Singular Value Decomposition Method to Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance

Protein Modeling with DEER Spectroscopy

Double electron-electron resonance (DEER) combined with site-directed spin labeling can provide distance distributions between selected protein residues to investigate protein structure and conformational heterogeneity. The utilization of the full quantitative information contained in DEER data requires effective protein and spin label modeling methods. Here, we review the application of DEER data to protein modeling. First, we discuss the significance of spin label modeling for accurate extraction of protein structural information and review the most popular label modeling methods. Next, we review several important aspects of protein modeling with DEER, including site selection, how DEER restraints are applied, common artifacts, and the unique potential of DEER data for modeling structural ensembles and conformational landscapes. Finally, we discuss common applications of protein modeling with DEER data and provide an outlook.

Rapid Analysis of DEER Signals Including Short Distances

Double electron electron resonance (DEER) spectroscopy is an important technique to measure distance distributions P(r) for studying protein structures and protein-protein interactions. DEER data analysis can at times become challenging due to the lack of a detailed analytical signal expression or numerical methods with rapid computation time. We have derived an analytical expression κFULL, which includes both the pseudo-secular dipolar coupling (PSDC) and the finite pulse effects, especially important for shorter distances. Analyses of experiments by κFULL yield accurate and consistent P(r) values for three DEER nitroxide-rulers with distances (rAVG) in the range of 15 to 32 Å, while the current standard analysis produces erroneous results for rAVG < 20 Å. Computation times for deriving P(r) vary between 1 min and 4 min, which is usually much shorter than previous methods that include pseudo-secular and other effects. The expression can be applied to all types of DEER spin probes with little or no modifications.

Localized Reconstruction of Multimodal Distance Distribution from DEER Data of Biopolymers

Pulsed Dipolar ESR Spectroscopy (PDS) is a uniquely powerful technique to characterize the structural property of intrinsically disordered proteins (IDPs) and polymers and the conformational evolution of IDPs and polymers, e.g. during assembly, by offering the probability distribution of segment end-to-end distances. However, it is challenging to determine distance distribution P(r) of IDPs by PDS because of the uncertain and broad shape information that is intrinsic to the distance distribution of IDPs. We demonstrate here that the Srivastava-Freed Singular Value Decomposition (SF-SVD) point-wise mathematical inversion method along with wavelet denoising (WavPDS) can aid in obtaining reliable shapes for the distance distribution, P(r), for IDPs. We show that broad regions of P(r) as well as mixed narrow and broad features within the captured distance distribution range can be effectively resolved and differentiated without a priori knowledge. The advantage of SF-SVD and WavPDS is that the methods are transparent, requiring no adjustable parameters, the processing of the magnitude for the probability distribution is performed separately for each distance increment, and the outcome of the analysis is independent of the user's judgement. We demonstrate the performance and present the application of WavPDS and SF-SVD on model ruler molecules, model polyethylene glycol polymers with end-to-end spin labeling, and IDPs with pairwise labeling spanning different segments of the protein tau to generate the transparent solutions to the P(r)'s including their uncertainties and error analysis.

MRI Denoising Using Pixel-Wise Threshold Selection

Magnetic resonance imaging (MRI) has emerged as a promising technique for non-invasive medical imaging. The primary challenge in MRI is the trade-off between image visual quality and acquisition time. Current MRI image denoising algorithms employ global thresholding to denoise the whole image, which leads to inadequate denoising or image distortion. This study introduces a novel pixel-wise (localized) thresholding approach of singular vectors, obtained from singular value decomposition, to denoise magnetic resonance (MR) images. The pixel-wise thresholding of singular vectors is performed using separate singular values as thresholds at each pixel, which is advantageous given the spatial noise variation throughout the image. The method presented is validated on MR images of a standard phantom approved by the magnetic resonance accreditation program (MRAP). The denoised images display superior visual quality and recover minute structural information otherwise suppressed in the noisy image. The increase in peak-signal-to-noise-ratio (PSNR) and contrast-to-noise-ratio (CNR) values of ≥ 18% and ≥ 200% of the denoised images, respectively, imply efficient noise removal and visual quality enhancement. The structural similarity index (SSIM) of ≥ 0.95 for denoised images indicates that the crucial structural information is recovered through the presented method. A comparison with the standard filtering methods widely used for MRI denoising establishes the superior performance of the presented method. The presented pixel-wise denoising technique reduces the scan time by 2-3 times and has the potential to be integrated into any MRI system to obtain faster and better quality images.

An analysis of double-quantum coherence ESR in an N-spin system: Analytical expressions and predictions

Electron spin resonance pulsed dipolar spectroscopy (PDS) has become popular in protein 3D structure analysis. PDS studies yield distance distributions between a pair or multiple pairs of spin probes attached to protein molecules, which can be used directly in structural studies or as constraints in theoretical predictions. Double-quantum coherence (DQC) is a highly sensitive and accurate PDS technique to study protein structures in the solid state and under physiologically relevant conditions. In this work, we have derived analytical expressions for the DQC signal for a system with N-dipolar coupled spin-1/2 particles in the solid state. The expressions are integrated over the relevant spatial parameters to obtain closed form DQC signal expressions. These expressions contain the concentration-dependent "instantaneous diffusion" and the background signal. For micromolar and lower concentrations, these effects are negligible. An approximate analysis is provided for cases of finite pulses. The expressions obtained in this work should improve the analysis of DQC experimental data significantly, and the analytical approach could be extended easily to a wide range of magnetic resonance phenomena.

