with different labeling position. While the distribution of the head groups is mainly consistent with the crystallographic data, the entry points of the binding sites are distributed much more homogeneously on the protein surface than suggested by the crystal structure. This symmetric distribution provides a straightforward explanation for the transport function of the protein as it facilitates a fast uptake and release of multiple fatty acids.

3.1 Introduction

Human serum albumin (HSA) is the most abundant protein in human blood plasma and serves as a transporting agent for various endogenous compounds and drug molecules [1, 2]. Especially, its capability to bind and transport multiple fatty acids (FA) has been studied extensively in the past [3, 4]. The research on HSA was severely hampered by the complexity of the protein and benefitted a lot from crystallographic high-resolution structures. Nearly 20 years ago, He and Carter reported the first crystal structure [5]. Up to date, a plentitude of crystal structures has been deposited in the Protein Data Bank.

Due to the pioneering work of Curry et al., crystal structures of various HSA–fatty acid complexes have become accessible allowing new insights into the FA binding properties of the protein [6–8]. In particular, they found that fatty acids are distributed highly asymmetrically in the protein crystal despite the fact that HSA exhibits a symmetric primary and secondary structure. Up to seven distinct binding sites were found for long chain fatty acids, most of which comprised of ionic anchoring units and long, hydrophobic pockets [8, 9]. The location of two to three high affinity binding sites [3, 10] was assigned by correlation of the X-ray structure with NMR studies on competitive binding of drugs replacing ¹³C-labeled fatty acids [11, 12]. Sites 2, 4, and 5 bind fatty acids with a high affinity, while sites 1, 3, 6, and 7 exhibit a somewhat lower affinity to fatty acids (see Fig. 3.1a).

Fig. 3.1

a Crystal structure (PDB 1e7i) of HSA co-crystallized with seven stearic acid molecules [8]. The oxygen atoms of the FA carboxylic acid head groups are displayed in red. b Chemical structure of the EPR active molecules, 5-doxylstearic acid (DSA) and 16-DSA. Reprinted with permission from [65, 66]. Copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim

On a more general note, there is a long standing debate to what extent protein crystal structures reflect the dynamic and functional structures of proteins in solution. This debate is often fueled by apparent discrepancies between X-ray crystallographic data and results from solution-state based techniques (e.g. NMR and other types of spectroscopy as well as neutron scattering) or from molecular dynamics simulations. Moreover, there is an increasing awareness that protein dynamics in solution is connected to its biological function. Recent NMR studies revealed that many proteins exhibit pronounced dynamic conformational flexibilities [13–15].

It is well known that, in particular, surface exposed parts of HSA show a high degree of flexibility which constitutes a key to the protein’s binding versatility towards various molecules. Already in the 1950s, Karush developed a concept which accounted for this conformational adaptability of the binding sites [16, 17]. Further, a model has been proposed, which takes into account the conformational entropy arising from the flexibility of the fatty acid alkyl chains [18].

This study aims at unraveling the functional structure of HSA with respect to its binding of fatty acids. An electron paramagnetic resonance (EPR) technique is applied to study the fatty acid binding site distribution in the protein in frozen solution by characterizing it from the fatty acids’ point of view. This is achieved by studying spin-labeled fatty acids, which alone give rise to an EPR signal [19–21]. Thus, the distribution of the FA binding sites is detected without any contribution from the complex protein itself (Fig. 3.1a). Structural information of the binding sites is obtained by determining the distance distributions between the fatty acids. These distance distributions are retrieved by double electron–electron resonance (DEER), a pulse EPR method, which utilizes the inherent distance dependence of the dipolar couplings (acting solely through space) between the unpaired electron spins [22–24]. In recent years, DEER has increasingly been used in structural studies on both synthetic [25, 26] and biological systems [27] with the focus on (membrane) proteins and nucleic acids [28–31].

To sample distance information from different positions along the methylene chain of the fatty acids in the respective binding sites, fatty acids with different labeling positions were applied. In 5-doxylstearic acid (5-DSA), the unpaired electron resides near the anchoring carboxylic acid group. In 16-DSA, it is located near the end of the methylene chain (Fig. 3.1b). Thus, information can be retrieved from the anchor positions in the protein as well as from the entry points into the fatty acid channel formed by the protein.

This chapter is divided into three parts. In the first section, the uptake of spin-labeled fatty acids by the protein is characterized with CW EPR spectroscopy. Following this, distance distributions are recorded when loading the protein with various amounts of fatty acids. The experimental results are then compared with the expected distributions as derived from the crystal structure and differences are discussed in terms of the protein function. In a more technical second part, spin systems with more than two unpaired electrons per protein molecules are studied. Spin counting is applied to quantify the number of coupled spins and limitations of the method for self-assembled systems are discussed. Further, distortions in the distance distribution due to multispin effects are characterized in detail. In the third section, a second compound is admixed to the protein beside fatty acids. Cu(II) protoporphyrin IX serves as an EPR probe with a large $g$ anisotropy. Via orientationally selective DEER, not only the distances but also the relative orientations of the fatty acid in the protein are accessed and compared to theoretical data as suggested by the crystal structure.

3.2 The Distribution of Fatty Acids in Human Serum Albumin in Solution

3.2.1 Results

All experiments in this chapter imply the addition of up to seven fatty acids to one HSA molecule to occupy all binding sites in the protein. To avoid artifacts and allow quantitative interpretation of the data, it is essential to limit the amount of EPR active, spin-labeled fatty acids to two per protein molecule. This avoids complications due to multispin effects (cf. Sect. 3.3) [32]. By simultaneously adding diamagnetic fatty acids, the degree of loading can be still varied in such spin-diluted systems, as the diamagnetic fatty acids compete with DSA for a binding site without giving rise to an EPR signal. By adjusting the ratio of diamagnetic fatty acid and DSA, two sites, statistically distributed among all sites, are then occupied by EPR active molecules. Thus, an artifact-free distance distribution with a complete set of distances from all fatty acid binding sites can be obtained.

The diamagnetic fatty acid was prepared by reduction of the corresponding DSA to the EPR-inactive hydroxylamine (rDSA). Details of the reaction are given in Appendix A.1.1. This molecule is structurally closely related to the paramagnetic DSA and exhibits comparable binding affinities, as checked by CW EPR spectroscopy (Appendix A.1.2). Stearic acid could also be used as spin diluting paramagnetic species, but suffers from a low solubility and a larger structural variation in comparison to DSA. Moreover, similar results are obtained independent of the nature of the spin diluting stearic acid (Appendix A.1.1).

Uptake of spin labeled fatty acids

The CW EPR spectra of both types of spin-labeled fatty acids, 5-DSA and 16-DSA, at different HSA–fatty acid ratios are displayed in Fig. 3.2. The spectra diplay signatures of rotationally restricted and freely tumbling nitroxides, as indicated by solid and dashed lines. These two species correspond to fatty acid molecules bound to DSA and free fatty acids in solution.

Fig. 3.2

CW EPR spectra of HSA–fatty acid mixtures with a 16-DSA and b 5-DSA recorded at 298 K. The rDSA:DSA values indicate the average number of reduced and EPR-active fatty acid per protein molecule. The characteristic signatures of the respective DSA bound to HSA are marked by solid lines, the signature of free fatty acids in solution is marked by dashed lines. For comparison, a reference spectrum of 0.2 mM DSA in aqueous solution is displayed on top. Reprinted with permission from [65, 66]. Copyright 2010 WILEY–VCH Verlag GmbH and Co. KGaA, Weinheim

Up to a HSA–fatty acid ratio of 1:3, no (5-DSA) or only a negligible (16-DSA) signature of free species is observed, indicating complete uptake of the fatty acids by the protein. This confirms the existence of three high affinity binding sites in full agreement with the literature. At higher fatty acid ratios, the relative amount of unbound DSA steadily increases. Yet, at a HSA–fatty acid ratio of 1:6, more than 99.7% of all fatty acids are still complexed by the protein as deduced from the spectral intensities of both species. This proves a nearly quantitative uptake of both types of DSA and confirms that the fatty acid uptake is not disturbed by spin labeling.

