The "long tail" of the protein tumbling correlation function: observation by (1)H NMR relaxometry in a wide frequency and concentration range

Multiscale Water Dynamics on Protein Surfaces: Protein-Specific Response to Surface Ions

Proteins function in crowded aqueous environments, interacting with a diverse range of compounds, and among them, dissolved ions. These interactions are water-mediated. In the present study, we combine field-dependent NMR relaxation (NMRD) and theory to probe water dynamics on the surface of proteins in concentrated aqueous solutions of hen egg-white lysozyme (LZM) and bovine serum albumin (BSA). The experiments reveal that the presence of salts (NaCl or NaI) leads to an opposite ion-specific response for the two proteins: an addition of salt to LZM solutions increases water relaxation rates with respect to the salt-free case, while for BSA solutions, a decrease is observed. The magnitude of the change depends on the ion identity. The developed model accounts for the non-Lorentzian shape of the NMRD profiles and reproduces the experimental data over four decades in Larmor frequency (10 kHz to 110 MHz). It is applicable up to high protein concentrations. The model incorporates the observed ion-specific effects via changes in the protein surface roughness, represented by the surface fractal dimension, and the accompanying changes in the surface water residence times. The response is protein-specific, linked to geometrical aspects of the individual protein surfaces, and goes beyond protein-independent Hofmeister-style ordering of ions.

Elucidating the 1H NMR Relaxation Mechanism in Polydisperse Polymers and Bitumen Using Measurements, MD Simulations, and Models

The mechanism behind the ¹H nuclear magnetic resonance (NMR) frequency dependence of T₁ and the viscosity dependence of T₂ for polydisperse polymers and bitumen remains elusive. We elucidate the matter through NMR relaxation measurements of polydisperse polymers over an extended range of frequencies (f₀ = 0.01-400 MHz) and viscosities (η = 385-102 000 cP) using T₁ and T₂ in static fields, T₁ field-cycling relaxometry, and T_1ρ in the rotating frame. We account for the anomalous behavior of the log-mean relaxation times T_1LM ∝ f₀ and T_2LM ∝ (η/T)^-1/2 with a phenomenological model of ¹H-¹H dipole-dipole relaxation, which includes a distribution in molecular correlation times and internal motions of the nonrigid polymer branches. We show that the model also accounts for the anomalous T_1LM and T_2LM in previously reported bitumen measurements. We find that molecular dynamics (MD) simulations of the T₁ ∝ f₀ dispersion and T₂ of similar polymers simulated over a range of viscosities (η = 1-1000 cP) are in good agreement with measurements and the model. The T₁ ∝ f₀ dispersion at high viscosities agrees with previously reported MD simulations of heptane confined in a polymer matrix, which suggests a common NMR relaxation mechanism between viscous polydisperse fluids and fluids under nanoconfinement, without the need to invoke paramagnetism.

Understanding the Nature of Nuclear Magnetic Resonance Relaxation by Means of Fast-Field-Cycling Relaxometry and Molecular Dynamics Simulations-The Validity of Relaxation Models

Fast-field-cycling relaxometry is a nuclear magnetic resonance method growing in popularity; yet, theoretical interpretation is limited to analytical models of uncertain accuracy. We present the first study calculating fast-field-cycling dipolar coupling directly from a molecular dynamics simulation trajectory. In principle, the frequency-resolved dispersion contains both rotational and translational diffusion information, among others. The present joint experimental/molecular dynamics study demonstrates that nuclear magnetic resonance properties calculated from the latter reproduce measured dispersion curves and temperature trends faithfully. Furthermore, molecular dynamics simulations can verify interpretation model assumptions by providing actual diffusion coefficients and correlation times.

The nuclear Overhauser Effect (NOE) as a tool to study macromolecular confinement: Elucidation and disentangling of crowding and encapsulation effects

We propose a methodology to capture short-lived but biophysically important contacts of biomacromolecules using the biomolecule-water nuclear Overhauser effect as an indirect microscope. Thus, instead of probing the direct correlation with the foreign biomolecule, we detect its presence by the disturbance it causes in the surrounding water. In addition, this information obtained is spatially resolved and can thus be attributed to specific sites. We extend this approach to the influence of more than one change in chemical environment and show a methodological way of resolution. This is achieved by taking double differences of corresponding σ_NOE/σ_ROE ratios of the systems studied and separating specific, unspecific, and intermediate influence. While applied to crowding and encapsulation in this study, this method is generally suitable for any combination of changes in chemical environment.

