Rotational diffusion of a tracer colloid particle: I. Short time orientational correlations

We extend the generalized Smoluchowski equation to descrbe the diffusional relaxation of position and orientation in a suspension of interacting spherical colloid particles. Considering a tracer particle which interacts with other particles through spherically symmetric pair potentials and with an external field we obtain a cluster expansion representation of the orientational time correlation functions for the tracer. The one and two body cluster contributions are studied explicitly at short times. Working to first order in volume fraction φ we show that the initial slope of the time correlation functions is described by a modified diffusion coefficient D^r = D^r₀(1 −C^rφ) where C^r is a number determined by hydrodynamic and potential interactions. We evaluate C^r numerically for spheres with slip-stick hydrodynamic boundary conditions and also for permeable spheres.     

Internal dynamics and hydration of solid proteins by1H NMR relaxation and FTIR spectroscopy

Temperature dependences of¹H nonselective nuclear magnetic resonanceT ₁ andT ₂ relaxation times measured at 27 MHz have been studied on solid human serum albumin (HSA) samples at various hydrations. The data were interpreted in terms of three kinds of internal motions in a protein and microdynamic parameters of the motions were obtained by a “model-free” approach. Two fast motions with correlation times lying in the range of tens to hundreds picoseconds were shown to be essentially insensitive to hydration. Unlike lysozyme and bovine albumin, HSA reveals relaxation transition due to slow motion in the room temperature range thus allowing one to obtain microdynamic parameters more precisely. Hydration leads to a shortening of the correlation time from hundreds to tens nanoseconds and to a less restricted movement. The comparison of the hydration dependence of relaxation parameters with infrared spectra of HSA side chain groups clearly shows that methyl protons are evidently involved in a slow motion, following the saturation of the protein globule surface by water. The same dependence correlating with solvent accessible surface areas was shown to exist for some other proteins. In addition to the main set of protons performing a solidlike movement, a small amount of much more mobile protons is also present with its proportion rising steeply with hydration and temperature. The origin of these protons is discussed.     

Longitudinal relaxation pathways in scalar-coupled systems

In applications to systems with resolved scalar couplings, the two-dimensional exchange experiment (NOESY) can provide greatly increased information if the flip angles of the two pulses that precede and follow the mixing interval τ_m are reduced (typically ,β ≈20°). The analysis of the amplitudes of individual signals within diagonal- and cross-peak multiplets allows one to gain insight into a variety of competing longitudinal relaxation mechanisms, not only for the fast- and slow-motion limits but also, in favorable cases, for critical correlation times.     

Origin of the Correlation Time Dependence of Coherence Transfer Distortions in Rotating Frame Cross-Relaxation Spectra

HOHAHA distortions in conventional (CW) ROESY experiments are known to be prominent when the frequency of the spin-lock field is near the midpoint between the resonance frequencies of a pair of coupled spins. That the disappearance of these distortions with offset from the midpoint is more rapid for large molecules than smaller ones is less widely known, and less well understood. We provide a quantitative explanation of the latter phenomenon using a combination of theory and numerical simulations. The cause of this effect can be found in the differential relaxation of the various magnetization modes which are involved in HOHAHA transfer. These modes experience enhanced relaxation far from a Hartmann–Hahn match. This enhancement is larger for molecules which have long correlation times.     

A method for evaluating correlation times for tumbling and internal motion in macromolecules using cross-relaxation rate constants from proton NMR spectra

A method of estimating the correlation times and extent of internal motion of macromolecules using ¹H NMR is proposed. The method relies on measuring the cross-relaxation rate constant between resolved, identified protons separated by a fixed distance, for example 2, 3 protons of tyrosine residues or 4, 5 protons of tryptophan residues in proteins, and the 5, 6 protons of cytosine residues in DNA. For a rigid body, the cross-relaxation rate constant yields directly an estimate of the tumbling time. Deviation of its dependence on viscosity and temperature from expectations for a rigid body allows one to estimate the degree to which internal motions contribute to the relaxation. The method is illustrated for Ribonuclease A and a 20 base pair fragment of DNA corresponding to the trp operator of Escherichia coli. The calculated correlation time of RNAse A is about 8 ns at 298 K, in good agreement with expectations from hydrodynamic measurements. Tyrosine 25 has significant internal motion, characterized by an apparent amplitude of 50–60°, a correlation time of about 5 ns, and low activation energy. The correlation time of the fragment of DNA is about 6.4 ns at 298 K, in agreement with expectations for a rigid rod. The apparent activation energy was 3.8 kcal/mol, close to the value for the dependence of the viscosity of D₂O on temperature. Further, the same result was obtained regardless of the position of the base in the sequence, indicating that bending motions are of small amplitude on the nanosecond time scale for short fragments of DNA.     

