Pulsed dynamic nuclear polarization: a comprehensive Floquet description.

Dynamic nuclear polarization (DNP) experiments using microwave (mw) pulse sequences are one approach to transfer the larger polarization on the electron spin to nuclear spins of interest. How the result of such experiments depends on the external magnetic field and the excitation power is part of an ongoing debate and of paramount importance for applications that require high chemical-shift resolution. To date numerical simulations using operator-based Floquet theory have been used to predict and explain experimental data. However, such numerical simulations provide only limited insight into parameters relevant for efficient polarization transfer, such as transition amplitudes or resonance offsets. Here we present an alternative method to describe pulsed DNP experiments by using matrix-based Floquet theory. This approach leads to analytical expressions for the transition amplitudes and resonance offsets. We validate the method by comparing computations by these analytical expressions to their numerical counterparts and to experimental results for the XiX, TOP and TPPM DNP sequences. Our results explain the experimental data and are in very good agreement with the numerical simulations. The analytical expressions allow for the discussion of the scaling behaviour of pulsed DNP experiments with respect to the external magnetic field. We find that the transition amplitudes scale inversely with the external magnetic field.

Cu2+-Induced self-assembly and amyloid formation of a cyclic D,L-α-peptide: structure and function.

In a wide spectrum of neurodegenerative diseases, self-assembly of pathogenic proteins to cytotoxic intermediates is accelerated by the presence of metal ions such as Cu2+. Only low concentrations of these early transient oligomeric intermediates are present in a mixture of species during fibril formation, and hence information on the extent of structuring of these oligomers is still largely unknown. Here, we investigate dimers as the first intermediates in the Cu2+-driven aggregation of a cyclic D,L-α-peptide architecture. The unique structural and functional properties of this model system recapitulate the self-assembling properties of amyloidogenic proteins including ß-sheet conformation and cross-interaction with pathogenic amyloids. We show that a histidine-rich cyclic D,L-α-octapeptide binds Cu2+ with high affinity and selectivity to generate amyloid-like cross-ß-sheet structures. By taking advantage of backbone amide methylation to arrest the self-assembly at the dimeric stage, we obtain structural information and characterize the degree of local order for the dimer. We found that, while catalytic amounts of Cu2+ promote aggregation of the peptide to fibrillar structures, higher concentrations dose-dependently reduce fibrillization and lead to formation of spherical particles, showing self-assembly to different polymorphs. For the initial self-assembly step to the dimers, we found that Cu2+ is coordinated on average by two histidines, similar to self-assembled peptides, indicating that a similar binding interface is perpetuated during Cu2+-driven oligomerization. The dimer itself is found in heterogeneous conformations that undergo dynamic exchange, leading to the formation of different polymorphs at the initial stage of the aggregation process.

Symmetry-based singlet-triplet excitation in solution nuclear magnetic resonance.

Coupled pairs of spin-1/2 nuclei support one singlet state and three triplet states. In many circumstances, the nuclear singlet order, defined as the difference between the singlet population and the mean of the triplet populations, is a long-lived state that persists for a relatively long time in solution. Various methods have been proposed for generating singlet order, starting from nuclear magnetization. This requires the stimulation of singlet-to-triplet transitions by modulated radiofrequency fields. We show that a recently described pulse sequence, known as PulsePol [Schwartz et al., Sci. Adv., 4, eaat8978 (2018)], is an efficient technique for converting magnetization into long-lived singlet order. We show that the operation of this pulse sequence may be understood by adapting the theory of symmetry-based recoupling sequences in magic-angle-spinning solid-state nuclear magnetic resonance (NMR). The concept of riffling allows PulsePol to be interpreted by using the theory of symmetry-based pulse sequences and explains its robustness. This theory is used to derive a range of new pulse sequences for performing singlet-triplet excitation and conversion in solution NMR. Schemes for further enhancing the robustness of the transformations are demonstrated.

ATP Analogues for Structural Investigations: Case Studies of a DnaB Helicase and an ABC Transporter.

