Benchmark Test and Guidelines for DEER/PELDOR Experiments on Nitroxide-Labeled Biomolecules

Distance distribution information obtained by pulsed dipolar EPR spectroscopy provides an important contribution to many studies in structural biology. Increasingly, such information is used in integrative structural modeling, where it delivers unique restraints on the width of conformational ensembles. In order to ensure reliability of the structural models and of biological conclusions, we herein define quality standards for sample preparation and characterization, for measurements of distributed dipole-dipole couplings between paramagnetic labels, for conversion of the primary time-domain data into distance distributions, for interpreting these distributions, and for reporting results. These guidelines are substantiated by a multi-laboratory benchmark study and by analysis of data sets with known distance distribution ground truth. The study and the guidelines focus on proteins labeled with nitroxides and on double electron-electron resonance (DEER aka PELDOR) measurements and provide suggestions on how to proceed analogously in other cases.

Protein functional dynamics from the rigorous global analysis of DEER data: Conditions, components, and conformations

The potential of spin labeling to reveal the dynamic dimension of macromolecules has been recognized since the dawn of the methodology in the 1960s. However, it was the development of pulsed electron paramagnetic resonance spectroscopy to detect dipolar coupling between spin labels and the availability of turnkey instrumentation in the 21st century that realized the full promise of spin labeling. Double electron-electron resonance (DEER) spectroscopy has seen widespread applications to channels, transporters, and receptors. In these studies, distance distributions between pairs of spin labels obtained under different biochemical conditions report the conformational states of macromolecules, illuminating the key movements underlying biological function. These experimental studies have spurred the development of methods for the rigorous analysis of DEER spectroscopic data along with methods for integrating these distributions into structural models. In this tutorial, we describe a model-based approach to obtaining a minimum set of components of the distance distribution that correspond to functionally relevant protein conformations with a set of fractional amplitudes that define the equilibrium between these conformations. Importantly, we review and elaborate on the error analysis reflecting the uncertainty in the various parameters, a critical step in rigorous structural interpretation of the spectroscopic data.

Confidence Analysis of DEER Data and Its Structural Interpretation with Ensemble-Biased Metadynamics

Given its ability to measure multicomponent distance distributions between electron-spin probes, double electron-electron resonance (DEER) spectroscopy has become a leading technique to assess the structural dynamics of biomolecules. However, methodologies to evaluate the statistical error of these distributions are not standard, often hampering a rigorous interpretation of the experimental results. Distance distributions are often determined from the experimental DEER data through a mathematical method known as Tikhonov regularization, but this approach makes rigorous error estimates difficult. Here, we build upon an alternative, model-based approach in which the distance probability distribution is represented as a sum of Gaussian components, and use propagation of errors to calculate an associated confidence band. Our approach considers all sources of uncertainty, including the experimental noise, the uncertainty in the fitted background signal, and the limited time span of the data collection. The resulting confidence band reveals the most and least reliable features of the probability distribution, thereby informing the structural interpretation of DEER experiments. To facilitate this interpretation, we also generalize the molecular simulation method known as ensemble-biased metadynamics (EBMetaD). This method, originally designed to generate maximal-entropy structural ensembles consistent with one or more probability distributions, now also accounts for the uncertainty in those target distributions exactly as dictated by their confidence bands. After careful benchmarks, we demonstrate the proposed techniques using DEER results from spin-labeled T4 lysozyme.

Long Distance Measurements up to 160 Å in the GroEL Tetradecamer Using Q-Band DEER EPR Spectroscopy

Current distance measurements between spin-labels on multimeric protonated proteins using double electron-electron resonance (DEER) EPR spectroscopy are generally limited to the 15-60 Å range. Here we show how DEER experiments can be extended to dipolar evolution times of ca. 80 μs, permitting distances up to 170 Å to be accessed in multimeric proteins. The method relies on sparse spin-labeling, supplemented by deuteration of protein and solvent, to minimize the deleterious impact of multispin effects and substantially increase the apparent spin-label phase memory relaxation time, complemented by high sensitivity afforded by measurements at Q-band. We demonstrate the approach using the tetradecameric molecular machine GroEL as an example. Two engineered surface-exposed mutants, R268C and E315C, are used to measure pairwise distance distributions with mean values ranging from 20 to 100 Å and from 30 to 160 Å, respectively, both within and between the two heptameric rings of GroEL. The measured distance distributions are consistent with the known crystal structure of apo GroEL. The methodology presented here should significantly expand the use of DEER for the structural characterization of conformational changes in higher order oligomers.

Assembly of Bak homodimers into higher order homooligomers in the mitochondrial apoptotic pore

In mitochondrial apoptosis, Bak is activated by death signals to form pores of unknown structure on the mitochondrial outer membrane via homooligomerization. Cytochrome c and other apoptotic factors are released from the intermembrane space through these pores, initiating downstream apoptosis events. Using chemical crosslinking and double electron electron resonance (DEER)-derived distance measurements between specific structural elements in Bak, here we clarify how the Bak pore is assembled. We propose that previously described BH3-in-groove homodimers (BGH) are juxtaposed via the 'α3/α5' interface, in which the C-termini of helices α3 and α5 are in close proximity between two neighboring Bak homodimers. This interface is observed concomitantly with the well-known 'α6:α6' interface. We also mapped the contacts between Bak homodimers and the lipid bilayer based on EPR spectroscopy topology studies. Our results suggest a model for the lipidic Bak pore, whereby the mitochondrial targeting C-terminal helix does not change topology to accommodate the lining of the pore lumen by BGH.

A Straightforward Approach to the Analysis of Double Electron-Electron Resonance Data

Double electron-electron resonance (DEER) is now widely utilized to measure distance distributions in the 20-70Å range. DEER is frequently applied to biological systems that have multiple conformational states leading to complex distance distributions. These complex distributions raise issues regarding the best approach to analyze DEER data. A widely used method utilizes a priori background correction followed by Tikhonov regularization. Unfortunately, the underlying assumptions of this approach can impact the analysis. In this chapter, a method of analyzing DEER data is presented that is ideally suited to obtain these complex distance distributions. The approach allows the fitting of raw experimental data without a priori background correction as well as the rigorous determination of uncertainties for all fitting parameters. This same methodological approach can be used for the simultaneous or global analysis of multiple DEER data sets using variable ratios of a common set of components, thus allowing direct correlation of distance components with functionally relevant conformational and biochemical states. Examples are given throughout to highlight this robust fitting approach.

