Transverse Spin Relaxation Rates Research Articles

Rapid Interpretation of Protein Backbone Rotation Dynamics Directly from Spin Relaxation Data.

Besides their structure, dynamics is pivotal for protein functions, particularly for intrinsically disordered proteins (IDPs) that do not fold into a fixed 3D structure. However, the detection of protein dynamics is difficult for IDPs and other disordered biomolecules. NMR spin relaxation rates are sensitive to the rapid rotations of chemical bonds, but their interpretation is arduous for IDPs or molecular assemblies with a complex dynamic landscape. Here we demonstrate numerically that the dynamics of a wide range of proteins, from short peptides to partially disordered proteins and peptides in micelles, can be characterized by calculating the total effective correlation times of protein backbone N-H bond rotations, τeff, from experimentally measured transverse 15N spin relaxation rates, R2, using a linear relation. Our results enable the determination of magnetic-field-independent and intuitively understandable parameters describing protein dynamics at different regions of the sequence directly from experiments. A practical advance of the approach is demonstrated by analyzing partially disordered proteins in which rotations of disordered regions occur with timescales of 1-2 ns, independent of their size, suggesting that rotations of disordered and folded regions are uncoupled in these proteins.

Global Dynamics of a Protein on the Surface of Anisotropic Lipid Nanoparticles Derived from Relaxation-Based NMR Spectroscopy.

The global motions of ubiquitin, a model protein, on the surface of anisotropically tumbling 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (POPG):1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC) bicelles are described. The shapes of POPG:DHPC bicelles prepared with high molar ratios q of POPG to DHPC can be approximated by prolate ellipsoids, with the ratio of ellipsoid dimensions and dimensions themselves increasing with higher values of q. Adaptation of the nuclear magnetic resonance (NMR) relaxation-based approach that we previously developed for interactions of ubiquitin with spherical POPG liposomes (Ceccon, A. J. Am. Chem. Soc. 2016, 138, 5789-5792) allowed us to quantitatively analyze the variation in lifetime line broadening of NMR signals (ΔR2) measured for ubiquitin in the presence of q = 2 POPG:DHPC bicelles and the associated transverse spin relaxation rates (R2,B) of bicelle-bound ubiquitin. Ubiquitin, transiently bound to POPG:DHPC bicelles, undergoes internal rotation about an axis orthogonal to the surface of the bicelle and perpendicular to the principal axis of its rotational diffusion tensor on the low microsecond time scale (∼3 μs), while the rotation axis itself wobbles in a cone on a submicrosecond time scale (≤ 500 ns).

Measurement of a129Xe transverse relaxation rate without the influence of Rb polarization-induced magnetic gradient.

We demonstrate the measurement of the transverse spin relaxation rate of Xe without the influence of the Rb polarization-induced magnetic field gradient. The optical pumping beam and probe beam turn on and off repeatedly during the measurement to reduce the relaxation originating from the Rb polarization-induced magnetic field gradient. During the absence of the optical pumping beam, the nuclear spin of the noble gas atom does not experience the alkali-polarization-induced magnetic field gradient so that the transverse spin relaxation rate (1/T2) decreases. When the duty cycle reaches zero, the measured transverse relaxation time T2 approaches the longitudinal spin relaxation time T1. Our method helps in roughly estimating the longitudinal spin relaxation time with a single measurement of the free induction decay.