Phosphorylation, disorder, and phase separation govern the behavior of Frequency in the fungal circadian clock

Circadian clocks are composed of transcription-translation negative feedback loops that pace rhythms of gene expression to the diurnal cycle. In the filamentous fungus Neurospora crassa, the proteins Frequency (FRQ), the FRQ-interacting RNA helicase (FRH), and Casein-Kinase I (CK1) form the FFC complex that represses expression of genes activated by the white-collar complex (WCC). FRQ orchestrates key molecular interactions of the clock despite containing little predicted tertiary structure. Spin labeling and pulse-dipolar electron spin resonance spectroscopy provide domain-specific structural insights into the 989-residue intrinsically disordered FRQ and the FFC. FRQ contains a compact core that associates and organizes FRH and CK1 to coordinate their roles in WCC repression. FRQ phosphorylation increases conformational flexibility and alters oligomeric state, but the changes in structure and dynamics are non-uniform. Full-length FRQ undergoes liquid-liquid phase separation (LLPS) to sequester FRH and CK1 and influence CK1 enzymatic activity. Although FRQ phosphorylation favors LLPS, LLPS feeds back to reduce FRQ phosphorylation by CK1 at higher temperatures. Live imaging of Neurospora hyphae reveals FRQ foci characteristic of condensates near the nuclear periphery. Analogous clock repressor proteins in higher organisms share little position-specific sequence identity with FRQ; yet, they contain amino acid compositions that promote LLPS. Hence, condensate formation may be a conserved feature of eukaryotic clocks.

Differentiating Unimodal and Multimodal Distributions in Pulsed Dipolar Spectroscopy Using Wavelet Transforms

Site directed spin labeling has enabled protein structure determination using electron spin resonance (ESR) pulsed dipolar spectroscopy (PDS). Small details in a distance distribution can be key to understanding important protein structure-function relationships. A major challenge has been to differentiate unimodal and overlapped multimodal distance distributions. They often yield similar distributions and dipolar signals. Current model-free distance reconstruction techniques such as Srivastava-Freed Singular Value Decomposition (SF-SVD) and Tikhonov regularization can suppress these small features in uncertainty and/or error bounds, despite being present. In this work, we demonstrate that continuous wavelet transform (CWT) can distinguish PDS signals from unimodal and multimodal distance distributions. We show that periodicity in CWT representation reflects unimodal distributions, which is masked for multimodal cases. This work is meant as a precursor to a cross-validation technique, which could indicate the modality of the distance distribution.

Dissecting the Interaction between Cryptochrome and Timeless Reveals Underpinnings of Light-Dependent Recognition

Circadian rhythms are determined by cell-autonomous transcription-translation feedback loops that entrain to environmental stimuli. In the model circadian clock of Drosophila melanogaster, the clock is set by the light-induced degradation of the core oscillator protein timeless (TIM) by the principal light-sensor cryptochrome (CRY). The cryo-EM structure of CRY bound to TIM revealed that within the extensive CRY:TIM interface, the TIM N-terminus binds into the CRY FAD pocket, in which FAD and the associated phosphate-binding loop (PBL) undergo substantial rearrangement. The TIM N-terminus involved in CRY binding varies in isoforms that facilitate the adaptation of flies to different light environments. Herein, we demonstrate, through peptide binding assays and pulsed-dipolar electron spin resonance (ESR) spectroscopy, that the TIM N-terminal peptide alone exhibits light-dependent binding to CRY and that the affinity of the interaction depends on the initiating methionine residue. Extensions to the TIM N-terminus that mimic less light-sensitive variants have substantially reduced interactions with CRY. Substitutions of CRY residues that couple to the flavin rearrangement in the CRY:TIM complex have dramatic effects on CRY light activation. CRY residues Arg237 on α8, Asn253, and Gln254 on the PBL are critical for the release of the CRY autoinhibitory C-terminal tail (CTT) and subsequent TIM binding. These key light-responsive elements of CRY are well conserved throughout Type I cryptochromes of invertebrates but not by cryptochromes of chordates and plants, which likely utilize a distinct light-activation mechanism.

Differentiating Unimodal and Multimodal Distributions in Pulsed Dipolar Spectroscopy Using Wavelet Transforms

Site directed spin labeling has enabled protein structure determination using electron spin resonance (ESR) pulsed dipolar spectroscopy (PDS). Small details in a distance distribution can be key to understanding important protein structure-function relationships. A major challenge has been to differentiate unimodal and overlapped multimodal distance distributions. They often yield similar distributions and dipolar signals. Current model-free distance reconstruction techniques such as Srivastava-Freed Singular Value Decomposition (SF-SVD) and Tikhonov regularization can suppress these small features in uncertainty and/or error bounds, despite being present. In this work, we demonstrate that continuous wavelet transform (CWT) can distinguish PDS signals from unimodal and multimodal distance distributions. We show that periodicity in CWT representation reflects unimodal distributions, which is masked for multimodal cases. This work is meant as a precursor to a cross-validation technique, which could indicate the modality of the distance distribution.

