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.

Pharmaceutical nanocrystals confined in porous host systems – interfacial effects and amorphous interphases

An amorphous acetaminophen nanolayer is shown to determine the surface energy of acetaminophen nanocrystals grown in controlled porous glasses.

Detection of Surface-Immobilized Components and Their Role in Viscoelastic Reinforcement of Rubber-Silica Nanocomposites

Immobilized polymer fractions have been claimed to be of pivotal importance for the large mechanical reinforcement observed in nanoparticle-filled elastomers but remained elusive in actual application-relevant materials. We here isolate the additive filler network contribution to the storage modulus of industrial styrene-butadiene rubber (SBR) nanocomposites filled with silica at different frequencies and temperatures and demonstrate that it is viscoelastic in nature. We further quantify the amount of immobilized polymer using solid-state NMR and establish a correlation with the mechanical reinforcement, identifying a direct, strongly nonlinear dependence on the immobilized polymer fraction. The observation of a temperature-independent filler percolation threshold suggests that immobilized polymer fractions may not necessarily form contiguous layers around the filler particles but could only reside in highly confined regions between closely packed filler particles, where they dominate the bending modulus of aggregated particles.

Structure of Poly(vinyl alcohol) Cryo-Hydrogels as Studied by Proton Low-Field NMR Spectroscopy

The network structure of poly(vinyl alcohol) (PVA) hydrogels obtained by freezing-thawing cycles was investigated by solid-state (1)H low-field NMR spectroscopy. By the application of multiple-quantum NMR experiments, we obtain information about the segmental order parameter, which is directly related to the restrictions on chain motion (cross-links) formed upon gelation. These measurements indicate that the network mesh size as well as the relative amount of nonelastic defects (i.e., non-cross-linked chains, dangling chains, loops) decrease with the number of freezing-thawing cycles but are independent of the polymer concentration. The formation of the PVA network is accompanied by an increasing fraction of polymer with fast magnetization decay ( approximately 20 mus). The quantitative study of this rigid phase with a specific refocusing pulse sequence shows that it is composed of a primary crystalline polymer phase ( approximately 5%), which constitutes the main support of the network structure and determines the mesh size, and a secondary population of more imperfect crystallites, which increase the number of elastic chain segments in the polymer gel but do not affect the average network mesh size appreciably. Correspondingly, progressive melting of the secondary crystallites with increasing temperature does not affect the network mesh size but only the amount of network defects, and melting of the main PVA crystallites at approximately 80 degrees C leads to the destruction of the network gel and the formation of an isotropic PVA solution.

Spin-diffusion NMR at low field for the study of multiphase solids

The use of spin-diffusion NMR for the measurement of domain sizes in multiphase materials is becoming increasingly popular, in particular for the study of heterogeneous polymers. Under conditions where T(1) relaxation can be neglected, which is mostly the case at high field, analytical and approximate solutions to the evolution of spin diffusion are available. In order to extend the technique to more general conditions, we performed a comprehensive study of the diffusion of magnetization in a model copolymer at low field, where T(1) tends to be of the same order of magnitude as the typical spin-diffusion time. In order to study the effects of T(1) and to delineate the optimal T(1) values for back correction prior to applying the initial-rate approximation, we developed a numerical simulation based on the diffusion equation and including longitudinal relaxation. We present and discuss the limits of simple correction strategies for initial-slope analysis based on apparent relaxation times from saturation-recovery experiments or the spin-diffusion experiments themselves. Our best strategy faithfully reproduces domain sizes obtained by both TEM investigations and full simultaneous fitting of spin-diffusion and saturation-recovery curves. Full fitting of such independent data sets not only yields correct domain sizes, but also the true longitudinal relaxation times, as well as spin-diffusion coefficients. Effects of interphases with distinct mobility on spin-diffusion curves, as well as practical hints concerning the reliable component decomposition of the detected low-resolution FID signal by help of different magnetization filters are also discussed in detail.

Memory effect in isothermal crystallization of syndiotactic polypropylene - role of melt structure and dynamics?

The crystalline-memory effect on the crystallization of syndiotactic polypropylene is investigated by differential scanning calorimetry and solid-state NMR spectroscopy. The influence of several parameters in the thermal (pre-)treatment and the crystallization conditions is studied in detail. In agreement with previous reports, the power law behavior of the overall crystal growth rate is found to be remarkably different for melts with and without memory. This has previously been interpreted in terms of changes in the structure and/or the dynamics of the melt (disentangled state, local order), and a variety of NMR experiments is used to detect such potential changes. All our NMR results are identical for melts with and without memory, therefore excluding any large effect of the "memory" on melt structure or dynamics exceeding the percent level of the whole sample volume, and thus supporting more conventional interpretations in terms of persisting nuclei. Samples that were pre-crystallized at lower temperatures exhibit a larger memory effect, and the potential nuclei fraction is a non-equilibrium structure and is restricted to the 0.1% level if it is crystalline or highly ordered.

