PDSFit: PDS data analysis in the presence of orientation selectivity, g-anisotropy, and exchange coupling

Pulsed dipolar electron paramagnetic resonance spectroscopy (PDS), encompassing techniques such as pulsed electron-electron double resonance (PELDOR or DEER) and relaxation-induced dipolar modulation enhancement (RIDME), is a valuable method in structural biology and materials science for obtaining nanometer-scale distance distributions between electron spin centers. An important aspect of PDS is the extraction of distance distributions from the measured time traces. Most software used for this PDS data analysis relies on simplifying assumptions, such as assuming isotropic g-factors of ~2 and neglecting orientation selectivity and exchange coupling. Here, the program PDSFit is introduced, which enables the analysis of PELDOR and RIDME time traces with or without orientation selectivity. It can be applied to spin systems consisting of up to two spin centers with anisotropic g-factors and to spin systems with exchange coupling. It employs a model-based fitting of the time traces using parametrized distance and angular distributions, and parametrized PDS background functions. The fitting procedure is followed by an error analysis for the optimized parameters of the distributions and backgrounds. Using five different experimental data sets published previously, the performance of PDSFit is tested and found to provide reliable solutions.

Differentiating between Label and Protein Conformers in Pulsed Dipolar EPR Spectroscopy with the dHis-Cu2+ (NTA) Motif

Pulsed dipolar EPR spectroscopy (PDS) in combination with site-directed spin labeling is a powerful tool in structural biology. However, the commonly used spin labels are conjugated to biomolecules via rather long and flexible linkers, which hampers the translation of distance distributions into biomolecular conformations. In contrast, the spin label copper(II)-nitrilotriacetic acid [Cu2+ (NTA)] bound to two histidines (dHis) is rigid and yields narrow distance distributions, which can be more easily translated into biomolecular conformations. Here, we use this label on the 71 kDa Yersinia outer protein O (YopO) to decipher whether a previously experimentally observed bimodal distance distribution is due to two conformations of the biomolecule or of the flexible spin labels. Two different PDS experiments, that is, pulsed electron-electron double resonance (PELDOR aka DEER) and relaxation-induced dipolar modulation enhancement (RIDME), yield unimodal distance distribution with the dHis-Cu2+ (NTA) motif; this result suggests that the α-helical backbone of YopO adopts a single conformation in frozen solution. In addition, we show that the Cu2+ (NTA) label preferentially binds to the target double histidine (dHis) sites even in the presence of 22 competing native histidine residues. Our results therefore suggest that the generation of a His-null background is not required for this spin labeling methodology. Together these results highlight the value of the dHis-Cu2+ (NTA) motif in PDS experiments.

A Comparison of Cysteine-Conjugated Nitroxide Spin Labels for Pulse Dipolar EPR Spectroscopy

The structure-function and materials paradigms drive research on the understanding of structures and structural heterogeneity of molecules and solids from materials science to structural biology. Functional insights into complex architectures are often gained from a suite of complementary physicochemical methods. In the context of biomacromolecular structures, the use of pulse dipolar electron paramagnetic resonance spectroscopy (PDS) has become increasingly popular. The main interest in PDS is providing long-range nanometre distance distributions that allow for identifying macromolecular topologies, validating structural models and conformational transitions as well as docking of quaternary complexes. Most commonly, cysteines are introduced into protein structures by site-directed mutagenesis and modified site-specifically to a spin-labelled side-chain such as a stable nitroxide radical. In this contribution, we investigate labelling by four different commercial labelling agents that react through different sulfur-specific reactions. Further, the distance distributions obtained are between spin-bearing moieties and need to be related to the protein structure via modelling approaches. Here, we compare two different approaches to modelling these distributions for all four side-chains. The results indicate that there are significant differences in the optimum labelling procedure. All four spin-labels show differences in the ease of labelling and purification. Further challenges arise from the different tether lengths and rotamers of spin-labelled side-chains; both influence the modelling and translation into structures. Our comparison indicates that the spin-label with the shortest tether in the spin-labelled side-group, (bis-(2,2,5,5-Tetramethyl-3-imidazoline-1-oxyl-4-yl) disulfide, may be underappreciated and could increase the resolution of structural studies by PDS if labelling conditions are optimised accordingly.