Enzymatic Spin-Labeling of Protein N- and C-Termini for Electron Paramagnetic Resonance Spectroscopy

Electron paramagnetic resonance (EPR) spectroscopy is a powerful tool for investigating the structure and dynamics of proteins. The introduction of paramagnetic moieties at specific positions in a protein enables precise measurement of local structure and dynamics. This technique, termed site-directed spin-labeling, has traditionally been performed using cysteine-reactive radical-containing probes. However, large proteins are more likely to contain multiple cysteine residues and cysteine labeling at specific sites may be infeasible or impede function. To address this concern, we applied three peptide-ligating enzymes (sortase, asparaginyl endopeptidase, and inteins) for nitroxide labeling of N- and C-termini of select monomeric and dimeric proteins. Continuous wave and pulsed EPR (double electron electron resonance) experiments reveal specific attachment of nitroxide probes to ether N-termini (OaAEP1) or C-termini (sortase and intein) across three test proteins (CheY, CheA, and iLOV), thereby enabling a straightforward, highly specific, and general method for protein labeling. Importantly, the linker length (3, 5, and 9 residues for OaAEP1, intein, and sortase reactions, respectively) between the probe and the target protein has a large impact on the utility of distance measurements by pulsed EPR, with longer linkers leading to broader distributions. As these methods are only dependent on accessible N- and C-termini, we anticipate application to a wide range of protein targets for biomolecular EPR spectroscopy.

Insights into the oligomeric structure of the HIV-1 Vpu protein

The HIV-1-encoded protein Vpu forms an oligomeric ion channel/pore in membranes and interacts with host proteins to support the virus lifecycle. However, Vpu molecular mechanisms are currently not well understood. Here, we report on the Vpu oligomeric organization under membrane and aqueous conditions and provide insights into how the Vpu environment affects the oligomer formation. For these studies, we designed a maltose-binding protein (MBP)-Vpu chimera protein and produced it in E. coli in soluble form. We analyzed this protein using analytical size-exclusion chromatography (SEC), negative staining electron microscopy (nsEM), and electron paramagnetic resonance (EPR) spectroscopy. Surprisingly, we found that MBP-Vpu formed stable oligomers in solution, seemingly driven by Vpu transmembrane domain self-association. A coarse modeling of nsEM data as well as SEC and EPR data suggests that these oligomers most likely are pentamers, similar to what was reported regarding membrane-bound Vpu. We also noticed reduced MBP-Vpu oligomer stability upon reconstitution of the protein in β-DDM detergent and mixtures of lyso-PC/PG or DHPC/DHPG. In these cases, we observed greater oligomer heterogeneity, with MBP-Vpu oligomeric order generally lower than in solution; however, larger oligomers were also present. Notably, we found that in lyso-PC/PG, above a certain protein concentration, MBP-Vpu assembles into extended structures, which had not been reported for Vpu. Therefore, we captured various Vpu oligomeric forms, which can shed light on Vpu quaternary organization. Our findings could be useful in understanding Vpu organization and function in cellular membranes and could provide information regarding the biophysical properties of single-pass transmembrane proteins.

Interdomain Linkers Regulate Histidine Kinase Activity by Controlling Subunit Interactions

Bacterial chemoreceptors regulate the cytosolic multidomain histidine kinase CheA through largely unknown mechanisms. Residue substitutions in the peptide linkers that connect the P4 kinase domain to the P3 dimerization and P5 regulatory domain affect CheA basal activity and activation. To understand the role that these linkers play in CheA activity, the P3-to-P4 linker (L3) and P4-to-P5 linker (L4) were extended and altered in variants of Thermotoga maritima (Tm) CheA. Flexible extensions of the L3 and L4 linkers in CheA-LV1 (linker variant 1) allowed for a well-folded kinase domain that retained wild-type (WT)-like binding affinities for nucleotide and normal interactions with the receptor-coupling protein CheW. However, CheA-LV1 autophosphorylation activity registered ∼50-fold lower compared to WT. Neither a WT nor LV1 dimer containing a single P4 domain could autophosphorylate the P1 substrate domain. Autophosphorylation activity was rescued in variants with extended L3 and L4 linkers that favor helical structure and heptad spacing. Autophosphorylation depended on linker spacing and flexibility and not on sequence. Pulse-dipolar electron-spin resonance (ESR) measurements with spin-labeled adenosine 5'-triphosphate (ATP) analogues indicated that CheA autophosphorylation activity inversely correlated with the proximity of the P4 domains within the dimers of the variants. Despite their separation in primary sequence and space, the L3 and L4 linkers also influence the mobility of the P1 substrate domains. In all, interactions of the P4 domains, as modulated by the L3 and L4 linkers, affect domain dynamics and autophosphorylation of CheA, thereby providing potential mechanisms for receptors to regulate the kinase.

Illuminating the Structural Basis of Tau Aggregation by Intramolecular Distance Tracking: A Perspective on Methods

The aggregation of the tau protein is central to several neurodegenerative diseases, collectively known as tauopathies. High-resolution views of tau tangles accumulated under pathological conditions in post-mortem brains have been revealed recently by cryogenic electron microscopy. One of the striking discoveries was that fibril folds are unique to and homogeneous within one disease family, but typically different between different tauopathies. It is widely believed that seeded aggregation can achieve structural propagation of tau fibrils and generate pathological fibril structures. However, direct molecular level measurement of structural evolution during aggregation is missing. Here, we discuss our perspective on the biophysical approaches that can contribute to the ongoing debate regarding the prion-like propagation of tau and the role of cofactors. We discuss the unique potential of double electron-electron resonance (DEER)-based intramolecular distance measurement, sensitive to two to several nanometers distances. DEER can track the structural evolution of tau along the course of aggregation from the completely disordered state, to partially ordered and highly ordered fibril states, and has the potential to be a key tool to elucidate the disease-specific tau aggregation pathways.

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.