CW dipolar broadening EPR spectroscopy and mechanically aligned bilayers used to measure distance and relative orientation between two TOAC spin labels on an antimicrobial peptide

An EPR membrane alignment technique was applied to measure distance and relative orientations between two spin labels on a protein oriented along the surface of the membrane. Previously we demonstrated an EPR membrane alignment technique for measuring distances and relative orientations between two spin labels using a dual TOAC-labeled integral transmembrane peptide (M2δ segment of Acetylcholine receptor) as a test system. In this study we further utilized this technique and successfully measured the distance and relative orientations between two spin labels on a membrane peripheral peptide (antimicrobial peptide magainin-2). The TOAC-labeled magainin-2 peptides were mechanically aligned using DMPC lipids on a planar quartz support, and CW-EPR spectra were recorded at specific orientations. Global analysis in combination with rigorous spectral simulation was used to simultaneously analyze data from two different sample orientations for both single- and double-labeled peptides. We measured an internitroxide distance of 15.3Å from a dual TOAC-labeled magainin-2 peptide at positions 8 and 14 that closely matches with the 13.3Å distance obtained from a model of the labeled magainin peptide. In addition, the angles determining the relative orientations of the two nitroxides have been determined, and the results compare favorably with molecular modeling. This study demonstrates the utility of the technique for proteins oriented along the surface of the membrane in addition to the previous results for proteins situated within the membrane bilayer.

Automated structure refinement for a protein heterodimer complex using limited EPR spectroscopic data and a rigid-body docking algorithm: a three-dimensional model for an ankyrin-CDB3 complex

We report here specialized functions incorporated recently in the rigid-body docking software toolkit TagDock to utilize electron paramagnetic resonance derived (EPR-derived) interresidue distance measurements and spin-label accessibility data. The TagDock package extensions include a custom methanethiosulfonate spin label rotamer library to enable explicit, all-atom spin-label side-chain modeling and scripts to evaluate spin-label surface accessibility. These software enhancements enable us to better utilize the biophysical data routinely available from various spin-labeling experiments. To illustrate the power and utility of these tools, we report the refinement of an ankyrin:CDB3 complex model that exhibits much improved agreement with the EPR distance measurements, compared to model structures published previously.

Competition between homodimerization and cholesterol binding to the C99 domain of the amyloid precursor protein

The 99-residue transmembrane C-terminal domain (C99, also known as β-CTF) of the amyloid precursor protein (APP) is the product of the β-secretase cleavage of the full-length APP and is the substrate for γ-secretase cleavage. The latter cleavage releases the amyloid-β polypeptides that are closely associated with Alzheimer's disease. C99 is thought to form homodimers; however, the free energy in favor of dimerization has not previously been quantitated. It was also recently documented that cholesterol forms a 1:1 complex with monomeric C99 in bicelles. Here, the affinities for both homodimerization and cholesterol binding to C99 were measured in bilayered lipid vesicles using both electron paramagnetic resonance (EPR) and Förster resonance energy transfer (FRET) methods. Homodimerization and cholesterol binding were seen to be competitive processes that center on the transmembrane G₇₀₀XXXG₇₀₄XXXG₇₀₈ glycine-zipper motif and adjacent Gly709. On one hand, the observed Kd for cholesterol binding (Kd = 2.7 ± 0.3 mol %) is on the low end of the physiological cholesterol concentration range in mammalian cell membranes. On the other hand, the observed K(d) for homodimerization (K(d) = 0.47 ± 0.15 mol %) likely exceeds the physiological concentration range for C99. These results suggest that the 1:1 cholesterol/C99 complex will be more highly populated than C99 homodimers under most physiological conditions. These observations are of relevance for understanding the γ-secretase cleavage of C99.

Structural arrangement of the intracellular Ca2+ binding domains of the cardiac Na+/Ca2+ exchanger (NCX1.1): effects of Ca2+ binding

The cardiac Na(+)/Ca(2+) exchanger (NCX1.1) serves as the primary means of Ca(2+) extrusion across the plasma membrane of cardiomyocytes after the rise in intracellular Ca(2+) during contraction. The exchanger is regulated by binding of Ca(2+) to its intracellular domain, which contains two structurally homologous Ca(2+) binding domains denoted as CBD1 and CBD2. NMR and x-ray crystallographic studies have provided structures for the isolated CBD1 and CBD2 domains and have shown how Ca(2+) binding affects their structures and motional dynamics. However, structural information on the entire Ca(2+) binding domain, denoted CBD12, and how binding of Ca(2+) alters its structure and dynamics is more limited. Site-directed spin labeling has been employed in this work to address these questions. Electron paramagnetic resonance measurements on singly labeled constructs of CBD12 have identified the regions that undergo changes in dynamics as a result of Ca(2+) binding. Double electron-electron resonance (DEER) measurements on doubly labeled constructs of CBD12 have shown that the β-sandwich regions of the CBD1 and CBD2 domains are largely insensitive to Ca(2+) binding and that these two domains are widely separated at their N and C termini. Interdomain distances measured by DEER have been employed to construct structural models for CBD12 in the presence and absence of Ca(2+). These models show that there is not a major change in the relative orientation of the two Ca(2+) binding domains as a result of Ca(2+) binding in the NCX1.1 isoform. Additional measurements have shown that there are significant changes in the dynamics of the F-G loop region of CBD2 that merit further characterization with regard to their possible involvement in regulation of NCX1.1 activity.

Inter-spin distance determination using L-band (1-2 GHz) non-adiabatic rapid sweep electron paramagnetic resonance (NARS EPR)

Site-directed spin-labeling electron paramagnetic resonance (SDSL EPR) provides insight into the local structure and motion of a spin probe strategically attached to a molecule. When a second spin is introduced to the system, macromolecular information can be obtained through measurement of inter-spin distances either by continuous wave (CW) or pulsed electron double resonance (ELDOR) techniques. If both methodologies are considered, inter-spin distances of 8-80 Å can be experimentally determined. However, there exists a region at the upper limit of the conventional X-band (9.5 GHz) CW technique and the lower limit of the four-pulse double electron-electron resonance (DEER) experiment where neither method is particularly reliable. The work presented here utilizes L-band (1.9 GHz) in combination with non-adiabatic rapid sweep (NARS) EPR to address this opportunity by increasing the upper limit of the CW technique. Because L-band linewidths are three to seven times narrower than those at X-band, dipolar broadenings that are small relative to the X-band inhomogeneous linewidth become observable, but the signal loss, due to the frequency dependence of the Boltzmann factor, has made L-band especially challenging. NARS has been shown to increase sensitivity by a factor of five, and overcomes much of this loss, making L-band distance determination more feasible. Two different systems are presented, and distances of 18-30 Å have been experimentally determined at physiologically relevant temperatures. Measurements are in excellent agreement with a helical model and values determined by DEER.