Assignment Strategies and Analysis of Cross-Peak Patterns and Intensities in the Three-Dimensional Homonuclear TOCSY-NOESY of RNA

The application of 3D TOCSY-NOESY to the analysis of RNA is presented, using a TOCSY-NOESY spectrum of the RNA duplex r(5′GGGCUGAAGCCU′). It is shown that for RNA molecules, 3D spectra can be obtained with a digital resolution comparable to that obtained for 2D NMR with full spectral information. The improvement in assignment over 2D methods is shown and discussed on the basis of an assignment strategy presented earlier. A simple and straightforward method for determining sugar puckers and γ backbone torsion angles is presented, which is derived from an analysis of cross-peak intensities originating from the TOCSY coherence transfer among sugar protons and HS′/5″ protons. The stereospecific assignment of the HS′/5″ resonances in 3D TOCSY-NOESY spectra is also discussed.     

Water proton relaxation in solutions of serum albumin from healthy donors and patients with liver and renal failures

These studies demonstrate possible connection between a decreased affinity of human serum albumin (HSA) in patients with liver and renal failures and changes of the HSA hydration state. The relaxation times,T ₁ andT ₂, of water protons in aqueous protein solution depend on the interaction of water molecules with biopolymer macromolecules. We compared these relaxation times for aqueous solutions of HSA from healthy and sick donors. For latter the amount and correlation time of the bound water are higher than those in healthy donors HSA solutions. The influence of long-chain fatty acids on the albumin hydration was found to be small.     

Evaluation of cross-peak volumes in 2D-spectra using 1D-fitting of line shapes

An interactive technique for the evaluation of cross-peak volumes in 2D-spectra is presented, based on a 1D nonlinear curve-fitting procedure. The effects of applied window functions, truncation of time domain data and cross-peak overlap on the evaluated cross-peak volumes are considered. The technique is applied to crowded NOESY spectra of the 34–65 and 163–231 fragments of bacterioopsin ofHalobacterium halobium. For these spectra 284 and 546 cross-peak volumes were measured with high accuracy.     

Response of lysozyme internal dynamics to hydration probed by13C and1H solid-state NMR relaxation

We have studied the hydration dependence of the internal protein dynamics of hen egg white lysozyme by naturally abundant¹³C and¹H nuclear magnetic resonance (NMR) relaxation. NMR relaxation timesT ₁, off-resonanceT _1p and proton-decoupled on-resonanceT _1p (only for carbon expriments) were measured in the temperature range from 0 to 50°C. The spectral resolution in carbon cross-polarization magic angle spinning spectrum allows to treat methine, methylene and methyl carbons separately, while proton experiments provide only one integral signal from all protons at a time. The relaxation times were quantitatively analyzed by the well-established correlation function formalism and model-free approach. The whole set of the data could be adequately described by a model assuming three types of motion having correlation times around 10^?4, 10^?9 and 10^?12 s. The slowest process originated from correlated conformational transitions between different energy minima, the intermediate process could be identified as librations within one energy minimum, and the fastest one is a fast rotation of methyl protons the symmetry axis of methyl groups. A comparison of the dynamic behavior of lysozyme and polylysine obtained from a previous study (A. Krushelnitsky, D. Faizullin, D. Reichert, Biopolymers 73, 1–15, 2004) reveals that in the dry state both biopolymers are rigid on both fast and slow time scales. Upon hydration, lysozyme and polylysine reveal a considerable enhancement of the internal mobility, however, in different ways. The side chains of polylysine are more mobile than those of lysozyme, whereas for the backbone a reversed picture is observed. This difference correlates with structural features of lysozyme and polylysine discussed in detail. Due to the presence of a fast spin diffusion, the analysis of proton relaxation data is a more difficult task. However, our data demonstrate that the correlation functions of motion obtained from carbon and proton experiments are substantially different. We explained this by the fact that these two types of NMR relaxation experiments probe the motion of different internuclear vectors. The comparison of the proton data with our previous results on proton relaxation timesT ₁ measured over a wide temperature range indicates that at low temperatures lysozyme undergoes structural rearrangements affecting the amplitudes and/or activation energies of motions.     

