Bayesian Probabilistic Inference of Nonparametric Distance Distributions in DEER Spectroscopy.

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, assuming a nonparametric distance distribution with a Tikhonov smoothness prior. The method uses Markov Chain Monte Carlo sampling with a compositional Gibbs sampler to determine a posterior probability distribution over the entire parameter space, including the distance distribution, given an experimental data set. This posterior contains all of the information available from the data, including a full quantification of the uncertainty about the model parameters. The corresponding uncertainty about the distance distribution is visually captured via an ensemble of posterior predictive distributions. Several examples are presented to illustrate the method. Compared with bootstrapping, it performs faster and provides slightly larger uncertainty intervals.

Determining electron-nucleus distances and Fermi contact couplings from ENDOR spectra.

The hyperfine coupling between an electron spin and a nuclear spin depends on the Fermi contact coupling aiso and, through dipolar coupling, the distance r between the electron and the nucleus. It is measured with electron-nuclear double resonance (ENDOR) spectroscopy and provides insight into the electronic and spatial structure of paramagnetic centers. The analysis and interpretation of ENDOR spectra is commonly done by ordinary least-squares fitting. As this is an ill-posed, inverse mathematical problem, this is challenging, in particular for spectra that show features from several nuclei or where the hyperfine coupling parameters are distributed. We introduce a novel Tikhonov-type regularization approach that analyzes an experimental ENDOR spectrum in terms of a complete non-parametric distribution over r and aiso. The approach uses a penalty function similar to the cross entropy between the fitted distribution and a Bayesian prior distribution that is derived from density functional theory calculations. Additionally, we show that smoothness regularization, commonly used for a similar purpose in double electron-electron resonance (DEER) spectroscopy, is not suited for ENDOR. We demonstrate that the novel approach is able to identify and quantitate ligand protons with electron-nucleus distances between 4 and 9 Å in a series of vanadyl porphyrin compounds.

Bayesian Probabilistic Analysis of DEER Spectroscopy Data Using Parametric Distance Distribution Models.

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.

Sensitivity enhancement by population transfer in Gd(III) spin labels.

In order to enhance echo signals observed with selective pulses, equilibrium populations of the energy levels of S = 7/2 Gd(III) spin labels are rearranged with frequency-swept passage pulses. To transfer population from as many energy levels as possible, the 2 µs long passage pulses range over more than 1 GHz. Application of this technique at Q-band frequencies to three different Gd(III) complexes and spin dynamics simulations reveal large signal enhancements beyond 100% for Gd(III) complexes with zero-field splitting parameters below 1 GHz. For complexes with larger splittings, experimental enhancements are on the order of 90%. Moreover, population transfer is combined with distance measurements on a model system with a pair of Gd(III) ions. As a result, a signal enhancement of 85% is achieved without inducing changes in the obtained distance information. Besides this enhancement by population transfer, a dipolar modulation depth of 9% is demonstrated, which results in a total enhancement of 3.3 with respect to data obtained with monochromatic rectangular pulses. The limitations of the population transfer technique are discussed. In particular, the extraordinary broad pulse bandwidths caused heating effects and pulse distortions, which constrain the pulse length and thus the achievable signal enhancement.

Copper ESEEM and HYSCORE through ultra-wideband chirp EPR spectroscopy.

The main limitation of pulse electron paramagnetic resonance (EPR) spectroscopy is its narrow excitation bandwidth. Ultra-wideband (UWB) excitation with frequency-swept chirp pulses over several hundreds of megahertz overcomes this drawback. This allows to excite electron spin echo envelope modulation (ESEEM) from paramagnetic copper centers in crystals, whereas up to now, only ESEEM of ligand nuclei like protons or nitrogens at lower frequencies could be detected. ESEEM spectra are recorded as two-dimensional correlation experiments, since the full digitization of the electron spin echo provides an additional Fourier transform EPR dimension. Thus, UWB hyperfine-sublevel correlation experiments generate a novel three-dimensional EPR-correlated nuclear modulation spectrum.

Beyond Stages: Predicting Individual Time Dependent Risk for Type 1 Diabetes.