Several publications dealing with the fatty acid binding properties of HSA use commercial HSA that is labeled fatty acid free. CW EPR studies, however, revealed a decreased uptake of fatty acids in such samples, which is indicative of partial protein degeneration (Appendix A.1.3). Hence, these studies were performed with commercially available HSA that was not explicitly fatty acid free but labeled non-denaturated. Potentially residual fatty acid molecules were regarded as a far less severe problem, since they can exchange with the EPR-active fatty acids and do not hamper a desired uniform distribution of DSA among all possible binding sites.

The degree of rotational freedom of the nitroxide can be estimated from the distance between the low field maximum and the high field minimum by spectral simulation [33, 34]. 5-DSA is rotationally more restricted than 16-DSA which has a roughly three times lower rotational correlation time. This trend is expected since the nitroxide unit of 5-DSA is placed in the tight hydrophobic binding channels near the anchoring point. The nitroxide group of 16-DSA, on the other hand, is located at the end of such a channel or even exceeds the end of a channel and will thus experience a higher degree of rotational freedom as reported by detailed CW EPR studies on the binding of spin-labeled fatty acids to different types of serum albumin [19–21].

Distances between the acid sites

To retrieve the desired information about the functional structure of HSA, the HSA–fatty acid complexes were further analyzed by DEER spectroscopy. The intramolecular part of the time-domain data and the extracted distance distributions are displayed in Fig. 3.3. For 16-DSA, well-defined dipolar modulations are observed which originate from narrow distance distributions with a dominating distance at 3.6 nm and two smaller contributions at 2.2 and 4.9 nm. For 5-DSA, such a pronounced modulation is missing, which is indicative of a broader distribution. In fact, a broad single distance peak is derived, which covers a range from 1.5 nm (the lower accessible limit with DEER) to 4 nm with a maximum around 2.5 nm.

Fig. 3.3

a, b Intramolecular part of the DEER time-domain data and c, d extracted distance distributions of spin-labeled stearic acids complexed in HSA with varying numbers of reduced and EPR active fatty acid per protein molecule: black (0:2), blue (2:2), green (4:2), orange (6:2). The data from 16-DSA are shown on top (a, c), the data from 5-DSA on the bottom (b, d). Reprinted with permission from [65, 66]. Copyright 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Remarkably, neither the 5-DSA nor the 16-DSA distance distributions change considerably when the protein is loaded with different amounts of fatty acids. Thus, higher loading does not result in the generation of new distinct distance contributions. It rather results in a broadening of the already existing distance peaks. This can be explained as follows. Although fatty acids possess different binding affinities to different protein binding sites, these differences seem not very pronounced. Hence, the binding sites are not filled up consecutively. Rather, all binding sites are populated to a certain degree even at low HSA–fatty acid ratios. The high affinity binding sites are only populated to a larger extent. Variations of the HSA–fatty acid ratio will then only lead to changes of the relative populations. This explanation is supported by NMR studies with ¹³C labeled fatty acids. Only subtle changes of the NMR peak ratios were observed when increasing the fatty acid ratio [11, 12].

3.2.2 Discussion

While the CW EPR data were collected at 298 K, DEER measurements were conducted at 50 K. For this purpose, the solution containing the HSA–fatty acid complexes was shock-frozen to obtain a vitrified solution. Thus, a snapshot of the protein ensemble in solution at the glass transition temperature of around 170 K is studied [35, 36]. Note that 20 vol% of glycerol were added to obtain such glassy samples. This is a standard treatment in pulse EPR and there is plenty of evidence that this small amount of non-aqueous solvent does not alter the structure of proteins but rather stabilizes the native structure in frozen solutions [28, 37]. This assumption is supported by CW EPR measurements at 298 K that did not show changes of the fatty acid binding dependent on the addition of glycerol. In contrast, only small amounts of ethanol (10 vol%) are sufficient to denature the tertiary structure of the protein. In this case, the DEER time-domain signal consists of a homogeneous exponential decay without underlying modulations (data not shown).

In this study, spin-labeled DSA is used as a substitute for natural fatty acids. The doxyl EPR reporter group causes only a minor structural variation, but could lead to different binding affinities since some fatty acid binding sites are reported as narrow tunnels. In this case, the presence or absence of a bulky doxyl group could be relevant. For 16-DSA, the spin label is located at the end of the methylene tail and, at least for some sites, is probably not even required to enter the binding site. In contrast, the doxyl group of 5-DSA is located in the vicinity to the ionic head group of the fatty acid. It may thus be argued that this alteration of the FA structure may result in potentially less efficient binding to HSA. However, CW EPR data reveal that both spin-labeled fatty acids are taken up equally by the protein. Both DSA variants are complexed almost completely at a HSA–fatty acid ratio of 1:6. Furthermore, they display competitive binding affinities in comparison to stearic acid. Thus, neither steric nor electronic variations severely affect the binding properties of the spin-labeled fatty acid. Considering the wide variety of saturated and unsaturated FA that can be bound by HSA [3, 8], it is thus not surprising that the binding of DSA molecules is comparable to that of other long chain fatty acids.

The different labeling positions allow for two different views on the functional structure of the protein. The position of the unpaired electron in 5-DSA is close to the carboxylic acid group of the fatty acid, which interacts with positively charged side groups of the protein. Hence, DEER delivers the characterization of the spatial distribution of the anchoring groups. With 16-DSA, on the other hand, the entry points into the fatty acid channels are probed. Information about the spatial distribution of these points is important to gain a better understanding of the uptake and release properties of the protein.

The 5-DSA (and thus the headgroup) distribution in solution is much broader than the distribution of 16-DSA (i.e. the entry points). Despite the increased flexibility of the doxyl moiety of 16-DSA, a very uniform distribution with a well-defined main distance is obtained. This suggests that the entry points of the fatty acid binding sites are distributed rather symmetrically on the surface of the protein molecule.

In Fig. 3.4, the experimental distance distributions in solution are compared with distributions retrieved from the crystal structure. These distributions were calculated assuming a full occupation of all binding sites and a Gaussian broadening of the distance peaks. The procedure is detailed in the experimental part (Sect. 3.6) and in Appendix A.1.6. Since the fatty acids in sites 1 and 7 are not resolved up to the C-16 atom of the methylene chain, they were extrapolated to this position. Additionally, Fig. 3.4 contains an alternative distribution without these two low affinity binding sites.

Fig. 3.4

Comparison of experimental distance distributions obtained by DEER (black) with calculated distributions obtained from the crystal structure (red, blue) for the a C-16 position and b C-5 position. The distribution in red is obtained assuming that all seven binding sites occupied. The distribution in blue results when the fatty acids in low affinity binding sites 1 and 7 are neglected which are not completely resolved in the crystal structure. Note that distances >6 nm cannot be accessed by DEER under the applied conditions. Reprinted with permission from [65, 66]. Copyright 2010 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim

The experimental distribution of 5-DSA show major similarities to that of the crystal structure assuming a full occupation of all binding sites. In both cases, broad distributions centered at a distance of about 3 nm are obtained. Indeed, the highly asymmetric distribution of fatty acid binding sites observed by crystallographic data can also be found in the DEER results, namely for position C-5, i.e. for the anchoring points. In that case, the distributions from both methods coincide remarkably well. First of all, this shows that the distance distributions determined from DEER are reliable. Second, it suggests that the anchoring point distribution in solution reflects the more rigid inner part of the protein, which does not differ too strongly in the crystal and in solution.