The amyloid precursor protein has a flexible transmembrane domain and binds cholesterol

C99 is the transmembrane carboxyl-terminal domain of the amyloid precursor protein that is cleaved by γ-secretase to release the amyloid-β polypeptides, which are associated with Alzheimer's disease. Nuclear magnetic resonance and electron paramagnetic resonance spectroscopy show that the extracellular amino terminus of C99 includes a surface-embedded "N-helix" followed by a short "N-loop" connecting to the transmembrane domain (TMD). The TMD is a flexibly curved α helix, making it well suited for processive cleavage by γ-secretase. Titration of C99 reveals a binding site for cholesterol, providing mechanistic insight into how cholesterol promotes amyloidogenesis. Membrane-buried GXXXG motifs (G, Gly; X, any amino acid), which have an established role in oligomerization, were also shown to play a key role in cholesterol binding. The structure and cholesterol binding properties of C99 may aid in the design of Alzheimer's therapeutics.

The global analysis of DEER data

Double Electron-Electron Resonance (DEER) has emerged as a powerful technique for measuring long range distances and distance distributions between paramagnetic centers in biomolecules. This information can then be used to characterize functionally relevant structural and dynamic properties of biological molecules and their macromolecular assemblies. Approaches have been developed for analyzing experimental data from standard four-pulse DEER experiments to extract distance distributions. However, these methods typically use an a priori baseline correction to account for background signals. In the current work an approach is described for direct fitting of the DEER signal using a model for the distance distribution which permits a rigorous error analysis of the fitting parameters. Moreover, this approach does not require a priori background correction of the experimental data and can take into account excluded volume effects on the background signal when necessary. The global analysis of multiple DEER data sets is also demonstrated. Global analysis has the potential to provide new capabilities for extracting distance distributions and additional structural parameters in a wide range of studies.

Distance measurements on a dual-labeled TOAC AChR M2δ peptide in mechanically aligned DMPC bilayers via dipolar broadening CW-EPR spectroscopy

A membrane alignment technique has been used to measure the distance between two TOAC nitroxide spin labels on the membrane-spanning M2δ, peptide of the nicotinic acetylcholine receptor (AChR), via CW-EPR spectroscopy. The TOAC-labeled M2δ peptides were mechanically aligned using DMPC lipids on a planar quartz support, and CW-EPR spectra were recorded at specific orientations. Global analysis in combination with rigorous spectral simulation was used to simultaneously analyze data from two different sample orientations for both single- and double-labeled peptides. We measured an internitroxide distance of 14.6 Å from a dual TOAC-labeled AChR M2δ peptide at positions 7 and 13 that closely matches with the 14.5 Å distance obtained from a model of the labeled AChR M2δ peptide. In addition, the angles determining the relative orientation of the two nitroxides have been determined, and the results compare favorably with molecular modeling. The global analysis of the data from the aligned samples gives much more precise estimates of the parameters defining the geometry of the two labels than can be obtained from a randomly dispersed sample.

Determination of structural models of the complex between the cytoplasmic domain of erythrocyte band 3 and ankyrin-R repeats 13-24

The adaptor protein ankyrin-R interacts via its membrane binding domain with the cytoplasmic domain of the anion exchange protein (AE1) and via its spectrin binding domain with the spectrin-based membrane skeleton in human erythrocytes. This set of interactions provides a bridge between the lipid bilayer and the membrane skeleton, thereby stabilizing the membrane. Crystal structures for the dimeric cytoplasmic domain of AE1 (cdb3) and for a 12-ankyrin repeat segment (repeats 13-24) from the membrane binding domain of ankyrin-R (AnkD34) have been reported. However, structural data on how these proteins assemble to form a stable complex have not been reported. In the current studies, site-directed spin labeling, in combination with electron paramagnetic resonance (EPR) and double electron-electron resonance, has been utilized to map the binding interfaces of the two proteins in the complex and to obtain inter-protein distance constraints. These data have been utilized to construct a family of structural models that are consistent with the full range of experimental data. These models indicate that an extensive area on the peripheral domain of cdb3 binds to ankyrin repeats 18-20 on the top loop surface of AnkD34 primarily through hydrophobic interactions. This is a previously uncharacterized surface for binding of cdb3 to AnkD34. Because a second dimer of cdb3 is known to bind to ankyrin repeats 7-12 of the membrane binding domain of ankyrin-R, the current models have significant implications regarding the structural nature of a tetrameric form of AE1 that is hypothesized to be involved in binding to full-length ankyrin-R in the erythrocyte membrane.

Conformational equilibria of bulged sites in duplex DNA studied by EPR spectroscopy

Conformational flexibility in nucleic acids provides a basis for complex structures, binding, and signaling. One-base bulges directly neighboring single-base mismatches in nucleic acids can be present in a minimum of two distinct conformations, complicating the examination of the thermodynamics by calorimetry or UV-monitored melting techniques. To provide additional information about such structures, we demonstrate how electron paramagnetic resonance (EPR) active spin-labeled base analogues, base-specifically incorporated into the DNA, are monitors of the superposition of different bulge-mismatch conformations. EPR spectra provide information about the dynamic environments of the probe. This information is cast in terms of "dynamic signatures" that have an underlying basis in structural variations. By examining the changes in the equilibrium of the different states across a range of temperatures, the enthalpy and entropy of the interconversion among possible conformations can be determined. The DNA constructs with a single bulge neighboring a single-base mismatch ("bulge-mismatches") may be approximately modeled as an equilibrium between two possible conformations. This structural information provides insight into the local composition of the bulge-mismatch sequences. Experiments on the bulge-mismatches show that basepairing across the helix can be understood in terms of purine and pyrimidine interactions, rather than specific bases. Measurements of the enthalpy and entropy of formation for the bulge-mismatches by differential scanning calorimetry and UV-monitored melting confirm that the formation of bulge-mismatches is in fact more complicated than a simple two-state process, consistent with the base-specific spectral data that bulge-mismatches exist in multiple conformations in the premelting temperature region. We find that the calculations with the nearest-neighbor (NN) model for the two likely conformations do not correlate well with the populations of structures and thermodynamic parameters inferred from the base-specific EPR dynamics probe. We report that the base-specific spin probes are able to identify a bistable, temperature dependent, switching between conformations for a particular complex bulged construct.

