Microsecond Exchange Processes Studied by Two-Dimensional ESR at 95 GHz

High-frequency high-power DNP/EPR spectrometer operating at 7 T magnetic field

One of the most essential prerequisites for the development of pulse Dynamic Nuclear Polarization (DNP) is the ability to generate high-power coherent mm-wave pulses at the electron precession frequencies corresponding to the magnetic fields of modern high-resolution NMR spectrometers. As a major step towards achieving this goal, an Extended Interaction Klystron (EIK) pulse amplifier custom-built by the Communications and Power Industries, Inc. and producing up to 140 W at 197.8 GHz, was integrated with in-house built NMR/DNP/EPR spectrometer operating at 7 T magnetic field. The spectrometer employs a Thomas Keating, Ltd. quasioptical bridge to direct mm-waves into a homebuilt DNP probe incorporating photonic bandgap (PBG) resonators to further boost electronic B1e fields. Three-pulse electron spin echo nutation experiments were employed to characterize the B1e fields at the sample by operating the homodyne 198 GHz bridge in an induction mode. Room-temperature experiments with a single-crystal high-pressure, high-temperature (HPHT) diamond and a polystyrene film doped with BDPA radical yielded < 9 ns π/2 pulses at ca. 50 W specified EIK output at the corresponding resonance frequencies and the PBG resonator quality factor of Q≈300. DNP experiments carried out in a "gated" mode by supplying 20 μs mm-wave pulses every 1 ms yielded 13C solid-effect DNP with gains up to 20 for the polystyrene-BDPA sample at natural 13C abundance. For a single-crystal HPHT diamond, the gated DNP mode yielded almost the same 13C enhancement as a low-power continuous wave (CW) mode at 0.4 W, whereas no DNP effect was observed for the BDPA/polystyrene sample in the latter case. To illustrate the versatility of our upgraded DNP spectrometer, room-temperature Overhauser DNP enhancements of 7-14 for 31P NMR signal were demonstrated using a liquid droplet of 1 M tri-phenyl phosphine co-dissolved with 100 mM of BDPA in toluene‑d8.

Integrating Electron Paramagnetic Resonance Spectroscopy and Computational Modeling to Measure Protein Structure and Dynamics

Electron paramagnetic resonance (EPR) has become a powerful probe of conformational heterogeneity and dynamics of biomolecules. In this Review, we discuss different computational modeling techniques that enrich the interpretation of EPR measurements of dynamics or distance restraints. A variety of spin labels are surveyed to provide a background for the discussion of modeling tools. Molecular dynamics (MD) simulations of models containing spin labels provide dynamical properties of biomolecules and their labels. These simulations can be used to predict EPR spectra, sample stable conformations and sample rotameric preferences of label sidechains. For molecular motions longer than milliseconds, enhanced sampling strategies and de novo prediction software incorporating or validated by EPR measurements are able to efficiently refine or predict protein conformations, respectively. To sample large-amplitude conformational transition, a coarse-grained or an atomistic weighted ensemble (WE) strategy can be guided with EPR insights. Looking forward, we anticipate an integrative strategy for efficient sampling of alternate conformations by de novo predictions, followed by validations by systematic EPR measurements and MD simulations. Continuous pathways between alternate states can be further sampled by WE-MD including all intermediate states.

Time-Frequency Analysis of Two-Dimensional Electron Spin Resonance Signals

Two-dimensional electron spin resonance (2D ESR) spectroscopy is a unique experimental technique for probing protein structure and dynamics, including processes that occur at the microsecond time scale. While it provides significant resolution enhancement over the one-dimensional experimental setup, spectral broadening and noise make extraction of spectral information highly challenging. Traditionally, two-dimensional Fourier transform (2D FT) is applied for the analysis of 2D ESR signals, although its efficiency is limited to stationary signals. In addition, it often fails to resolve overlapping peaks in 2D ESR. In this work, we propose a time-frequency analysis of 2D time-domain signals, which identifies all frequency peaks by decoupling a signal into its distinct constituent components via projection on the time-frequency plane. The method utilizes 2D undecimated discrete wavelet transform (2D UDWT) as an intermediate step in the analysis, followed by signal reconstruction and 2D FT. We have applied the method to a simulated 2D double quantum coherence (DQC) signal for validation and a set of experimental 2D ESR signals, demonstrating its efficiency in resolving overlapping peaks in the frequency domain, while displaying frequency evolution with time in case of non-stationary data.

Single-pulse terahertz spectroscopy monitoring sub-millisecond time dynamics at a rate of 50 kHz

Slow motion movies allow us to see intricate details of the mechanical dynamics of complex phenomena. If the images in each frame are replaced by terahertz (THz) waves, such movies can monitor low-energy resonances and reveal fast structural or chemical transitions. Here, we combine THz spectroscopy as a non-invasive optical probe with a real-time monitoring technique to demonstrate the ability to resolve non-reproducible phenomena at 50k frames per second, extracting each of the generated THz waveforms every 20 μs. The concept, based on a photonic time-stretch technique to achieve unprecedented data acquisition speeds, is demonstrated by monitoring sub-millisecond dynamics of hot carriers injected in silicon by successive resonant pulses as a saturation density is established. Our experimental configuration will play a crucial role in revealing fast irreversible physical and chemical processes at THz frequencies with microsecond resolution to enable new applications in fundamental research as well as in industry.

Microsecond dynamics in proteins by two-dimensional ESR. II. Addressing computational challenges

Two-dimensional electron-electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. In previous work, we provided simulations for the case of domain motions within proteins that are themselves slowly tumbling in a solution. In order to perform these simulations, it was found that the standard approach of solving the relevant stochastic Liouville equation using the efficient Lanczos algorithm for this case breaks down, so algorithms were employed that rely on the Arnoldi iteration. While they lead to accurate simulations, they are very time-consuming. In this work, we focus on a variant known as the rational Arnoldi algorithm. We show that this can achieve a significant reduction in computation time. The stochastic Liouville matrix, which is of very large dimension, N, is first reduced to a much smaller dimension, m, e.g., from N ∼ O(10⁴) to m ∼ 60, that spans the relevant Krylov subspace from which the spectrum is predicted. This requires the selection of the m frequency shifts to be utilized. A method of adaptive shift choice is introduced to optimize this selection. We also find that these procedures help in optimizing the pruning procedure that greatly reduces the dimension of the initial N dimensional stochastic Liouville matrix in such subsequent computations.