In contrast, the distance distribution of the entry points (16-DSA) strongly deviates from the crystal structure, taking into account that distances greater than 6 nm cannot be accessed by DEER under the applied conditions. The crystal structure distribution exhibits three major peaks at 2.5, 3.5, and 4.5 nm. While the peak positions roughly agree with the DEER data, the relative intensities deviate considerably. Experimentally, the peak around 3.6 nm by far dominates all other peaks, which remarkably simplifies the distance distribution as compared to that derived from the crystal structure. It suggests that the entry points are distributed much more symmetrically and homogeneously over the protein surface than it would be expected from the crystal structure. Note that it is even impossible to reconcile the dominant (5- and 16-DSA) distances found from DEER measurements with those of the crystal structure. This is explained in detail in Appendix A.1.7. A homogeneous distance distribution of six binding sites suggests high symmetry. Considering the six sites to form an octahedron, on expects 12 vertex–vertex distances with length r and 3 distances with length $\sqrt 2 r$. With the dominating distance r = 3.6 nm, a diagonal distance of 5.1 nm results, which is in remarkable agreement with the observed distance of 4.9 nm. Indeed, an octahedron constitutes the most favorable distribution for the entries of six fatty acid binding sites on a sphere, as they are then easily accessible from every side of the protein and assume the maximum distance with respect to each other. However, such an octahedron model can only account for the entry points of six fatty acid binding sites. Moreover, it does not account for the structure of the protein, which is rather heart-shaped than sphere-like.

One may speculate that the more homogeneous distribution of the entry points arises from the conformational flexibility of HSA. Furthermore, it may even mirror the optimization of the protein to allow for a fast and facilitated uptake and release of the fatty acids. For this, an optimized average distribution of FA entry points as well as large conformational flexibility are prerequisites. A large flexibility on or close to the protein surface may also be entropically favored. The gain in entropy by only small conformational variations is much larger than for changes in the interior of the protein.

A homogeneous distribution of binding sites on an octahedron is also in accord with the fact that the DEER distance distributions effectively do not change when the fatty acid ratio is varied. Even if the binding sites were filled up consecutively, they would all give rise to similar distances due to their symmetric distribution on the protein surface.

To check the probability of such a symmetric distribution of the entry points, a molecular dynamics (MD) simulation on the crystal structure (1e7i) was performed for a period of 6.5 ns. Though no substantial deviation from the overall crystal structure is observed, it was found that the C-16 position of the fatty acids is more strongly affected by small changes of secondary structure elements than position C-5 (for details, see Appendix A.1.8). This is an additional hint that the anchoring region of the protein is rigid while the entry points have a substantial higher degree of freedom and flexibility.

3.3 Multispin Contributions to DEER Spectra

In this section, it will be studied in detail how the DEER data are affected when multiple paramagnetic centers are clustered in the protein. Special emphasis is placed on the differences between these multispin systems and the spin-diluted systems that were discussed in the previous section. Specifically, it is elucidated here how multispin interactions affect the experimental distance distributions and hamper the correct interpretation of the data.

3.3.1 Spin Counting

In Fig. 3.5, the intramolecular parts of the DEER time-domain data and the corresponding distance distributions are shown when the protein is loaded with 1–8 paramagnetic 16-DSA molecules. At first sight, the distance distributions for high loading exhibit considerable deviations to the distributions of the spin-diluted systems displayed in Fig. 3.3b. This issue will be discussed in detail in the next part of this section, while in the subsequent paragraphs the DEER time-domain data of HSA complexed with multiple EPR-active 16-DSA units is analyzed.

Fig. 3.5

a Background corrected DEER time-domain data of HSA complexed with 2–8 equivalents of 16-DSA with a graphical illustration of the definition of the modulation depth $\Updelta$. b Corresponding distance distributions by Tikhonov regularization with a regularization parameter of 100 normalized to the height of the peak at 3.6 nm. Reprinted with permission from [67]. Copyright 2011 Elsevier Inc

As mentioned in the last section, the fraction of fatty acids bound to HSA can be determined by CW EPR measurements. It was already discussed that 16-DSA is almost completely bound to the protein in HSA–fatty acid mixtures up to a ratio of 1:6 (cf. Appendix A.1.2). DEER provides a different means to quantify the fatty acid molecules per protein by the determination of the number of dipolar coupled spins N [38], which can be accessed by the relation [39]

$$ N = \frac{{\ln \left( {1 - \Updelta } \right)}}{{\ln \left( {1 - \lambda } \right)}} + 1. $$

(3.1)

$\Updelta$ is the modulation depth and $\lambda$ the inversion efficiency. The modulation depth, illustrated graphically in Fig. 3.5a is defined by

$$ \Updelta = 1 - \mathop {\lim }\limits_{t \to \infty } V\left( t \right)/V\left( 0 \right) $$

(3.2)

and can easily be determined from the background corrected DEER time trace. The inversion efficiency is accessed experimentally using a biradical (N = 2, $\Updelta = \lambda$). Note that $\lambda$ is proportional but not identical to the experimental inversion efficiency $\lambda_{\exp }$ that is mentioned later in this section. The latter variable characterizes the inversion efficiency of selected spin packets in a narrow frequency range, while $\lambda$ quantifies the average inversion efficiency for the pumped spins.

As can be seen in Fig. 3.5a, the modulation depth increases as more spin-labeled fatty acid equivalents are added to the protein. It reaches a constant value for HSA–fatty acid ratios ≥ 1:5. As expected, the increase of the average number of spins per protein molecule is reflected in the increase of the modulation depth.

The inversion efficiency was determined with a rigid phenylene-ethynylene based biradical with a spin–spin distance of 2.8 nm dissolved in o-terphenyl [40]. $\lambda$ depends on a variety of parameters such as the length of the pump pulse, the shape and width of the resonator mode, the spectral line shape, and the position of the pump pulse in the spectrum and in the resonator mode [41]. For this reason, all experimental conditions were kept constant for the biradical and the HSA–fatty acid complexes.

However, using the biradical as a reference, the average number of coupled spins varies from 1.49 to 2.81 for all HSA–DSA mixtures (Table 3.1). This suggests that the protein is able to complex less than three DSA molecules on average, which is in clear disagreement with the data obtained by CW EPR measurements. On the contrary, reasonable N values are obtained when the inversion efficiency is approximated by the modulation depth of a 1:2 HSA–DSA mixture (Table 3.1). Mixtures with 3–5 equivalents of fatty acid give rise to values N = 2.93, 3.76, and 4.65, which correlate well with the expected average number of fatty acids per molecule.

Table 3.1 Modulation depths and average numbers of spins in HSA–fatty acid Complexes (reproduced with permission from [67])

The difference in the inversion efficiency of the biradical and the HSA–fatty acid mixtures is far too pronounced to be explained by the slightly narrower EPR spectrum of the biradical (Appendix A.1.9). Further, no angular correlations of the DSA molecules were observed, which would lead to an orientation dependence of $\lambda$ as indicated by Eq. 2.100 (Appendix A.1.10). This is easily comprehensible since the spin-bearing hydrocarbon ring is still able to rotate rather freely about the methylene chain of the fatty acid, even if the position of the fatty acids is restricted due to narrow protein channels. On the contrary, a slight orientation selection of the spins in the rigid biradical was found (data not shown). While a strong orientation selection would account for the observed deviation in $\lambda$ [31, 42], the slight orientational dependence observed here does not.