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.

Application of spherical harmonics for DEER data analysis in systems with a conformational distribution

Double electron-electron resonance (DEER) and other pulse electron paramagnetic resonance (EPR) techniques are valuable tools for determining distances between paramagnetic centres. DEER theory is well developed for a scenario where relative orientations of paramagnetic centres do not affect the DEER data. In particular, such theory enables a number of approaches for extracting distance distributions. However, in a more general case, when orientation selection effects become substantial, the analytical theory of DEER is less well developed, therefore quite commonly researchers rely on a comparison of some model-based simulations with experimental data. This work elaborates the theory of DEER with orientation selection effects, focusing on a scenario of a moderate conformational disorder, leading to an orientation distribution in a pair of paramagnetic centres. The analytical treatment based on expansions into spherical harmonics, provides important insights into the structure of DEER data. As follows from this treatment, DEER spectra with orientation selection can be represented as a linear combination of modified Pake pattern (MPP) components. The conformational disorder has a filtering effect on the weights of MPP components, specifically by significantly suppressing MPP components of higher degrees. The developed theory provides a pathway for model-based simulations of DEER data where orientation distribution is defined by analytical functions with parameters. The theory based on spherical harmonics expansions was also applied to develop an iterative processing algorithm based on Tikhonov regularization, which disentangles the distance and orientation information in a model-free manner. As an input, this procedure takes several DEER datasets measured at various positions of an EPR line, and outputs a distance distribution and orientation distribution information encoded in a set of coefficients related to the weights of MPP components. The model-based and model-free approaches based on the developed theory were validated for a nitroxide biradical and a spin-labelled protein.

Structural and dynamic origins of ESR lineshapes in spin-labeled GB1 domain: the insights from spin dynamics simulations based on long MD trajectories

Site-directed spin labeling (SDSL) ESR is a valuable tool to probe protein systems that are not amenable to characterization by x-ray crystallography, NMR or EM. While general principles that govern the shape of SDSL ESR spectra are known, its precise relationship with protein structure and dynamics is still not fully understood. To address this problem, we designed seven variants of GB1 domain bearing R1 spin label and recorded the corresponding MD trajectories (combined length 180 μs). The MD data were subsequently used to calculate time evolution of the relevant spin density matrix and thus predict the ESR spectra. The simulated spectra proved to be in good agreement with the experiment. Further analysis confirmed that the spectral shape primarily reflects the degree of steric confinement of the R1 tag and, for the well-folded protein such as GB1, offers little information on local backbone dynamics. The rotameric preferences of R1 side chain are determined by the type of the secondary structure at the attachment site. The rotameric jumps involving dihedral angles χ1 and χ2 are sufficiently fast to directly influence the ESR lineshapes. However, the jumps involving multiple dihedral angles tend to occur in (anti)correlated manner, causing smaller-than-expected movements of the R1 proxyl ring. Of interest, ESR spectra of GB1 domain with solvent-exposed spin label can be accurately reproduced by means of Redfield theory. In particular, the asymmetric character of the spectra is attributable to Redfield-type cross-correlations. We envisage that the current MD-based, experimentally validated approach should lead to a more definitive, accurate picture of SDSL ESR experiments.

