Time Scales of Slow Motions in Ubiquitin Explored by Heteronuclear Double Resonance

Paramagnetic relaxation enhancement-assisted structural characterization of a partially disordered conformation of ubiquitin

Nuclear magnetic resonance (NMR) is a powerful tool to study three-dimensional structures as well as protein conformational fluctuations in solution, but it is compromised by increases in peak widths and missing signals. We previously reported that ubiquitin has two folded conformations, N₁ and N₂ and plus another folded conformation, I, in which some amide group signals of residues 33-41 almost disappeared above 3 kbar at pH 4.5 and 273 K. Thus, well-converged structural models could not be obtained for this region owing to the absence of distance restraints. Here, we reexamine the problem using the ubiquitin Q41N variant as a model for this locally disordered conformation, I. We demonstrate that the variant shows pressure-induced loss of backbone amide group signals at residues 28, 33, 36, and 39-41 like the wild-type, with a similar but smaller effect on CαH and CβH signals. In order to characterize this I structure, we measured paramagnetic relaxation enhancement (PRE) under high pressure to obtain distance restraints, and calculated the structure assisted by Bayesian inference. We conclude that the more disordered I conformation observed at pH 4.0, 278 K, and 2.5 kbar largely retained the N₂ conformation, although the amide groups at residues 33-41 have more heterogeneous conformations and more contact with water, which differ from the N₁ and N₂ states. The PRE-assisted strategy has the potential to improve structural characterization of proteins that lack NMR signals, especially for relatively more open and hydrated protein conformations.

Quantifying proton NMR coherent linewidth in proteins under fast MAS conditions: a second moment approach

Proton detected solid-state NMR under fast magic-angle-spinning (MAS) conditions is currently redefining the applications of solid-state NMR, in particular in structural biology. Understanding the contributions to the spectral linewidth is thereby of paramount importance. When disregarding the sample-dependent inhomogeneous contributions, the NMR proton linewidth is defined by homogeneous broadening, which has incoherent and coherent contributions. Understanding and disentangling these different contributions in multi-spin systems like proteins is still an open issue. The coherent contribution is mainly caused by the dipolar interaction under MAS and is determined by the molecular structure and the proton chemical shifts. Numerical simulation approaches based on numerically exact direct integration of the Liouville-von Neumann equation can give valuable information about the lineshape, but are limited to small spin systems (<12 spins). We present an alternative simulation method for the coherent contributions based on the rapid and partially analytic calculation of the second moments of large spin systems. We first validate the method on a simple system by predicting the ¹⁹F linewidth in CaF₂ under MAS. We compare simulation results to experimental data for microcrystalline ubiquitin (deuterated 100% back-exchanged at 110 kHz and fully-protonated at 125 kHz). Our results quantitatively explain the observed linewidth per-residue basis for the vast majority of residues.

15N transverse relaxation measurements for the characterization of µs-ms dynamics are deteriorated by the deuterium isotope effect on 15N resulting from solvent exchange

¹⁵N R₂ relaxation measurements are key for the elucidation of the dynamics of both folded and intrinsically disordered proteins (IDPs). Here we show, on the example of the intrinsically disordered protein α-synuclein and the folded domain PDZ2, that at physiological pH and near physiological temperatures amide-water exchange can severely skew Hahn-echo based ¹⁵N R₂ relaxation measurements as well as low frequency data points in CPMG relaxation dispersion experiments. The nature thereof is the solvent exchange with deuterium in the sample buffer, which modulates the ¹⁵N chemical shift tensor via the deuterium isotope effect, adding to the apparent relaxation decay which leads to systematic errors in the relaxation data. This results in an artificial increase of the measured apparent ¹⁵N R₂ rate constants-which should not be mistaken with protein inherent chemical exchange contributions, R_ex, to ¹⁵N R₂. For measurements of ¹⁵N R₂ rate constants of IDPs and folded proteins at physiological temperatures and pH, we recommend therefore the use of a very low D₂O molar fraction in the sample buffer, as low as 1%, or the use of an external D₂O reference along with a modified ¹⁵N R₂ Hahn-echo based experiment. This combination allows for the measurement of R_ex contributions to ¹⁵N R₂ originating from conformational exchange in a time window from µs to ms.