It is well known, that the modulation depth is partly suppressed for dipolar pairs with short distances and the dipole–dipole couplings in the range of or larger than the excitation bandwidth of the pump pulse [41]. But as discussed in detail in the last section, a homogeneous distribution with a main contribution at 3.6 nm is observed, and even the crystallographic data suggests only two distances <2 nm (Table A.1). Additionally, no indications for strong dipolar couplings can be found in ESE detected spectra, as spectral broadenings are absent (Appendix A.1.9). Hence, the reason for the apparent deviation of the inversion efficiency remains unclear.

More realistic values of N are obtained using the 1:2 HSA–DSA mixture as reference. Still, the obtained values are slightly lower than the expected ones with a bigger deviation for large numbers of coupled fatty acids. For an average of 3, 4, and 5 coupled spins, values of 2.93, 3.76, and 4.65 are calculated.

In fact, the modulation depth is slightly overestimated for protein complexes with a high fatty acid content. This is due to the fact that the apparent background dimensionality of 3.8 is based on the assumption of a single electron spin in the center of a sphere with a radius of 2.5 nm (Appendix A.1.5). If more spins are located in the same sphere, the probability of intermolecular distances <5 nm increases and the apparent dimensionality is reduced.

However, this slight overestimation of N is counteracted by a second and larger effect. Bode et al. observed that the contributions from mixtures with a varying number of coupled spins to the overall modulation depth are weighted with a scaling factor which depends on the transverse relaxation time $T_{2}$ of the spins in the cluster [39]. Clusters with more coupled spins exhibit a decreased $T_{2}$ time, hence their spectral contribution is underrepresented (Appendix A.1.9). On a different note, the height of the central peak of the EPR spectrum is more strongly decreased by the enhanced relaxation times than the flanks. Thus, the inversion efficiency for highly loaded HSA samples is slightly decreased as well (as the pump pulse is located in the spectral center). Since the relaxation time of the isolated spin oligomers could not be accessed, a quantification of this influence according to the method proposed in Ref. [39] was not feasible.

For even higher amounts of spin-labeled fatty acid molecules, the obtained values deviate significantly from the expected values (4.67 vs. 6 and 4.45 vs. 8). In addition to the above mentioned factors, the modulation depth is additionally decreased by contributions from free, uncomplexed spin probes. This effect is most prominent for the 1:8 mixture, which exhibits an even smaller modulation depth than the 1:6 sample. This is in line with CW EPR studies showing that the fraction of unbound DSA is substantially increased for the 1:8 mixture (data not shown). The decrease of the modulation depth due to unbound DSA is also manifested for the spin-diluted systems examined in the last section (Fig. 3.3a). The addition of rDSA molecules leads to an increasing fraction of unbound DSA and to a decrease of the modulation depth.

In conclusion, the modulation depth serves as a means to qualitatively assess the average number of spins in self-assembled systems. A quantitative interpretation is mainly hampered by the existance of spin clusters with a varying number of coupled spins and contributions from unbound spin-labeled material, which decrease the modulation depth. In this study, large deviations are observed for $\ge5$ coupled spins in a total of seven potential binding sites.

3.3.2 Quantification of Multispin Artifacts

As already mentioned, the time-domain data in Fig. 3.5a give rise to distance distributions that deviate considerably from the results of the spin-diluted systems for a high degree of loading. While the distance distributions of the spin-diluted systems hardly change with the number of fatty acids (Fig. 3.3b), the distributions with only spin-labeled fatty acids undergo pronounced changes depending on how many DSA molecules are added to the protein (Fig. 3.5b). In addition to a substantial broadening of all distance peaks, their relative ratio is significantly altered. The contribution of the small distance at 2.2 nm increases relative to the dominant contribution at 3.6 nm, while the large distance at ~5 nm vanishes for HSA–fatty acid mixtures with more than three equivalents of DSA.

In the following, flip angle dependent DEER measurements are performed to reveal the influence of multispin contributions to the changes of the distance distributions. The experiment is based on the dependence of N-spin contributions on the inversion efficiency, which can be roughly approximated by

$$ V_{N - {\tt {spin}}} \propto \lambda^{N - 1} . $$

(3.3)

A detailed description of the theoretical background is given in Ref. [32]. Each contribution is affected to a different degree by a variation of the inversion efficiency, which can be controlled by the flip angle of the pump pulse. Hence, a series of measurements at different flip angles allows for the separation of the N-spin interactions. Since three-spin interactions constitute the by far dominant part of the multispin interactions for $\lambda \gg 1,$ only the separation of the two- and three-spin contribution is considered in analogy to the method described by Jeschke et al. [32]. As multispin interactions with N > 3 are neglected in the analysis, the 1:3 HSA–DSA mixture and the comparison to the spin-diluted samples are discussed in detail.

Intramolecular DEER time-domain signals for six different flip angles of the pump pulse are shown in Fig. 3.6a, b. The flip angles were varied by selective attenuation of the microwave power of the pump pulse channel and the resulting inversion efficiencies were quantified by an inversion recovery sequence. The relation of the modulation depth and the inversion efficiency is given by the relation [32]

$$ \Updelta \left( \lambda \right) = \sum\limits_{i = 1}^{N - 1} {d_{i} \lambda^{i} } . $$

(3.4)

Fig. 3.6

a, b Intramolecular time-domain data of flip angle dependent DEER measurements for 16-DSA (left) and 5-DSA (right). The inversion efficiency of the pump pulse was decreased by attenuation of the microwave power output ranging from 0 to 10 dB. c, d Plots of the total modulation depth $\Updelta$ as function of the inversion efficiency $\lambda_{\exp }$ (determined by inversion recovery). The data points were fitted with a second-order polynomial (red) accounting for two- and three-spin contributions to the DEER signal and a straight line, which neglects three-spin contributions. Reprinted with permission from [67]. Copyright 2011 Elsevier Inc

For pure two-spin contributions a linear relationship is expected. Any contribution from multispin interactions gives rise to deviations from this linear dependency due to the admixture of higher order polynomials. Indeed, a slight deviation is observed for 1:3 mixtures of HSA with both 16-DSA and 5-DSA (Fig. 3.6c, d), which is absent if the ratio is decreased to 1:2 (data not shown). This is a clear indication that multispin interactions contribute to the overall DEER signal. The deviation from the linear curve is not as strong as expected for a triradical [32], since the sample contains a mixture of proteins with one, two, three, and higher amounts of spin-labeled fatty acids.

Having visualized the contributions due to multispin interactions, one can now focus on the resulting artifacts in the respective distance distribution. For this purpose, pair and three-spin contributions are extracted from the raw DEER data. In Fig. 3.7, the distance distribution obtained from the pair contribution is compared to the distribution obtained from the original DEER data, which is distorted by multispin interactions.

Fig. 3.7

Comparison of the distance distribution obtained from the raw time-domain data of a 1:3 mixture of HSA and DSA (black) and from the extracted two-spin contributions (red) for 16-DSA (a) and 5-DSA (b). The observed differences, indicated by black arrows for 16-DSA, are compared to the deviations observed for HSA molecules fully loaded with purely paramagnetic DSA (blue) and a spin-diluted mixture of rDSA and DSA (orange). Reprinted with permission from [67]. Copyright 2011 Elsevier Inc

The observed changes are most pronounced for 16-DSA, since the distribution contains well-resolved peaks, but are also manifested in the distribution of 5-DSA. The multispin effects, present in the raw DEER data, lead to a slight broadening of the observed distance peaks. More severely, contributions from small distances are overestimated while large distances are suppressed. These observations are in full agreement with the multispin effects observed for model triradicals [32].