Signal enhancement using 45 degrees water flipback for 3D 15N-edited ROESY and NOESY HMQC and HSQC.

A novel implementation of the water flipback technique employing a 45 degrees flip-angle water-selective pulse is presented. The use of this water flipback technique is shown to significantly enhance signal in 3D 15N-edited ROESY in a 20 kDa complex of the vnd/NK-2 homeodomain bound to DNA. The enhancement is seen relative to the same experiment using weak water presaturation during the recovery delay. This enhancement is observed for the signals from both labile and nonlabile protons. ROESY and NOESY pulse sequences with 45 degrees water flipback are presented using both HMQC and HSQC for the 15N dimension. The 45 degrees flipback pulse is followed by a gradient, a water selective 180 degrees pulse, and another gradient to remove quadrature images and crosspeak phase distortion near the water frequency. Radiation damping of the water magnetization during the t1 and t2 evolution periods is suppressed using gradients. Water resonance planes from NOESY-HMQC and NOESY-HSQC spectra show that the HMQC version of the pulse sequences can provide stronger signal for very fast exchanging protons. The HSQC versions of the ROESY and NOESY pulse sequences are designed for the quantitative determination of protein-water crossrelaxation rates, with no water-selective pulses during the mixing time and with phase cycling and other measures for reducing axial artifacts in the water signal.     

Signal Enhancement Using 45° Water Flipback for 3D N-Edited ROESY and NOESY HMQC and HSQC

A novel implementation of the water flipback technique employing a 45° flip-angle water-selective pulse is presented. The use of this water flipback technique is shown to significantly enhance signal in 3D ¹⁵N-edited ROESY in a 20 kDa complex of the vnd/NK-2 homeodomain bound to DNA. The enhancement is seen relative to the same experiment using weak water presaturation during the recovery delay. This enhancement is observed for the signals from both labile and nonlabile protons. ROESY and NOESY pulse sequences with 45° water flipback are presented using both HMQC and HSQC for the ¹⁵N dimension. The 45° flipback pulse is followed by a gradient, a water selective 180° pulse, and another gradient to remove quadrature images and crosspeak phase distortion near the water frequency. Radiation damping of the water magnetization during the t₁ and t₂ evolution periods is suppressed using gradients. Water resonance planes from NOESY–HMQC and NOESY–HSQC spectra show that the HMQC version of the pulse sequences can provide stronger signal for very fast exchanging protons. The HSQC versions of the ROESY and NOESY pulse sequences are designed for the quantitative determination of protein–water crossrelaxation rates, with no water-selective pulses during the mixing time and with phase cycling and other measures for reducing axial artifacts in the water signal.     

对相干态与级联三能级原子相互作用过程中原子与场的动力学特性

研究对相干态与级联三能原子相互作用的动力学特性。结果表明，无论场模与原子的中间能级是否失谐，拉比振荡和互关联函数的时间演化都呈现崩溃与回复现象，但崩溃的持续时间随失谐量的增加而迅速延长，且两模之间随时间的演化即出现关联也出现反关联。     

NMR Study of Spatial Structure and Internal Dynamic of Adducts of Ninhydrin-Derived Azomethine Ylide with Cyclopropenes