Highly Basic Clusters in the Herpes Simplex Virus 1 Nuclear Egress Complex Drive Membrane Budding by Inducing Lipid Ordering

During replication of herpesviruses, capsids escape from the nucleus into the cytoplasm by budding at the inner nuclear membrane. This unusual process is mediated by the viral nuclear egress complex (NEC) that deforms the membrane around the capsid by oligomerizing into a hexagonal, membrane-bound scaffold. Here, we found that highly basic membrane-proximal regions (MPRs) of the NEC alter lipid order by inserting into the lipid headgroups and promote negative Gaussian curvature. We also find that the electrostatic interactions between the MPRs and the membranes are essential for membrane deformation. One of the MPRs is phosphorylated by a viral kinase during infection, and the corresponding phosphomimicking mutations block capsid nuclear egress. We show that the same phosphomimicking mutations disrupt the NEC-membrane interactions and inhibit NEC-mediated budding in vitro, providing a biophysical explanation for the in vivo phenomenon. Our data suggest that the NEC generates negative membrane curvature by both lipid ordering and protein scaffolding and that phosphorylation acts as an off switch that inhibits the membrane-budding activity of the NEC to prevent capsid-less budding. IMPORTANCE Herpesviruses are large viruses that infect nearly all vertebrates and some invertebrates and cause lifelong infections in most of the world's population. During replication, herpesviruses export their capsids from the nucleus into the cytoplasm by an unusual mechanism in which the viral nuclear egress complex (NEC) deforms the nuclear membrane around the capsid. However, how membrane deformation is achieved is unclear. Here, we show that the NEC from herpes simplex virus 1, a prototypical herpesvirus, uses clusters of positive charges to bind membranes and order membrane lipids. Reducing the positive charge or introducing negative charges weakens the membrane deforming ability of the NEC. We propose that the virus employs electrostatics to deform nuclear membrane around the capsid and can control this process by changing the NEC charge through phosphorylation. Blocking NEC-membrane interactions could be exploited as a therapeutic strategy.

Methodology for rigorous modeling of protein conformational changes by Rosetta using DEER distance restraints

We describe an approach for integrating distance restraints from Double Electron-Electron Resonance (DEER) spectroscopy into Rosetta with the purpose of modeling alternative protein conformations from an initial experimental structure. Fundamental to this approach is a multilateration algorithm that harnesses sets of interconnected spin label pairs to identify optimal rotamer ensembles at each residue that fit the DEER decay in the time domain. Benchmarked relative to data analysis packages, the algorithm yields comparable distance distributions with the advantage that fitting the DEER decay and rotamer ensemble optimization are coupled. We demonstrate this approach by modeling the protonation-dependent transition of the multidrug transporter PfMATE to an inward facing conformation with a deviation to the experimental structure of less than 2Å Cα RMSD. By decreasing spin label rotamer entropy, this approach engenders more accurate Rosetta models that are also more closely clustered, thus setting the stage for more robust modeling of protein conformational changes.

Non-uniform sampling in pulse dipolar spectroscopy by EPR: the redistribution of noise and the optimization of data acquisition

Pulse dipolar spectroscopy (PDS) in Electron Paramagnetic Resonance (EPR) is the method of choice for determining the distance distribution function for mono-, bi- or multi- spin-labeled macromolecules and nanostructures. PDS acquisition schemes conventionally use uniform sampling of the dipolar trace, but non-uniform sampling (NUS) schemes can decrease the total measurement time or increase the accuracy of the resulting distance distributions. NUS requires optimization of the data acquisition scheme, as well as changes in data processing algorithms to accommodate the non-uniformly sampled data. We investigate in silico the applicability of the NUS approach in PDS, considering its effect on random, truncation and sampling noise in the experimental data. Each type of noise in the time-domain data propagates differently and non-uniformly into the distance spectrum as errors in the distance distribution. NUS schemes seem to be a valid approach for increasing sensitivity and/or throughput in PDS by decreasing and redistributing noise in the distance spectrum so that it has less impact on the distance spectrum.

Studies of transmembrane peptides by pulse dipolar spectroscopy with semi-rigid TOPP spin labels

Electron paramagnetic resonance (EPR)-based pulsed dipolar spectroscopy measures the dipolar interaction between paramagnetic centers that are separated by distances in the range of about 1.5-10 nm. Its application to transmembrane (TM) peptides in combination with modern spin labelling techniques provides a valuable tool to study peptide-to-lipid interactions at a molecular level, which permits access to key parameters characterizing the structural adaptation of model peptides incorporated in natural membranes. In this mini-review, we summarize our approach for distance and orientation measurements in lipid environment using novel semi-rigid TOPP [4-(3,3,5,5-tetramethyl-2,6-dioxo-4-oxylpiperazin-1-yl)-L-phenylglycine] labels specifically designed for incorporation in TM peptides. TOPP labels can report single peak distance distributions with sub-angstrom resolution, thus offering new capabilities for a variety of TM peptide investigations, such as monitoring of various helix conformations or measuring of tilt angles in membranes.