Simulation of nitroxide electron paramagnetic resonance spectra from brownian trajectories and molecular dynamics simulations

A simulated continuous wave electron paramagnetic resonance spectrum of a nitroxide spin label can be obtained from the Fourier transform of a free induction decay. It has been previously shown that the free induction decay can be calculated by solving the time-dependent stochastic Liouville equation for a set of Brownian trajectories defining the rotational dynamics of the label. In this work, a quaternion-based Monte Carlo algorithm has been developed to generate Brownian trajectories describing the global rotational diffusion of a spin-labeled protein. Also, molecular dynamics simulations of two spin-labeled mutants of T4 lysozyme, T4L F153R1, and T4L K65R1 have been used to generate trajectories describing the internal dynamics of the protein and the local dynamics of the spin-label side chain. Trajectories from the molecular dynamics simulations combined with trajectories describing the global rotational diffusion of the protein are used to account for all of the dynamics of a spin-labeled protein. Spectra calculated from these combined trajectories correspond well to the experimental spectra for the buried site T4L F153R1 and the helix surface site T4L K65R1. This work provides a framework to further explore the modeling of the dynamics of the spin-label side chain in the wide variety of labeling environments encountered in site-directed spin labeling studies.

Carbon-centered radicals in isolated soy proteins

Solid-state electron paramagnetic resonance (EPR) spectroscopy of commercial samples of isolated soy proteins (ISP) revealed a symmetrical free-radical signal typical of carbon-centered radicals (g= 2.005) ranging from 2.96 x 10(14) to 6.42 x 10(14) spins/g. The level of free radicals in ISP was 14 times greater than similar radicals in sodium caseinate, 29 times greater than egg albumin, and about 100 times greater levels than casein. Nine soy protein powdered drink mixes contained similar types of free radicals up to 4.10 x 10(15) spins/g of drink mix, or up to 6.4 times greater than the highest free-radical content found in commercial ISP. ISP samples prepared in the laboratory contained trapped radicals similar to the levels in commercial ISP samples. When ISP was hydrated in 2.3 mM sodium erythorbate or 8.3 mM L-cysteine, frozen and dried, the level of trapped free radicals increased by about 17- and 19-fold, respectively. The ESR spectrum of defatted soybean flakes contained overlapping signals from the primary free-radical peak (g= 2.005) and a sextet pattern typical of manganese-II. The manganese signal was reduced in the laboratory ISP and very weak in the commercial ISP.

Structure of the cytoplasmic domain of erythrocyte band 3 hereditary spherocytosis variant P327R: band 3 Tuscaloosa

Previous studies have shown that a single P327R point mutation in the cytoplasmic domain of band 3 (cdb3) protein, known as band 3 Tuscaloosa, leads to a reduction in protein 4.2 content of the erythrocyte membrane and hemolytic anemia. Recent studies have shown that this point mutation does not dissociate the cdb3 dimer, nor does it lead to large-scale rearrangement of the protein structure (Bustos, S. P., and Reithmeier, R. A. F. (2006) Biochemistry 45, 1026-1034). To better define the structural changes in cdb3 that lead to the hemolytic anemia phenotype, site-directed spin labeling (SDSL), in combination with continuous wave electron paramagnetic resonance (EPR) and pulsed double electron-electron resonance (DEER) spectroscopies, has been employed in this study to compare the structure of the R327 variant with wild type P327 cdb3. It is confirmed that the P327R mutation does not dissociate the cdb3 dimer, nor does it change the spatial orientation of the two peripheral domains relative to the dimer interface. However, it does affect the packing of the C-terminal end of helix 10 of the dimerization arms in a subpopulation of cdb3 dimers, it leads to spectral changes at some residues in beta-strand 11 and in the N-terminal end of helix10, and it produces measurable spectral changes at other residues that are near the mutation site. The data indicate that the structural changes are subtle and are localized to one surface of the cdb3 dimer. The spectroscopic description of structural features of the P327R variant provides important clues about the location of one potential protein 4.2 binding surface on cdb3 as well as new insight into the structural basis of the membrane destabilization.

Solution structure of the cytoplasmic domain of erythrocyte membrane band 3 determined by site-directed spin labeling

The cytoplasmic domain of the anion exchange protein (cdb3) serves as a critical organizing center for protein-protein interactions that stabilize the erythrocyte membrane. The structure of the central core of cdb3, determined by X-ray crystallography from crystals grown at pH 4.8, revealed a compact dimer for residues 55-356 and unresolved N- and C-termini on each monomer [Zhang et al. (2000) Blood 96, 2925-2933]. Given that previous studies had suggested a highly asymmetric structure for cdb3 and that pH dependent structural transitions of cdb3 have been reported, the structure of cdb3 in solution at neutral pH was investigated via site-directed spin labeling in combination with conventional electron paramagnetic resonance (EPR) and double electron electron resonance (DEER) spectroscopies. These studies show that the structure of the central compact dimer (residues 55-356) is indistinguishable from the crystal structure determined at pH 4.8. N-Terminal residues 1-54 and C-terminal residues 357-379 are dynamically disordered and show no indications of stable secondary structure. These results establish a structural model for cdb3 in solution at neutral pH which represents an important next step in characterizing structural details of the protein-protein interactions that stabilize the erythrocyte membrane.