BACKGROUND: Essentially all individuals with multiple autoantibodies will develop clinical type 1 diabetes. Multiple AABs and normal glucose tolerance define Stage 1 diabetes; abnormal glucose tolerance defines Stage 2. However, the rate of progression within these stages is heterogeneous, necessitating personalized risk calculators to improve clinical implementation. METHODS: We developed 3 models using TrialNet's Pathway to Prevention data to accommodate the reality that not all risk variables are clinically available. The Small model included AAB status, fasting glucose, HbA1c and age, while the Medium and Large models added predictors of disease progression measured via oral glucose tolerance testing. FINDINGS: All models markedly improved granularity regarding personalized risk missing from current categories of stages of T1D. Model derived risk calculations are consistent with the expected reduction of risk with increasing age and increase in risk with higher glucose and lower insulin secretion, illustrating the suitability of the models. Adding glucose and insulin secretion data altered model predicted probabilities within Stages. In those with high 2-hour glucose, a high C-peptide markedly decreased predicted risk; lower C-peptide obviated the age-dependent risk of 2-hour glucose alone, providing a more nuanced estimate of rate of disease progression within Stage 2. CONCLUSIONS: While essentially all those with multiple AABs will develop type 1 diabetes, the rate of progression is heterogeneous and not explained by any individual single risk variable. The model-based probabilities developed here provide an adaptable personalized risk calculator to better inform decisions about how and when to monitor disease progression in clinical practice.

Linking candidate causal autoimmune variants to T cell networks using genetic and epigenetic screens in primary human T cells.

Genetic variants associated with autoimmune diseases are highly enriched within putative cis -regulatory regions of CD4 + T cells, suggesting that they alter disease risk via changes in gene regulation. However, very few genetic variants have been shown to affect T cell gene expression or function. We tested >18,000 autoimmune disease-associated variants for allele-specific expression using massively parallel reporter assays in primary human CD4 + T cells. The 545 expression-modulating variants (emVars) identified greatly enrich for likely causal variants. We provide evidence that many emVars are mediated by common upstream regulatory conduits, and that putative target genes of primary T cell emVars are highly enriched within a lymphocyte activation network. Using bulk and single-cell CRISPR-interference screens, we confirm that emVar-containing T cell cis -regulatory elements modulate both known and novel target genes that regulate T cell proliferation, providing plausible mechanisms by which these variants alter autoimmune disease risk.

Identification of biomarkers for COVID-19 associated secondary hemophagocytic lymphohistiocytosis.

OBJECTIVES: We aimed to define and validate novel biomarkers that could identify individuals with COVID-19 associated secondary hemophagocytic lymphohistiocytosis (sHLH) and to test whether fatalities due to COVID-19 in the presence of sHLH were associated with specific defects in the immune system. DESIGN: In two cohorts of adult patients presenting with COVID-19 in 2020 and 2021, clinical lab values and serum proteomics were assessed. Subjects identified as having sHLH were compared to those with COVID-19 without sHLH. Eight deceased patients defined as COVID-sHLH underwent genomic sequencing in order to identify variants in immune-related genes. SETTING: Two tertiary care hospitals in Seattle, Washington (Virginia Mason Medical Center and Harborview Medical Center). PATIENTS: 186 patients with COVID-19. INTERVENTIONS: None. MEASUREMENTS AND MAIN RESULTS: Nine percent of enrolled COVID-19 subjects met our defined criteria for sHLH. Using broad serum proteomic approaches (O-link and SomaScan), we identified three biomarkers for COVID-19 associated sHLH (soluble PD-L1, TNF-R1, and IL-18BP), supporting a role for proteins previously associated with other forms of sHLH (IL-18BP and sTNF-R1). We also identified novel biomarkers and pathways of COVID-sHLH, including sPD-L1 and the syntaxin pathway. We detected variants in several genes involved in immune responses in individuals with COVID-sHLH, including in DOCK8 and in TMPRSS15, suggesting that genetic alterations in immune-related genes may contribute to hyperinflammation and fatal outcomes in COVID-19. CONCLUSIONS: Biomarkers of COVID-19 associated sHLH, such as soluble PD-L1, and pathways, such as the syntaxin pathway, and variants in immune genes in these individuals, suggest critical roles for the immune response in driving sHLH in the context of COVID-19.

Abatacept increases T cell exhaustion in early RA individuals who carry HLA risk alleles.

Exhausted CD8 T cells (TEX) are associated with worse outcome in cancer yet better outcome in autoimmunity. Building on our past findings of increased TIGIT+KLRG1+ TEX with teplizumab therapy in type 1 diabetes (T1D), in the absence of treatment we found that the frequency of TIGIT+KLRG1+ TEX is stable within an individual but differs across individuals in both T1D and healthy control (HC) cohorts. This TIGIT+KLRG1+ CD8 TEX population shares an exhaustion-associated EOMES gene signature in HC, T1D, rheumatoid arthritis (RA), and cancer subjects, expresses multiple inhibitory receptors, and is hyporesponsive in vitro, together suggesting co-expression of TIGIT and KLRG1 may broadly define human peripheral exhausted cells. In HC and RA subjects, lower levels of EOMES transcriptional modules and frequency of TIGIT+KLRG1+ TEX were associated with RA HLA risk alleles (DR0401, 0404, 0405, 0408, 1001) even when considering disease status and cytomegalovirus (CMV) seropositivity. Moreover, the frequency of TIGIT+KLRG1+ TEX was significantly increased in RA HLA risk but not non-risk subjects treated with abatacept (CTLA4Ig). The DR4 association and selective modulation with abatacept suggests that therapeutic modulation of TEX may be more effective in DR4 subjects and TEX may be indirectly influenced by cellular interactions that are blocked by abatacept.