Interactions Controlling the Slow Dynamic Conformational Motions of Ubiquitin

Rational mutation of proteins based on their structural and dynamic characteristics is a useful strategy for amplifying specific fluctuations in proteins. Here, we show the effects of mutation on the conformational fluctuations and thermodynamic stability of ubiquitin. In particular, we focus on the salt bridge between K11 and E34 and the hydrogen bond between I36 and Q41, which are predicted to control the fluctuation between the basic folded state, N₁, and the alternatively folded state, N₂, of the protein, using high-pressure NMR spectroscopy. The E34A mutation, which disrupts the salt bridge, did not alter picosecond–to–nanosecond, microsecond–to–millisecond dynamic motions, and stability of the protein, while the Q41N mutation, which destabilizes the hydrogen bond, specifically amplified the N₁–N₂ conformational fluctuation and decreased stability. Based on the observed thermodynamic stabilities of the various conformational states, we showed that in the Q41N mutant, the N₁ state is more significantly destabilized than the N₂ state, resulting in an increase in the relative population of N₂. Identifying the interactions controlling specific motions of a protein will facilitate molecular design to achieve functional dynamics beyond native state dynamics.

Slow conformational exchange and overall rocking motion in ubiquitin protein crystals

Proteins perform their functions in solution but their structures are most frequently studied inside crystals. Here we probe how the crystal packing alters microsecond dynamics, using solid-state NMR measurements and multi-microsecond MD simulations of different crystal forms of ubiquitin. In particular, near-rotary-resonance relaxation dispersion (NERRD) experiments probe angular backbone motion, while Bloch–McConnell relaxation dispersion data report on fluctuations of the local electronic environment. These experiments and simulations reveal that the packing of the protein can significantly alter the thermodynamics and kinetics of local conformational exchange. Moreover, we report small-amplitude reorientational motion of protein molecules in the crystal lattice with an ~3–5° amplitude on a tens-of-microseconds time scale in one of the crystals, but not in others. An intriguing possibility arises that overall motion is to some extent coupled to local dynamics. Our study highlights the importance of considering the packing when analyzing dynamics of crystalline proteins.

X-ray crystallography is the main method for protein structure determination. Here the authors combine solid-state NMR measurements and molecular dynamics simulations and show that crystal packing alters the thermodynamics and kinetics of local conformational exchange as well as overall rocking motion of protein molecules in the crystal lattice.

Studying Dynamics by Magic-Angle Spinning Solid-State NMR Spectroscopy: Principles and Applications to Biomolecules

Magic-angle spinning solid-state NMR spectroscopy is an important technique to study molecular structure, dynamics and interactions, and is rapidly gaining importance in biomolecular sciences. Here we provide an overview of experimental approaches to study molecular dynamics by MAS solid-state NMR, with an emphasis on the underlying theoretical concepts and differences of MAS solid-state NMR compared to solution-state NMR. The theoretical foundations of nuclear spin relaxation are revisited, focusing on the particularities of spin relaxation in solid samples under magic-angle spinning. We discuss the range of validity of Redfield theory, as well as the inherent multi-exponential behavior of relaxation in solids. Experimental challenges for measuring relaxation parameters in MAS solid-state NMR and a few recently proposed relaxation approaches are discussed, which provide information about time scales and amplitudes of motions ranging from picoseconds to milliseconds. We also discuss the theoretical basis and experimental measurements of anisotropic interactions (chemical-shift anisotropies, dipolar and quadrupolar couplings), which give direct information about the amplitude of motions. The potential of combining relaxation data with such measurements of dynamically-averaged anisotropic interactions is discussed. Although the focus of this review is on the theoretical foundations of dynamics studies rather than their application, we close by discussing a small number of recent dynamics studies, where the dynamic properties of proteins in crystals are compared to those in solution.

Allosteric switch regulates protein-protein binding through collective motion

Many biological processes depend on allosteric communication between different parts of a protein, but the role of internal protein motion in propagating signals through the structure remains largely unknown. Through an experimental and computational analysis of the ground state dynamics in ubiquitin, we identify a collective global motion that is specifically linked to a conformational switch distant from the binding interface. This allosteric coupling is also present in crystal structures and is found to facilitate multispecificity, particularly binding to the ubiquitin-specific protease (USP) family of deubiquitinases. The collective motion that enables this allosteric communication does not affect binding through localized changes but, instead, depends on expansion and contraction of the entire protein domain. The characterization of these collective motions represents a promising avenue for finding and manipulating allosteric networks.

