Molecular theory for nuclear magnetic relaxation in protein solutions and tissue: Surface diffusion and free-volume analogy

Decoupling Protein Concentration and Aggregate Content Using Diffusion and Water NMR

Protein-based biopharmaceutical drugs, such as monoclonal antibodies, account for the majority of the best-selling drugs globally in recent years. For bioprocesses, key performance indicators are the concentration and aggregate level for the product being produced. In water NMR (wNMR), the use of the water transverse relaxation rate [R2(1H2O)] has been previously used to determine protein concentration and aggregate level; however, it cannot be used to separate between them without using an additional technique. This work shows that it is possible to "decouple" these two key characteristics by recording the water diffusion coefficient [D(1H2O)] in conjunction with R2(1H2O), even in the event of overlap in either D(1H2O) or R2(1H2O). This method is demonstrated on three different systems, following appropriate D(1H2O) or R2(1H2O) calibration data acquisition for a protein of interest. Our method highlights the potential use of benchtop NMR as an at-line process analytical technique.

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 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).

The magnetic field dependence of water T1 in tissues

The magnetic field dependence of the composite (1)H(2)O nuclear magnetic resonance signal T(1) was measured for excised samples of rat liver, muscle, and kidney over the field range from 0.7 to 7 T (35-300 MHz) with a nuclear magnetic resonance spectrometer using sample-shuttle methods. Based on extensive measurements on simpler component systems, the magnetic field dependence of T(1) of all tissues studied are readily fitted at Larmor frequencies above 1 MHz with a simple relaxation equation consisting of three contributions: a power law, A*ω(-0.60) related to the interaction of water with long-lived-protein binding sites, a logarithmic term B*τ(d) *log(1+1/(ωτ(d))(2)) related to water diffusion at macromolecular interfacial regions, and a constant term associated with the high frequency limit of water-spin-lattice relaxation. The parameters A and B include the concentration and surface area dependences respectively. The logarithmic diffusion term becomes significant at high magnetic fields and is consistent with rapid translational dynamics at macromolecular surfaces. The data are fitted well with translational correlation times of approximately 15 ps for human brain white matter, but with a B value three times larger than gray matter tissues. This analysis suggests that the water-surface translational correlation time is approximately three times longer than in gray matter.

Molecular Dynamics of Monomer, Oligomer, and Polymer Liquids in Porous Media: A Field-Cycling Nmr Relaxometry and NMR Field-Gradient Diffusometry Study

The molecular dynamics of fluids in porous media has been studied using field-cycling NMR relaxometry and NMR field-gradient diffusometry. The frequency dependences of the 1H and 2H spin-lattice relaxation times T1 of various liquids in porous glass reveal weak and strong adsorption behaviour depending on the polarity of the adsorbates. Correlation times eight orders of magnitude longer than in bulk have been observed. The T1 dispersion moreover reflects geometrical details of the matrix in a length scale three orders of magnitude longer than the adsorbate molecules. The mean-square displacements of adsorbate molecules on the surface are only one order of magnitude less than in bulk. The global diffusivity is reduced by tortuosity and porosity effects. The observed phenomena may be explained by bulk-mediated surface diffusion, i.e., Lévy walks. The dynamics of polymer chains much longer than the pore size is characteristicly different from that in bulk melts. There is evidence that the reptation mechanism explains at least a part of the phenomena observed for the porous matrix in contrast to findings with bulk polymer melts.

NMR Experiments on Molecular Dynamics in Nanoporous Media: Evidence for Lévy Walk Statistics

Field-cycling 1H and 2H NMR relaxometry and field-gradient 1H NMR diffusometry were applied to polar and nonpolar liquids filled into porous glasses and fineparticle agglomerates (SiO2, ZnO, TiO2, globular proteins). The orders of magnitude of the length scales of the pore spaces ranged from 100 to several 102 nm. Pronounced differences of the spin-lattice relaxation dispersion for “weak” (nonpolar) and “strong” (polar) adsorption were found. In the latter case, the correlation times of the adsorbate orientation are up to eight orders of magnitude longer than in bulk. Trans-lational diffusion in liquid surface layers was directly studied with the aid of field-gradient NMR diffusometry in systems where the free liquid was frozen. The spin-lattice relaxation dispersion can be explained on the basis of reorientations mediated by translational displacements (RMTD) of adsorbate molecules on the surfaces. Thisprocess appears to be enhanced by a Levy walk mechanism so that the propagator adopts the form of a Cauchy distribution. The evaluated surface correlation functions are characterized by surface correlation lengths in the same order as the pore diameters, that is, up to three orders ofmagnitude larger than the length scale of dipolar interaction.