Nucleoside triphosphates (NTPs) are used as chemical energy source in a variety of cell systems. Structural snapshots along the NTP hydrolysis reaction coordinate are typically obtained by adding stable, nonhydrolyzable adenosine triphosphate (ATP) -analogues to the proteins, with the goal to arrest a state that mimics as closely as possible a physiologically relevant state, e.g., the pre-hydrolytic, transition and post-hydrolytic states. We here present the lessons learned on two distinct ATPases on the best use and unexpected pitfalls observed for different analogues. The proteins investigated are the bacterial DnaB helicase from Helicobacter pylori and the multidrug ATP binding cassette (ABC) transporter BmrA from Bacillus subtilis, both belonging to the same division of P-loop fold NTPases. We review the magnetic-resonance strategies which can be of use to probe the binding of the ATP-mimics, and present carbon-13, phosphorus-31, and vanadium-51 solid-state nuclear magnetic resonance (NMR) spectra of the proteins or the bound molecules to unravel conformational and dynamic changes upon binding of the ATP-mimics. Electron paramagnetic resonance (EPR), and in particular W-band electron-electron double resonance (ELDOR)-detected NMR, is of complementary use to assess binding of vanadate. We discuss which analogues best mimic the different hydrolysis states for the DnaB helicase and the ABC transporter BmrA. These might be relevant also to structural and functional studies of other NTPases.

ELDOR-detected NMR beyond hyperfine couplings: a case study with Cu(ii)-porphyrin dimers.

The pulse EPR method ELDOR-detected NMR (EDNMR) is applied to two Cu(ii)-porphyrin dimers that are suitable building blocks for molecular wires. One of the dimers is meso-meso singly linked, the other one is ß, meso, ß-fused. We show experimentally and theoretically that EDNMR spectra contain information about the electron-electron couplings. The spectra of the singly linked dimer are consistent with a perpendicular arrangement of the porphyrin planes and negligible exchange coupling. In addition, the resolution is good enough to distinguish 63Cu and 65Cu in frozen glassy solution and to resolve a metal-ion nuclear quadrupole coupling of 32 MHz. In the case of the fused dimer, we observe so far unreported signal enhancements, or anti-holes, in the EDNMR spectra. These are readily explained in a generalized framework based on [Cox et al., J. Magn. Reson., 2017, 280, 63-78], if an effective spin of S = 1 is assumed, in accordance with SQUID measurements. The positions of the anti-holes encode a zero-field splitting with |D| = 240 MHz, which is about twice as large as expected from the point-dipole approximation. These findings demonstrate the previously unrecognized applicability and versatility of the EDNMR technique in the quantitative study of complex paramagnetic compounds.

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.

Reverse dynamic nuclear polarisation for indirect detection of nuclear spins close to unpaired electrons.

Polarisation transfer schemes and indirect detection are central to magnetic resonance. Using the trityl radical OX063 and a pulse electron paramagnetic resonance spectrometer operating in the Q-band (35 GHz, 1.2 T), we show here that it is possible to use pulsed dynamic nuclear polarisation (DNP) to transfer polarisation from electrons to protons and back. The latter is achieved by first saturating the electrons and then simply using a reverse DNP step. A variable mixing time between DNP and reverse DNP allows us to investigate the decay of polarisation on protons in the vicinity of the electrons. We qualitatively investigate the influence of solvent deuteration, temperature, and electron concentration. We expect reverse DNP to be useful in the investigation of nuclear spin diffusion and envisage its use in electron-nuclear double-resonance (ENDOR) experiments.

Designing broadband pulsed dynamic nuclear polarization sequences in static solids.

Dynamic nuclear polarization (DNP) is a nuclear magnetic resonance (NMR) hyperpolarization technique that mediates polarization transfer from unpaired electrons with large thermal polarization to NMR-active nuclei via microwave (mw) irradiation. The ability to generate arbitrarily shaped mw pulses using arbitrary waveform generators allows for remarkable improvement of the robustness and versatility of DNP. We present here novel design principles based on single-spin vector effective Hamiltonian theory to develop new broadband DNP pulse sequences, namely, an adiabatic version of XiX (X-inverse X)-DNP and a broadband excitation by amplitude modulation (BEAM)-DNP experiment. We demonstrate that the adiabatic BEAM-DNP pulse sequence may achieve a 1H enhancement factor of ∼360, which is better than ramped-amplitude NOVEL (nuclear spin orientation via electron spin locking) at ∼0.35 T and 80 K in static solids doped with trityl radicals. In addition, the bandwidth of the BEAM-DNP experiments (~50 MHz) is about three times the 1H Larmor frequency. The generality of our theoretical approach will be helpful in the development of new pulsed DNP sequences.

Spectroscopic glimpses of the transition state of ATP hydrolysis trapped in a bacterial DnaB helicase.