Protein stabilizer, NDSB-195, enhances the dynamics of the β4 -α2 loop of ubiquitin

Non-detergent sulfobetaines (NDSBs) are a new group of small, synthetic protein stabilizers, which have advantages over classical compatible osmolytes, such as polyol, amines, and amino acids: they do not increase solution viscosity, unlike polyols, and they are zwitterionic at all pH ranges, unlike amines and amino acids. NDSBs also facilitate the crystallization and refolding of proteins. The mechanism whereby NDSBs exhibit such activities, however, remains elusive. To gain insight into this mechanism, we studied, using nuclear magnetic resonance (NMR), the effects of dimethylethylammonium propane sulfonate (NDSB-195) on the dynamics of ubiquitin, on which a wealth of information has been accumulated. By analyzing the line width of amide proton resonances and the transverse relaxation rates of nitrogen atoms, we found that NDSB-195 enhances the microsecond-millisecond dynamics of a β4 -α2 loop of ubiquitin. Although those compounds that enhance protein dynamics are generally considered to destabilize protein molecules, NDSB-195 enhanced the stability of ubiquitin against guanidium chloride denaturation. Thus, the simultaneous enhancement of stability and flexibility by a single compound can be attained.

NMR Method for Characterizing Microsecond-to-Millisecond Chemical Exchanges Utilizing Differential Multiple-Quantum Relaxation in High Molecular Weight Proteins

Chemical exchange processes of proteins on the order of microseconds (μs) to milliseconds (ms) play critical roles in biological functions. Developments in methyl-transverse relaxation optimized spectroscopy (methyl-TROSY), which observes the slowly relaxing multiple quantum (MQ) coherences, have enabled the studies of biologically important large proteins. However, the analyses of μs to ms chemical exchange processes based on the methyl-TROSY principle are still challenging, because the interpretation of the chemical exchange contributions to the MQ relaxation profiles is complicated, as significant chemical shift differences occur in both (1)H and (13)C nuclei. Here, we report a new methyl-based NMR method for characterizing chemical exchanges, utilizing differential MQ relaxation rates and a heteronuclear double resonance pulse technique. The method enables quantitative evaluations of the chemical exchange processes, in which significant chemical shift differences exist in both the (1)H and (13)C nuclei. The versatility of the method is demonstrated with the application to KirBac1.1, with an apparent molecular mass of 200 kDa.

Metainference: A Bayesian inference method for heterogeneous systems

Modeling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model and thus to obtain better predictions about the behavior of the corresponding system. This approach, however, is affected by a variety of different errors, especially when a system simultaneously populates an ensemble of different states and experimental data are measured as averages over such states. To address this problem, we present a Bayesian inference method, called "metainference," that is able to deal with errors in experimental measurements and with experimental measurements averaged over multiple states. To achieve this goal, metainference models a finite sample of the distribution of models using a replica approach, in the spirit of the replica-averaging modeling based on the maximum entropy principle. To illustrate the method, we present its application to a heterogeneous model system and to the determination of an ensemble of structures corresponding to the thermal fluctuations of a protein molecule. Metainference thus provides an approach to modeling complex systems with heterogeneous components and interconverting between different states by taking into account all possible sources of errors.

The membrane anchor of the transcriptional activator SREBP is characterized by intrinsic conformational flexibility

Regulated intramembrane proteolysis (RIP) is a conserved mechanism crucial for numerous cellular processes, including signaling, transcriptional regulation, axon guidance, cell adhesion, cellular stress responses, and transmembrane protein fragment degradation. Importantly, it is relevant in various diseases including Alzheimer's disease, cardiovascular diseases, and cancers. Even though a number of structures of different intramembrane proteases have been solved recently, fundamental questions concerning mechanistic underpinnings of RIP and therapeutic interventions remain. In particular, this includes substrate recognition, what properties render a given substrate amenable for RIP, and how the lipid environment affects the substrate cleavage. Members of the sterol regulatory element-binding protein (SREBP) family of transcription factors are critical regulators of genes involved in cholesterol/lipid homeostasis. After site-1 protease cleavage of the inactive SREBP transmembrane precursor protein, RIP of the anchor intermediate by site-2 protease generates the mature transcription factor. In this work, we have investigated the labile anchor intermediate of SREBP-1 using NMR spectroscopy. Surprisingly, NMR chemical shifts, site-resolved solvent exposure, and relaxation studies show that the cleavage site of the lipid-signaling protein intermediate bears rigid α-helical topology. An evolutionary conserved motif, by contrast, interrupts the secondary structure ∼9-10 residues C-terminal of the scissile bond and acts as an inducer of conformational flexibility within the carboxyl-terminal transmembrane region. These results are consistent with molecular dynamics simulations. Topology, stability, and site-resolved dynamics data suggest that the cleavage of the α-helical substrate in the case of RIP may be associated with a hinge motion triggered by the molecular environment.