Molecular basis of water proton relaxation in gels and tissue

An extensive set of water-1H magnetic relaxation dispersion (MRD) data are presented for aqueous agarose and gelatin gels. It is demonstrated that the EMOR model, which was developed in a companion paper to this study (see Halle, this issue), accounts for the dependence of the water-1H spin-lattice relaxation rate on resonance frequency over more than four decades and on pH. The parameter values deduced from analysis of the 1H MRD data are consistent with values derived from 2H MRD profiles from the same gels and with small-molecule reference data. This agreement indicates that the water-1H relaxation dispersion in aqueous biopolymer gels is produced directly by exchange-mediated orientational randomization of internal water molecules or labile biopolymer protons, with little or no role played by collective biopolymer vibrations or coherent spin diffusion. This ubiquitous mechanism is proposed to be the principal source of water-1H spin-lattice relaxation at low magnetic fields in all aqueous systems with rotationally immobile biopolymers, including biological tissue. The same mechanism also contributes to transverse and rotating-frame relaxation and magnetization transfer at high fields.

Molecular theory of field-dependent proton spin-lattice relaxation in tissue

A molecular theory is presented for the field-dependent spin-lattice relaxation time of water in tissue. The theory attributes the large relaxation enhancement observed at low frequencies to intermediary protons in labile groups or internal water molecules that act as relaxation sinks for the bulk water protons. Exchange of intermediary protons not only transfers magnetization to bulk water protons, it also drives relaxation by a mechanism of exchange-mediated orientational randomization (EMOR). An analytical expression for T1 is derived that remains valid outside the motional-narrowing regime. Cross-relaxation between intermediary protons and polymer protons plays an important role, whereas spin diffusion among polymer protons can be neglected. For sufficiently slow exchange, the dispersion midpoint is determined by the local dipolar field rather than by molecular motions, which makes the dispersion frequency insensitive to temperature and system composition. The EMOR model differs fundamentally from previous models that identify collective polymer vibrations or hydration water dynamics as the molecular motion responsible for spin relaxation. Unlike previous models, the EMOR model accounts quantitatively for 1H magnetic relaxation dispersion (MRD) profiles from tissue model systems without invoking unrealistic parameter values.

NMR relaxation and water self-diffusion studies in whey protein solutions and gels

The changes in water proton transverse relaxation behavior induced by aggregation of whey proteins are explained in terms of the simple molecular processes of diffusion and chemical exchange. The water self-diffusion coefficient was measured in whey protein solutions and gels by the pulsed field gradient NMR method. As expected, water self-diffusion was reduced with increased protein concentrations. Whatever the concentration, the water molecules were free to diffuse over distances varying from 15 to 47 mum. Water diffusion was constant over these distances, demonstrating that no restrictions were found to explain the water hindrance. The modification in protein structure by gelation induced a decrease in water diffusion. The effects of protein concentration on water diffusion are discussed and modeled. Two approaches were compared, the obstruction effect induced by a spherical particle and the cell model, which considered two water compartments with specific self-diffusion coefficients.

Magnetic field dependence of proton spin-lattice relaxation times

The magnetic field dependence of the water-proton spin-lattice relaxation rate (1/T(1)) in tissues results from magnetic coupling to the protons of the rotationally immobilized components of the tissue. As a consequence, the magnetic field dependence of the water-proton (1/T(1)) is a scaled report of the field dependence of the (1/T(1)) rate of the solid components of the tissue. The proton spin-lattice relaxation rate may be represented generally as a power law: 1/T(1)omega = A omega(-b), where b is usually found to be in the range of 0.5-0.8. We have shown that this power law may arise naturally from localized structural fluctuations along the backbone in biopolymers that modulate the proton dipole-dipole couplings. The protons in a protein form a spin communication network described by a fractal dimension that is less than the Euclidean dimension. The model proposed accounts quantitatively for the proton spin-lattice relaxation rates measured in immobilized protein systems at different water contents, and provides a fundamental basis for understanding the parametric dependence of proton spin-lattice relaxation rates in dynamically heterogeneous systems, such as tissues.