The protein-water nuclear Overhauser effect (NOE) as an indirect microscope for molecular surface mapping of interaction patterns

In this computational study, the intermolecular solute-solvent Nuclear Overhauser Effect (NOE) of the model protein ubiquitin in different chemical environments (free, bound to a partner protein and encapsulated) is investigated. Short-ranged NOE observables such as the NOE/ROE ratio reveal hydration phenomena on absolute timescales such as fast hydration sites and slow water clefts. We demonstrate the ability of solute-solvent NOE differences measured of the same protein in different chemical environments to reveal hydration changes on the relative timescale. The resulting NOE/ROE-surface maps are shown to be a central key for analyzing biologically relevant chemical influences such as complexation and confinement: the presence of a complexing macromolecule or a confining surface wall modulates the water mobility in the vicinity of the probe protein, hence revealing which residues of said protein are proximate to the foreign interface and which are chemically unaffected. This way, hydration phenomena can serve to indirectly map the precise influence (position) of other molecules or interfaces onto the protein surface. This proposed one-protein many-solvents approach may offer experimental benefits over classical one-protein other-protein pseudo-intermolecular transient NOEs. Furthermore, combined influences such as complexation and confinement may exert non-additive influences on the protein compared to a reference state. We offer a mathematical method to disentangle the influence of these two different chemical environments.

NMR Assessment of Therapeutic Peptides and Proteins: Correlations That Reveal Interactions and Motions

NMR measurements of rotational and translational diffusion are used to characterize the solution behavior of a wide variety of therapeutic proteins and peptides. The timescales of motions sampled in these experiments reveal complicated intrinsic solution behavior such as flexibility, that is central to function, as well as self-interactions, stress-induced conformational changes and other critical attributes that can be discovery and development liabilities. Trends from proton transverse relaxation (R₂ ) and hydrodynamic radius (R_h ) are correlated and used to identify and differentiate intermolecular from intramolecular interactions. In this study, peptide behavior is consistent with complicated multimer self-assembly, while multi-domain protein behavior is dominated by intramolecular interactions. These observations are supplemented by simulations that include effects from slow transient interactions and rapid internal motions. R₂ -R_h correlations provide a means to profile protein motions as well as interactions. The approach is completely general and can be applied to therapeutic and target protein characterization.

Changes in protein hydration dynamics by encapsulation or crowding of ubiquitin: strong correlation between time-dependent Stokes shift and intermolecular nuclear Overhauser effect

The local changes in protein hydration dynamics upon encapsulation of the protein or macromolecular crowding are essential to understand protein function in cellular environments. We were able to obtain a spatially-resolved picture of the influence of confinement and crowding on the hydration dynamics of the protein ubiquitin by analyzing the time-dependent Stokes shift (TDSS), as well as the intermolecular Nuclear Overhauser Effect (NOE) at different sites of the protein by large-scale computer simulation of single and multiple proteins in water and confined in reverse micelles. Besides high advanced space resolved information on hydration dynamics we found a strong correlation of the change in NOE upon crowding or encapsulation and the change in the integral TDSS relaxation times in all investigated systems relative to the signals in a diluted protein solution.

Changes in local protein hydration dynamics caused by encapsulation or crowding are reflected in the TDSS and the intermolecular NOE alike.