Dipolar coupling between nitroxide spin labels: the development and application of a tether-in-a-cone model

A tether-in-a-cone model is developed for the simulation of electron paramagnetic resonance spectra of dipolar coupled nitroxide spin labels attached to tethers statically disordered within cones of variable halfwidth. In this model, the nitroxides adopt a range of interprobe distances and orientations. The aim is to develop tools for determining both the distance distribution and the relative orientation of the labels from experimental spectra. Simulations demonstrate the sensitivity of electron paramagnetic resonance spectra to the orientation of the cones as a function of cone halfwidth and other parameters. For small cone halfwidths (< approximately 40 degrees ), simulated spectra are strongly dependent on the relative orientation of the cones. For larger cone halfwidths, spectra become independent of cone orientation. Tether-in-a-cone model simulations are analyzed using a convolution approach based on Fourier transforms. Spectra obtained by the Fourier convolution method more closely fit the tether-in-a-cone simulations as the halfwidth of the cone increases. The Fourier convolution method gives a reasonable estimate of the correct average distance, though the distance distribution obtained can be significantly distorted. Finally, the tether-in-a-cone model is successfully used to analyze experimental spectra from T4 lysozyme. These results demonstrate the utility of the model and highlight directions for further development.

High field/high frequency saturation transfer electron paramagnetic resonance spectroscopy: increased sensitivity to very slow rotational motions

Saturation transfer electron paramagnetic resonance (ST-EPR) spectroscopy has been employed to characterize the very slow microsecond to millisecond rotational dynamics of a wide range of nitroxide spin-labeled proteins and other macromolecules in the past three decades. The vast majority of this previous work has been carried out on spectrometers that operate at X-band ( approximately 9 GHz) microwave frequency with a few investigations reported at Q-band ( approximately 34 GHz). EPR spectrometers that operate in the 94-250-GHz range and that are capable of making conventional linear EPR measurements on small aqueous samples have now been developed. This work addresses potential advantages of utilizing these same high frequencies for ST-EPR studies that seek to quantitatively analyze the very slow rotational dynamics of spin-labeled macromolecules. For example, the uniaxial rotational diffusion (URD) model has been shown to be particularly applicable to the study of the rotational dynamics of integral membrane proteins. Computational algorithms have been employed to define the sensitivity of ST-EPR signals at 94, 140, and 250 GHz to the correlation time for URD, to the amplitude of constrained URD, and to the orientation of the spin label relative to the URD axis. The calculations presented in this work demonstrate that these higher microwave frequencies provide substantial increases in sensitivity to the correlation time for URD, to small constraints in URD, and to the geometry of the spin label relative to the URD axis as compared with measurements made at X-band. Moreover, the calculations at these higher frequencies indicate sensitivity to rotational motions in the 1-100-ms time window, particularly at 250 GHz, thereby extending the slow motion limit for ST-EPR by two orders of magnitude relative to X- and Q-bands.

Formulation of Zeeman modulation as a signal filter

The Bloch equation containing a Zeeman modulation field is solved analytically by treating the Zeeman modulation frequency as a perturbation. The absorption and dispersion signals at both 0 degrees and 90 degrees modulation phase are obtained. The solutions are valid to first order in the modulation frequency, but are otherwise valid for any value of modulation amplitude or microwave amplitude. A first order treatment of modulation frequency is shown to be a valid approximation over a wide range of typical experimental EPR conditions. The solutions derived from the Bloch equation suggest that the effect of over-modulation on first and second harmonic EPR spectra can be formulated as a mathematical filter that smoothes and broadens the under-modulated signal. The only adjustable filter parameter is a width that is equivalent to the applied peak-to-peak modulation amplitude. The true spin-spin and spin-lattice relaxation rates are completely determined from the under-modulated spectrum. The filters derived from the analytic solutions of the Bloch equation in the linear limit of modulation frequency are tested against numerical solutions of the Bloch equation that are valid for any modulation frequency to show their applicability. The filters are further tested using experimental EPR spectra. Experimental under-modulated spectra are mathematically filtered and compared with the experimental over-modulated spectra. The application of modulation filters to STEPR spectra is explored and limitations are discussed.

Rotational dynamics of the epidermal growth factor receptor

We have examined the rotational mobility of SL-EGF, a bifunctional adduct of bis(sulfo-N-succinimidyl)-[(15)N,(2)H(16)]-doxyl-2-spiro-4'-pimelate and [Lys3,Tyr22]-murine epidermal growth factor, bound to the EGF receptor in A431 membrane vesicles. The linear EPR spectrum indicated that there was essentially no free SL-EGF in the bound complex preparation. To better define the rotational mobility of the SL-EGF bound to the EGF receptor, ST-EPR spectra were obtained at multiple Zeeman field modulation frequencies. Global analysis with a uniaxial rotational diffusion model of the ST-EPR data yielded two minima that have differences in rotational mobility and in orientation of the SL-EGF relative to the membrane normal axis. The rotational mobilities of the two rotational species are consistent with monomers and dimers or somewhat larger oligomers, such as trimers or tetramers, arguing against a role for higher order receptor clustering in receptor activation. Considering the two minima and previous observations that A431 membrane vesicles contain two distinguishable ligand-binding populations, the ST-EPR spectra were fit with a model having two uniaxial rotating species. This yielded two components that were similar to those obtained from the two original one-component fits, either fast or slow rotational mobility, with different orientations. The model-dependent results obtained suggest that there are potential conformational and rotational differences in the two populations and provide a plausible description for the origin of high- and low-affinity EGF-binding sites that can be tested in future experiments.

The sensitivity of saturation transfer electron paramagnetic resonance spectra to restricted amplitude uniaxial rotational diffusion

Computational methods have been developed to model the effects of constrained or restricted amplitude uniaxial rotational diffusion (URD) on saturation transfer electron paramagnetic resonance (ST-EPR) signals observed from nitroxide spin labels. These methods, which have been developed to model the global rotational motion of intrinsic membrane proteins that can interact with the cytoskeleton or other peripheral proteins, are an extension of previous work that described computationally efficient algorithms for calculating ST-EPR spectra for unconstrained URD (Hustedt and Beth, 1995, Biophys. J. 69:1409-1423). Calculations are presented that demonstrate the dependence of the ST-EPR signal (V'(2)) on the width (Delta) of a square-well potential as a function of the microwave frequency, the correlation time for URD, and the orientation of the spin-label with respect to the URD axis. At a correlation time of 10 micros, the V'(2) signal is very sensitive to Delta in the range from 0 to 60 degrees, marginally sensitive from 60 degrees to 90 degrees, and insensitive beyond 90 degrees. Sensitivity to Delta depends on the correlation time for URD with higher sensitivity to large values of Delta at the shorter correlation times, on the microwave frequency, and on the orientation of the spin-label relative to the URD axis. The computational algorithm has been incorporated into a global nonlinear least-squares analysis approach, based upon the Marquardt-Levenberg method (Blackman et al., 2001, Biophys. J. 81:3363-3376). This has permitted determination of the correlation time for URD and the width of the square-well potential by automated fitting of experimental ST-EPR data sets obtained from a spin-labeled membrane protein and provided a new automated method for analysis of data obtained from any system that exhibits restricted amplitude URD.