Freezing of molecular rotation in a paramagnetic crystal studied by P31 NMR

We present a detailed $^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) study of the molecular rotation in the compound $[\mathrm{Cu}{(\mathrm{pz})}_{2}{(2\ensuremath{-}\mathrm{HOpy})}_{2}]{({\mathrm{PF}}_{6})}_{2}$, where $\mathrm{pz}={\mathrm{C}}_{4}{\mathrm{H}}_{4}{\mathrm{N}}_{2}$ and $2\ensuremath{-}\mathrm{HOpy}={\mathrm{C}}_{5}{\mathrm{H}}_{4}\mathrm{NHO}$. Here, a freezing of the ${\mathrm{PF}}_{6}$ rotation modes is revealed by several steplike increases of the temperature-dependent second spectral moment, with accompanying broad peaks of the longitudinal and transverse nuclear spin-relaxation rates. An analysis based on the Bloembergen-Purcell-Pound (BPP) theory quantifies the related activation energies as ${E}_{a}/{k}_{B}=250$ and 1400 K. Further, the anisotropy of the second spectral moment of the $^{31}\mathrm{P}$ absorption line was calculated for the rigid lattice, as well as in the presence of several sets of ${\mathrm{PF}}_{6}$ reorientation modes, and is in excellent agreement with the experimental data. Whereas the anisotropy of the frequency shift and enhancement of nuclear spin-relaxation rates is driven by the molecular rotation with respect to the dipole fields stemming from the Cu ions, the second spectral moment is determined by the intramolecular interaction of nuclear $^{19}\mathrm{F}$ and $^{31}\mathrm{P}$ moments in the presence of the distinct rotation modes.

Optimized selection of slow-relaxing 13C transitions in methyl groups of proteins: application to relaxation dispersion.

Optimized selection of the slow-relaxing components of single-quantum 13C magnetization in 13CH3 methyl groups of proteins using acute (< 90°) angle 1H radio-frequency pulses, is described. The optimal selection scheme is more relaxation-tolerant and provides sensitivity gains in comparison to the experiment where the undesired (fast-relaxing) components of 13C magnetization are simply 'filtered-out' and only 90° 1H pulses are employed for magnetization transfer to and from 13C nuclei. When applied to methyl 13C single-quantum Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion experiments for studies of chemical exchange, the selection of the slow-relaxing 13C transitions results in a significant decrease in intrinsic (exchange-free) transverse spin relaxation rates of all exchanging species. For exchanging systems involving high-molecular-weight species, the lower transverse relaxation rates translate into an increase in the information content of the resulting relaxation dispersion profiles.

Magic-Angle-Pulse Driven Separation of Degenerate 1 H Transitions in Methyl Groups of Proteins: Application to Studies of Methyl Axis Dynamics.

Dynamics of protein side chains is one of the principal determinants of conformational entropy in protein structures and molecular recognition events. We describe NMR experiments that rely on the use of magic-angle pulses for efficient isolation of degenerate 1 H transitions of the I=3/2 manifold of 13 CH3 methyl groups, and serve as 'building blocks' for the measurement of transverse spin relaxation rates of the fast- and slow-relaxing 1 H transitions - the primary quantitative reporters of methyl axis dynamics in selectively {13 CH3 }-methyl-labelled, highly deuterated proteins. The magic-angle-pulse driven experiments are technically simpler and, in the absence of relaxation, predicted to be 2.3-fold more sensitive than previously developed analogous schemes. Validation of the methodology on a sample of {13 CH3 }-labeled ubiquitin demonstrates quantitative agreement between order parameters of methyl three-fold symmetry axis obtained with magic-angle-pulse driven experiments and other established NMR techniques, paving the way for studies of methyl axis dynamics in human DNAJB6b chaperone, a protein that undergoes exchange with high-molecular-weight oligomeric species.

Effects of an HIV-1 maturation inhibitor on the structure and dynamics of CA-SP1 junction helices in virus-like particles

HIV-1 maturation involves conversion of the immature Gag polyprotein lattice, which lines the inner surface of the viral membrane, to the mature capsid protein (CA) lattice, which encloses the viral RNA. Maturation inhibitors such as bevirimat (BVM) bind within six-helix bundles, formed by a segment that spans the junction between the CA and spacer peptide 1 (SP1) subunits of Gag, and interfere with cleavage between CA and SP1 catalyzed by the HIV-1 protease (PR). We report solid-state NMR (ssNMR) measurements on spherical virus-like particles (VLPs), facilitated by segmental isotopic labeling, that provide information about effects of BVM on the structure and dynamics of CA-SP1 junction helices in the immature lattice. Although BVM strongly blocks PR-catalyzed CA-SP1 cleavage in VLPs and blocks conversion of VLPs to tubular CA assemblies, 15N and 13C ssNMR chemical shifts of segmentally labeled VLPs with and without BVM are very similar, indicating that interaction with BVM does not alter the six-helix bundle structure appreciably. Only the 15N chemical shift of A280 (the first residue of SP1) changes significantly, consistent with BVM binding to an internal ring of hydrophobic side chains of L279 residues. Measurements of transverse 15N spin relaxation rates reveal a reduction in the amplitudes and/or timescales of backbone N-H bond motions, corresponding to a rigidification of the six-helix bundles. Overall, our data show that inhibition of HIV-1 maturation by BVM involves changes in structure and dynamics that are surprisingly subtle, but still sufficient to produce a large effect on CA-SP1 cleavage.