Quantitative NMR study of heat-induced aggregation of eye-lens crystallin proteins under crowding conditions

The eye lens contains a highly concentrated, polydisperse mixture of crystallins, and a loss in transparency during cataract formation is attributed to the aggregation of these proteins. Most biochemical and biophysical studies of crystallins have been performed in diluted samples because of various physical limitations of the respective method at physiological concentrations of up to 200-400 mg/mL. We introduce a straightforward proton NMR transverse relaxometry method to quantify simultaneously proteins in the dissolved and aggregated states at these elevated concentrations, because these states significantly differ in their transverse relaxation properties. The key feature of this method is a direct observation of the protein signal in a wide range of relaxation delays, from few microseconds up to few hundred milliseconds. We applied this method to follow heat-induced aggregation of bovine α- and γB-crystallin between 60 and 200 mg/mL. We find that at 60 °C, a temperature where both crystallins still comprise a native tertiary structure, γB-crystallin aggregated at these high protein concentrations with a time constant of about 30-40 h. α-crystallin remained soluble at 60 mg/mL but formed a transparent gel at 200 mg/mL. This quantitative NMR method can be applied to investigations of other proteins and their mixtures under various aggregation conditions.

Microsecond motions probed by near-rotary-resonance R1ρ15N MAS NMR experiments: the model case of protein overall-rocking in crystals

Solid-state near-rotary-resonance measurements of the spin-lattice relaxation rate in the rotating frame (R_1ρ) is a powerful NMR technique for studying molecular dynamics in the microsecond time scale. The small difference between the spin-lock (SL) and magic-angle-spinning (MAS) frequencies allows sampling very slow motions, at the same time it brings up some methodological challenges. In this work, several issues affecting correct measurements and analysis of ¹⁵N R_1ρ data are considered in detail. Among them are signal amplitude as a function of the difference between SL and MAS frequencies, "dead time" in the initial part of the relaxation decay caused by transient spin-dynamic oscillations, measurements under HORROR condition and proper treatment of the multi-exponential relaxation decays. The multiple ¹⁵N R_1ρ measurements at different SL fields and temperatures have been conducted in 1D mode (i.e. without site-specific resolution) for a set of four different microcrystalline protein samples (GB1, SH3, MPD-ubiquitin and cubic-PEG-ubiquitin) to study the overall protein rocking in a crystal. While the amplitude of this motion varies very significantly, its correlation time for all four sample is practically the same, 30-50 μs. The amplitude of the rocking motion correlates with the packing density of a protein crystal. It has been suggested that the rocking motion is not diffusive but likely a jump-like dynamic process.

Fast Magic-Angle-Spinning 19F Spin Exchange NMR for Determining Nanometer 19F-19F Distances in Proteins and Pharmaceutical Compounds

Internuclear distances measured using NMR provide crucial constraints of three-dimensional structures but are often restricted to about 5 Å due to the weakness of nuclear-spin dipolar couplings. For studying macromolecular assemblies in biology and materials science, distance constraints beyond 1 nm will be extremely valuable. Here we present an extensive and quantitative analysis of the feasibility of 19F spin exchange NMR for precise and robust measurements of interatomic distances up to 1.6 nm at a magnetic field of 14.1 T, under 20-40 kHz magic-angle spinning (MAS). The measured distances are comparable to those achievable from paramagnetic relaxation enhancement but have higher precision, which is better than ±1 Å for short distances and ±2 Å for long distances. For 19F spins with the same isotropic chemical shift but different anisotropic chemical shifts, intermediate MAS frequencies of 15-25 kHz without 1H irradiation accelerate spin exchange. For spectrally resolved 19F-19F spin exchange, 1H-19F dipolar recoupling significantly speeds up 19F-19F spin exchange. On the basis of data from five fluorinated synthetic, pharmaceutical, and biological compounds, we obtained two general curves for spin exchange between CF groups and between CF3 and CF groups. These curves allow 19F-19F distances to be extracted from the measured spin exchange rates after taking into account 19F chemical shifts. These results demonstrate the robustness of 19F spin exchange NMR for distance measurements in a wide range of biological and chemical systems.

1H NMR at Larmor frequencies down to 3Hz by means of Field-Cycling techniques

Field-Cycling (FC) NMR experiments were carried out at ¹H Larmor frequencies down to about 3Hz. This could be achieved by fast switching a high polarizing magnetic field down to a low evolution field which is tilted with respect to the polarization field. Then, the low frequency Larmor precession of the nuclear spin magnetization about this evolution field is registered by means of FIDs in a high detection field. The crucial technical point of the experiment is the stabilization of the evolution field, which is achieved by compensating for temporal magnetic field fluctuations of all three spatial components. The paper reports on some other basic low field experiments such as the simultaneous measurement of the Larmor frequency and the spin-lattice relaxation time in such small fields as well as the irradiation of oscillating transversal magnetic field pulses at very low frequencies as a novel method for field calibration in low field FC NMR. The potential of low field FC is exemplified by the ¹H relaxation dispersion of water at frequencies below about 2kHz stemming from the slow proton exchange process.

