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

Double electron-electron resonance (DEER) spectroscopy measures distance distributions between spin labels in proteins, yielding important structural and energetic information about conformational landscapes. Analysis of an experimental DEER signal in terms of a distance distribution is a nontrivial task due to the ill-posed nature of the underlying mathematical inversion problem. This work introduces a Bayesian probabilistic inference approach to analyze DEER data, using a multi-Gauss mixture model for the distance distribution. The method uses Markov chain Monte Carlo (MCMC) sampling to determine a posterior probability distribution over model parameter space. This distribution contains all the information available from the data, including a full quantification of the uncertainty about the parameters. The corresponding uncertainty about the distance distribution is captured via an ensemble of posterior predictive distributions. Several synthetic examples illustrate the method. An experimental example shows the importance of model checking and comparison using residual analysis and Bayes factors. Overall, the Bayesian approach allows for more robust inference about protein conformations from DEER spectroscopy.

Prediction and Selection of Spin Label Rotamers for High-Resolution Insight into Protein Structures by DEER Spectroscopy

Modular assembly of bio-inspired supramolecular polymers is a powerful technique to develop new soft nanomaterials, and protein folding is a versatile basis for preparing such materials. Previous work demonstrated a significant difference in the physical properties of closely related supramolecular polymers composed of building blocks in which identical coiled-coil-forming peptides are cross-linked by one of two subtly different organic linkers (one flexible and the other rigid). Herein, we investigate the molecular basis for this observation by isolating a single subunit of the supramolecular polymer chain and probing its structure and conformational flexibility by double electron–electron resonance (DEER) spectroscopy. Experimental spin–spin distance distributions for two different labeling sites coupled with molecular dynamics simulations provide insights into how the linker structure impacts chain dynamics in the coiled-coil supramolecular polymer.

The signaling state of the photoactive yellow protein (PYP) photoreceptor is transiently developed via isomerization of its blue-light-absorbing chromophore. The associated structural rearrangements have large amplitude but, due to its transient nature and chemical exchange reactions that complicate NMR detection, its accurate three-dimensional structure in solution has been elusive. Here we report on direct structural observation of the transient signaling state by combining double electron electron resonance spectroscopy (DEER), NMR, and time-resolved pump-probe X-ray solution scattering (TR-SAXS/WAXS). Measurement of distance distributions for doubly spin-labeled photoreceptor constructs using DEER spectroscopy suggests that the signaling state is well ordered and shows that interspin-label distances change reversibly up to 19 Å upon illumination. The SAXS/WAXS difference signal for the signaling state relative to the ground state indicates the transient formation of an ordered and rearranged conformation, which has an increased radius of gyration, an increased maximum dimension, and a reduced excluded volume. Dynamical annealing calculations using the DEER derived long-range distance restraints in combination with short-range distance information from (1)H-(15)N HSQC perturbation spectroscopy give strong indication for a rearrangement that places part of the N-terminal domain in contact with the exposed chromophore binding cleft while the terminal residues extend away from the core. Time-resolved global structural information from pump-probe TR-SAXS/WAXS data supports this conformation and allows subsequent structural refinement that includes the combined energy terms from DEER, NMR, and SAXS/WAXS together. The resulting ensemble simultaneously satisfies all restraints, and the inclusion of TR-SAXS/WAXS effectively reduces the uncertainty arising from the possible spin-label orientations. The observations are essentially compatible with reduced folding of the I(2)' state (also referred to as the 'pB' state) that is widely reported, but indicates it to be relatively ordered and rearranged. Furthermore, there is direct evidence for the repositioning of the N-terminal region in the I(2)' state, which is structurally modeled by dynamical annealing and refinement calculations.

Optimal Tikhonov regularization for DEER spectroscopy

Structural Dynamics of Calmodulin using Bifunctional Spin Labels and Double Electron-Electron Resonance

Analytical distance distributions in systems of spherical symmetry with applications to double electron–electron resonance

Shape models are in these days frequently transmitted over Internet and the research of their compression has been started. Considering the large portion of shape model can be normal vectors, a new scheme was recently presented to compress normal vectors using clustering and mixed indexing scheme. Presented in this paper is a mathematical investigation of the scheme to analyze the probability distribution of normal index distances in Normal Index array which is critical for the compression. The probability distribution is formulated so that the values can be easily calculated once the relative probabilities of C, R, E, S, and L op-codes in Edgebreaker are known. It can be shown that the distribution of index distances can be easily transformed into a few measures for the compression performance of the proposed algorithm.

<strong class="journal-contentHeaderColor">Abstract.</strong> Double electron–electron resonance (DEER) spectroscopy measures the distribution of distances between two electron spins in the nanometer range, often on doubly spin-labeled proteins, via the modulation of a refocused spin echo by the dipolar interaction between the spins. DEER is commonly conducted under conditions where the polarization of the spins is small. Here, we examine the DEER signal under conditions of high spin polarization, thermally obtainable at low temperatures and high magnetic fields, and show that the signal acquires a polarization-dependent out-of-phase component both for the intramolecular and intermolecular contributions. For the latter, this corresponds to a phase shift of the spin echo that is linear in the pump pulse position. We derive a compact analytical form of this phase shift and show experimental measurements using monoradical and biradical nitroxides at several fields and temperatures. The effect highlights a novel aspect of the fundamental spin physics underlying DEER spectroscopy.

