Slow Internal Protein Dynamics from Water 1H Magnetic Relaxation Dispersion

Dynamical properties of solid and hydrated collagen: Insight from nuclear magnetic resonance relaxometry

1H spin-lattice Nuclear Magnetic Resonance relaxometry experiments have been performed for collagen and collagen-based artificial tissues in the frequency range of 10 kHz-20 MHz. The studies were performed for non-hydrated and hydrated materials. The relaxation data have been interpreted as including relaxation contributions originating from 1H-1H and 1H-14N dipole-dipole interactions, the latter leading to Quadrupole Relaxation Enhancement effects. The 1H-1H relaxation contributions have been decomposed into terms associated with dynamical processes on different time scales. A comparison of the parameters for the non-hydrated and hydrated systems has shown that hydration leads to a decrease in the dipolar relaxation constants without significantly affecting the dynamical processes. In the next step, the relaxation data for the hydrated systems were interpreted in terms of a model assuming two-dimensional translational diffusion of water molecules in the vicinity of the macromolecular surfaces and a sub-diffusive motion leading to a power law of the frequency dependencies of the relaxation rates. It was found that the water diffusion process is slowed down by at least two orders of magnitude compared to bulk water diffusion. The frequency dependencies of the relaxation rates in hydrated tissues and hydrated collagen are characterized by different power laws (ωH-β, where ωH denotes the 1H resonance frequency): the first of about 0.4 and the second close to unity.

A Highly Ordered Nitroxide Side Chain for Distance Mapping and Monitoring Slow Structural Fluctuations in Proteins

Site-directed spin labeling electron paramagnetic resonance (SDSL-EPR) is an established tool for exploring protein structure and dynamics. Although nitroxide side chains attached to a single cysteine via a disulfide linkage are commonly employed in SDSL-EPR, their internal flexibility complicates applications to monitor slow internal motions in proteins and to structure determination by distance mapping. Moreover, the labile disulfide linkage prohibits the use of reducing agents often needed for protein stability. To enable the application of SDSL-EPR to the measurement of slow internal dynamics, new spin labels with hindered internal motion are desired. Here, we introduce a highly ordered nitroxide side chain, designated R9, attached at a single cysteine residue via a non-reducible thioether linkage. The reaction to introduce R9 is highly selective for solvent-exposed cysteine residues. Structures of R9 at two helical sites in T4 Lysozyme were determined by X-ray crystallography and the mobility in helical sequences was characterized by EPR spectral lineshape analysis, Saturation Transfer EPR, and Saturation Recovery EPR. In addition, interspin distance measurements between pairs of R9 residues are reported. Collectively, all data indicate that R9 will be useful for monitoring slow internal structural fluctuations, and applications to distance mapping via dipolar spectroscopy and relaxation enhancement methods are anticipated.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00723-023-01618-8.

Ion influence on surface water dynamics and proton exchange at protein surfaces - A unified model for transverse and longitudinal NMR relaxation dispersion

In all biologically relevant media, proteins interact in the presence of surrounding ions, and such interactions are water-mediated. Water molecules play a crucial role in the restructuring of proteins in solution and indeed in their biological activity. Surface water dynamics and proton exchange at protein surfaces is investigated here using NMR relaxometry, for two well-known globular proteins, lysozyme and bovine serum albumin, with particular attention to the role of surface ions. We present a unified model of surface water dynamics and proton exchange, accounting simultaneously for the observed longitudinal and transverse relaxation rates. The most notable effect of salt (0.1 M) concerns the slow surface water dynamics, related to rare water molecules embedded in energy wells on the protein surface. This response is protein-specific. On the other hand, the proton exchange time between labile protein-protons and water-protons at the protein surface seems to be very similar for the two proteins and is insensitive to the addition of salts at the concentration studied.