NMR investigations on binding and dynamics of imidazolium-based ionic liquids with HEWL.

Molecular level insights on protein-ionic liquid (P-IL) interactions are beneficial for assessing protein stability, binding and dynamics. In the present work, interactions of ILs, namely, 1-butyl 3-methylimidazolium methyl sulfate (IL1), 1-butyl 3-methylimidazolium octyl sulfate (IL2) and 1-butyl 3-methylimidazolium chloride (IL3) with hen egg white lysozyme (HEWL) protein were investigated using solution-state nuclear magnetic resonance (NMR) spectroscopy. To ascertain the binding and dynamics from the perspective of both protein and IL, various ligand based NMR approaches such as selective and non-selective nuclear spin-relaxation (R1SEL and R1NS), saturation transfer difference (STD), difference of inversion recovery rate with and without target irradiation (DIRECTION), 35Cl line-shape and spin-relaxation, and protein back bone amide chemical shift perturbations (CSPs) from 1H-15N HSQC were utilized. Among the ILs investigated, IL2 experiences significant interaction relative to those of IL1 and IL3, as revealed by the combined R1SEL and R1NS analysis, which is further supported by STD NMR. CSP analyses of 1H-15N HSQC spectra of aqueous P-IL mixtures enabled to identify the potential binding sites of ILs with HEWL. Whereas, 15N longitudinal (R1) and transverse (R2) spin-relaxation rates and 15N{1H} heteronuclear nuclear Overhauser effect (hetNOE) data subjected to the model free analysis for IL2 yielded the rotational correlation times and order parameters of various residues of HEWL. Furthermore, the results could discern the nature of interactions between studied ILs and HEWL in terms of specific and non-specific interactions.

Decorrelating Kinetic and Relaxation Parameters in Exchange Saturation Transfer NMR: A Case Study of N-Terminal Huntingtin Peptides Binding to Unilamellar Lipid Vesicles.

Dark state exchange saturation transfer (DEST) and lifetime line-broadening (Δ R2, the difference in the measured transverse relaxation rates for the observable species in the presence and absence of exchange with a species characterized by very large intrinsic transverse relaxation rates) have proven to be powerful NMR tools for studying exchange phenomena between a NMR visible species and a high-molecular weight, "dark", NMR invisible state. However, in the exchange regime, where the transverse spin relaxation rates in the bound state ( R2bound) are smaller than the strength of the DEST saturation radio frequency field, typically corresponding to systems below ∼6 MDa, the combination of DEST and Δ R2 data, while sufficient to define the apparent association rate constant, cannot unambiguously determine the population of the bound state pB and R2bound values independently. We show that the latter exchange and relaxation parameters can be decorrelated by the measurement of the maximal value of the contribution of the fast-relaxing magnetization component to the total NMR signal, Cfastmax, an observable that is directly proportional to pB. When integrated into the analysis of DEST/Δ R2 data, Cfastmax provides an indispensable source of information for quantitative studies of exchange involving high-molecular-weight dark states. We demonstrate the utility of this approach by investigating the binding kinetics of two huntingtin exon-1-derived peptides to small unilamellar lipid vesicles (SUV), ∼ 31 nm in diameter and 4.3 MDa in molecular weight. The interaction of the N-terminal amphiphilic domain of huntingtin exon-1 with membrane surfaces promotes polyglutamine-mediated aggregation and, as such, is thought to play a role in the etiology of Huntington's disease, an autosomal dominant fatal neurodegenerative condition. The first peptide comprises the 16-residue N-terminal amphiphilic domain (httNT) alone, while the second contains an additional seven residue polyglutamine tract at the C-terminus (httNTQ7). At a peptide-to-lipid molar ratio of 1:4, the population of peptide bound to the SUV surface is substantial, ∼ 7-8%, while exchange between the free and SUV-bound peptide is slow on the relaxation time-scale ( kex ∼ 200 s-1). The last two C-terminal residues of httNT and the last 9 of httNTQ7 remain flexible in the SUV-bound form due to transient detachment from the lipid surface that occurs on a time-scale several-fold faster than binding.