Using NMR spectroscopy, the structure of the new products obtained in reaction of ninhydrin-derived azomethine ylide with cyclopropenes was established and conformational mobility was studied. Complete signal assignments in 1H and 13C spectra on base analysis of some homo- and heteronuclear correlation spectra were made, and qualitative comparison of the cross-peak intensities in the NOESY spectrum confirmed the structure of compounds 4a–4c in which three aromatic rings “a”, “b” and “c” at carbons of the cyclopropane ring are facing to us and the side substitute group at carbon C10 is situated in back direction. The hindered rotations of these aromatic rings in rigid part of molecules under study were found and values of free energy activation ∆G≠ of these rotations were evaluated on base coalescence temperature (Tc) and frequency difference (∆ν) data. The existence of fast in NMR time-scale conformational equilibrium in the solution associated with hindered rotation of side substitute group around C10–C14 bond was proved. In case of adduct 4c, the ratio 68:32 of two preferable conformers has been determined at room temperature in CDCl3 on base a comparison of calculated and experimental values of vicinal constant 3J10α–14β. This scalar constant turned out to be 1.0 Hz more for adduct 4a and this reflects an increase in the population of the main conformer almost by 10%. In the NOESY spectra of all studied adducts, a very rare phenomenon of scalar relaxation was found. It manifests itself in appearance of the additional scalar input into the effective cross-relaxation rate between two protons, and in case ωoτc ≪ 1, it may lead to a change in the sign of the cross-peak to the opposite if the scalar constant between them JH–H turns out to be time-dependent (scalar relaxation of the first kind) or in case of quadrupole nuclear situated near from one of these protons (scalar relaxation of the second kind). Thus, the conformational mobility which is connected with fast (in NMR time scale) nitrogen inversion in five-membered ring of adducts under study was proved due to the presence of the so-called scalar relaxation effects in NOESY spectra which look as a change cross-peak sign in comparison with the usual case.     

Electron spin relaxation by spin-rotation interaction in benzoyl and other acyl type radicals

In various studies of the spin dynamics in radical pairs, benzoyl-type radicals have been one of the two paramagnetic pair species. Their electron spin relaxation has been assumed to be slow enough to be neglected in the data analysis. This assumption is checked by measuring the electron spin relaxation in a sequence of three acyl radicals (benzoyl, 2,4,6-trimethylbenzoyl and hexahydrobenzoyl) by time-resolved electron paramagnetic resonance spectroscopy. In contrast to the assumed slow relaxation, rather short spin-lattice relaxation times (100–400 ns) are found for benzoyl and 2,4,6-trimethylbenzoyl radicals from the decay of the integral initial electron polarization to thermal equilibrium at different temperatures and viscosities. The relaxation is induced by a spin-rotation coupling arising from two different types of radical movements: overall rotation of the whole radical and hindered internal rotation of the CO group. The predominant second contribution depends on the barrier of the internal rotation. The obtained results are well explained in the frame of Bull’s theory when using a modified rotational correlation time τ _J . The size of the spin-rotation coupling due to the internal CO group rotation in benzoyl radicals is estimated to be |C _α|=1510 MHz.     

Elucidation of cross relaxation in liquids by two-dimensional N.M.R. spectroscopy

Two-dimensional N.M.R. spectroscopy is applied to the elucidation of cross relaxation pathways in liquids. The theory underlying two dimensional studies of cross relaxation and of transient nuclear Overhauser effects is developed. The influence of the correlation time of the molecular random process is investigated. It is found that in the limit of short correlation times (extreme narrowing limit) weak negative cross-peaks are observed. However, for long correlation times (spin diffusion limit) strong positive cross-peaks can be obtained. The technique appears particularly promising for the study of cross relaxation in macromolecules. Examples of intra- and intermolecular cross relaxation in the extreme narrowing limit are presented.     

Proton Strong Coupling in Heteronuclear Systems. Theoretical and Experimental Evaluation in Quantitative Analysis of SQC NOESY Spectra of Biopolymers

Hydrogen-detected NOE-relayed heteronuclear correlation via single-quantum coherence spectra (SQC-NOESY) may be affected by second-order anomalies when |(ω_I ± πJ_IS) − ω_I′| ≤ 20πJ_II′, where I and I′ are protons and S the heterospin coupled only to I. When the above condition applies, coherences of type S_αI_β (α, β = x, y, z) undergo oscillatory transfer to S_αI′_β coherences without the need for any pulse perturbation. Thus the INEPT transfers, as well as the t₁ precession step of the SQC-NOESY scheme, will no longer be effective in sorting out only antiphase or transverse coherences of the proton spin directly coupled to the heteronucleus S. In practice the process leads to measurable amplitude contributions to both auto- and cross-peak volumes, despite the fact that the effects developed during the INEPT steps are often negligible and the theoretical net transfer expected from the t₁ evolution is null. Since during t_m and t₂ (provided heteronuclear decoupling is applied) no effect is expected from the direct-heteronuclear-coupling operator, any strong-coupling contribution arising in these conditions can be computed using the specific parameters of the system under investigation. Thus auto- and cross-peak volumes can be corrected before internuclear distances are evaluated, In natural-abundance or slightly enriched ¹H-¹³C biopolymer systems, assuming J_II′/J_IS = 0.06 and t₁ = 10-20 ms, a correction amounting to 0-7% of the auto- and cross-peak volume sum should be applied to the connectivities of the strongly coupled pair, depending on Δω_I.     