Pulsed triple electron resonance (TRIER) for dipolar correlation spectroscopy.

A new pulse sequence is presented for correlating dipolar frequencies in molecules with more than two paramagnetic centers. This triple electron resonance experiment (TRIER) is an extension the double electron-electron resonance (DEER) experiment, which is widely used for distance determination in the nanometer range. We use linear chirp pulses with smoothed edges to create a refocused observer echo, and two hyperbolic secant pulses with distinct excitation windows to excite two other subsets of spins. These pumped spins are coupled to the observed spin through the dipole-dipole interaction. A two-dimensional dipolar modulation pattern is recorded by variation of the position of the two pump pulses. By two-dimensional Fourier transform of the echo integral, a plot is obtained that correlates dipolar frequencies within the same molecule. Such correlation patterns can be used in conjunction with DEER, with which distance distributions are usually determined for several doubly labeled molecules with different spin-labeling sites. In the presence of two conformers, DEER traces give two distances and assignment to an individual conformer is not trivial and usually requires a trial and error approach. TRIER can potentially provide the missing connection between distances as correlations between dipolar frequencies.

SPIDYAN, a MATLAB library for simulating pulse EPR experiments with arbitrary waveform excitation.

Frequency-swept chirp pulses, created with arbitrary waveform generators (AWGs), can achieve inversion over a range of several hundreds of MHz. Such passage pulses provide defined flip angles and increase sensitivity. The fact that spectra are not excited at once, but single transitions are passed one after another, can cause new effects in established pulse EPR sequences. We developed a MATLAB library for simulation of pulse EPR, which is especially suited for modeling spin dynamics in ultra-wideband (UWB) EPR experiments, but can also be used for other experiments and NMR. At present the command line controlled SPin DYnamics ANalysis (SPIDYAN) package supports one-spin and two-spin systems with arbitrary spin quantum numbers. By providing the program with appropriate spin operators and Hamiltonian matrices any spin system is accessible, with limits set only by available memory and computation time. Any pulse sequence using rectangular and linearly or variable-rate frequency-swept chirp pulses, including phase cycling can be quickly created. To keep track of spin evolution the user can choose from a vast variety of detection operators, including transition selective operators. If relaxation effects can be neglected, the program solves the Liouville-von Neumann equation and propagates spin density matrices. In the other cases SPIDYAN uses the quantum mechanical master equation and Liouvillians for propagation. In order to consider the resonator response function, which on the scale of UWB excitation limits bandwidth, the program includes a simple RLC circuit model. Another subroutine can compute waveforms that, for a given resonator, maintain a constant critical adiabaticity factor over the excitation band. Computational efficiency is enhanced by precomputing propagator lookup tables for the whole set of AWG output levels. The features of the software library are discussed and demonstrated with spin-echo and population transfer simulations.

Transverse interference peaks in chirp FT-EPR correlated three-pulse ESEEM spectra.

Fourier transform (FT) electron paramagnetic resonance (EPR) correlation spectroscopy usually requires broader excitation bandwidth than can be achieved by monochromatic rectangular pulses. Replacement of such pulses by frequency-swept pulses affords the correlation spectra, which, however, may not look the same as those that would be obtained with sufficiently broad-banded monochromatic rectangular pulses. This was recently observed for correlating nuclear frequencies to FT-EPR spectra by a three-pulse electron spin echo envelope modulation experiment. Here we analyze the origin of the additional cross peaks, whose position depends on the direction of the frequency sweep. We find that such peaks arise if coherence or polarization is transferred to an electron spin transition already before this transition is actually passed during the frequency sweep. This happens by excitation of a chain of transitions that connect levels of the source transition, where coherence resides before mixing, and the target transition, where it resides after mixing. The correlation spectra can be simplified by combining data from frequency up and down sweeps.

Coherence Transfer by Passage Pulses in Electron Paramagnetic Resonance Spectroscopy.

