Focus: Two-dimensional electron-electron double resonance and molecular motions: The challenge of higher frequencies

Phosphorylation, disorder, and phase separation govern the behavior of Frequency in the fungal circadian clock

Circadian clocks are composed of transcription-translation negative feedback loops that pace rhythms of gene expression to the diurnal cycle. In the filamentous fungus Neurospora crassa, the proteins Frequency (FRQ), the FRQ-interacting RNA helicase (FRH), and Casein-Kinase I (CK1) form the FFC complex that represses expression of genes activated by the white-collar complex (WCC). FRQ orchestrates key molecular interactions of the clock despite containing little predicted tertiary structure. Spin labeling and pulse-dipolar electron spin resonance spectroscopy provide domain-specific structural insights into the 989-residue intrinsically disordered FRQ and the FFC. FRQ contains a compact core that associates and organizes FRH and CK1 to coordinate their roles in WCC repression. FRQ phosphorylation increases conformational flexibility and alters oligomeric state, but the changes in structure and dynamics are non-uniform. Full-length FRQ undergoes liquid-liquid phase separation (LLPS) to sequester FRH and CK1 and influence CK1 enzymatic activity. Although FRQ phosphorylation favors LLPS, LLPS feeds back to reduce FRQ phosphorylation by CK1 at higher temperatures. Live imaging of Neurospora hyphae reveals FRQ foci characteristic of condensates near the nuclear periphery. Analogous clock repressor proteins in higher organisms share little position-specific sequence identity with FRQ; yet, they contain amino acid compositions that promote LLPS. Hence, condensate formation may be a conserved feature of eukaryotic clocks.

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.

Regulation of membrane protein structure and function by their lipid nano-environment

Transmembrane proteins comprise ~30% of the mammalian proteome, mediating metabolism, signalling, transport and many other functions required for cellular life. The microenvironment of integral membrane proteins (IMPs) is intrinsically different from that of cytoplasmic proteins, with IMPs solvated by a compositionally and biophysically complex lipid matrix. These solvating lipids affect protein structure and function in a variety of ways, from stereospecific, high-affinity protein-lipid interactions to modulation by bulk membrane properties. Specific examples of functional modulation of IMPs by their solvating membranes have been reported for various transporters, channels and signal receptors; however, generalizable mechanistic principles governing IMP regulation by lipid environments are neither widely appreciated nor completely understood. Here, we review recent insights into the inter-relationships between complex lipidomes of mammalian membranes, the membrane physicochemical properties resulting from such lipid collectives, and the regulation of IMPs by either or both. The recent proliferation of high-resolution methods to study such lipid-protein interactions has led to generalizable insights, which we synthesize into a general framework termed the 'functional paralipidome' to understand the mutual regulation between membrane proteins and their surrounding lipid microenvironments.

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.

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

Exchange processes which include conformational change, protonation/deprotonation, and binding equilibria are routinely studied by 2D exchange NMR techniques, where information about the exchange of nuclei between environments with different NMR shifts is obtained from the development of cross-peaks. Whereas 2D NMR enables the real time study of millisecond and slower exchange processes, 2D ESR in the form of 2D-ELDOR (two-dimensional electron-electron double resonance) has the potential for such studies over the nanosecond to microsecond real time scales. Cross-peak development due to chemical exchange has been seen previously for semiquinones in ESR, but this is not possible for most common ESR probes, such as nitroxides, studied at typical ESR frequencies because, unlike NMR, the exchanging states yield ESR signals that are not resolved from each other within their respective line widths. But at 95 GHz, it becomes possible to resolve them in many cases because of the increased g-factor resolution. The 95 GHz instrumental developments occurring at ACERT now enable such studies. We demonstrate these new capabilities in two studies: (A) the protonation/deprotonation process for a pH-sensitive imidazoline spin label in aqueous solution where the exchange rate and the population ratio of the exchanging states are controlled by the concentration and pH of the buffer solution, respectively, and (B) a nitroxide radical partitioning between polar (aqueous) and nonpolar (phospholipid) environments in multilamellar lipid vesicles, where the cross-peak development arises from the exchange of the nitroxide between the two phases. This work represents the first example of the observation and analysis of cross-peaks arising from chemical exchange processes involving nitroxide spin labels.

Microsecond dynamics in proteins by two-dimensional ESR: Predictions

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 this work, simulations are provided for the example of domain motions within proteins that are themselves slowly tumbling in solution. These show the nature of the exchange cross-peaks that are predicted to develop in real time from such domain motions. However, we find that the existing theoretical methods for computing 2D-ELDOR experiments over a wide motional range begin to fail seriously when applied to very slow motions characteristic of proteins in solution. One reason is the failure to obtain accurate eigenvectors and eigenvalues of the complex symmetric stochastic Liouville matrices describing the experiment when computed by the efficient Lanczos algorithm in the range of very slow motion. Another, perhaps more serious, issue is that these matrices are "non-normal," such that for the very slow motional range even rigorous diagonalization algorithms do not yield the correct eigenvalues and eigenvectors. We have employed algorithms that overcome both these issues and lead to valid 2D-ELDOR predictions even for motions approaching the rigid limit. They are utilized to describe the development of cross-peaks in 2D-ELDOR at 95 GHz for a particular case of domain motion.

Preface: Special Topic on Multidimensional Spectroscopy

Multidimensional signals are generated by subjecting molecules to sequences of short optical pulses and recording correlation plots related to the various controlled delay periods. These techniques which span all the way from the THz to the x-ray regimes provide qualitatively new structural and dynamical molecular information not available from conventional one-dimensional techniques. This issue surveys the recent experimental and theoretical progresses in this rapidly developing 20 year old field which illustrates the novel insights provided by multidimensional techniques into electronic and nuclear motions. It should serve as a valuable source for experts in the field and help introduce newcomers to this exciting and challenging branch of nonlinear spectroscopy.