Rapid Simulation of Unprocessed DEER Decay Data for Protein Fold Prediction

Despite advances in sampling and scoring strategies, Monte Carlo modeling methods still struggle to accurately predict de novo the structures of large proteins, membrane proteins, or proteins of complex topologies. Previous approaches have addressed these shortcomings by leveraging sparse distance data gathered using site-directed spin labeling and electron paramagnetic resonance spectroscopy to improve protein structure prediction and refinement outcomes. However, existing computational implementations entail compromises between coarse-grained models of the spin label that lower the resolution and explicit models that lead to resource-intense simulations. These methods are further limited by their reliance on distance distributions, which are calculated from a primary refocused echo decay signal and contain uncertainties that may require manual refinement. Here, we addressed these challenges by developing RosettaDEER, a scoring method within the Rosetta software suite capable of simulating double electron-electron resonance spectroscopy decay traces and distance distributions between spin labels fast enough to fold proteins de novo. We demonstrate that the accuracy of resulting distance distributions match or exceed those generated by more computationally intensive methods. Moreover, decay traces generated from these distributions recapitulate intermolecular background coupling parameters even when the time window of data collection is truncated. As a result, RosettaDEER can discriminate between poorly folded and native-like models by using decay traces that cannot be accurately converted into distance distributions using regularized fitting approaches. Finally, using two challenging test cases, we demonstrate that RosettaDEER leverages these experimental data for protein fold prediction more effectively than previous methods. These benchmarking results confirm that RosettaDEER can effectively leverage sparse experimental data for a wide array of modeling applications built into the Rosetta software suite.

Modeling of spin–spin distance distributions for nitroxide labeled biomacromolecules

Combining CREST and MD simulations based on GFN-FF for the automated computation of distance distributions for nitroxide labeled (metallo-) proteins.

Site Selective and Efficient Spin Labeling of Proteins with a Maleimide-Functionalized Trityl Radical for Pulsed Dipolar EPR Spectroscopy

Pulsed dipolar electron paramagnetic resonance spectroscopy (PDS) in combination with site-directed spin labeling (SDSL) of proteins and oligonucleotides is a powerful tool in structural biology. Instead of using the commonly employed gem-dimethyl-nitroxide labels, triarylmethyl (trityl) spin labels enable such studies at room temperature, within the cells and with single-frequency electron paramagnetic resonance (EPR) experiments. However, it has been repeatedly reported that labeling of proteins with trityl radicals led to low labeling efficiencies, unspecific labeling and label aggregation. Therefore, this work introduces the synthesis and characterization of a maleimide-functionalized trityl spin label and its corresponding labeling protocol for cysteine residues in proteins. The label is highly cysteine-selective, provides high labeling efficiencies and outperforms the previously employed methanethiosulfonate-functionalized trityl label. Finally, the new label is successfully tested in PDS measurements on a set of doubly labeled Yersinia outer protein O (YopO) mutants.

Pulsed EPR Dipolar Spectroscopy under the Breakdown of the High-Field Approximation: The High-Spin Iron(III) Case

Pulsed EPR dipolar spectroscopy (PDS) offers several methods for measuring dipolar coupling and thus the distance between electron-spin centers. To date, PDS measurements to metal centers were limited to ions that adhere to the high-field approximation. Here, the PDS methodology is extended to cases where the high-field approximation breaks down on the example of the high-spin Fe³⁺ /nitroxide spin-pair. First, the theory developed by Maryasov et al. (Appl. Magn. Reson. 2006, 30, 683-702) was adapted to derive equations for the dipolar coupling constant, which revealed that the dipolar spectrum does not only depend on the length and orientation of the interspin distance vector with respect to the applied magnetic field but also on its orientation to the effective g-tensor of the Fe³⁺ ion. Then, it is shown on a model system and a heme protein that a PDS method called relaxation-induced dipolar modulation enhancement (RIDME) is well-suited to measuring such spectra and that the experimentally obtained dipolar spectra are in full agreement with the derived equations. Finally, a RIDME data analysis procedure was developed, which facilitates the determination of distance and angular distributions from the RIDME data. Thus, this study enables the application of PDS to for example, the highly relevant class of high-spin Fe³⁺ heme proteins.