Flexibility of the cytoplasmic domain of the anion exchange protein, band 3, in human erythrocytes

The rotational flexibility of the cytoplasmic domain of band 3, in the region that is proximal to the inner membrane surface, has been investigated using a combination of time-resolved optical anisotropy (TOA) and saturation-transfer electron paramagnetic resonance (ST-EPR) spectroscopies. TOA studies of rotational diffusion of the transmembrane domain of band 3 show a dramatic decrease in residual anisotropy following cleavage of the link with the cytoplasmic domain by trypsin (E. A. Nigg and R. J. Cherry, 1980, Proc. Natl. Acad. Sci. U.S.A. 77:4702-4706). This result is compatible with two independent hypotheses: 1) trypsin cleavage leads to dissociation of large clusters of band 3 that are immobile on the millisecond time scale, or 2) trypsin cleavage leads to release of a constraint to uniaxial rotational diffusion of the transmembrane domain. ST-EPR studies at X- and Q-band microwave frequencies detect rotational diffusion of the transmembrane domain of band 3 about the membrane normal axis of reasonably large amplitude that does not change upon cleavage with trypsin. These ST-EPR results are not consistent with dissociation of clusters of band 3 as a result of cleavage with trypsin. Global analyses of the ST-EPR data using a newly developed algorithm indicate that any constraint to rotational diffusion of the transmembrane domain of band 3 via interactions of the cytoplasmic domain with the membrane skeleton must be sufficiently weak to allow rotational excursions in excess of 32 degrees full-width for a square-well potential. In support of this result, analyses of the TOA data in terms of restricted amplitude uniaxial rotational diffusion models suggest that the membrane-spanning domain of that population of band 3 that is linked to the membrane skeleton is constrained to diffuse in a square-well of approximately 73 degrees full-width. This degree of flexibility may be necessary for providing the unique mechanical properties of the erythrocyte membrane.

Nitroxide spin-spin interactions: applications to protein structure and dynamics

Measurement of the distance between two spin label probes in proteins permits the spatial orientation of elements of defined secondary structure. By using site-directed spin labeling, it is possible to determine multiple distance constraints and thereby build tertiary and quaternary structural models as well as measure the kinetics of structural changes. New analytical methods for determining interprobe distances and relative orientations for uniquely oriented spin labels have been developed using global analysis of multifrequency electron paramagnetic resonance data. New methods have also been developed for determining interprobe distances for randomly oriented spin labels. These methods are being applied to a wide range of structural problems, including peptides, soluble proteins, and membrane proteins, that are not readily characterized by other structural techniques.

Molecular distances from dipolar coupled spin-labels: the global analysis of multifrequency continuous wave electron paramagnetic resonance data

For immobilized nitroxide spin-labels with a well-defined interprobe geometry, resolved dipolar splittings can be observed in continuous wave electron paramagnetic resonance (CW-EPR) spectra for interelectron distances as large as 30 A using perdeuterated probes. In this work, algorithms are developed for calculating CW-EPR spectra of immobilized, dipolar coupled nitroxides, and then used to define the limits of sensitivity to the interelectron distance as a function of geometry and microwave frequency. Secondly, the CW-EPR spectra of N epsilon-spin-labeled coenzyme NAD+ bound to microcrystalline, tetrameric glyceraldehyde-3-phosphate dehydrogenase (GAPDH) have been collected at 9.8, 34, and 94 GHz. These data have been analyzed, using a combination of simulated annealing and global analysis, to obtain a unique fit to the data. The values of the intermitroxide distance and the five angles defining the relative orientation of the two nitroxides are in reasonable agreement with a molecular model built from the known crystal structure. Finally, the effect of rigid body isotropic rotational diffusion on the CW-EPR spectra of dipolar coupled nitroxides has been investigated using an algorithm based on Brownian dynamics trajectories. These calculations demonstrate the sensitivity of CW-EPR spectra to dipolar coupling in the presence of rigid body rotational diffusion.

Increased rotational mobility and extractability of band 3 from protein 4.2-deficient erythrocyte membranes: evidence of a role for protein 4.2 in strengthening the band 3-cytoskeleton linkage

Band 3 (anion-exchange protein 1-[AE1]) is the major integral membrane protein of human erythrocytes and links the membrane to the underlying cytoskeleton via high-affinity binding to ankyrin. It is unclear whether other cytoskeletal proteins participate in strengthening the ankyrin-band 3 linkage, but a putative role for protein 4.2 (P4.2) has been proposed based on the increased osmotic fragility and spherocytic morphology of P4.2-deficient red blood cells (RBCs). The present study was designed to investigate the hypothesis that P4.2 has a direct role in strengthening the band 3-cytoskeleton linkage in human RBCs, by measuring independent features of this interaction in normal and P4.2-deficient RBCs. The features examined were the rotational mobility of band 3 assayed by time-resolved phosphorescence emission anisotropy (TPA), and the extractability of band 3 by octyl-beta-glucoside, the latter being a nonionic detergent that selectively extracts only band 3 that is not anchored to the cytoskeleton. We find that the amplitude of the most rapidly rotating population of band 3 (correlation time, approximately 30 to 60 microseconds) is increased 81% and 67% in P4.2-deficient ghosts (P4.2NIPPON and band 3MONTEFIORE, respectively) compared with control ghosts. The amplitude of the intermediate speed rotating population of band 3 (correlation time, approximately 200 to 500 microseconds) is increased 23% and 8% in P4.2-deficient ghosts (P4.2NIPPON and band 3MONTEFIORE, respectively) compared with control ghosts, at the expense of the slowly rotating component (correlation time, approximately 2,000 to 3,000 microseconds, amplitude decreased 43% and 39% in P4.2NIPPON and band 3MONTEFIORE, respectively) and immobile component (immobile on this experimental time scale; amplitude decreased 26% and 10% in P4.2NIPPON and band 3MONTEFIORE, respectively) of band 3. These results demonstrate that P4.2 deficiency partially removes band 3 rotational constraints, ie, it increases band 3 rotational mobility. The nonionic detergent octyl-beta-glucoside, which does not disturb band 3-cytoskeleton associations, ie, it extracts only band 3 that is not attached to the cytoskeleton, extracted 30% and 61% more band 3 from P4.2NIPPON and band 3MONTEFIORE ghost membranes, respectively, compared with control ghosts. The octyl-beta-glucoside ghost extracts from both P4.2-deficient phenotypes were enriched in band 3 oligomeric species (tetramers, higher-order oligomers, and aggregates) compared with controls. Since band 3 oligomers selectively associate with the cytoskeleton, these results are consistent with a weakened band 3-cytoskeleton linkage in P4.2-deficient RBC membranes. P4.2 deficiency does not affect band 3 anion transport activity, since uptake of radiolabeled sulfate was similar for control and P4.2-deficient RBCs. Thus, we propose that P4.2 directly participates in strengthening the band 3-cytoskeleton linkage.