Linear passage pulses provide a simple approach to ultra-wideband electron paramagnetic resonance (EPR) spectroscopy. We show by numerical simulations that the efficiency of inversion of polarization or coherence order on a single transition by idealized passage pulses is an exponential function of critical adiabaticity during passage, which allows for defining an effective flip angle for fast passage. This result is confirmed by experiments on E' centers in Herasil glass. Deviations from the exponential law arise due to relaxation and a distribution of the adiabaticity parameter that comes from inhomogeneity of the irradiation field. Such inhomogeneity effects as well as edge effects in finite sweep bands cause a distribution of dynamic phase shifts, which can be partially refocused in echo experiments. In multilevel systems, passage of several transitions leads to generation of coherence on formally forbidden transitions that can also be described by the concept of an effective flip angle. On the one hand, such transfer to coherence on forbidden transitions is a significant magnetization loss mechanism for dipole-dipole coupled electron spin pairs at distances below about 2 nm. On the other hand, it can potentially be harnessed for electron spin echo envelope modulation (ESEEM) experiments, where matching of the irradiation field strength to the nuclear Zeeman frequency leads to efficient generation of nuclear coherence and efficient back transfer to electron coherence on allowed transitions at high adiabaticity.

Gd(III)-Gd(III) distance measurements with chirp pump pulses.

The broad EPR spectrum of Gd(III) spin labels restricts the dipolar modulation depth in distance measurements between Gd(III) pairs to a few percent. To overcome this limitation, frequency-swept chirp pulses are utilized as pump pulses in the DEER experiment. Using a model system with 3.4 nm Gd-Gd distance, application of one single chirp pump pulse at Q-band frequencies leads to modulation depths beyond 10%. However, the larger modulation depth is counteracted by a reduction of the absolute echo intensity due to the pump pulse. As supported by spin dynamics simulations, this effect is primarily driven by signal loss to double-quantum coherence and specific to the Gd(III) high spin state of S=7/2. In order to balance modulation depth and echo intensity for optimum sensitivity, a simple experimental procedure is proposed. An additional improvement by 25% in DEER sensitivity is achieved with two consecutive chirp pump pulses. These pulses pump the Gd(III) spectrum symmetrically around the observation position, therefore mutually compensating for dynamical Bloch-Siegert phase shifts at the observer spins. The improved sensitivity of the DEER data with modulation depths on the order of 20% is due to mitigation of the echo reduction effects by the consecutive pump pulses. In particular, the second pump pulse does not lead to additional signal loss if perfect inversion is assumed. Moreover, the compensation of the dynamical Bloch-Siegert phase prevents signal loss due to spatial dependence of the dynamical phase, which is caused by inhomogeneities in the driving field. The new methodology is combined with pre-polarization techniques to measure long distances up to 8.6 nm, where signal intensity and modulation depth become attenuated by long dipolar evolution windows. In addition, the influence of the zero-field splitting parameters on the echo intensity is studied with simulations. Herein, larger sensitivity is anticipated for Gd(III) complexes with zero-field splitting that is smaller than for the employed Gd-PyMTA complex.

Adiabatic and fast passage ultra-wideband inversion in pulsed EPR.

We demonstrate that adiabatic and fast passage ultra-wideband (UWB) pulses can achieve inversion over several hundreds of MHz and thus enhance the measurement sensitivity, as shown by two selected experiments. Technically, frequency-swept pulses are generated by a 12 GS/s arbitrary waveform generator and upconverted to X-band frequencies. This pulsed UWB source is utilized as an incoherent channel in an ordinary pulsed EPR spectrometer. We discuss experimental methodologies and modeling techniques to account for the response of the resonator, which can strongly limit the excitation bandwidth of the entire non-linear excitation chain. Aided by these procedures, pulses compensated for bandwidth or variations in group delay reveal enhanced inversion efficiency. The degree of bandwidth compensation is shown to depend critically on the time available for excitation. As a result, we demonstrate optimized inversion recovery and double electron electron resonance (DEER) experiments. First, virtually complete inversion of the nitroxide spectrum with an adiabatic pulse of 128ns length is achieved. Consequently, spectral diffusion between inverted and non-inverted spins is largely suppressed and the observation bandwidth can be increased to increase measurement sensitivity. Second, DEER is performed on a terpyridine-based copper (II) complex with a nitroxide-copper distance of 2.5nm. As previously demonstrated on this complex, when pumping copper spins and observing nitroxide spins, the modulation depth is severely limited by the excitation bandwidth of the pump pulse. By using fast passage UWB pulses with a maximum length of 64ns, we achieve up to threefold enhancement of the modulation depth. Associated artifacts in distance distributions when increasing the bandwidth of the pump pulse are shown to be small.