With the data at hand, the apparent deviation between the distance distributions of fully loaded HSA samples can solely be related to multispin effects. In a 1:8 mixture of HSA and 16-DSA or in a 1:4 mixture of HSA and 5-DSA, multispin effects lead to an overestimation of small distances and to a broadening of the peaks in full analogy to the flip angle dependent DEER results. Hence, a spin-diluted system is an indispensible prerequisite for retrieving artifact- and distortion-free distance distributions when self-assembled systems with a more than two potential paramagnetic centers are studied.

Even for protein samples with a high number of paramagnetic centers, all observed changes are described well by three-spin contributions. It can thus be assumed that contributions from multiple spin interactions with N > 3 are negligible, even if as much as seven spins are coupled. Note that, in principle, three-spin contributions can be analyzed in addition to pair contributions. They do not only contain information about the distance, but also about the relative orientation of the three interacting spins [32]. However, this analysis is not carried out in this section due to the plentitude of coupled spins, which generates various possibilities for three spin contributions with different distances and orientations. Instead, orientational information will be accessed in the next section by employing an EPR-active transition metal.

3.4 Orientation Selectivity in DEER: Beyond Distances

Besides fatty acids, HSA binds and transports a large variety of endogenous compounds and drugs. Most drugs are bound in two distinct binding sites located in subdomains IIA and IIIA of the protein [5, 43], which overlap with fatty acid binding sites 2, and 3/4 [11, 12]. Among the endogenous ligands, hemin, bilirubin, and tyroxine are the most important. Hemin and bilirubin bind to subdomain IB (fatty acid site 1) [44–46], whereas thyroxine binds to subdomain IIA (fatty acid site 7) [47].

Hemin is a particularly interesting ligand for EPR studies since it contains a paramagnetic Fe³⁺ central ion, which is complexed by a porphyrin derivative. It fits snugly into the hydrophobic cavity of the protein with its two propionate groups interacting with basic side chain residues of the protein [44]. In that sense, its binding mode resembles that of fatty acids. In fact, hemin exhibits a higher affinity to the protein binding site than the fatty acids. Thus, the addition of one equivalent of hemin is sufficient to quantitatively replace the fatty acid bound to site 1. The crystal structure PDB 1o9x of HSA co-crystallized with hemin and myristic acid is shown in Fig. 3.8 [44].

Fig. 3.8

a Crystal structure (PDB 1o9x) of HSA co-crystallized with hemin and six myristic acid molecules [44]. b Chemical structure of the EPR active substitutes for hemin and myristic acid, Cu(II) protoporphyrin IX and 16-DSA. Reprinted with permission from [68]. Copyright 2011 Biophysical Society

Although Fe³⁺ itself possesses a quadrupolar electron spin with S = 5/2, which leads to substantial broadening of the EPR spectrum (Appendix A.1.11), it can easily be substituted by a variety of transition metal ions. Cu²⁺ (S = 1/2) is the ion of choice for EPR applications, since its spectra exhibit comparably narrow spectral widths. Due to the relatively high spectral density, Cu²⁺ can even be utilized as a probe in DEER distance measurements (see below, cf. Sect. 4.4) [48, 49].

By the addition of Cu(II) protoporphyrin IX (replacing hemin) and 16-doxyl stearic acid (replacing myristic acid) to HSA, a self-assembled ternary system is obtained that allows a structural characterization of the protein in analogy to Sect. 3.2 (Fig. 3.9). In fact, the spectral separation of copper and nitroxide contributions opens the possibility to solely retrieve distances between the Cu²⁺ ion in the center of the porphyrin and the nitroxide groups of the fatty acids. Thus, the total number of distances probed by the system is significantly reduced from 21 (FA–FA) to 6 (hemin–FA). According to the crystal structure, these six distances range from 2.36 to 4.25 nm (C-16 position of the fatty acids). Hence, they are well in the distance regime that can be accessed by DEER (Fig. 3.9).

Fig. 3.9

Relative positions of Cu(II) protoporphyrin IX and the stearic acid molecules in the protein. The structural model was obtained by inserting hemin in the crystal structure PDB 1e7i of HSA complexed with seven stearic acid molecules (cf. Sect. 3.6) [8]. The C-16 positions of the stearic acids are highlighted in orange and the last resolved carbon atom of stearic acid in site 7 is colored yellow. The structural relationship between Cu(II) and position C-16 of the stearic acids is sufficiently described by the distance and the angle $\delta$ between the connecting vector and the z-axis of the molecular Cu(II) frame. In the inset, the expected distance distribution is shown assuming Gaussian peaks with $\sigma =$ 0.14 nm. The methylene chain of the stearic acid in site 7 was linearly extrapolated to its C-16 position. Reprinted with permission from [68]. Copyright 2011 Biophysical Society

Further, the major disadvantage of the selective excitation of only few Cu²⁺ spin packets by a single microwave pulse can be used as an advantage, as the excited spins possess a defined orientation with respect to the external magnetic field. Due to this orientation selection, DEER does not only provide information about the spin–spin distance, but also contains information about the relative orientation of the spin–spin vector with respect to the molecular frames of the paramagnetic centers [50, 51]. Note that the ternary system based on HSA also constitutes a fully self-assembled biological model system for orientation selection in DEER.

The effect of orientation selection on a DEER spectrum can be utilized if the $g$ anisotropy of at least one of the paramagnetic centers is resolved. For nitroxides, sufficient resolution is provided at high magnetic fields of $\ge95$ GHz and spin pair geometries can be accessed [42, 52–55]. However, orientationally selective DEER measurements on nitroxides are also possible at X-band, since a variation of the observer pulse position in the low field part of the spectrum slightly affects the orientation of the excited spins [31, 56].

Transition metals give rise to strong angular effects even at X-band due to the significantly broader $g$ anisotropy. In particular, a variety of Cu²⁺ containing compounds was studied by DEER. Copper–nitroxide distances and orientations were accessed for terpyridine and porphyrin model complexes [48, 57], and even copper–copper distances could be estimated for several biological systems [48, 58, 59].

Several sophisticated methods were developed for the analysis of orientation selection in DEER [42, 55, 56, 60]. A direct conversion of the dipolar data into a distance distribution is not possible, since the orientation dependence of the DEER data is a priori unknown. Hence, a structural model is used to retrieve distance and mutual spin orientations. Based on this model, dipolar couplings are calculated and fitted to the experimental time-domain data or its Fourier transform. All reported methods explicitly calculate the orientation selection of both observer and pump spin. The mutual orientation of the paramagnetic centers in then accounted for by Euler angle transformation of the molecular frame of spin B in the molecular frame of spin A. Finally, the resulting excitation pattern is related to the mutual orientation of spin A to the spin–spin connecting vector.

Hence, this thorough methodology completely describes the mutual orientation of the whole spin system. However, in many cases no defined relationship between both spins exists. This is particularly true for flexible spin labels that can assume a large range of orientations and also applies to the spin labels of the fatty acids in this study, as confirmed by field-swept DEER measurements (Appendix A.1.10). Thus, the orientation selection is almost exclusively governed by the transition metal ion, which exhibits a fixed position with respect to the spin–spin vector and a substantially more pronounced g anisotropy.

In the next paragraphs, a particularly simple method for the analysis of the orientation-selective DEER data is presented, which only considers the orientation-selective excitation of the copper spins.

In the first step, the EPR parameters of the Cu(II) porphyrin system are retrieved by simulation of the copper contribution to the EPR spectrum. With these parameters, the relative fractions of excited spins at each angular orientation with respect to the external magnetic field are calculated with the Easyspin routine ‘orisel’ for each field position of the observer pulse [34]. Typically, the data are calculated in an angular grid of $\theta \times \varphi = 100$ $\times$100, giving rise to 10,000 orientations.