Electron charge and spin delocalization revealed in the optically probed longitudinal and transverse spin dynamics in n -GaAs

The evolution of the electron spin dynamics as consequence of carrier delocalization in $n$-type GaAs is investigated by the recently developed extended pump-probe Kerr/Faraday rotation spectroscopy. We find that isolated electrons localized on donors demonstrate a prominent difference between the longitudinal and transverse spin relaxation rates in magnetic field, which is almost absent in the metallic phase. The inhomogeneous transverse dephasing time $T_2^*$ of the spin ensemble strongly increases upon electron delocalization as a result of motional narrowing that can be induced by increasing either the donor concentration or the temperature. An unexpected relation between $T_2^*$ and the longitudinal spin relaxation time $T_1$ is found, namely that their product is about constant, as explained by the magnetic field effect on the spin diffusion. We observe a two-stage longitudinal spin relaxation which suggests the establishment of spin temperature in the system of exchange-coupled donor-bound electrons.

Dynamics of a globular protein adsorbed to liposomal nanoparticles.

A solution-state NMR method is proposed to investigate the dynamics of proteins that undergo reversible association with nanoparticles (NPs). We applied the recently developed dark-state exchange saturation transfer experiment to obtain residue-level dynamic information on a NP-adsorbed protein in the form of transverse spin relaxation rates, R2bound. Based on dynamic light scattering, fluorescence, circular dichroism, and NMR spectroscopy data, we show that the test protein, human liver fatty acid binding protein, interacts reversibly and peripherally with liposomal NPs without experiencing significant structural changes. The significant but modest saturation transfer from the bound state observed at 14.1 and 23.5 T static magnetic fields, and the small determined R2bound values were consistent with a largely unrestricted global motion at the lipid surface. Amino acid residues displaying faster spin relaxation mapped to a region that could represent the epitope of interaction with an extended phospholipid chain constituting the protein anchor. These results prove that atomic-resolution protein dynamics is accessible even after association with NPs, supporting the use of saturation transfer methods as powerful tools in bionanoscience.

Site-Specific Structural Variations Accompanying Tubular Assembly of the HIV-1 Capsid Protein

The 231-residue capsid (CA) protein of human immunodeficiency virus type 1 (HIV-1) spontaneously self-assembles into tubes with a hexagonal lattice that is believed to mimic the surface lattice of conical capsid cores within intact virions. We report the results of solid-state nuclear magnetic resonance (NMR) measurements on HIV-1 CA tubes that provide new information regarding changes in molecular structure that accompany CA self-assembly, local dynamics within CA tubes, and possible mechanisms for the generation of lattice curvature. This information is contained in site-specific assignments of signals in two- and three-dimensional solid-state NMR spectra, conformation-dependent 15N and 13C NMR chemical shifts, detection of highly dynamic residues under solution NMR conditions, measurements of local variations in transverse spin relaxation rates of amide 1H nuclei, and quantitative measurements of site-specific 15N–15N dipole–dipole couplings. Our data show that most of the CA sequence is conformationally ordered and relatively rigid in tubular assemblies and that structures of the N-terminal domain (NTD) and the C-terminal domain (CTD) observed in solution are largely retained. However, specific segments, including the N-terminal β-hairpin, the cyclophilin A binding loop, the inter-domain linker, segments involved in intermolecular NTD–CTD interactions, and the C-terminal tail, have substantial static or dynamical disorder in tubular assemblies. Other segments, including the 310-helical segment in CTD, undergo clear conformational changes. Structural variations associated with curvature of the CA lattice appear to be localized in the inter-domain linker and intermolecular NTD–CTD interface, while structural variations within NTD hexamers, around local 3-fold symmetry axes, and in CTD–CTD dimerization interfaces are less significant.

