CIDME: Short distances measured with long chirp pulses

Enhanced sensitivity for pulse dipolar EPR spectroscopy using variable-time RIDME

Pulse dipolar EPR spectroscopy (PDS) measurements are an important complementary tool in structural biology and are increasingly applied to macromolecular assemblies implicated in human health and disease at physiological concentrations. This requires ever higher sensitivity, and recent advances have driven PDS measurements into the mid-nanomolar concentration regime, though optimization and acquisition of such measurements remains experimentally demanding and time expensive. One important consideration is that constant-time acquisition represents a hard limit for measurement sensitivity, depending on the maximum measured distance. Determining this distance a priori has been facilitated by machine-learning structure prediction (AlphaFold2 and RoseTTAFold) but is often confounded by non-representative behaviour in frozen solution that may mandate multiple rounds of optimization and acquisition. Herein, we endeavour to simultaneously enhance sensitivity and streamline PDS measurement optimization to one-step by benchmarking a variable-time acquisition RIDME experiment applied to CuII-nitroxide and CuII-CuII model systems. Results demonstrate marked sensitivity improvements of both 5- and 6-pulse variable-time RIDME of between 2- and 5-fold over the constant-time analogues.

"Store-bought is fine": Sensitivity considerations using shaped pulses for DEER measurements on Cu(II) labels

The narrow excitation bandwidth of monochromic pulses is a sensitivity limitation for pulsed dipolar spectroscopy on Cu(II)-based measurements. In response, frequency-swept pulses with large excitation bandwidths have been adopted to probe a greater range of the EPR spectrum. However, much of the work utilizing frequency-swept pulses in Cu(II) distance measurements has been carried out on home-built spectrometers and equipment. Herein, we carry out systematic Cu(II) based distance measurements to demonstrate the capability of chirp pulses on commercial instrumentation. More importantly we delineate sensitivity considerations under acquisition schemes that are necessary for robust distance measurements using Cu(II) labels for proteins. We show that a 200 MHz sweeping bandwidth chirp pulse can improve the sensitivity of long-range distance measurements by factors of three to four. The sensitivity of short-range distances only increases slightly due to special considerations for the chirp pulse duration relative to the period length of the modulated dipolar signal. Enhancements in sensitivity also dramatically reduce measurement collection times enabling rapid collection of orientationally averaged Cu(II) distance measurements in under two hours.

Light-induced pulsed dipolar EPR spectroscopy for distance and orientation analysis

Measuring distances in biology at the molecular level is of great importance for understanding the structure and function of proteins, nucleic acids and other biological molecules and their complexes. Pulsed Dipolar Spectroscopy (PDS) offers advantages with respect to other methods as it is uniquely sensitive and specific to electronic spin centers and allows measurements in near-native conditions, comprising the in-cell environment. PDS methods measure the electron spin-spin dipolar interaction, therefore they require the presence of at least two paramagnetic centers, which are often stable radicals. Recent developments have introduced transient triplet states, photo-activated by a laser pulse, as spin labels and probes, thereby establishing a new family of techniques-Light-induced PDS (LiPDS). In this chapter, an overview of these methods is provided, looking at the chromophores that can be used for LiPDS and some of the technical aspects of the experiments. A guide to the choice of technique that can yield the best results, depending on the type of system studied and the information required, is provided. Examples of previous LiPDS studies of model systems and proteins are given. Characterization data for the chromophores used in these studies is tabulated to help selection of appropriate triplet state probes in future studies.

A Low-Spin CoII/Nitroxide Complex for Distance Measurements at Q-Band Frequencies

Pulse dipolar electron paramagnetic resonance spectroscopy (PDS) is continuously furthering the understanding of chemical and biological assemblies through distance measurements in the nanometer range. New paramagnets and pulse sequences can provide structural insights not accessible through other techniques. In the pursuit of alternative spin centers for PDS, we synthesized a low-spin CoII complex bearing a nitroxide (NO) moiety, where both the CoII and NO have an electron spin S of 1/2. We measured CoII-NO distances with the well-established double electron–electron resonance (DEER aka PELDOR) experiment, as well as with the five- and six-pulse relaxation-induced dipolar modulation enhancement (RIDME) spectroscopies at Q-band frequencies (34 GHz). We first identified challenges related to the stability of the complex in solution via DEER and X-ray crystallography and showed that even in cases where complex disproportionation is unavoidable, CoII-NO PDS measurements are feasible and give good signal-to-noise (SNR) ratios. Specifically, DEER and five-pulse RIDME exhibited an SNR of ~100, and while the six-pulse RIDME exhibited compromised SNR, it helped us minimize unwanted signals from the RIDME traces. Last, we demonstrated RIDME at a 10 μM sample concentration. Our results demonstrate paramagnetic CoII to be a feasible spin center in medium magnetic fields with opportunities for PDS studies involving CoII ions.