Tuning flavin environment to detect and control light-induced conformational switching in Drosophila cryptochrome

Light-induction of an anionic semiquinone (SQ) flavin radical in Drosophila cryptochrome (dCRY) alters the dCRY conformation to promote binding and degradation of the circadian clock protein Timeless (TIM). Specific peptide ligation with sortase A attaches a nitroxide spin-probe to the dCRY C-terminal tail (CTT) while avoiding deleterious side reactions. Pulse dipolar electron-spin resonance spectroscopy from the CTT nitroxide to the SQ shows that flavin photoreduction shifts the CTT ~1 nm and increases its motion, without causing full displacement from the protein. dCRY engineered to form the neutral SQ serves as a dark-state proxy to reveal that the CTT remains docked when the flavin ring is reduced but uncharged. Substitutions of flavin-proximal His378 promote CTT undocking in the dark or diminish undocking in the light, consistent with molecular dynamics simulations and TIM degradation activity. The His378 variants inform on recognition motifs for dCRY cellular turnover and strategies for developing optogenetic tools.

Chandrasekaran et al. engineered the Drosophila circadian clock protein Cryptochrome (dCRY) to form the neutral semiquinone, which serves as a dark-state proxy. They find that the C-terminal tail of dCRY remains docked when the flavin ring is reduced but uncharged. dCRY His378 variants provide insights into the recognition motifs for dCRY turnover and strategies for optogenetic tools.

Engineered chemotaxis core signaling units indicate a constrained kinase-off state

Bacterial chemoreceptors, the histidine kinase CheA, and the coupling protein CheW form transmembrane molecular arrays with remarkable sensing properties. The receptors inhibit or stimulate CheA kinase activity depending on the presence of attractants or repellants, respectively. We engineered chemoreceptor cytoplasmic regions to assume a trimer of receptor dimers configuration that formed well-defined complexes with CheA and CheW and promoted a CheA kinase-off state. These mimics of core signaling units were assembled to homogeneity and investigated by site-directed spin-labeling with pulse-dipolar electron-spin resonance spectroscopy (PDS), small-angle x-ray scattering, targeted protein cross-linking, and cryo-electron microscopy. The kinase-off state was especially stable, had relatively low domain mobility, and associated the histidine substrate and docking domains with the kinase core, thus preventing catalytic activity. Together, these data provide an experimentally restrained model for the inhibited state of the core signaling unit and suggest that chemoreceptors indirectly sequester the kinase and substrate domains to limit histidine autophosphorylation.

DeerLab: a comprehensive software package for analyzing dipolar electron paramagnetic resonance spectroscopy data

Dipolar EPR spectroscopy (DEER and other techniques) enables the structural characterization of macromolecular and biological systems by measurement of distance distributions between unpaired electrons on a nanometer scale. The inference of these distributions from the measured signals is challenging due to the ill-posed nature of the inverse problem. Existing analysis tools are scattered over several applications with specialized graphical user interfaces. This renders comparison, reproducibility, and method development difficult. To remedy this situation, we present DeerLab, an open-source software package for analyzing dipolar EPR data that is modular and implements a wide range of methods. We show that DeerLab can perform one-step analysis based on separable non-linear least squares, fit dipolar multi-pathway models to multi-pulse DEER data, run global analysis with non-parametric distributions, and use a bootstrapping approach to fully quantify the uncertainty in the analysis.

Tm filtering by 1H-methyl labeling in a deuterated protein for pulsed double electron-electron resonance EPR

Modulating the phase-memory relaxation time (Tm) of a spin label by introducing 1H-methyl groups in a perdeuterated protein background is used in DEER experiments to assign interactions in multimodal P(r) distributions. Proof of principle is demonstrated using Protein A where one nitroxide label occupies two distinct regions of conformational space. The presence of a single protonated methyl group in close proximity (4-8 Å) to only one of the two nitroxide rotamer ensembles results in a selective and substantial decrease in Tm, manifested by differential decay of the peak intensities in the bimodal P(r) distance distribution as a function of the total dipolar evolution time. This form of Tm filtering will facilitate DEER structural analysis of biomolecular systems with three spin labels, including complexes involving multimeric proteins.

Conformational Dynamics in Extended RGD-Containing Peptides

RGD is a prolific example of a tripeptide used in biomaterials for cell adhesion, but the potency of free or surface-bound RGD tripeptide is orders-of-magnitude less than the RGD domain within natural proteins. We designed a set of peptides with varying lengths, composed of fragments of fibronectin protein whose central three residues are RGD, in order to vary their conformational behavior without changing the binding site's chemical environment. With these peptides, we measure the conformational dynamics and transient structure of the active site. Our studies reveal how flanking residues affect conformational behavior and integrin binding. We find that disorder of the binding site is important to the potency of RGD peptides and that transient hydrogen bonding near the RGD site affects both the energy landscape roughness of the peptides and peptide binding. This phenomenon is independent of longer-range folding interactions and helps explain why short binding sequences, including RGD itself, do not fully replicate the integrin-targeting properties of extracellular matrix proteins. Our studies reinforce that peptide binding is a holistic event and fragments larger than those directly involved in binding should be considered in the design of peptide epitopes for functional biomaterials.

Submillisecond Freezing Permits Cryoprotectant-Free EPR Double Electron-Electron Resonance Spectroscopy

Double electron-electron resonance (DEER) EPR spectroscopy is a powerful method for obtaining distance distributions between pairs of engineered nitroxide spin-labels in proteins and other biological macromolecules. These measurements require the use of cryogenic temperatures (77 K or less) to prolong the phase memory relaxation time (T_m ) sufficiently to enable detection of a DEER echo curve. Generally, a cryoprotectant such as glycerol is added to protein samples to facilitate glass formation and avoid protein clustering (which can result in a large decrease in T_m ) during relatively slow flash freezing in liquid N₂ . However, cryoprotectants are osmolytes and can influence protein folding/unfolding equilibria, as well as species populations in weak multimeric systems. Here we show that submillisecond rapid freezing, achieved by high velocity spraying of the sample onto a rapidly spinning, liquid nitrogen cooled copper disc obviates the requirement for cryoprotectants and permits high quality DEER data to be obtained in absence of glycerol. We demonstrate this approach on five different protein systems: protein A, the metastable drkN SH3 domain, urea-unfolded drkN SH3, HIV-1 reverse transcriptase, and the transmembrane domain of HIV-1 gp41 in lipid bicelles.