Determination of the orientation of a band 3 affinity spin-label relative to the membrane normal axis of the human erythrocyte

The orientation of the nitroxide moiety of an isotopically substituted spin-labeled derivative of dihydrostilbenedisulfonate ([15N,2H13]-SL-H2DADS-maleimide) covalently coupled at the extracellular stilbenedisulfonate binding site of the human erythrocyte anion exchange protein, band 3, has been determined relative to the membrane normal axis of intact cells. The X-band linear electron paramagnetic resonance (EPR) spectra of [15N,2H13]-SL-H2DADS-maleimide-labeled band 3 in intact erythrocytes oriented by flow through an EPR flat cell have been obtained for two orthogonal orientations of the sample in the DC magnetic field. Two different methods of analysis have provided very similar values for the angles alpha 1 and beta 1 which uniquely define the orientation of the nitroxide axis frame relative to the membrane normal axis. In the first approach, a variable fraction of the cells, f, were taken to be biconcave disks perfectly oriented relative to the flat cell surface with the remainder, 1-f, isotropically oriented. Simultaneous nonlinear least squares analysis of the spectra obtained at the two sample orientations yielded best fit values of f = 0.60, alpha 1 = 58 degrees, and beta 1 = 36 degrees. In the second approach, the EPR spectra of flow-oriented intact erythrocytes labeled with the fatty acid spin-label, [15N,2H12]-5-nitroxyl stearate, have been obtained at the two sample orientations. These two spectra have been used to determine a model-independent distribution of membrane normal orientations in the sample. Using this experimentally determined membrane normal orientation distribution, the EPR spectra of [15N,2H13]-SL-H2DADS-maleimide-labeled erythrocytes were then reanalyzed to obtain a second determination of the nitroxide orientation, alpha 1 = 61 degrees and beta 1 = 37 degrees. The orientation of the nitroxide with respect to the membrane normal axis determined in the present study is nearly identical to the orientation of the nitroxide with respect to the uniaxial rotational diffusion axis, alpha = 66 degrees and beta = 34 degrees, as determined from saturation transfer EPR (ST-EPR) studies [Hustedt, E. H., & Beth, A. H. (1995) Biophys. J. 69, 1409-1423]. This result supports the conclusion that the motion observed using ST-EPR spectroscopy is, in fact, the uniaxial rotational diffusion of band 3 about the membrane normal.

Synthesis and characterization of a novel spin-labeled affinity probe of human erythrocyte band 3: characteristics of the stilbenedisulfonate binding site

A new spin-labeled maleimide derivative of the anion exchange inhibitor 4-4'-diaminodihydrostilbene-2,2'-disulfonate (H2DADS) has been synthesized as a site-specific molecular probe of the stilbenedisulfonate binding site of the anion exchange protein 1 (AE-1; band 3) in human erythrocytes. This probe, SL-H2DADS-maleimide, specifically and covalently labels the Mr 17 kDa integral membrane segment of band 3 with a 1:1 stoichiometry and inhibits essentially 100% of the band 3-mediated anion exchange. The linear V1 EPR spectrum of spin-labeled intact erythrocytes is indicative of a spatially isolated probe which is effectively immobilized on the submicrosecond time scale. Several independent lines of experimental evidence have shown that the nitroxide moiety of SL-H2DADS-maleimide-labeled band 3 is sequestered in a highly protected protein environment. These results are consistent with the observation that the spin-label is rigidly linked to band 3 in a fixed orientation with respect to the membrane normal axis [Hustedt, E. J., & Beth, A. H., (1996) Biochemistry 35, 6944-6954]. The nitroxide moieties of the SL-H2DADS-maleimide-labeled band 3 dimer are greater than 20 A from each other and are also more than 20 A from a monomer-monomer contact surface defined by cross-linking with the spin-labeled reagent BSSDA [bis(sulfo-N-succinimidyl)doxyl-2-spiro-5'-azelate]. These properties make SL-H2DADS-maleimide an extremely useful molecular probe for characterization of the physical properties of the band 3 stilbenedisulfonate binding site, determination of distances between the stilbenedisulfonate site and other segments of band 3, and investigation of the global rotational dynamics of human erythrocyte band 3.

Analysis of saturation transfer electron paramagnetic resonance spectra of a spin-labeled integral membrane protein, band 3, in terms of the uniaxial rotational diffusion model

Algorithms have been developed for the calculation of saturation transfer electron paramagnetic resonance (ST-EPR) spectra of a nitroxide spin-label assuming uniaxial rotational diffusion, a model that is frequently used to describe the global rotational dynamics of large integral membrane proteins. One algorithm explicitly includes terms describing Zeeman overmodulation effects, whereas the second more rapid algorithm treats these effects approximately using modified electron spin-lattice and spin-spin relaxation times. Simulations are presented to demonstrate the sensitivity of X-band ST-EPR spectra to the rate of uniaxial rotational diffusion and the orientation of the nitroxide probe with respect to the diffusion axis. Results obtained by using the algorithms presented, which are based on the transition-rate formalism, are in close agreement with those obtained by using an eigenfunction expansion approach. The effects of various approximations used in the simulation algorithms are considered in detail. Optimizing the transition-rate formalism to model uniaxial rotational diffusion results in over an order of magnitude reduction in computation time while allowing treatment of nonaxial A- and g-tensors. The algorithms presented here are used to perform nonlinear least-squares analyses of ST-EPR spectra of the anion exchange protein of the human erythrocyte membrane, band 3, which has been affinity spin-labeled with a recently developed dihydrostilbene disulfonate derivative, [15N,2H13]-SL-H2DADS-MAL. These results suggest that all copies of band 3 present in intact erythrocytes undergo rotational diffusion about the membrane normal axis at a rate consistent with a band 3 dimer.