Optimising broadband pulses for DEER depends on concentration and distance range of interest

EPR distance determination in the nanometre region has become an important tool for studying the structure and interaction of macromolecules. Arbitrary waveform generators (AWGs), which have recently become commercially available for EPR spectrometers, have the potential to increase the sensitivity of the most common technique, double electron-electron resonance (DEER, also called PELDOR), as they allow the generation of broadband pulses. There are several families of broadband pulses, which are different in general pulse shape and the parameters that define them. Here, we compare the most common broadband pulses. When broadband pulses lead to a larger modulation depth, they also increase the background decay of the DEER trace. Depending on the dipolar evolution time, this can significantly increase the noise level towards the end of the form factor and limit the potential increase in the modulation-to-noise ratio (MNR). We found asymmetric hyperbolic secant (HS{ 1 , 6 } ) pulses to perform best for short DEER traces, leading to a MNR improvement of up to 86 % compared to rectangular pulses. For longer traces we found symmetric hyperbolic secant (HS{ 1 , 1 } ) pulses to perform best; however, the increase compared to rectangular pulses goes down to 43 %.

Enhancing sensitivity of Double Electron-Electron Resonance (DEER) by using Relaxation-Optimized Acquisition Length Distribution (RELOAD) scheme

Over the past decades pulsed electron-electron double resonance (PELDOR), often called double electron-electron resonance (DEER), became one of the major spectroscopic tools for measurements of nanometer-scale distances and distance distributions in non-crystalline biological and chemical systems. The method is based on detecting the amplitude of the primary (3-pulse DEER) or refocused (4-pulse DEER) spin echo for the so-called "observer" spins when the other spins coupled to the former by a dipolar interaction are flipped by a "pump" pulse at another EPR frequency. While the timing of the pump pulse is varied in steps, the positions of the observer pulses are typically fixed. For such a detection scheme the total length of the observer pulse train and the electron spin memory time determine the amplitude of the detected echo signal. Usually, the distance range considerations in DEER experiments dictate the total length of the observer pulse train to exceed the phase memory time by a factor of few and this leads to a dramatic loss of the signal-to-noise ratio (SNR). While the acquisition of the DEER signal seems to be irrational under such conditions, it is currently the preferred way to conduct DEER because of an effective filtering out of all other unwanted interactions. Here we propose a novel albeit simple approach to improve DEER sensitivity and decrease data acquisition time by introducing the signal acquisition scheme based on RELaxation Optimized Acquisition (Length) Distribution (DEER-RELOAD). In DEER-RELOAD the dipolar phase evolution signal is acquired in multiple segments in which the observer pulses are fixed at the positions to optimize SNR just for that specific segment. The length of the segment is chosen to maximize the signal acquisition efficiency according the phase relaxation properties of the spin system. The total DEER trace is then obtained by "stitching" the multiple segments into a one continuous trace. The utility of the DEER-RELOAD acquisition scheme has been demonstrated on an example of the standard 4-pulse DEER sequence applied to two membrane protein complexes labeled with nitroxides. While theoretical gains from the DEER-RELOAD scheme increase with the number of stitched segments, in practice, even dividing the acquisition of the DEER trace into two segments may improve SNR by a factor of >3, as it has been demonstrated for one of these two membrane proteins.

Improved signal fidelity in 4-pulse DEER with Gaussian pulses

The introduction of arbitrary waveform generator (AWG) technology and the availability of high power microwave amplifiers mark a "new era" in pulse EPR due to significant sensitivity improvements and the possibility to perform novel types of experiments. We present an optimized 4-pulse DEER setup that uses Gaussian observer pulses (GaussDEER) in connection with a Gaussian/shaped pump pulse. Gaussian pulses allow to experimentally remove the "2+1" pulse train ESE signal which is intrinsically present in any DEER experiment performed with rectangular pulses. Further signal improvements are obtained with shaped pump pulses, which can significantly increase the modulation depth of the DEER experiment due to their tailored excitation bandwidth. Although sequences like CP (Carr-Purcell) DEER offer advantages such as a prolongation of the dipolar evolution time, they suffer from post-processing of the time-domain data to remove artifacts. Therefore, it is worth having a 4-pulse DEER experiment free of residual "2+1" signal since this is still the main dipolar spectroscopic technique used in structural biology. In this work we focus on nitroxides, which are the spin probes primarily used in site-directed spin labeling studies of biomolecules, however, the advantages introduced by Gaussian pulses can be extended to any spin type.