The ATP hydrolysis transition state of motor proteins is a weakly populated protein state that can be stabilized and investigated by replacing ATP with chemical mimics. We present atomic-level structural and dynamic insights on a state created by ADP aluminum fluoride binding to the bacterial DnaB helicase from Helicobacter pylori. We determined the positioning of the metal ion cofactor within the active site using electron paramagnetic resonance, and identified the protein protons coordinating to the phosphate groups of ADP and DNA using proton-detected 31P,1H solid-state nuclear magnetic resonance spectroscopy at fast magic-angle spinning > 100 kHz, as well as temperature-dependent proton chemical-shift values to prove their engagements in hydrogen bonds. 19F and 27Al MAS NMR spectra reveal a highly mobile, fast-rotating aluminum fluoride unit pointing to the capture of a late ATP hydrolysis transition state in which the phosphoryl unit is already detached from the arginine and lysine fingers.

Using nutation-frequency-selective pulses to reduce radio-frequency field inhomogeneity in solid-state NMR.

Radio-frequency (rf) field inhomogeneity is a common problem in NMR which leads to non-ideal rotations of spins in parts of the sample. Often, a physical volume restriction of the sample is used to reduce the effects of rf-field inhomogeneity, especially in solid-state NMR where spacers are inserted to reduce the sample volume to the centre of the coil. We show that band-selective pulses in the spin-lock frame can be used to apply B1-field selective inversions to spins that experience selected parts of the rf-field distribution. Any frequency band-selective pulse can be used for this purpose, but we chose the family of I-BURP pulses (Geen and Freeman, 1991) for the measurements demonstrated here. As an example, we show that the implementation of such pulses improves homonuclear frequency-switched Lee-Goldburg decoupling in solid-state NMR.

Distance measurement between trityl radicals by pulse dressed electron paramagnetic resonance with phase modulation.

Distance measurement in the nanometre range is among the most important applications of pulse electron paramagnetic resonance today, especially in biological applications. The longest distance that can be measured by all presently used pulse sequences is determined by the phase memory time Tm of the observed spins. Here we show that one can measure the dipolar coupling during strong microwave irradiation by using an appropriate frequency- or phase-modulation scheme, i.e. by applying pulse sequences in the nutating frame. This decouples the electron spins from the surrounding nuclear spins and thus leads to significantly longer relaxation times of the microwave-dressed spins (i.e. the rotating frame relaxation times T1ρ and T2ρ) compared to Tm. The electron-electron dipolar coupling is not decoupled as long as both spins are excited, which can be implemented for trityl radicals at Q-band frequencies (35 GHz, 1.2 T). We show results for two bis-trityl rulers with inter-electron distances of about 4.1 and 5.3 nm and discuss technical challenges and possible next steps.

Molecular and supported Ti(iii)-alkyls: efficient ethylene polymerization driven by the π-character of metal-carbon bonds and back donation from a singly occupied molecular orbital.

While Ti(iii) alkyl species are the proposed active sites in Ziegler-Natta ethylene polymerization catalysts, the corresponding well-defined homogeneous catalysts are not known. We report that well-defined neutral ß-diiminato Ti(iii) alkyl species, namely [Ti(nacnac)(CH2 t Bu)2] and its alumina-grafted derivative [(AlsO)Ti(nacnac)(CH2 t Bu)], are active towards ethylene polymerization at moderate pressures and temperatures and possess an electron configuration well-adapted to insertion of ethylene. Advanced EPR spectroscopy showed that ethylene insertion into a Ti(iii)-C bond takes place during polymerization from Ti(nacnac)(CH2 t Bu)2. A combination of pulsed EPR spectroscopy and DFT calculations, based on a crystal structure of [Ti(nacnac)(CH2 t Bu)2], enabled us to reveal details about the structure and electronic configurations of both molecular and surface-grafted species. For both compounds, the α-agostic C-H interaction, which involves the singly occupied molecular orbital, indicates a π character of the metal-carbon bond; this π character is enhanced upon ethylene coordination, leading to a nearly barrier-less C2H4 insertion into Ti(iii)-C bonds after this first step. During coordination, back donation from the SOMO to the π*(C2H4) occurs, leading to stabilization of π-ethylene complexes and to a significant lowering of the overall energy of the C2H4 insertion transition state. In d1 alkyl complexes, ethylene insertion follows an original "augmented" Cossee-Arlman mechanism that involves the delocalization of unpaired electrons between the SOMO, π*(C2H4) and σ*(Ti-C) in the transition state, which further favors ethylene insertion. All these factors facilitate ethylene polymerization on Ti(iii) neutral alkyl species and make d1 alkyl complexes potentially more effective polymerization catalysts than their d0 analogues.

