Andrin Doll

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.

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.

Fourier-transform electron spin resonance with bandwidth-compensated chirp pulses.

Electron spin echo experiments using chirp pulses at X-band around 9GHz have been performed with a home-built spectrometer based on an arbitrary waveform generator. Primary echoes without phase dispersion were obtained by employing the Böhlen-Bodenhausen scheme with the refocusing pulse being half as long as the coherence-generating pulse. To account for physical bandwidth limitation by the resonator, the instantaneous sweep rate of the chirps was adapted to the spectrometers frequency response function, which can be recorded from the sample under study within a few minutes. Such bandwidth-compensated chirp pulses are experimentally shown to achieve an almost uniform excitation bandwidth that exceeds the resonator bandwidth. This uniform excitation allows for computing frequency-domain spectra by Fourier-transformation (FT) of the echo signal. For a nitroxide in dilute solid solution with a spectral width of 200MHz, the FT EPR spectrum agrees remarkably well with a field-swept echo-detected EPR spectrum. The overall spectral perturbation for operation far beyond the resonator bandwidth was characterized by acquiring a 700MHz wide spectral range of a copper (II) EPR spectrum with nearly uniform amplitude with excitation and refocusing pulses of 200 and 100ns, respectively. Furthermore, peculiarities were observed in solid-state FT EPR spectra of disordered systems. To understand these peculiarities two-dimensional data sets were acquired that correlate the FT EPR spectrum to inversion recovery or nuclear modulation. The echo envelope modulation experiments reveal echo decay rates increased by enhanced instantaneous diffusion and passage-specific effects in the nuclear modulations. The latter effect can be suppressed by nuclear modulation averaging. Apparent longitudinal relaxation times for a given subset of orientations are influenced by nuclear modulation effects. Proper extraction of orientation-dependent relaxation times thus requires an experimental setup that minimizes the modulations.

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.

Liquid state DNP for water accessibility measurements on spin-labeled membrane proteins at physiological temperatures

We demonstrate the application of continuous wave dynamic nuclear polarization (DNP) at 0.35 T for site-specific water accessibility studies on spin-labeled membrane proteins at concentrations in the 10-100 μM range. The DNP effects at such low concentrations are weak and the experimentally achievable dynamic nuclear polarizations can be below the equilibrium polarization. This sensitivity problem is solved with an optimized home-built DNP probe head consisting of a dielectric microwave resonator and a saddle coil as close as possible to the sample. The performance of the probe head is demonstrated with both a modified pulsed EPR spectrometer and a dedicated CW EPR spectrometer equipped with a commercial NMR console. In comparison to a commercial pulsed ENDOR resonator, the home-built resonator has an FID detection sensitivity improvement of 2.15 and an electron spin excitation field improvement of 1.2. The reproducibility of the DNP results is tested on the water soluble maltose binding protein MalE of the ABC maltose importer, where we determine a net standard deviation of 9% in the primary DNP data in the concentration range between 10 and 100 μM. DNP parameters are measured in a spin-labeled membrane protein, namely the vitamin B(12) importer BtuCD in both detergent-solubilized and reconstituted states. The data obtained in different nucleotide states in the presence and absence of binding protein BtuF reveal the applicability of this technique to qualitatively extract water accessibility changes between different conformations by the ratio of primary DNP parameters ϵ. The ϵ-ratio unveils the physiologically relevant transmembrane communication in the transporter in terms of changes in water accessibility at the cytoplasmic gate of the protein induced by both BtuF binding at the periplasmic region of the transporter and ATP binding at the cytoplasmic nucleotide binding domains.

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.

Water accessibility in a membrane-inserting peptide comparing Overhauser DNP and pulse EPR methods

Water accessibility is a key parameter for the understanding of the structure of biomolecules, especially membrane proteins. Several experimental techniques based on the combination of electron paramagnetic resonance (EPR) spectroscopy with site-directed spin labeling are currently available. Among those, we compare relaxation time measurements and electron spin echo envelope modulation (ESEEM) experiments using pulse EPR with Overhauser dynamic nuclear polarization (DNP) at X-band frequency and a magnetic field of 0.33 T. Overhauser DNP transfers the electron spin polarization to nuclear spins via cross-relaxation. The change in the intensity of the (1)H NMR spectrum of H2O at a Larmor frequency of 14 MHz under a continuous-wave microwave irradiation of the nitroxide spin label contains information on the water accessibility of the labeled site. As a model system for a membrane protein, we use the hydrophobic α-helical peptide WALP23 in unilamellar liposomes of DOPC. Water accessibility measurements with all techniques are conducted for eight peptides with different spin label positions and low radical concentrations (10-20 μM). Consistently in all experiments, the water accessibility appears to be very low, even for labels positioned near the end of the helix. The best profile is obtained by Overhauser DNP, which is the only technique that succeeds in discriminating neighboring positions in WALP23. Since the concentration of the spin-labeled peptides varied, we normalized the DNP parameter ϵ, being the relative change of the NMR intensity, by the electron spin concentration, which was determined from a continuous-wave EPR spectrum.

Averaging of nuclear modulation artefacts in RIDME experiments

The presence of artefacts due to Electron Spin Echo Envelope Modulation (ESEEM) complicates the analysis of dipolar evolution data in Relaxation Induced Dipolar Modulation Enhancement (RIDME) experiments. Here we demonstrate that averaging over the two delay times in the refocused RIDME experiment allows for nearly quantitative removal of the ESEEM artefacts, resulting in potentially much better performance than the so far used methods. The analytical equations are presented and analyzed for the case of electron and nuclear spins S=1/2,I=1/2. The presented analysis is also relevant for Double Electron Electron Resonance (DEER) and Chirp-Induced Dipolar Modulation Enhancement (CIDME) techniques. The applicability of the ESEEM averaging approach is demonstrated on a Gd(III)-Gd(III) rigid ruler compound in deuterated frozen solution at Q band (35GHz).

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.