Characterizing monoclonal antibody formulations in arginine glutamate solutions using 1H NMR spectroscopy

Assessing how excipients affect the self-association of monoclonal antibodies (mAbs) requires informative and direct in situ measurements for highly concentrated solutions, without sample dilution or perturbation. This study explores the application of solution nuclear magnetic resonance (NMR) spectroscopy for characterization of typical mAb behavior in formulations containing arginine glutamate. The data show that the analysis of signal intensities in 1D ¹H NMR spectra, when compensated for changes in buffer viscosity, is invaluable for identifying conditions where protein-protein interactions are minimized. NMR-derived molecular translational diffusion rates for concentrated solutions are less useful than transverse relaxation rates as parameters defining optimal formulation. Furthermore, NMR reports on the solution viscosity and mAb aggregation during accelerated stability study assessment, generating data consistent with that acquired by size-exclusion chromatography. The methodology developed here offers NMR spectroscopy as a new tool providing complementary information useful to formulation development of mAbs and other large therapeutic proteins.

Coupling and Decoupling of Rotational and Translational Diffusion of Proteins under Crowding Conditions

Molecular motion of biopolymers in vivo is known to be strongly influenced by the high concentration of organic matter inside cells, usually referred to as crowding conditions. To elucidate the effect of intermolecular interactions on Brownian motion of proteins, we performed (1)H pulsed-field gradient NMR and fluorescence correlation spectroscopy (FCS) experiments combined with small-angle X-ray scattering (SAXS) and viscosity measurements for three proteins, αB-crystalline (αBc), bovine serum albumin, and hen egg-white lysozyme (HEWL) in aqueous solution. Our results demonstrate that long-time translational diffusion quantitatively follows the expected increase of macro-viscosity upon increasing the protein concentration in all cases, while rotational diffusion as assessed by polarized FCS and previous multi-frequency (1)H NMR relaxometry experiments reveals protein-specific behavior spanning the full range between the limiting cases of full decoupling from (αBc) and full coupling to (HEWL) the macro-viscosity. SAXS was used to study the interactions between the proteins in solution, whereby it is shown that the three cases cover the range between a weakly interacting hard-sphere system (αBc) and screened Coulomb repulsion combined with short-range attraction (HEWL). Our results, as well as insights from the recent literature, suggest that the unusual rotational-translational coupling may be due to anisotropic interactions originating from hydrodynamic shape effects combined with high charge and possibly a patchy charge distribution.

Transient binding accounts for apparent violation of the generalized Stokes-Einstein relation in crowded protein solutions

The effect of high concentration, also referred to as crowding conditions, on Brownian motion is of central relevance for the understanding of the physical, chemical and biological properties of proteins in their native environment. Specifically, the simple inverse relationship between the translational diffusion coefficient and the macroscopic solution viscosity as predicted by the generalized Stokes-Einstein (GSE) relation has been the subject of many studies, yet a consensus on its applicability has not been reached. Here, we use isotope-filtered pulsed-field gradient NMR to separately assess the μm-scale diffusivity of two proteins, BSA and an SH3 domain, in mixtures as well as single-protein solutions, and demonstrate that transient binding can account for an apparent violation of the GSE relation. Whereas GSE behavior applies for the single-protein solutions, it does not hold for the protein mixtures. Transient binding behavior in the concentrated mixtures is evidenced by calorimetric experiments and by a significantly increased apparent activation energy of diffusion. In contrast, the temperature dependence of the viscosity, as well as of the diffusivity in single-component solutions, is always dominated by the flow activation energy of pure water. As a practically relevant second result, we further show that, for high protein concentrations, the diffusion of small molecules such as dioxane or water is not generally a suitable probe for the viscosity experienced by the diffusing proteins.