A Structural Model of a P450-Ferredoxin Complex from Orientation-Selective Double Electron-Electron Resonance Spectroscopy

Cytochrome P450 (CYP) monooxygenases catalyze the oxidation of chemically inert carbon-hydrogen bonds in diverse endogenous and exogenous organic compounds by atmospheric oxygen. This C-H bond oxy-functionalization activity has huge potential in biotechnological applications. Class I CYPs receive the two electrons required for oxygen activation from NAD(P)H via a ferredoxin reductase and ferredoxin. The interaction of Class I CYPs with their cognate ferredoxin is specific. In order to reconstitute the activity of diverse CYPs, structural characterization of CYP-ferredoxin complexes is necessary, but little structural information is available. Here we report a structural model of such a complex (CYP199A2-HaPux) in frozen solution derived from distance and orientation restraints gathered by the EPR technique of orientation-selective double electron-electron resonance (os-DEER). The long-lived oscillations in the os-DEER spectra were well modeled by a single orientation of the CYP199A2-HaPux complex. The structure is different from the two known Class I CYP-Fdx structures: CYP11A1-Adx and CYP101A1-Pdx. At the protein interface, HaPux residues in the [Fe₂S₂] cluster-binding loop and the α3 helix and the C-terminus residue interact with CYP199A2 residues in the proximal loop and the C helix. These residue contacts are consistent with biochemical data on CYP199A2-ferredoxin binding and electron transfer. Electron-tunneling calculations indicate an efficient electron-transfer pathway from the [Fe₂S₂] cluster to the heme. This new structural model of a CYP-Fdx complex provides the basis for tailoring CYP enzymes for which the cognate ferredoxin is not known, to accept electrons from HaPux and display monooxygenase activity.

PELDOR Spectroscopy Reveals Two Defined States of a Sialic Acid TRAP Transporter SBP in Solution

The tripartite ATP-independent periplasmic (TRAP) transporters are a widespread class of membrane transporters in bacteria and archaea. Typical substrates for TRAP transporters are organic acids including the sialic acid N-acetylneuraminic acid. The substrate binding proteins (SBP) of TRAP transporters are the best studied component and are responsible for initial high-affinity substrate binding. To better understand the dynamics of the ligand binding process, pulsed electron-electron double resonance (PELDOR, also known as DEER) spectroscopy was applied to study the conformational changes in the N-acetylneuraminic acid-specific SBP VcSiaP. The protein is the SBP of VcSiaPQM, a sialic acid TRAP transporter from Vibrio cholerae. Spin-labeled double-cysteine mutants of VcSiaP were analyzed in the substrate-bound and -free state and the measured distances were compared to available crystal structures. The data were compatible with two clear states only, which are consistent with the open and closed forms seen in TRAP SBP crystal structures. Substrate titration experiments demonstrated the transition of the population from one state to the other with no other observed forms. Mutants of key residues involved in ligand binding and/or proposed to be involved in domain closure were produced and the corresponding PELDOR experiments reveal important insights into the open-closed transition. The results are in excellent agreement with previous in vivo sialylation experiments. The structure of the spin-labeled Q54R1/L173R1 R125A mutant was solved at 2.1 Å resolution, revealing no significant changes in the protein structure. Thus, the loss of domain closure appears to be solely due to loss of binding. In conclusion, these data are consistent with TRAP SBPs undergoing a simple two-state transition from an open-unliganded to closed-liganded state during the transport cycle.

Measuring Spin⋅⋅⋅Spin Interactions between Heterospins in a Hybrid [2]Rotaxane

Use of molecular electron spins as qubits for quantum computing will depend on the ability to produce molecules with weak but measurable interactions between the qubits. Here we demonstrate use of pulsed EPR spectroscopy to measure the interaction between two inequivalent spins in a hybrid rotaxane molecule.

Quantitative FRET studies and integrative modeling unravel the structure and dynamics of biomolecular systems

Förster Resonance Energy Transfer (FRET) combined with single-molecule spectroscopy probes macromolecular structure and dynamics and identifies coexisting conformational states. We review recent methodological developments in integrative structural modeling by satisfying spatial restraints on networks of FRET pairs (hybrid-FRET). We discuss procedures to incorporate prior structural knowledge and to obtain optimal distance networks. Finally, a workflow for hybrid-FRET is presented that automates integrative structural modeling and experiment planning to put hybrid-FRET on rails. To test this workflow, we simulate realistic single-molecule experiments and resolve three protein conformers, exchanging at 30μs and 10ms, with accuracies of 1-3Å RMSD versus the target structure. Incorporation of data from other spectroscopies and imaging is also discussed.