Nuclear magnetic relaxation by the dipolar EMOR mechanism: Three-spin systems

In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. Starting from the stochastic Liouville equation, we have developed a non-perturbative theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole couplings, and Larmor frequencies. Here, we implement the general dipolar EMOR theory for a macromolecule-bound three-spin system, where one, two, or all three spins exchange with the bulk solution phase. In contrast to the previously studied two-spin system with a single dipole coupling, there are now three dipole couplings, so relaxation is affected by distinct correlations as well as by self-correlations. Moreover, relaxation can now couple the magnetizations with three-spin modes and, in the presence of a static dipole coupling, with two-spin modes. As a result of this complexity, three secondary dispersion steps with different physical origins can appear in the longitudinal relaxation dispersion profile, in addition to the primary dispersion step at the Larmor frequency matching the exchange rate. Furthermore, and in contrast to the two-spin system, longitudinal relaxation can be significantly affected by chemical shifts and by the odd-valued ("imaginary") part of the spectral density function. We anticipate that the detailed studies of two-spin and three-spin systems that have now been completed will provide the foundation for developing an approximate multi-spin dipolar EMOR theory sufficiently accurate and computationally efficient to allow quantitative molecular-level interpretation of frequency-dependent water-proton longitudinal relaxation data from biophysical model systems and soft biological tissue.

New applications and perspectives of fast field cycling NMR relaxometry

The field cycling NMR relaxometry method (also known as fast field cycling (FFC) when instruments employing fast electrical switching of the magnetic field are used) allows determination of the spin-lattice relaxation time (T1 ) continuously over five decades of Larmor frequency. The method can be exploited to observe the T1 frequency dependence of protons, as well as any other NMR-sensitive nuclei, such as (2) H, (13) C, (31) P, and (19) F in a wide range of substances and materials. The information obtained is directly correlated with the physical/chemical properties of the compound and can be represented as a 'nuclear magnetic resonance dispersion' curve. We present some recent academic and industrial applications showing the relevance of exploiting FFC NMR relaxometry in complex materials to study the molecular dynamics or, simply, for fingerprinting or quality control purposes. The basic nuclear magnetic resonance dispersion features are outlined in representative examples of magnetic resonance imaging (MRI) contrast agents, porous media, proteins, and food stuffs. We will focus on the new directions and perspectives for the FFC technique. For instance, the introduction of the latest Wide Bore FFC NMR relaxometers allows probing, for the first time, of the dynamics of confined surface water contained in the macro-pores of carbonate rock cores. We also evidence the use of the latest field cycling technology with a new cryogen-free variable-field electromagnet, which enhances the range of available frequencies in the 2D T1 -T2 correlation spectrum for separating oil and water in crude oil. Copyright © 2015 John Wiley & Sons, Ltd.

Nuclear magnetic relaxation by the dipolar EMOR mechanism: General theory with applications to two-spin systems

In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. We have embarked on a systematic program to develop, from the stochastic Liouville equation, a general and rigorous theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole coupling strengths, and Larmor frequencies. Here, we present a general theoretical framework applicable to spin systems of arbitrary size with symmetric or asymmetric exchange. So far, the dipolar EMOR theory is only available for a two-spin system with symmetric exchange. Asymmetric exchange, when the spin system is fragmented by the exchange, introduces new and unexpected phenomena. Notably, the anisotropic dipole couplings of non-exchanging spins break the axial symmetry in spin Liouville space, thereby opening up new relaxation channels in the locally anisotropic sites, including longitudinal-transverse cross relaxation. Such cross-mode relaxation operates only at low fields; at higher fields it becomes nonsecular, leading to an unusual inverted relaxation dispersion that splits the extreme-narrowing regime into two sub-regimes. The general dipolar EMOR theory is illustrated here by a detailed analysis of the asymmetric two-spin case, for which we present relaxation dispersion profiles over a wide range of conditions as well as analytical results for integral relaxation rates and time-dependent spin modes in the zero-field and motional-narrowing regimes. The general theoretical framework presented here will enable a quantitative analysis of frequency-dependent water-proton longitudinal relaxation in model systems with immobilized macromolecules and, ultimately, will provide a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters.