Monitoring DNA dynamics using spin-labels with different independent mobilities

The electron paramagnetic resonance (EPR) spectra of spin-labeled DNA duplexes, both bound to DEAE-Sephadex and free in solution, have been analyzed. The nitroxide spin-labels are covalently linked to a deoxyuridine residue using either a monoacetylene or diacetylene tether. This difference in tether length produces a dramatic difference in the independent mobility of the nitroxide relative to the DNA. In the case of the monoacetylene tether, the motion of the nitroxide has previously been shown to be tightly coupled to that of the DNA duplex. With the diacetylene tether, there is considerable independent motion of the probe. The diacetylene tether is intended to minimize the possibility of the nitroxide producing a perturbation of the dynamics of DNA. It is demonstrated here that, when coupled via the diacetylene tether, the nitroxide undergoes a rapid uniaxial rotation about the tether. A detailed analysis of the EPR spectrum of duplex DNA in solution, spin-labeled using the diacetylene tether, demonstrates that the motion of the nitroxide can be modeled in terms of this independent uniaxial rotation together with motion of the DNA which is consistent with the global tumbling of the duplex. As was previously found using the monoacetylene tether, there is no evidence of rapid, large-amplitude motions of the base pair in the EPR spectrum of a nitroxide coupled to duplex DNA via the diacetylene tether. This result confirms the small amplitudes of internal motion, local and collective, previously observed in duplex DNA with the monoacetylene-tethered nitroxide.

Protein rotational dynamics investigated with a dual EPR/optical molecular probe. Spin-labeled eosin

An acyl spin-label derivative of 5-aminoeosin (5-SLE) was chemically synthesized and employed in studies of rotational dynamics of the free probe and of the probe when bound noncovalently to bovine serum albumin using the spectroscopic techniques of fluorescence anisotropy decay and electron paramagnetic resonance (EPR) and their long-lifetime counterparts phosphorescence anisotropy decay and saturation transfer EPR. Previous work (Beth, A. H., Cobb, C. E., and J. M. Beechem, 1992. Synthesis and characterization of a combined fluorescence, phosphorescence, and electron paramagnetic resonance probe. Society of Photo-Optical Instrumentation Engineers. Time-Resolved Laser Spectroscopy III. 504-512) has shown that the spin-label moiety only slightly altered the fluorescence and phosphorescence lifetimes and quantum yields of 5-SLE when compared with 5-SLE whose nitroxide had been reduced with ascorbate and with the diamagnetic homolog 5-acetyleosin. In the present work, we have utilized time-resolved fluorescence anisotropy decay and linear EPR spectroscopies to observe and quantitate the psec motions of 5-SLE in solution and the nsec motions of the 5-SLE-bovine serum albumin complex. Time-resolved phosphorescence anisotropy decay and saturation transfer EPR studies have been carried out to observe and quantitate the microseconds motions of the 5-SLE-albumin complex in glycerol/buffer solutions of varying viscosity. These latter studies have enabled a rigorous comparison of rotational correlation times obtained from these complementary techniques to be made with a single probe. The studies described demonstrate that it is possible to employ a single molecular probe to carry out the full range of fluorescence, phosphorescence, EPR, and saturation transfer EPR studies. It is anticipated that "dual" molecular probes of this general type will significantly enhance capabilities for extracting dynamics and structural information from macromolecules and their functional assemblies.

Measurement of rotational dynamics by the simultaneous nonlinear analysis of optical and EPR data

In the preceding companion article in this issue, an optical dye and a nitroxide radical were combined in a new dual function probe, 5-SLE. In this report, it is demonstrated that time-resolved optical anisotropy and electron paramagnetic resonance (EPR) data can be combined in a single analysis to measure rotational dynamics. Rigid-limit and rotational diffusion models for simulating nitroxide EPR data have been incorporated into a general non-linear least-squares procedure based on the Marquardt-Levenberg algorithm. Simultaneous fits to simulated time-resolved fluorescence anisotropy and linear EPR data, together with simultaneous fits to experimental time-resolved phosphorescence anisotropy decays and saturation transfer EPR (ST-EPR) spectra of 5-SLE noncovalently bound to bovine serum albumin (BSA) have been performed. These results demonstrate that data from optical and EPR experiments can be combined and globally fit to a single dynamic model.

Motions of short DNA duplexes: an analysis of DNA dynamics using an EPR-active probe

The dynamics of a series of four DNA duplexes of length 12, 24, 48, and 96 base pairs have been studied using an electron paramagnetic resonance (EPR) active nitroxide spin-label covalently attached to a thymidine located near the center of each duplex. The linear EPR spectra were simulated by solving the stochastic Liouville equation for anisotropic rotational diffusion. The diffusion tensor for global rotation of the duplex was predicted from hydrodynamic theory for a right circular cylinder. All internal motions, assumed to be rapid, are modeled by reduced electron Zeeman and hyperfine tensor anisotropies. Best fit simulations to the data were then obtained by adjusting the total amplitude of all internal dynamics. The local, length-independent and the collective, length-dependent contributions to the internal dynamics were separated by determining the total amplitude of internal motion as a function of duplex length. The major axis of the spin tensors was determined to be tilted 20 degrees from the helix axis. As a result, the spin-label is most sensitive to flexural motions of the DNA duplex. It is found that the global tumbling of duplex is accurately modeled by hydrodynamic theory. The length-independent motion is characterized by a root-mean-squared amplitude of oscillation of 10 degrees in two dimensions at 20 degrees C and has a strong temperature dependence, indicating that the local structure of the DNA changes with temperature. The length dependence of the internal dynamics leads to an estimate of the dynamic flexural persistence length of 2500 +/- 340 A. There was no statistically significant difference between models assuming a harmonic or a square-well local bending potential.