Double electron-electron resonance (DEER) spectroscopy measures the distribution of distances between two electron spins in the nanometer range, often on doubly spin-labeled proteins, via the modulation of a refocused spin echo by the dipolar interaction between the spins. DEER is commonly conducted under conditions where the polarization of the spins is small. Here, we examine the DEER signal under conditions of high spin polarization, thermally obtainable at low temperatures and high magnetic fields, and show that the signal acquires a polarization-dependent out-of-phase component, both for the intra- and the inter-molecular contribution. For the latter, this corresponds to a phase shift of the spin echo that is linear in the pump pulse position. We derive a compact analytical form of this phase shift and show experimental measurements using monoradical and biradical nitroxides at several fields and temperatures. The effect highlights a novel aspect of the fundamental spin physics underlying DEER spectroscopy.

Spectroscopy experiments are crucial to study membrane proteins for which traditional structure determination methods still prove challenging. Double electron-electron resonance (DEER) spectroscopy experiments provide protein residue-pair distance distributions that are indicative of their conformational heterogeneity. Atomistic molecular dynamics (MD) simulations are another tool that have been proven to be vital to study the structural dynamics of membrane proteins such as to identify inward-open, occluded, and outward-open conformations of transporter membrane proteins, among other partially open or closed states of the protein. Yet, studies have reported that there is no direct consensus between the distributional data from DEER experiments and MD simulations, which has challenged validation of structures obtained from long-timescale simulations and using simulations to design experiments. Current coping strategies for comparisons rely on heuristics, such as mapping the nearest matching peaks between two ensembles or biased simulations. Here we examine the differences in residue-pair distance distributions arising due to the choice of membranes around the protein and covalent modification of a pair of residues to nitroxide spin labels in DEER experiments. Through comparing MD simulations of two proteins, PepTSo and LeuT-both of which have been characterized using DEER experiments previously-we show that the proteins' dynamics are similar despite the choice of the detergent micelle as a membrane mimetic in DEER experiments. On the other hand, covalently modified residues show slight local differences in their dynamics and a huge divergence when the oxygen atom pair distances between spin labeled residues are measured rather than protein backbone distances. Given the computational expense associated with pairwise MTSSL labeled MD simulations, we examine the use of biased simulations to explore the conformational dynamics of the spin labels only to reveal that such simulations alter the underlying protein dynamics. Our study identifies the main cause for the mismatch between DEER experiments and MD simulations and will accelerate the development of potential mitigation strategies to improve the match.

Capturing Conformational Changes of the Tau Protein Upon Aggregation

Conducting a three-pulse DEER experiment without dead time: A review

Sodium-dependent transporters couple the flow of Na+ ions down their electrochemical potential gradient to the uphill transport of various ligands. Many of these transporters share a common core structure composed of a five-helix inverted repeat and deliver their cargo utilizing an alternating-access mechanism. A detailed characterization of inward-facing conformations of the Na+-dependent sugar transporter from Vibrio parahaemolyticus (vSGLT) has previously been reported, but structural details on additional conformations and on how Na+ and ligand influence the equilibrium between other states remains unknown. Here, double electron-electron resonance spectroscopy, structural modeling, and molecular dynamics are utilized to deduce ligand-dependent equilibria shifts of vSGLT in micelles. In the absence and presence of saturating amounts of Na+, vSGLT favors an inward-facing conformation. Upon binding both Na+ and sugar, the equilibrium shifts toward either an outward-facing or occluded conformation. While Na+ alone does not stabilize the outward-facing state, gating charge calculations together with a kinetic model of transport suggest that the resting negative membrane potential of the cell, absent in detergent-solubilized samples, may stabilize vSGLT in an outward-open conformation where it is poised for binding external sugars. In total, these findings provide insights into ligand-induced conformational selection and delineate the transport cycle of vSGLT.

Ibuprofen is a non-steroidal anti-inflammatory drug (NSAID) with analgesic and antipyretic effects. Understanding the molecular mechanisms of drug interaction with cell membranes is important to improving drug delivery, uptake by cells, possible side effects, etc. Double electron-electron resonance spectroscopy (DEER, also known as PELDOR) provides information on the nanoscale spatial arrangement of spin-labeled molecules. Here, DEER was applied to study (mono-)spin-labeled ibuprofen (ibuprofen-SL) in a bilayer of palmitoyl-oleoyl-sn-glycerophosphocholine (POPC). The results obtained show that the ibuprofen-SL molecules are located within a plane in each bilayer leaflet. At their low molar concentration in the bilayer χ, the found surface concentration of ibuprofen-SL is two times higher than χ, which can be explained by alternative assembling in the two leaflets of the bilayer. When χ > 2 mol%, these assemblies merge. The findings shed new light on the nanoscale spatial arrangement of ibuprofen in biological membranes.