Absolute oxygen R1eimaging in vivo with pulse electron paramagnetic resonance

Tissue oxygen (O2) levels are among the most important and most quantifiable stimuli to which cells and tissues respond through inducible signaling pathways. Tumor O2 levels are major determinants of the response to cancer therapy. Developing more accurate measurements and images of tissue O2 partial pressure (pO2), assumes enormous practical, biological, and medical importance. We present a fundamentally new technique to image pO2 in tumors and tissues with pulse electron paramagnetic resonance (EPR) imaging enabled by an injected, nontoxic, triaryl methyl (trityl) spin probe whose unpaired electron's slow relaxation rates report the tissue pO2. Heretofore, virtually all in vivo EPR O2 imaging measures pO2 with the transverse electron spin relaxation rate, R2e, which is susceptible to the self-relaxation confounding O2 sensitivity. We found that the trityl electron longitudinal relaxation rate, R1e, is an order of magnitude less sensitive to confounding self-relaxation. R1e imaging has greater accuracy and brings EPR O2 images to an absolute pO2 image, within uncertainties. R1e imaging more accurately determines oxygenation of cancer and normal tissue in animal models than has been available. It will enable enhanced, rapid, noninvasive O2 images for understanding oxygen biology and the relationship of oxygenation patterns to therapy outcome in living animal systems.

Magnetic field effects on the finite-frequency noise and ac conductance of a Kondo quantum dot out of equilibrium

We present analytic results for the finite-frequency current noise and the nonequilibrium ac conductance for a Kondo quantum dot in presence of a magnetic field. Using the real-time renormalization group method, we determine the line shape close to resonances and show that while all resonances in the ac conductance are broadened by the transverse spin relaxation rate, the noise at finite field additionally involves the longitudinal rate as well as sharp kinks resulting in singular derivatives. Our results provide a consistent theoretical description of recent experimental data for the emission noise at zero magnetic field, and we propose the extension to finite field for which we present a detailed prediction.

Biomechanics of Synthetic Elastin: Insights from Magnetic Resonance Microimaging

We used Magnetic Resonance microimaging (MRI) to study the compressive behaviour of synthetic elastin. Compression-induced changes in the elastin sample were quantified using longitudinal and transverse spin relaxation rates (R1 and R2, respectively). Spatially-resolved maps of each spin relaxation rate were obtained, allowing the heterogeneous texture of the sample to be observed with and without compression. Compression resulted in an increase of both the mean R1 and the mean R2, but most of this increase was due to sub-locations that exhibited relatively low R1 and R2 in the uncompressed state. This behaviour can be described by differential compression, where local domains in the hydrogel with a relatively low biopolymer content compress more than those with a relatively high biopolymer content.

Erratum: Measurement of longitudinal and transverse spin relaxation rates using the ground-state Hanle effect [Phys. Rev. A84, 053421 (2011)

Erratum: Measurement of longitudinal and transverse spin relaxation rates using the ground-state Hanle effect [Phys. Rev. A<b>84</b>, 053421 (2011)

Measurement of longitudinal and transverse spin relaxation rates using the ground-state Hanle effect

We present a theoretical and experimental study of the resonant circularly-polarized-light-induced Hanle effect in the ground state of Cs vapor atoms in a paraffin-coated cell. The effect manifests itself as a narrow resonance (centered at $B=0$) in the dependence of the optical transmission coefficient of the vapor on the magnitude of an external magnetic field $\stackrel{P\vec}{B}$. We develop a theoretical model that yields an algebraic expression for the shape of these resonances for arbitrary field orientations and arbitrary angular momenta of the states coupled by the exciting light, provided that the light power is kept sufficiently small. An experimental procedure for assessing the range of validity of the model is given. Experiments were carried out on the laser-driven Cs ${D}_{1}$ transition both in longitudinal and transverse field geometries, and the observed line shapes of the corresponding bright and dark resonances give an excellent confirmation of the model predictions. The method is applied for determining the intrinsic longitudinal and transverse relaxation rates of the vector magnetization in the vapor and their dependence on light power.