Theoretical tools for the design of NMR relaxation dispersion pulse sequences

Recent decades have witnessed tremendous progress in the development of new experimental methods for studying biomolecules, particularly in the field of NMR relaxation dispersion. Here we review the theoretical frameworks that provided the insights necessary for such progress. The effect of radio-frequency manipulations on spin systems is discussed using Average Hamiltonian Theory (AHT), Average Liouvillian Theory (ALT), and Bloch-Wangsness-Redfield (BWR) relaxation theory. We illustrate these concepts using the case of Heteronuclear Double Resonance (HDR) methods.

Integrative, dynamic structural biology at atomic resolution--it's about time

Biomolecules adopt a dynamic ensemble of conformations, each with the potential to interact with binding partners or perform the chemical reactions required for a multitude of cellular functions. Recent advances in X-ray crystallography, nuclear magnetic resonance (NMR) spectroscopy and other techniques are helping us realize the dream of seeing--in atomic detail--how different parts of biomolecules shift between functional substates using concerted motions. Integrative structural biology has advanced our understanding of the formation of large macromolecular complexes and how their components interact in assemblies by leveraging data from many low-resolution methods. Here, we review the growing opportunities for integrative, dynamic structural biology at the atomic scale, contending there is increasing synergistic potential between X-ray crystallography, NMR and computer simulations to reveal a structural basis for protein conformational dynamics at high resolution.

High-Pressure NMR Spectroscopy Reveals Functional Sub-states of Ubiquitin and Ubiquitin-Like Proteins

High-pressure nuclear magnetic resonance (NMR) spectroscopy has revealed that ubiquitin has at least two high-energy states--an alternatively folded state N2 and a locally disordered state I--between the basic folded state N1 and totally unfolded U state. The high-energy states are conserved among ubiquitin-like post-translational modifiers, ubiquitin, NEDD8, and SUMO-2, showing the E1-E2-E3 cascade reaction. It is quite intriguing that structurally similar high-energy states are evolutionally conserved in the ubiquitin-like modifiers, and the thermodynamic stabilities vary among the proteins. To investigate atomic details of the high-energy states, a Q41N mutant of ubiquitin was created as a structural model of N2, which is 71% populated even at atmospheric pressure. The convergent structure of the "pure" N2 state was obtained by nuclear Overhauser effect (NOE)-based structural analysis of the Q41N mutant at 2.5 kbar, where the N2 state is 97% populated. The N2 state of ubiquitin is closely similar to the conformation of the protein bound to the ubiquitin-activating enzyme E1. The recognition of E1 by ubiquitin is best explained by conformational selection rather than by induced-fit motion.

Chemical exchange in biomacromolecules: past, present, and future

The perspective reviews quantitative investigations of chemical exchange phenomena in proteins and other biological macromolecules using NMR spectroscopy, particularly relaxation dispersion methods. The emphasis is on techniques and applications that quantify the populations, interconversion kinetics, and structural features of sparsely populated conformational states in equilibrium with a highly populated ground state. Applications to folding, molecular recognition, catalysis, and allostery by proteins and nucleic acids are highlighted.

Probing transient conformational states of proteins by solid-state R(1ρ) relaxation-dispersion NMR spectroscopy

The function of proteins depends on their ability to sample a variety of states differing in structure and free energy. Deciphering how the various thermally accessible conformations are connected, and understanding their structures and relative energies is crucial in rationalizing protein function. Many biomolecular reactions take place within microseconds to milliseconds, and this timescale is therefore of central functional importance. Here we show that R_1ρ relaxation dispersion experiments in magic-angle-spinning solid-state NMR spectroscopy make it possible to investigate the thermodynamics and kinetics of such exchange process, and gain insight into structural features of short-lived states.