The lengths r of the spin–spin vectors and their angles to the Cu²⁺ molecular z-axis $\delta$ were obtained from the crystal structure (Fig. 3.9). The position of the electron spin of the nitroxide was approximated by the C-16 position of the fatty acid. The relative positions of the nitroxides to the Cu(II) porphyrin are fully described by r and $\delta$ due to the axial symmetry of the Cu²⁺ molecular frame.

For each orientation, the angle between the external magnetic field and the spin–spin vector $\theta_{\hbox{AB}} ,$ and the effective $\hbox{ g}_{\hbox{Cu}} \left( \theta \right)$ value (Eq. 2.46) were determined. These values were then used to calculate the dipolar frequency at each magnetic field position (Eq. 2.101). Dipolar spectra were obtained by weighting the dipolar frequencies (positive and negative) with the calculated fraction of excited spins and by $\rm{sin}\,\theta$ and subsequent summation for all orientations. Time-domain signals were calculated by Eq. 2.100.

This calculation yields DEER data originating from infinitely sharp distance peaks. More realistic data were obtained by assuming a Gaussian broadening of each distance (usually $\sigma =$ 0.14 nm). Each peak was subdivided into 40 equally spaced sub-distances with $\Updelta r$ = 0.05 nm, for which the above-mentioned calculation was repeated. To reduce the calculation times, negligible angular and distance contributions were not considered. The cut-off values were 1% (orientation) and 5% (distance) of the maximum value. For six distances, the calculation time was less than 30 min. The source code of the program is given in Appendix A.1.13.

A typical EPR spectrum of HSA complexed with Cu(II) protoporphyrin IX and 16-DSA is displayed in Fig. 3.10 (top). The most prominent feature of the spectrum is due to the nitroxide contribution, which is visualized separately in blue. By subtraction of this contribution, the contribution from the paramagnetic Cu²⁺ was obtained, which could then be subjected to a spectral simulation (red). Uniaxial parameters $g_{ \bot } =$ 2.053, $g_{\parallel } =$ 2.194, $A_{ \bot }{\rm(Cu)}$ = 58.8 MHz, and $A_{\parallel }{\rm(Cu)}$ = 616 MHz were retrieved, further superhyperfine couplings to four strongly coupled ¹⁴N atoms with magnitudes $A_{ \bot } {\rm(N)}$ = 50.4 MHz and $A_{\parallel }{\rm(N)}$ = 37.8 MHz. These values correspond well to reported values on similar Cu(II) porphyrin systems [61].

Fig. 3.10

ESE detected EPR absorption spectrum of HSA complexed with 1 eq. Cu(II) protoporphyrin IX and 1 eq. 16-DSA at 10 K (black, top). The nitroxide contribution, approximated by a 1:2 mixture of HSA and 16-DSA at 50 K (blue), was subtracted. The residual spectrum was pseudomodulated (black, bottom) and simulated (red). The simulations were used to calculate the Cu(II) orientations (Easyspin function ‘orisel’) that are excited by a 32 ns pulse at a certain spectral position. In the performed DEER experiments, the frequency of the pump pulse was kept at the maximum of the nitroxide spectrum and in the center of the resonator mode while the position of the observer pulse was varied within the copper spectrum. The orientation selection for these magnetic field positions is displayed in unit sphere plots with warm colors indicating high excitation efficiencies. Reprinted with permission from [68]. Copyright 2011 Biophysical Society

For the DEER measurements, the pump pulse was positioned at the maximum of the nitroxide spectrum to minimize orientation selection from these spins and to provide for a large fraction of pumped spins. The position of the observer pulse was varied within the copper spectrum. Orientational unit spheres for three typical positions are depicted in Fig. 3.10. Significant fractions of excited spins along the unique axis of the distorted octahedral frame are only obtained at a low magnetic field. However, the observer pulse position z₂ exhibits a frequency offset of 500 MHz to the pump pulse position at the spectral maximum, which severely decreases the signal-to-noise ratio as the flank of the resonator mode is approached and as the spectral density is decreased. Nonetheless, Bode et al. and Lovett et al., performing DEER measurement on comparable Cu(II) porphyrins, chose this option to achieve the desired orientations along z [57, 60]. Luckily, comparable orientations can also be selected at the high field flank of the spectrum (position z₁), which is a result of the strong hyperfine coupling of the strongly coordinated Cu²⁺ ion. As depicted in Appendix A.1.12, both observer pulse positions give rise to similar DEER spectra—with a substantially increased SNR for position z₁.

The obtained DEER time-domain data and frequency spectra for observer pulse positions xy and z₁ are displayed in Fig. 3.11. Note that spin-diluted systems were used in analogy to the fatty acid studies in Sect. 3.2. On average, a protein molecule contains one Cu²⁺ spin and one EPR-active 16-DSA molecule. Occupation of all available fatty acid binding sites is achieved by addition of rDSA. Non-diluted systems give rise to multispin effects as identified in the previous section (Appendix A.1.12).

Fig. 3.11

Background-corrected DEER time-domain data and dipolar spectra of HSA complexed with 1 eq. of Cu(II) protoporphyrin IX and 16-DSA, and varying amounts of 16-rDSA, as indicated by the central digit. Observer pulses were applied at field positions exciting Cu(II) orientations either predominantly in the xy-plane of the porphyrin ring (a, position xy) or outerdiagonal elements towards the molecular z-axis (b, position z₁). Reprinted with permission from [68]. Copyright 2011 Biophysical Society

Comparing the time traces in Fig. 3.11, a pronounced orientation selection is observed. At the xy position of the observer pulse, the dipolar modulations oscillate with a frequency twice that at the z₁ position. At this position, the dipolar contribution from angles $\theta_{\hbox{AB}} =$ 0° are far more pronounced than in a Pake pattern of a disordered system with no orientational relationship (cf. Fig. 2.23). At the same time, the dipolar singularities at $\theta_{\hbox{AB}} =$ 90° are the only pronounced feature of the dipolar spectrum at an observer position z₁, as contributions from $\theta_{\rm {AB}} =$ 0° are effectively suppressed.

Remarkably, the dipolar spectra do not undergo considerable changes when the total amount of fatty acid is varied. This observation is in full agreement with the results in Sect. 3.2. It supports the conclusion that the fatty acid sites do either not show pronounced preferences for certain binding sites, or that the binding sites are rather symmetrically distributed within the protein.

One should note that Cu(II) porphyrin does not only serve as EPR probe but also blocks the fatty acid binding site 1. When adding two equivalents of 16-DSA, nitroxide–nitroxide distances can be accessed, which hardly deviate from the data obtained in Sect. 3.2 with seven available binding sites (data not shown). Together with the observations in Sect. 3.2, it can be seen as further indication for a homogeneous, rather symmetric distribution of the entry points to the binding sites in the protein.

In Fig. 3.12, the measured dipolar data are compared to data calculated from the crystal structure, assuming full occupation of all binding sites. The dominating feature of the measured spectra is remarkably well reproduced by the calculated data as concerns both strength and orientation of the dipolar coupling. At the xy position, the enhanced contribution from dipolar angles $\theta_{\hbox{AB}} =$ 0° is clearly visible in the calculated spectra, although it is less pronounced than in the calculated data. In contrast, strong dipolar couplings due to small distances of ~2.5 nm are almost entirely absent in the measured data, though suggested by the crystallographic data.