High-yield production in E. coli and characterization of full-length functional p13II protein from human T-cell leukemia virus type 1

Human T-cell leukemia virus type 1 is an oncovirus that causes aggressive adult T-cell leukemia but is also responsible for severe neurodegenerative and endocrine disorders. Combatting HTLV-1 infections requires a detailed understanding of the viral mechanisms in the host. Therefore, in vitro studies of important virus-encoded proteins would be critical. Our focus herein is on the HTLV-1-encoded regulatory protein p13^II, which interacts with the inner mitochondrial membrane, increasing its permeability to cations (predominantly potassium, K⁺). Thereby, this protein affects mitochondrial homeostasis. We report on our progress in developing specific protocols for heterologous expression of p13^II in E. coli, and methods for its purification and characterization. We succeeded in producing large quantities of highly-pure full-length p13^II, deemed to be its fully functional form. Importantly, our particular approach based on the fusion of ubiquitin to the p13^II C-terminus was instrumental in increasing the persistently low expression of soluble p13^II in its native form. We subsequently developed approaches for protein spin labeling and a conformation study using double electron-electron resonance (DEER) spectroscopy and a fluorescence-based cation uptake assay for p13^II in liposomes. Our DEER results point to large protein conformation changes occurring upon transition from the soluble to the membrane-bound state. The functional assay on p13^II-assisted transport of thallium (Tl⁺) through the membrane, wherein Tl⁺ substituted for K⁺, suggests transmembrane potential involvement in p13^II function. Our study lays the foundation for expansion of in vitro functional and structural investigations on p13^II and would aid in the development of structure-based protein inhibitors and markers.

Supramolecular Approach to Electron Paramagnetic Resonance Distance Measurement of Spin-Labeled Proteins

We demonstrate a host-guest molecular recognition approach to advance double electron-electron resonance (DEER) distance measurements of spin-labeled proteins. We synthesized an iodoacetamide derivative of 2,6-diazaadamantane nitroxide (DZD) spin label that could be doubly incorporated into T4 Lysozyme (T4L) by site-directed spin labeling with efficiency up to 50% per cysteine. The rigidity of the fused ring structure and absence of mobile methyl groups increase the spin echo dephasing time (T_m) at temperatures above 80 K. This enables DEER measurements of distances >4 nm in DZD-labeled T4L in glycerol/water at temperatures up to 150 K with increased sensitivity compared to that of a common spin label such as MTSL. Addition of β-cyclodextrin reduces the rotational correlation time of the label, slightly increases T_m, and most importantly, narrows (and slightly lengthens) the interspin distance distributions. The distance distributions are in good agreement with simulated distance distributions obtained by rotamer libraries. These results provide a foundation for developing supramolecular recognition to facilitate long-distance DEER measurements at near physiological temperatures.

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.

Measurement of Angstrom to Nanometer Molecular Distances with 19 F Nuclear Spins by EPR/ENDOR Spectroscopy

Spectroscopic and biophysical methods for structural determination at atomic resolution are fundamental in studies of biological function. Here we introduce an approach to measure molecular distances in bio-macromolecules using 19 F nuclear spins and nitroxide radicals in combination with high-frequency (94 GHz/3.4 T) electron-nuclear double resonance (ENDOR). The small size and large gyromagnetic ratio of the 19 F label enables to access distances up to about 1.5 nm with an accuracy of 0.1-1 Å. The experiment is not limited by the size of the bio-macromolecule. Performance is illustrated on synthesized fluorinated model compounds as well as spin-labelled RNA duplexes. The results demonstrate that our simple but strategic spin-labelling procedure combined with state-of-the-art spectroscopy accesses a distance range crucial to elucidate active sites of nucleic acids or proteins in the solution state.

General regularization framework for DEER spectroscopy

Tikhonov regularization is the standard processing technique for the inversion of double electron-electron resonance (DEER) data to distance distributions without assuming a parametrized model. In other fields it has been surpassed by modern regularization methods. We analyze such alternative regularization methods based on the Tikhonov, total variation (TV) and Huber penalties with and without the use of Bregman iterations. For this, we provide a general mathematical framework and its open-source software implementation. We extend an earlier approach by Edwards and Stoll for the selection of an optimal regularization parameter to all of these penalties and use their big test data set of noisy DEER traces with known ground truth for assessment. The results indicate that regularization methods based on Bregman iterations provide an improvement upon Tikhonov regularization in recognizing features and recovering distribution width at moderate signal-to-noise ratio, provided that noise variance is known. Bregman-iterative methods are robust with respect to the method used in the choice of regularization parameter.