Nanosecond time scale motions in proteins revealed by high-resolution NMR relaxometry

Understanding the molecular determinants underlying protein function requires the characterization of both structure and dynamics at atomic resolution. Nuclear relaxation rates allow a precise characterization of protein dynamics at the Larmor frequencies of spins. This usually limits the sampling of motions to a narrow range of frequencies corresponding to high magnetic fields. At lower fields one cannot achieve sufficient sensitivity and resolution in NMR. Here, we use a fast shuttle device where the polarization builds up and the signals are detected at high field, while longitudinal relaxation takes place at low fields 0.5 < B₀ < 14.1 T. The sample is propelled over a distance up to 50 cm by a blowgun-like system in about 50 ms. The analysis of nitrogen-15 relaxation in the protein ubiquitin over such a wide range of magnetic fields offers unprecedented insights into molecular dynamics. Some key regions of the protein feature structural fluctuations on nanosecond time scales, which have so far been overlooked in high-field relaxation studies. Nanosecond motions in proteins may have been underestimated by traditional high-field approaches, and slower supra-τ_c motions that have no effect on relaxation may have been overestimated. High-resolution relaxometry thus opens the way to a quantitative characterization of nanosecond motions in proteins.

Measuring dynamic and kinetic information in the previously inaccessible supra-τ(c) window of nanoseconds to microseconds by solution NMR spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool that has enabled experimentalists to characterize molecular dynamics and kinetics spanning a wide range of time-scales from picoseconds to days. This review focuses on addressing the previously inaccessible supra-tc window (defined as τ(c) < supra-τ(c) < 40 μs; in which tc is the overall tumbling time of a molecule) from the perspective of local inter-nuclear vector dynamics extracted from residual dipolar couplings (RDCs) and from the perspective of conformational exchange captured by relaxation dispersion measurements (RD). The goal of the first section is to present a detailed analysis of how to extract protein dynamics encoded in RDCs and how to relate this information to protein functionality within the previously inaccessible supra-τ(c) window. In the second section, the current state of the art for RD is analyzed, as well as the considerable progress toward pushing the sensitivity of RD further into the supra-τ(c) scale by up to a factor of two (motion up to 25 μs). From the data obtained with these techniques and methodology, the importance of the supra-τ(c) scale for protein function and molecular recognition is becoming increasingly clearer as the connection between motion on the supra-τ(c) scale and protein functionality from the experimental side is further strengthened with results from molecular dynamics simulations.

Site-resolved measurement of microsecond-to-millisecond conformational-exchange processes in proteins by solid-state NMR spectroscopy

We demonstrate that conformational exchange processes in proteins on microsecond-to-millisecond time scales can be detected and quantified by solid-state NMR spectroscopy. We show two independent approaches that measure the effect of conformational exchange on transverse relaxation parameters, namely Carr-Purcell-Meiboom-Gill relaxation-dispersion experiments and measurement of differential multiple-quantum coherence decay. Long coherence lifetimes, as required for these experiments, are achieved by the use of highly deuterated samples and fast magic-angle spinning. The usefulness of the approaches is demonstrated by application to microcrystalline ubiquitin. We detect a conformational exchange process in a region of the protein for which dynamics have also been observed in solution. Interestingly, quantitative analysis of the data reveals that the exchange process is more than 1 order of magnitude slower than in solution, and this points to the impact of the crystalline environment on free energy barriers.

Exceeding the limit of dynamics studies on biomolecules using high spin-lock field strengths with a cryogenically cooled probehead

Internal motions in the microsecond timescale have been proposed to play an active part in a protein's biological function. Nuclear magnetic resonance (NMR) relaxation dispersion is a robust method sensitive to this timescale with atomic resolution. However, due to technical limitations, the observation of motions faster than ∼40 μs for ¹⁵N nuclei was not possible. We show that with a cryogenically cooled NMR probehead, a high spin-lock field strength can be generated that is able to detect motions as fast as 25 μs. We apply this high spin-lock field strength in an NMR experiment used for characterizing dynamical processes. An on-resonance rotating-frame transverse relaxation experiment was implemented that allows for the detection of a 25 μs process from a dispersion curve, and transverse relaxation rates were compared at low and high spin-lock field strengths showing that at high field strengths contributions from chemical exchange with lifetimes up to 25 μs can be removed. Due to the increase in sensitivity towards fast motion, relaxation dispersion for a residue that undergoes smaller chemical shift variations due to dynamics was identified. This technique reduces the previously inaccessible window between the correlation time and the relaxation dispersion window that covers four orders of magnitude by a factor of 2.