Facile generation of giant unilamellar vesicles using polyacrylamide gels.

Giant unilamellar vesicles (GUVs) are model cell-sized systems that have broad applications including drug delivery, analysis of membrane biophysics, and synthetic reconstitution of cellular machineries. Although numerous methods for the generation of free-floating GUVs have been established over the past few decades, only a fraction have successfully produced uniform vesicle populations both from charged lipids and in buffers of physiological ionic strength. In the method described here, we generate large numbers of free-floating GUVs through the rehydration of lipid films deposited on soft polyacrylamide (PAA) gels. We show that this technique produces high GUV concentrations for a range of lipid types, including charged ones, independently of the ionic strength of the buffer used. We demonstrate that the gentle hydration of PAA gels results in predominantly unilamellar vesicles, which is in contrast to comparable methods analyzed in this work. Unilamellarity is a defining feature of GUVs and the generation of uniform populations is key for many downstream applications. The PAA method is widely applicable and can be easily implemented with commonly utilized laboratory reagents, making it an appealing platform for the study of membrane biophysics.

Simulation and evaluation of 3D traction force microscopy.

Measuring cell-generated forces by Traction Force Microscopy (TFM) has become a standard tool in cell mechanobiology. Although widely used in two dimensional (2D) experiments, only a few methods exist to measure traction in three-dimensional (3D) cell culture, since 3D volumetric high-resolution microscopy and more demanding computational approaches are required. Although it is commonly known that the selected experimental and computational setup highly influence the quality and accuracy of the results, no existing methods can adequately assess the errors involved in this process. We present a fully integrated simulation and evaluation platform that allows one to simulate TFM images and quantify errors of an applied approach for traction stress reconstruction, in order to improve experiments that attempt to measure mechanical interaction in cellular systems. In this context, we show that a careful parameter selection can decrease the reconstructed traction error by up to 40%.

Chirp echo Fourier transform EPR-detected NMR.

A new ultra-wide band (UWB) pulse EPR method is introduced for observing all nuclear frequencies of a paramagnetic center in a single shot. It is based on burning spectral holes with a high turning angle (HTA) pulse that excites forbidden transitions and subsequent detection of the hole pattern by a chirp echo. We term this method Chirp Echo Epr SpectroscopY (CHEESY)-detected NMR. The approach is a revival of FT EPR-detected NMR. It yields similar spectra and the same type of information as electron-electron double resonance (ELDOR)-detected NMR, but with a multiplex advantage. We apply CHEESY-detected NMR in Q band to nitroxides and correlate the hyperfine spectrum to the EPR spectrum by varying the frequency of the HTA pulse. Furthermore, a selective π pulse before the HTA pulse allows for detecting hyperfine sublevel correlations between transitions of one nucleus and for elucidating the coupling regime, the same information as revealed by the HYSCORE experiment. This is demonstrated on hexaaquamanganese(II). We expect that CHEESY-detected NMR is generally applicable to disordered systems and that our results further motivate the development of EPR spectrometers capable of coherent UWB excitation and detection, especially at higher fields and frequencies.

Transient effects in π-pulse sequences in MAS solid-state NMR.

Dipolar recoupling techniques that use isolated rotor-synchronized π pulses are commonly used in solid-state NMR spectroscopy to gain insight into the structure of biological molecules. These sequences excel through their simplicity, stability towards radio-frequency (rf) inhomogeneity, and low rf requirements. For a theoretical understanding of such sequences, we present a Floquet treatment based on an interaction-frame transformation including the chemical-shift offset dependence. This approach is applied to the homonuclear dipolar-recoupling sequence Radio-Frequency Driven Recoupling (RFDR) and the heteronuclear recoupling sequence Rotational Echo Double Resonance (REDOR). Based on the Floquet approach, we show the influence of effective fields caused by pulse transients and discuss the advantages of pulse-transient compensation. We demonstrate experimentally that the transfer efficiency for homonuclear recoupling can be doubled in some cases in model compounds as well as in simple peptides if pulse-transient compensation is applied to the π pulses. Additionally, we discuss the influence of various phase cycles on the recoupling efficiency in order to reduce the magnitude of effective fields. Based on the findings from RFDR, we are able to explain why the REDOR sequence does not suffer in the recoupling efficiency despite the presence of effective fields.

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.