Insights into histidine kinase activation mechanisms from the monomeric blue light sensor EL346

Translation of environmental cues into cellular behavior is a necessary process in all forms of life. In bacteria, this process frequently involves two-component systems in which a sensor histidine kinase (HK) autophosphorylates in response to a stimulus before subsequently transferring the phosphoryl group to a response regulator that controls downstream effectors. Many details of the molecular mechanisms of HK activation are still unclear due to complications associated with the multiple signaling states of these large, multidomain proteins. To address these challenges, we combined complementary solution biophysical approaches to examine the conformational changes upon activation of a minimal, blue-light-sensing histidine kinase from Erythrobacter litoralis HTCC2594, EL346. Our data show that multiple conformations coexist in the dark state of EL346 in solution, which may explain the enzyme's residual dark-state activity. We also observe that activation involves destabilization of the helices in the dimerization and histidine phosphotransfer-like domain, where the phosphoacceptor histidine resides, and their interactions with the catalytic domain. Similar light-induced changes occur to some extent even in constitutively active or inactive mutants, showing that light sensing can be decoupled from activation of kinase activity. These structural changes mirror those inferred by comparing X-ray crystal structures of inactive and active HK fragments, suggesting that they are at the core of conformational changes leading to HK activation. More broadly, our findings uncover surprising complexity in this simple system and allow us to outline a mechanism of the multiple steps of HK activation.

Singular Value Decomposition Method To Determine Distance Distributions in Pulsed Dipolar Electron Spin Resonance: II. Estimating Uncertainty

This paper is a continuation of the method introduced by Srivastava and Freed (2017) that is a new method based on truncated singular value decomposition (TSVD) for obtaining physical results from experimental signals without any need for Tikhonov regularization or other similar methods that require a regularization parameter. We show here how to estimate the uncertainty in the SVD-generated solutions. The uncertainty in the solution may be obtained by finding the minimum and maximum values over which the solution remains converged. These are obtained from the optimum range of singular value contributions, where the width of this region depends on the solution point location (e.g., distance) and the signal-to-noise ratio (SNR) of the signal. The uncertainty levels typically found are very small with substantial SNR of the (denoised) signal, emphasizing the reliability of the method. With poorer SNR, the method is still satisfactory but with greater uncertainty, as expected. Pulsed dipolar electron spin resonance spectroscopy experiments are used as an example, but this TSVD approach is general and thus applicable to any similar experimental method wherein singular matrix inversion is needed to obtain the physically relevant result. We show that the Srivastava-Freed TSVD method along with the estimate of uncertainty can be effectively applied to pulsed dipolar electron spin resonance signals with SNR > 30, and even for a weak signal (e.g., SNR ≈ 3) reliable results are obtained by this method, provided the signal is first denoised using wavelet transforms (WavPDS).

Cofactors are essential constituents of stable and seeding-active tau fibrils

Amyloid fibrils are cross-β-rich aggregates that are exceptionally stable forms of protein assembly. Accumulation of tau amyloid fibrils is involved in many neurodegenerative diseases, including Alzheimer's disease (AD). Heparin-induced aggregates have been widely used and assumed to be a good tau amyloid fibril model for most biophysical studies. Here we show that mature fibrils made of 4R tau variants, prepared with heparin or RNA, spontaneously depolymerize and release monomers when their cofactors are removed. We demonstrate that the cross-β-sheet assembly formed in vitro with polyanion addition is unstable at room temperature. We furthermore demonstrate high seeding capacity with transgenic AD mouse brain-extracted tau fibrils in vitro that, however, is exhausted after one generation, while supplementation with RNA cofactors resulted in sustained seeding over multiple generations. We suggest that tau fibrils formed in brains are supported by unknown cofactors and inhere higher-quality packing, as reflected in a more distinct conformational arrangement in the mouse fibril-seeded, compared with heparin-induced, tau fibrils. Our study suggests that the role of cofactors in tauopathies is a worthy focus of future studies, as they may be viable targets for diagnosis and therapeutics.

Nucleotide Spin Labeling for ESR Spectroscopy of ATP-Binding Proteins

Site-directed spin labeling of proteins by chemical modification of engineered cysteine residues with the molecule MTSSL (1-Oxyl-2,2,5,5-tetramethylpyrroline-3-methyl methanethiosulfonate) has been an invaluable tool for conducting double electron electron resonance (DEER) spectroscopy experiments. However, this method is generally limited to recombinant proteins with a limited number of reactive Cys residues that when modified will not impair protein function. Here we present a method that allows for spin-labeling of protein nucleotide binding sites by adenosine diphosphate (ADP) modified with a nitroxide moiety on the β-phosphate (ADP-β-S-SL). The synthesis of this ADP analog is straightforward and isolation of pure product is readily achieved on a standard reverse-phase high-performance liquid chromatography (HPLC) system. Furthermore, analyses of isolated ADP-β-S-SL by LC-mass spectrometry confirm that the molecule is extremely stable under ambient conditions. The crystal structure of ADP-β-S-SL bound to the ATP pocket of the histidine kinase CheA reveals specific targeting of the probe, whose nitroxide moiety is mobile on the protein surface. Continuous wave and pulsed ESR measurements demonstrate the capability of ADP-β-S-SL to report on active site environment and provide reliable DEER distance constraints.