Protein-bound water molecule counting by resolution of (1)H spin-lattice relaxation mechanisms

Water proton spin-lattice relaxation is studied in dilute solutions of bovine serum albumin as a function of magnetic field strength, oxygen concentration, and solvent deuteration. In contrast to previous studies conducted at high protein concentrations, the observed relaxation dispersion is accurately Lorentzian with an effective correlation time of 41 +/- 3 ns when measured at low proton and low protein concentrations to minimize protein aggregation. Elimination of oxygen flattens the relaxation dispersion profile above the rotational inflection frequency, nearly eliminating the high field tail previously attributed to a distribution of exchange times for either whole water molecules or individual protons at the protein-water interface. The small high-field dispersion that remains is attributed to motion of the bound water molecules on the protein or to internal protein motions on a time scale of order one ns. Measurements as a function of isotope composition permit separation of intramolecular and intermolecular relaxation contributions. The magnitude of the intramolecular proton-proton relaxation rate constant is interpreted in terms of 25 +/- 4 water molecules that are bound rigidly to the protein for a time long compared with the rotational correlation time of 42 ns. This number of bound water molecules neglects the possibility of local motions of the water in the binding site; inclusion of these effects may increase the number of bound water molecules by 50%.

Surface fractals probed by adsorbate spin-lattice relaxation dispersion

Spin-lattice relaxation of strong adsorbates confined in disordered structures such as porous silica glass is treated on the basis of a relaxation mechanism due to "reorientation mediated by translational displacements." In such a situation the low-frequency spin-lattice relaxation dispersion beyond the regime where local reorientations dominate reflects molecular dynamics as well as the surface geometry on a length scale longer than 1 nm. It is shown that the power law frequently observed for the spin-lattice relaxation dispersion in porous media can be traced back to surface fractality. The fractal properties of rough surfaces and the statistics governing surface displacements enter explicitly in the expression for the dipolar correlation function. The surface fractal dimension can thus be evaluated from the low-frequency spin-lattice relaxation dispersion accessible by field-cycling NMR relaxometry.

Microstructure of porous media probed by NMR techniques in sub-micrometer length scales

It is shown that field-cycling NMR relaxation spectroscopy in combination with pulsed-gradient spin-echo diffusion studies especially in the supercon fringe field version are suitable techniques for the investigation of length scales of porous media in the range 10 A to 10 microns. Data for water adsorbed in fine particle agglomerates, porous glass and ceramics are reported. An orientational structure factor is introduced permitting the characterization of hydrated surfaces on the basis of reorientations mediated by translational displacements of the adsorbed molecules. Known lengths such as the mean pore or particle size have been reproduced in this way. In length scales beyond these structural elements, the geometry of the internal surfaces can be discussed in terms of wavenumber-space fractals.

T1 rho dispersion imaging and localized T1 rho dispersion relaxometry: application in vivo to mouse adenocarcinoma

The dispersion (frequency dependence) of the spin-lattice relaxation time in the rotating frame, T1 rho, is considered for tissue characterization. Methods for the volume-selective determination of the proper T1 rho dispersion and for imaging of parameters characterizing this frequency dependence are described. On- and off-resonance versions of the techniques are demonstrated. In vitro studies of excised rat tissues and in vivo applications to mice with implanted adenocarcinoma are reported. T1 rho dispersion images show clear contrasts of the malignant tissue, whereas muscle tissue is completely suppressed. No contrast agent is required. The measuring time is only twice as long as that for conventional magnetic resonance images. The results suggest that the T1 rho dispersion is less susceptible to the biological variability than the absolute values of the relaxation times.