Fig. 3.12

Comparison of the recorded dipolar spectra (HSA complexed with 1:4:1 equivalents of Cu(II):rDSA:DSA) and of the calculated Pake patterns for observer pulse positions xy (a) and z₁ (b). Full occupation of all fatty acid binding sites 2–7 is assumed. Reprinted with permission from [68]. Copyright 2011 Biophysical Society

The dominant contribution in the measured spectra can be unraveled by spectral simulations. Interestingly, this contribution is reproduced by a single dipolar interaction to a coupled nitroxide group (Fig. 3.13a). The qualitative consideration of the last paragraph is confirmed by the quantitative simulation, which yields a distance r = 3.85 nm and an angular orientation $\delta =$ 90°. Note that the contributions from $\theta_{\rm{AB}} =$ 0° even exceed the maximum achievable contribution at the given Cu²⁺ orientation selection for the xy observer position.

Fig. 3.13

a Recorded dipolar spectra (HSA with 1:1:1 Cu(II):rDSA:DSA) and best fit based on a dipolar coupling to a single electron spin placed in the extended xy-plane of the porphyrin ring ($\delta =$ 90°) with a distance $r =$ 3.85 nm. b Structural relation of the dominant DEER contribution to the fatty acid positions of the crystal structure. Potential positions for the dipolar coupled electron spin are indicated by a circle that is located close to the C-16 position of the stearic acid in site 6. Reprinted with permission from [68]. Copyright 2011 Biophysical Society

The obtained parameters correspond to a circle in the porphyrin plane, which is depicted graphically in Fig. 3.13b. Indeed, circular positions almost coincide with the C-16 position of the stearic acid in binding site 6 (r = 3.82 nm, $\delta =$ 88.1°). This site was already identified as the main contributor to the dominant 16-DSA–16-DSA distance peak by a strict comparison of the EPR data with the crystal structure (Appendix A.1.7).

However, given the fact that the found distance is close to the dominating 16-DSA–16-DSA distance and considering an almost complete absence of other distances, a different explanation is more probable. All observations can be accounted for by a symmetric distribution of the fatty acids tails and the entries to the fatty acid binding sites in the protein, as already proposed in Sect. 3.2. The pronounced orientation selection reflects the fact that the porphyrin ring is roughly aligned to the main plane of the more or less flat protein. Thus, fatty acids are predominantly located at angles close to $\delta =$ 90° as suggested by the crystal structure.

In summary, the orientation selective DEER measurements between the hemin substitute Cu(II) protoporphyrin and 16-DSA confirm the surprising nitroxide distance measurements between two 16-DSA molecules. Again, one dominant dipolar contribution is found, which indicates a symmetric distribution of the binding site entries into the protein.

3.5 Conclusions

DEER and orientationally selective DEER were applied to unravel the functional structure of HSA in solution. It was found that spin-diluted systems are an indispensible prerequisite for artifact-free measurements since multispin effects lead to major distortions of the distance distributions.

From these data one can conclude that HSA in solution is optimized for its function as a transporter of fatty acids. Specifically, the uptake and release of fatty acids is facilitated by a symmetric distribution of the binding sites’ entry points. The observed entry point distribution significantly differs from that expected from the crystal structure. While the crystal structure shows an asymmetric distribution of the entry points, a remarkably homogeneous and symmetric distribution is found. Contrary to that, the experimentally derived broad distribution of the ionic head groups as anchoring points shows major similarities with the crystal structure, indicating the reliability of the spectroscopic technique.

In general, the functional solution structures of proteins may differ, even significantly, from the crystal structure. This structure can be accessed by double electron–electron resonance spectroscopy. Using the selectivity of the spin probing approach, only signals from the fatty acids are obtained, which are directly related to the protein’s function of interest. This results in a tremendous simplification, but delivers a selective characterization of the functionality of the protein.

3.6 Materials and Methods

Materials. Non-denaturated human serum albumin (HSA, >95%, Calbiochem), 5- and 16-doxylstearic acid (DSA, Aldrich), hemin(chloride) (>98%, Roth), Cu(II) protoporphyrin IX (Frontier Scientific), and 87 wt% glycerol (Fluka) were used as received. The DSA derivatives were partly reduced to EPR-inactive hydroxylamines (rDSA) by addition of phenylhydrazine (97%, Aldrich) as described in detail in Appendix A.1.1.

Sample Preparation. 0.2 M phosphate buffered solutions of pH 6.4 with and without 2 mM HSA and 6.7 mM solutions of DSA and rDSA in 0.1 M KOH were mixed in the appropriate ratios to obtain HSA–fatty acid complexes in a 100 mM phosphate buffer solution of pH 7.4. In Sect. 3.2, the combined concentration of DSA and rDSA was kept constant at 2 mM with varying ratios from 2/0 to 2/6 per protein molecule. This method provides for isolated spin pairs in combination with a varying total occupation of the fatty acid binding sites. In Sect. 3.3, up to eight equivalents of EPR active DSA were added to HSA to study the effect of multispin artifacts in a biological sample. In Sect. 3.4, a ternary mixture of 1 eq. Cu(II) protoporphyrin IX, 1 eq. 16-DSA, and up to 4 eq. of 16-rDSA was complexed with HSA. In addition to already mentioned stock solutions, a 6.7 mM solution of the porphyrin derivative in 0.1 M KOH was prepared for this reason. For DEER measurements, 20 vol% glycerol were added to the final solutions to prevent crystallization upon freezing. The solutions were filled into 3 mm o.d. quartz tubes and shock-frozen in N₂(l) cooled iso-pentane (below –100 °C).

Analysis of the Crystal Structure (Sect. 3.2). Distances $r_{i}$ between the C-16 (or C-5) atoms of the fatty acids in all sites (1–7) were determined from the crystal structure PDB 1e7i (Tables A.1 and A.2 in Appendix A.1.6). The distance peaks were broadened assuming a Gaussian distribution $f\left( r \right) = \sum\nolimits_{i} {\exp \left\{ {\left( {r - r_{i} } \right)^{2} /2\sigma^{2} } \right\}.}$ Distributions with widths comparable to those of the DEER distributions were obtained with $\sigma =$ 0.21 nm (16-DSA) and $\sigma =$ 0.28 nm (5-DSA). While two binding modes were suggested for the stearic acid in site 4 [8], the configuration was chosen that is common for all fatty acids and offers electrostatic attachment of the carboxylic acid group. The stearic acid molecules in binding sites 1 and 7 are not fully resolved and were extrapolated to their C-16 position (cf. Appendix A.1.6).

CW EPR Measurements. Continuous wave (CW) EPR spectra were recorded on a Miniscope MS200 (Magnettech, Berlin, Germany) benchtop spectrometer working at X-band (~9.4 GHz) with a modulation amplitude of 0.04 mT and a microwave power of 50 mW. The temperature was adjusted to 293 K with the temperature control unit TC H02 (Magnettech). No change of the spectra was observed upon addition of glycerol.