Conformational Flexibility of a Human Immunoglobulin Light Chain Variable Domain by Relaxation Dispersion Nuclear Magnetic Resonance Spectroscopy: Implications for Protein Misfolding and Amyloid Assembly

The conformational flexibility of a human immunoglobulin κIV light-chain variable domain, LEN, which can undergo conversion to amyloid under destabilizing conditions, was investigated at physiological and acidic pH on a residue-specific basis by multidimensional solution-state nuclear magnetic resonance (NMR) methods. Measurements of backbone chemical shifts and amide (15)N longitudinal and transverse spin relaxation rates and steady-state nuclear Overhauser enhancements indicate that, on the whole, LEN retains its native three-dimensional fold and dimeric state at pH 2 and that the protein backbone exhibits limited fast motions on the picosecond to nanosecond time scale. On the other hand, (15)N Carr--Purcell--Meiboom--Gill (CPMG) relaxation dispersion NMR data show that LEN experiences considerable slower, millisecond time scale dynamics, confined primarily to three contiguous segments of about 5-20 residues and encompassing the N-terminal β-strand and complementarity determining loop regions 2 and 3 in the vicinity of the dimer interface. Quantitative analysis of the CPMG relaxation dispersion data reveals that at physiological pH these slow backbone motions are associated with relatively low excited-state protein conformer populations, in the ~2-4% range. Upon acidification, the minor conformer populations increase significantly, to ~10-15%, with most residues involved in stabilizing interactions across the dimer interface displaying increased flexibility. These findings provide molecular-level insights about partial protein unfolding at low pH and point to the LEN dimer dissociation, initiated by increased conformational flexibility in several well-defined regions, as being one of the important early events leading to amyloid assembly.

Near-resonance spin-noise spectroscopy

Spectroscopy of atomic spin noise allows the determination of many sample properties such as energy-level structures and transverse-spin relaxation rates without the need to drive the system away from equilibrium with applied fields. Analysis of noise measurements can also reveal the processes that limit the sensitivity of a measured signal. Standard methods for spectroscopic noise measurements in atomic vapors rely on far-off-resonant optical probing. We present a method for investigating spin noise with a probe beam frequency relatively close to resonance and show how the back action of the probe on the atomic state can be subtracted from the recorded noise spectra. We verify this method experimentally by showing noise data that scale with the square root of the number of atoms, after the probe back action has been properly subtracted.

Limits on possible new nucleon monopole-dipole interactions from the spin relaxation rate of polarizedHe3gas

Various theories beyond the standard model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A $P$-odd and $T$-odd interaction between polarized and unpolarized nucleons proportional to $\stackrel{\ensuremath{\rightarrow}}{s}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{r}$ involving a scalar coupling ${g}_{s}$ at one vertex and a pseudoscalar coupling ${g}_{p}$ at the other vertex is one such possibility. We show that measurements of the transverse spin relaxation rate ${\ensuremath{\Gamma}}_{2}$ for polarized gas can be used to set limits on ${g}_{s}{g}_{p}$ for boson masses in the $10\ensuremath{\mu}$eV to $100$ meV range, corresponding to distances from centimeters to micrometers. We present limits from both a reanalysis of previous measurements of ${\ensuremath{\Gamma}}_{2}$ in $^{3}\mathrm{He}$ spin exchange cells and from data in a test experiment searching for a change in ${\ensuremath{\Gamma}}_{2}$ upon the motion of an unpolarized test mass. The outlook for more sensitive measurements using this technique is discussed.