Maximizing NMR signal per unit time by facilitating the e-e-n cross effect DNP rate

The dynamic nuclear polarization (DNP) efficiency is critically dependent on the properties of the radical, solvent, and solute constituting the sample system. In this study, we focused on the three spin e-e-n cross effect (CE)'s influence on the nuclear longitudinal relaxation time constant T1n, the build-up time constants of nuclear magnetic resonance (NMR) signal, TDNP and DNP-enhancement of NMR signal. The dipolar interaction strength between the electron spins driving the e-e-n process was systematically modulated using mono-, di-, tri-, and dendritic-nitroxide radicals, while maintaining a constant global electron spin concentration of 10 mM. Experimental results showed that an increase in electron spin clustering led to an increased electron spin depolarization, as mapped by electron double resonance (ELDOR), and a dramatically shortened T1n and TDNP time constants under static and magic angle spinning (MAS) conditions. A theoretical analysis reveals that strong e-e interactions, caused by electron spin clustering, increase the CE rate. The three spin e-e-n CE is a hitherto little recognized mechanism for shortening T1n and TDNP in solid-state NMR experiments at cryogenic temperatures, and offers a design principle to enhance the effective CE DNP enhancement per unit time. Fast CE rates will benefit DNP at liquid helium temperatures, or at higher magnetic fields and pulsed DNP, where slow e-e-n polarization transfer rate is a key bottleneck to achieving maximal DNP performance.

Site-Specific Incorporation of a Cu2+ Spin Label into Proteins for Measuring Distances by Pulsed Dipolar Electron Spin Resonance Spectroscopy

Pulsed dipolar electron spin resonance spectroscopy (PDS) is a powerful tool for measuring distances in solution-state macromolecules. Paramagnetic metal ions, such as Cu²⁺, are used as spin probes because they can report on metalloprotein features and can be spectroscopically distinguished from traditional nitroxide (NO)-based labels. Here, we demonstrate site-specific incorporation of Cu²⁺ into non-metalloproteins through the use of a genetically encodable non-natural amino acid, 3-pyrazolyltyrosine (PyTyr). We first incorporate PyTyr in cyan fluorescent protein to measure Cu²⁺-to-NO distances and examine the effects of solvent conditions on Cu²⁺ binding and protein aggregation. We then apply the method to characterize the complex formed by the histidine kinase CheA and its target response regulator CheY. The X-ray structure of CheY-PyTyr confirms Cu labeling at PyTyr but also reveals a secondary Cu site. Cu²⁺-to-NO and Cu²⁺-to-Cu²⁺ PDS measurements of CheY-PyTyr with nitroxide-labeled CheA provide new insights into the conformational landscape of the phosphotransfer complex and have implications for kinase regulation.

Global analysis of complex PELDOR time traces

Pulsed electron-electron double resonance (PELDOR, alternatively called DEER for double electron-electron resonance) pulse sequences allow for the detection of echo decay curves that are modulated by dipole-dipole-coupling frequencies of interacting electron spins. With increasing distance between them, the echo decay needs to be monitored over a progressively extended time period. However, since the echo intensity typically falls off exponentially with increasing time, this might be problematic with respect to the minimum signal-to-noise ratio required for a sound data analysis. In this contribution we present the new PELDOR analysis tool GloPel (Global analysis of PELDOR data), an open-source Python-based application, that allows to extract improved-quality distance distributions from PELDOR data for which no ideal signal-to-noise ratio can be achieved for a very long observation window. By using Tikhonov regularization, GloPel allows for the simultaneous analysis of two time traces acquired for a sample in two different observation time windows, thus taking advantage of both, the typically high signal-to-noise ratio of the time trace acquired at early times of the echo decay, and the best possible background function fitted for the decay at later times, which is in most cases superimposed with considerable noise. In this way, short distances are not overseen in the higher noise of the longer time traces while long distances are not artificially shortened by limiting the observation time window of the experiment. Following our suggested data acquisition procedure, a significant reduction of the measurement time may also be achieved.

Deep neural network processing of DEER data

The established model-free methods for the processing of two-electron dipolar spectroscopy data [DEER (double electron-electron resonance), PELDOR (pulsed electron double resonance), DQ-EPR (double-quantum electron paramagnetic resonance), RIDME (relaxation-induced dipolar modulation enhancement), etc.] use regularized fitting. In this communication, we describe an attempt to process DEER data using artificial neural networks trained on large databases of simulated data. Accuracy and reliability of neural network outputs from real experimental data were found to be unexpectedly high. The networks are also able to reject exchange interactions and to return a measure of uncertainty in the resulting distance distributions. This paper describes the design of the training databases, discusses the training process, and rationalizes the observed performance. Neural networks produced in this work are incorporated as options into Spinach and DeerAnalysis packages.

Optimal Tikhonov regularization for DEER spectroscopy

Tikhonov regularization is the most commonly used method for extracting distance distributions from experimental double electron-electron resonance (DEER) spectroscopy data. This method requires the selection of a regularization parameter, α, and a regularization operator, L. We analyze the performance of a large set of α selection methods and several regularization operators, using a test set of over half a million synthetic noisy DEER traces. These are generated from distance distributions obtained from in silico double labeling of a protein crystal structure of T4 lysozyme with the spin label MTSSL. We compare the methods and operators based on their ability to recover the model distance distributions from the noisy time traces. The results indicate that several α selection methods perform quite well, among them the Akaike information criterion and the generalized cross validation method with either the first- or second-derivative operator. They perform significantly better than currently utilized L-curve methods.

Analytical solution of the PELDOR inverse problem using the integral Mellin transform

We describe a new model-free approach to solve the inverse problem in pulsed double electron-electron resonance (PELDOR, also known as DEER) spectroscopy and obtain the distance distribution function between two radicals from time-domain PELDOR data. The approach is based on analytical solutions of the Fredholm integral equations of the first kind using integral Mellin transforms to provide the distance distribution function directly. The approach appears to confine the noise in the computed distance distribution to short distances and does not introduce systematic distortions. Thus, the proposed analysis method can be a useful supplement to current methods to determine complicated distance distributions.