DEER Measurements and Analysis (Sect. 3.2). Dipolar time evolution data were obtained at X-band frequencies (9.2–9.4 GHz) with a Bruker Elexsys 580 spectrometer equipped with a Bruker Flexline split-ring resonator ER4118X_MS3 using the four-pulse DEER experiment with the pulse sequence [23, 24]. The dipolar evolution time t was varied, whereas $\tau_{1}$ and $\tau_{2} =$ 2.5 μs were kept constant. Proton modulation was averaged by addition of eight time traces of variable $\tau_{1} ,$ starting with $\tau_{1,0} =$ 200 ns and incrementing by $\Updelta \tau_{1} =$ 8 ns [62]. The resonator was overcoupled to $Q \approx$ 100. The pump frequency $v_{\hbox {pump}}$ was set to the maximum of the EPR spectrum. The observer frequency $v_{\hbox {obs}}$ was set to $v_{\hbox {pump}} + 61.6$ MHz, coinciding with the low field local maximum of the nitroxide spectrum. The observer pulse lengths were 32 ns for both $\pi /2$ and $\pi$ pulses and the pump pulse length was 12 ns. The temperature was set to 50 K by cooling with a closed cycle cryostat (ARS AF204, customized for pulse EPR, ARS, Macungie, PA, USA). The total measurement time for each sample was around 6 h. The raw time domain DEER data were processed with the program package DeerAnalysis 2008 [41]. Intermolecular contributions were removed by division by an exponential decay with a fractal dimension of $d =$ 3.8. The deviation from $d =$ 3.0 originates from excluded volume effects due to the size of the protein (see Appendix A.1.5). The resulting time traces were normalized to $t =$ 0. Distance distributions were obtained by Tikhonov regularization using regularization parameters of 100 (16-DSA) and 1000 (5-DSA).

Flip Angle Dependent DEER and Data Analysis (Sect. 3.3). The flip angle of the pump pulse $\beta_{\hbox {pump}}$ was adjusted by the inversion recovery sequence $\beta_{\hbox {pump}}- T - \left( {\pi /2} \right)_{\hbox {obs}} - \tau - \pi_{\hbox {obs}} - \tau - {\hbox {echo}}$ with T = 400 ns and $\tau =$ 200 ns on the maximum of the nitroxide spectrum. A maximum inversion efficiency $\lambda_{\max }$ is achieved at a flip angle $\pi_{\hbox {pump} }$. The inversion efficiency was defined by $\lambda = 0.5\left( {1 - I_{\max } /I_{\hbox {inv}} } \right)$ with $I_{\max }$ being the echo amplitude without inversion by a pump pulse and $I_{\hbox {inv}}$ the signed amplitude of the inverted echo [32]. The flip angle of the pump pulse was decreased by attenuation (A) of the power output of the external microwave source with a step attenuator DC-18 GHz (Narda Microwave Corporation, New York) to obtain nominal flip angles $\beta = \pi \cdot 10^{ - A/20\hbox{dB}}$ [32]. Attenuator settings of 0, 2, 3, 5, 7, and 10 dB were chosen for each flip angle dependent DEER experiment. The length of the pump pulse was kept at $t_{\hbox{pump}} =$ 12 ns to provide for a constant excitation bandwidth. The actual experimental flip angles were calculated by $\beta = \arccos \left( {1 - 2\lambda /\lambda_{\max } } \right)$ [32]. Dipolar time evolution data for each attenuator setting were obtained with the four-pulse DEER experiment as specified in the previous paragraph. $\tau_{2}$ was set to 2.2 μs for mixtures of HSA and 16-DSA and to 2.0 μs for samples containing 5-DSA. The measurement time of a single time trace was around 4 h, resulting in a total measurement time of 24 h for each sample. Intermolecular contributions were removed by division by an exponential decay with a fractal dimension of $d =$ 3.8. Two-spin and three-spin contributions were extracted from the background-corrected time-domain data with a slightly modified Matlab program kindly provided by Gunnar Jeschke. Details of the data analysis are described in Ref. [32].

Cu(II)–Nitroxide DEER with Orientation Selection (Sect. 3.4). First, an ESE detected spectrum of the combined copper and nitroxide spectrum was recorded with the primary echo sequence $\pi /2 - \tau - \pi - \tau - {\hbox{echo}}$ with $\tau =$ 200 ns. The temperature was set to 10 K. The nitroxide contribution was partly removed by subtraction of a nitroxide spectrum from a 1:2 mixture of HSA and 16-DSA. The residual spectrum was pseudomodulated with a modulation amplitude of 1 mT and simulated with a home-written Matlab program, which utilizes the slow motion routine of the Easyspin software package for EPR (see Sect. 2.7) [34, 63]. Collinear uni-axial g and A tensors and a natural isotopic composition of Cu (69.2% ⁶³Cu, 30.8% ⁶⁵Cu) were assumed. Dipolar time evolution data were obtained with the four-pulse DEER experiment (see above). The frequency of the pump pulse was kept at the maximum of the nitroxide spectrum and at the center of the resonator mode while the position of the observer pulse was varied in the copper spectrum (cf. Fig. 3.10).

Simulation of the DEER Spectra. The simulation of the copper spectrum was used to calculate the orientation selection at different observer pulse positions (routine ‘orisel’ in Easyspin). The orientational weights were implemented in a home-written Matlab program, which simulated DEER time-domain data and frequency spectra on the basis of available crystallographic data. In crystal structure PDB 1o9x, HSA is co-crystallized with hemin and six myristic acid molecules [44], while HSA is co-crystallized with seven stearic acid molecules in PDB 1e7i [8]. The distances and relative orientations between the central atom of the porphyrin complex (representing Cu²⁺) and the C-16 positions of the fatty acids (as an approximation for the free nitroxide electron) were obtained by merging the two crystal structures in one common coordinate system. Specifically, hemin was inserted in the crystal structure PDB 1e7i. Its relative position with respect to the fatty acids was calculated utilizing the C-1 atoms of the fatty acids in sites 2–6 as references. The orientational relationship between porphyrin and fatty acid was expressed by the angle $\delta$ between the connecting vector (Cu(II)–C-16) and the z-axis of the molecular Cu(II) frame. The C-16 position of the stearic acid in site 7 was obtained by linear extrapolation. The structural relation of Cu(II) to all stearic acids in sites 2–7 gave rise to six distance–angle pairs $\left( {r,\delta } \right)$: (2.36 nm, 64.7°), (2.98 nm, 56.2°), (2.38 nm, 85.7°), (4.25 nm, 73.2°), (3.93 nm, 88.5°), and (2.67 nm, 75.8°). The distances were broadened by a Gaussian distribution with $\sigma =$ 0.14 nm. Each distance peak was divided into 40 equally spaced contributions ($\Updelta r =$ 0.05 nm), which were weighted according to the Gaussian distribution.

The molecular coordinate frame of Cu²⁺ served as reference frame, since only copper was assumed to exhibit a pronounced orientation selection. Using Eq. 2.101, 10,000 dipolar frequencies were calculated for each distance contribution of each distance–angle pair, originating from an array of 100$\times$100 orientations of the magnetic field vector in the unit sphere. The effective $g$-value for each orientation of the magnetic field vector was obtained by Eq. 2.46. The dipolar frequencies were multiplied with the orientational weight for the respective magnetic field orientation, as obtained by ‘orisel’, and by $\hbox{sin}\,\theta$. These frequency contributions were added to generate dipolar spectra and were used to calculate time-domain data according to Eq. 2.100. To shorten the calculation time, only magnetic field vector orientations with weights >1% and distance contributions >5% of the maximum values were considered. One simulation run was completed within 30 min.

MD Simulations. Energy minimization and all MD simulations were performed in the YASARA program package [64]. The crystal structure of HSA co-crystallized with 7 stearic acids (1e7i) was first energy-minimized using the YASARA force field. The energy-minimized protein was put in a 10$\times$10$\times$10 nm box and filled with water molecules (pH 7.4) to obtain a density of ~1030 g/l. The temperature was set to 298 K. The individual time step was 2 fs and a snapshot of the box was taken every 5 ps. The averaged protein structure obtained of 1200 snapshots (corresponding to relaxation times 0.425–6.425 ns) was analyzed. All distances between the C-16 and C-5 positions of the stearic acids in this structure are summarized in Tables A.3 and A.4 in Appendix A.1.8.