Treating Biomacromolecular Conformational Variability

The function of a biomacromolecule is related not only to its structure but also to the different conformations that its structural elements can sample. It is therefore important to determine the extent of the structural fluctuations and to identify the states that are actually populated as a result of the rearrangement. However, this accomplishment is undermined by an intrinsic limitation: the amount of experimental data is by and large inferior to the number of the states that a biomacromolecule can actually sample. This means that additional, a priori information must be applied in order to derive the most from the available experimental data but not to run into overinterpretation. In this chapter we will give a summary of the experimental observables that can be used towards the reconstruction of structural ensembles, how the data can be profitably combined and to what extent the data are affected by error; finally we will give an overview of the computational methods that have been developed to model structural ensembles, highlighting their difference and similarities, advantages and disadvantages.

Refocused Out-Of-Phase (ROOPh) DEER: A pulse scheme for suppressing an unmodulated background in double electron-electron resonance experiments

EPR pulsed dipolar spectroscopy (PDS) is indispensable for measurements of nm-scale distances between electronic spins in biological and other systems. While several useful modifications and pulse sequences for PDS have been developed in recent years, DEER experiments utilizing pump and observer pulses at two different frequencies remain the most popular for practical applications. One of the major drawbacks of all the available DEER approaches is the presence of a significant unmodulated fraction in the detected signal that arises from an incomplete inversion of the coupled spins by the pump pulse. The latter fraction is perceived as one of the major sources of error for the reconstructed distance distributions. We describe an alternative detection scheme - a Refocused Out-Of-Phase DEER (ROOPh-DEER) - to acquire only the modulated fraction of the dipolar DEER signal. When Zeeman splitting is small compared to the temperature, the out-of-phase magnetization components cancel each other and are not observed in 4-pulse DEER experiment. In ROOPh-DEER these components are refocused by an additional pump pulse while the in-phase component containing an unmodulated background is filtered out by a pulse at the observed frequency applied right at the position of the refocused echo. Experimental implementation of the ROOPh-DEER detection scheme requires at least three additional pulses as was demonstrated on an example of a 7-pulse sequence. The application of 7-pulse ROOPh-DEER sequence to a model biradical yielded the interspin distance of 1.94 ± 0.07 nm identical to the one obtained with the conventional 4-pulse DEER, however, without the unmodulated background present as a dominant fraction in the latter signal.

Integration of a versatile bridge concept in a 34 GHz pulsed/CW EPR spectrometer

We present a 34 GHz continuous wave (CW)/pulsed electron paramagnetic resonance (EPR) spectrometer capable of pulse-shaping that is based on a versatile microwave bridge design. The bridge radio frequency (RF)-in/RF-out design (500 MHz to 1 GHz input/output passband, 500 MHz instantaneous input/output bandwidth) creates a flexible platform with which to compare a variety of excitation and detection methods utilizing commercially available equipment external to the bridge. We use three sources of RF input to implement typical functions associated with CW and pulse EPR spectroscopic measurements. The bridge output is processed via high speed digitizer and an in-phase/quadrature (I/Q) demodulator for pulsed work or sent to a wideband, high dynamic range log detector for CW. Combining this bridge with additional commercial hardware and new acquisition and control electronics, we have designed and constructed an adaptable EPR spectrometer that builds upon previous work in the literature and is functionally comparable to other available systems.

Artefact suppression in 5-pulse double electron electron resonance for distance distribution measurements

A 5-pulse version of the Double Electron Electron Resonance (DEER) experiment with Carr-Purcell delays and an additional pump pulse has been shown to significantly extend the experimentally accessible distance range in cases where nuclear spin diffusion dominates electron spin phase memory loss [Borbat et al., J. Phys. Chem. Lett., 2013, 4, 170]. We show that the sequence also prolongs coherence decay for spin labels in or near lipid bilayers, where this decay is mono-exponential. Compared to 4-pulse DEER, 5-pulse DEER suffers from additional artefacts that stem from pulse imperfection and excitation band overlap. Only some of these artefacts can be suppressed by phase cycling and the remaining ones have hindered widespread utilization of the method. Here, we report previously unknown additional artefact contributions stemming from overlap between the excitation bands of the microwave pulses that introduce additional dipolar evolution pathways. Experimental conditions are analyzed in detail that suppress these as well as the already known artefacts. Such suppression results in data that contain at most the partial excitation artefact, which can be deliberately shifted in time by a change in pulse timing without affecting the wanted contribution.