Nuclear magnetic relaxation induced by exchange-mediated orientational randomization: longitudinal relaxation dispersion for a dipole-coupled spin-1/2 pair

In complex biological or colloidal samples, magnetic relaxation dispersion (MRD) experiments using the field-cycling technique can characterize molecular motions on time scales ranging from nanoseconds to microseconds, provided that a rigorous theory of nuclear spin relaxation is available. In gels, cross-linked proteins, and biological tissues, where an immobilized macromolecular component coexists with a mobile solvent phase, nuclear spins residing in solvent (or cosolvent) species relax predominantly via exchange-mediated orientational randomization (EMOR) of anisotropic nuclear (electric quadrupole or magnetic dipole) couplings. The physical or chemical exchange processes that dominate the MRD typically occur on a time scale of microseconds or longer, where the conventional perturbation theory of spin relaxation breaks down. There is thus a need for a more general relaxation theory. Such a theory, based on the stochastic Liouville equation (SLE) for the EMOR mechanism, is available for a single quadrupolar spin I = 1. Here, we present the corresponding theory for a dipole-coupled spin-1/2 pair. To our knowledge, this is the first treatment of dipolar MRD outside the motional-narrowing regime. Based on an analytical solution of the spatial part of the SLE, we show how the integral longitudinal relaxation rate can be computed efficiently. Both like and unlike spins, with selective or non-selective excitation, are treated. For the experimentally important dilute regime, where only a small fraction of the spin pairs are immobilized, we obtain simple analytical expressions for the auto-relaxation and cross-relaxation rates which generalize the well-known Solomon equations. These generalized results will be useful in biophysical studies, e.g., of intermittent protein dynamics. In addition, they represent a first step towards a rigorous theory of water (1)H relaxation in biological tissues, which is a prerequisite for unravelling the molecular basis of soft-tissue contrast in clinical magnetic resonance imaging.

A compact high-speed mechanical sample shuttle for field-dependent high-resolution solution NMR

Analysis of NMR relaxation data has provided significant insight on molecular dynamic, leading to a more comprehensive understanding of macromolecular functions. However, traditional methodology allows relaxation measurements performed only at a few fixed high fields, thus severely restricting their potential for extracting more complete dynamic information. Here we report the design and performance of a compact high-speed servo-mechanical shuttle assembly adapted to a commercial 600 MHz high-field superconducting magnet. The assembly is capable of shuttling the sample in a regular NMR tube from the center of the magnet to the top (fringe field ∼0.01 T) in 100 ms with no loss of sensitivity other than that due to intrinsic relaxation. The shuttle device can be installed by a single experienced user in 30 min. Excellent 2D-(15)N-HSQC spectra of (u-(13)C, (15)N)-ubiquitin with relaxation at low fields (3.77 T) and detection at 14.1T were obtained to illustrate its utility in R(1) measurements of macromolecules at low fields. Field-dependent (13)C-R(1) data of (3,3,3-d)-alanine at various field strengths were determined and analyzed to assess CSA and (1)H-(13)C dipolar contributions to the carboxyl (13)C-R(1).

Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model

We consider nuclear spin-lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin-lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole-dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin-lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.

Mechanism of 1H-14N cross-relaxation in immobilized proteins

A resonant enhancement of the water-1H relaxation rate at three distinct frequencies in the range 0.5-3 MHz has been observed in a variety of aqueous biological systems. These so-called quadrupole (Q) peaks have been linked to a dipolar flip-flop polarization transfer from 1H nuclei to rapidly relaxing amide 14N nuclei in rotationally immobilized proteins. While the Q-peak frequencies conform to the known amide 14N quadrupole coupling parameters, a molecular model that accounts for the intensity and shape of the Q peaks has not been available. Here, we present such a model and test it against an extensive set of Q-peak data from two fully hydrated crosslinked proteins under conditions of variable temperature, pH and H/D isotope composition. We propose that polarization transfer from bulk water to amide 14N occurs in three steps: from bulk water to a so-called intermediary proton via material diffusion/exchange, from intermediary to amide proton by cross-relaxation driven by exchange-mediated orientational randomization of their mutual dipole coupling, and from amide proton to 14N by resonant dipolar relaxation 'of the second kind', driven by 14N spin fluctuations, which, in turn, are induced by restricted rigid-body motions of the protein. An essentially equivalent description of the last step can be formulated in terms of coherent 1H-->14N polarization transfer followed by fast 14N relaxation. Using independent structural and kinetic information, we show that the Q peaks from these two proteins involve approximately 7 intermediary protons in internal water molecules and side-chain hydroxyl groups with residence times of order 10(-5) s. The model not only accounts quantitatively for the extensive data set, but also explains why Q peaks are hardly observed from gelatin gels.