In phase selective excitation of overlapping multiplets by gradient-enhanced chemical shift selective filters

We have developed gradient-enhanced chemical shift selective filters (ge-CSSF) for inphase excitation of overlapping multiplets 1H. This method relies on the constructive addition of on resonance signal while off resonance magnetization is eliminated by destructive interference due to variable chemical shift evolution. This is achieved by co-addition of several FIDs acquired with a gradually incremented chemical shift evolution period. Two variable-time and one constant-time ge-CSSFs are proposed that can be combined with TOCSY, NOESY, and ROESY mixing schemes yielding highly selective 1D experiments. Analytical and numerical expressions are derived to calculate the excitation profiles of the ge-CSSFs and to examine the effects of spin-spin relaxation, the length of the CSSF increment, and selective inversion pulses. We demonstrate, both theoretically and experimentally, that CSSFs yield fast signal separation for compounds with a range of spin-spin relaxation times and chemical shift differences as small as 1-2 Hz. The use of pulsed field gradients ensures that very clean spectra are obtained. The main application of these techniques lies in analysis of mixtures where severe spectral overlap prevents the use of simple 1D selective methods.     

Dynamical renormalization group approach to relaxation in quantum field theory

The real time evolution and relaxation of expectation values of quantum fields and of quantum states are computed as initial value problems by implementing the dynamical renormalization group (DRG). Linear response is invoked to set up the renormalized initial value problem to study the dynamics of the expectation value of quantum fields. The perturbative solution of the equations of motion for the field expectation values of quantum fields as well as the evolution of quantum states features secular terms, namely terms that grow in time and invalidate the perturbative expansion for late times. The DRG provides a consistent framework to resum these secular terms and yields a uniform asymptotic expansion at long times. Several relevant cases are studied in detail, including those of threshold infrared divergences which appear in gauge theories at finite temperature and lead to anomalous relaxation. In these cases the DRG is shown to provide a resummation akin to Bloch-Nordsieck but directly in real time and that goes beyond the scope of Bloch-Nordsieck and Dyson resummations. The nature of the resummation program is discussed in several examples. The DRG provides a framework that is consistent, systematic, and easy to implement to study the non-equilibrium relaxational dynamics directly in real time that does not rely on the concept of quasiparticle widths.     

Magnetic Resonance Imaging of Rat C6 Glioma Model Enhanced by Using Water-Soluble Gadolinium Fullerene

Water-soluble gadofullerene Gd@Ful with composition Gd³⁺@C₈₂(OH) _X ^3– (x ~ 20) was synthesized for theranostic study. Nanosuspensions of Gd@Ful were used for magnetic relaxation measurements in vitro and for magnetic resonance imaging of a rat with intracranially implanted C6 glioma. Gd@Ful was shown to reduce proton relaxation times in vitro and provide dual contrast of T ₁- and T ₂-weighted images in a rat brain tumor model after paramagnetic intravenous delivery. Magnetic relaxation times of water protons under action of Gd@Ful were strongly shortened due to cluster formation and increase of motional correlation times of protons in the vicinity of the fullerene cage. The Gd@Ful administration promoted the improvement of glioma contrast enhancement at T ₂-weighted images due to accumulation of paramagnetic substance at the tumor site. The contrast efficiency of Gd@Ful corresponds to the characteristics of negative contrast agent. The Gd@Ful nanosuspension is shown to be a contrast enhancer with high anti-tumor therapeutic potency. The retention of the Gd@Ful in the tumor resulted in a 75 % increase in survival times of the tumor-bearing animals.