Double electron-electron resonance with multiple non-selective chirp refocusing

A new approach to double electron-electron resonance (DEER) for distance determination involving nitroxide spin labels at dilute concentrations is presented. In general, DEER pulse sequences rely on double resonance between pump and observer spins excited by selective pulses at two distinct microwave frequencies. In the new approach abbreviated as nDEER, non-selective chirp pulses that refocus all relevant spin pairs are combined with DEER. This non-selective refocusing results in suppression of unmodulated contributions, such as the constant contribution as well as the background curvature due to inter-molecular spin partners in ordinary DEER data. Due to this dipolar attenuation effect, primary nDEER data are closer to the dipolar modulation of primary interest than ordinary DEER data. Restrictions of nDEER are that secondary information related to these unmodulated contributions becomes difficult to retrieve. Accordingly, incomplete deconvolution of the inter-molecular background prevents the application of nDEER to rigid spin pairs at high concentrations. A key advantage of nDEER is the high fidelity of the chirp refocusing pulses, which is important for nDEER schemes that incorporate dynamical decoupling to access longer distances. In this context, nDEER with Carr-Purcell (CP) pulse trains having N = 2 and N = 4 refocusing pulses are demonstrated. These CP nDEER sequences require a total of N + 2 pulses, which is less than the 2N + 1 pulses required for CP DEER schemes. The pump pulse position is incremented throughout the refocusing pulses, which restricts the minimum time increment to 96 ns on our spectrometer and therefore complicates application to distances below 3 nm. At Q-band frequencies, unwanted modulations related to pulse imperfections contribute only 3.5% relative to the principal nDEER modulation. Accordingly, there is no need for dedicated data reconstruction methods as in CP DEER methods.

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.

Wideband frequency-swept excitation in pulsed EPR spectroscopy

Excitation of electron spins with monochromatic rectangular pulses is limited to bandwidths that are smaller than the spectral widths of most organic radicals and much smaller than the spectral widths of transition and rare earth metal ions. With frequency-swept pulses, bandwidths of up to 800MHz have previously been attained for excitation and detection of spin packets at frequencies of about 9.6GHz and bandwidths of up to 2.5GHz in a polarization transfer experiment at frequencies of about 34GHz. The remaining limitations, mainly due to resonator bandwidth and due to pulse length restrictions are discussed. Flip angles for state-space rotations on passage of a transition can generally be computed from the critical adiabaticity by the Landau-Zener-Stückelberg-Majorana expression. For hyperbolic secant pulses, the Demkov-Kunike model describes excitation for spin packets within and outside the sweep range. Well within the sweep range, the Bloch-Siegert phase shift is proportional to critical adiabaticity to a very good approximation. Because of the dependence of both flip angle and coherence phase on critical adiabaticity, it is advantageous to use pairs of amplitude and frequency modulation functions that provide such offset-independent adiabaticity. Compensation for the resonator response function should restore offset-independent adiabaticity. Whereas resonance offsets and Bloch-Siegert phase can be refocused at certain pulse length ratios, phase dispersion in coupled spin systems cannot generally be refocused. Based on the bandwidth limitations that arise from spin dynamics, requirements are derived for a spectrometer that achieves precise spin control over wide bands. The design of such a spectrometer and hardware characterization by EPR experiments are discussed.

Perspectives of shaped pulses for EPR spectroscopy

This article describes current uses of shaped pulses, generated by an arbitrary waveform generator, in the field of EPR spectroscopy. We show applications of sech/tanh and WURST pulses to dipolar spectroscopy, including new pulse schemes and procedures, and discuss the more general concept of optimum-control-based pulses for applications in EPR spectroscopy. The article also describes a procedure to correct for experimental imperfections, mostly introduced by the microwave resonator, and discusses further potential applications and limitations of such pulses.

Computing distance distributions from dipolar evolution data with overtones: RIDME spectroscopy with Gd(iii)-based spin labels

Extraction of distance distributions between high-spin paramagnetic centers from relaxation induced dipolar modulation enhancement (RIDME) data is affected by the presence of overtones of dipolar frequencies.