Segmental order in end-linked polymer networks: a Monte Carlo study

Segmental order in end-linked monomodal and bimodal polymer networks is investigated by means of bond-fluctuation Monte Carlo simulations. The tensor order parameter, which is a central observable in NMR experiments, is not uniquely related to simple vectorial order. The relaxation of NMR-detected tensorial interactions towards their finite long-time limit is best described by a power law and occurs over much longer time scales than the relaxation of vectorial order. The well-known prediction for the segmental order of Gaussian chains as a simple function of the segment number between constraints is not straightforwardly obeyed, neither in dry nor in swollen networks. Excluded-volume interactions tend to significantly reduce the tensorial order, as is clearly observed in single-chain simulations. A distribution extends along the chain, where order is increased in a region of 30-40 bonds around the cross-links in networks. The dominating contribution to the order parameter distribution arises from the frozen-in distribution of end-to-end separations. We find strong deviations from the Gamma distribution, which has so far been implicitly used in most NMR works, as it is a straightforward consequence of a Gaussian distribution of end separations. Specifically, we find narrower distributions, as small values of the tensor order parameter are strongly suppressed, most probably as a result of trapped entanglements. The markedly subaffine behavior of the average order parameter and the changes in its distribution on swelling are assigned to orientation processes of strands which compensate for the non-affine local deformation. Our central observations and interpretations are well supported by our previous experimental and theoretical work.

An investigation of the hydrogen-bonding structure in bilirubin by 1H double-quantum magic-angle spinning solid-state NMR spectroscopy

The complex hydrogen-bonding arrangement in the biologically important molecule bilirubin IXalpha is probed by using 1H double-quantum (DQ) magic-angle spinning (MAS) NMR spectroscopy. Employing fast MAS (30 kHz) and a high magnetic field (16.4 T), three low-field resonances corresponding to the different hydrogen-bonding protons are resolved in a 1H MAS NMR spectrum of bilirubin. These resonances are assigned on the basis of the proton-proton proximities identified from a two-dimensional rotor-synchronized 1H DQ MAS NMR spectrum. An analysis of 1H DQ MAS spinning-sideband patterns for the NH protons in bilirubin allows the quantitative determination of proton-proton distances and the geometry. The validity of this procedure is proven by simulated spectra for a model three-spin system, which show that the shortest distance can be determined to a very high degree of accuracy. The distance between the lactam and pyrrole NH protons in bilirubin is determined to be 0.186 +/- 0.002 nm (corresponding to a dominant dipolar coupling constant of 18.5 +/- 0.5 kHz). The analysis also yields a distance between the lactam NH and carboxylic acid OH protons of 0.230 +/- 0.008 nm (corresponding to a perturbing dipolar coupling constant of 9.9 +/- 1.0 kHz) and an H-H-H angle of 122 +/- 4 degrees. Finally, a comparison of 1H DQ MAS spinning-sideband patterns for bilirubin and its dimethyl ester reveals a significantly longer distance between the two NH protons in the latter case.

Recoupled polarization-transfer methods for solid-state (1)H--(13)C heteronuclear correlation in the limit of fast MAS

An in-depth account of the effects of homonuclear couplings and multiple heteronuclear couplings is given for a recently published technique for (1)H--(13)C dipolar correlation in solids under very fast MAS, where the heteronuclear dipolar coupling is recoupled by means of REDOR pi-pulse trains. The method bears similarities to well-known solution-state NMR techniques, which form the framework of a heteronuclear multiple-quantum experiment. The so-called recoupled polarization-transfer (REPT) technique is versatile in that rotor-synchronized (1)H--(13)C shift correlation spectra can be recorded. In addition, weak heteronuclear dipolar coupling constants can be extracted by means of spinning sideband analysis in the indirect dimension of the experiment. These sidebands are generated by rotor encoding of the reconversion Hamiltonian. We present generalized variants of the initially described heteronuclear multiple-quantum correlation (HMQC) experiment, which are better suited for certain applications. Using these techniques, measurements on model compounds with (13)C in natural abundance, as well as simulations, confirm the very weak effect of (1)H--(1)H homonuclear couplings on the spectra recorded with spinning frequencies of 25--30 kHz. The effect of remote heteronuclear couplings on the spinning-sideband patterns of CH(n) groups is discussed, and (13)C spectral editing of rigid organic solids is shown to be practicable with these techniques.

Sideband patterns from rotor-encoded longitudinal magnetization in MAS recoupling experiments

Recent multiple-quantum MAS NMR experiments have shown that a change in the rotor phase (and, hence, in the Hamiltonian) between the excitation and reconversion periods can lead to informative spinning-sideband patterns. However, such "rotor encoding" is not limited to multiple-quantum experiments. Here it is shown that longitudinal magnetization can also be rotor-encoded. Both homonuclear and heteronuclear rotor encoding of longitudinal magnetization (RELM) experiments are performed on dipolar-coupled spin-1/2 systems, and the corresponding sideband patterns in the indirect dimension are analyzed. In both cases, only even-order sidebands are produced, and their intensity distribution depends on the durations of the recoupling periods. In heteronuclear experiments using REDOR-type recoupling, purely dipolar sideband patterns that are entirely free of effects due to the chemical-shielding anisotropy can be generated. Advantages and disadvantages of the heteronuclear RELM experiment are discussed in the context of other methods used to measure heteronuclear dipolar couplings.

Recoupled polarization transfer heteronuclear 1H-13C multiple-quantum correlation in solids under ultra-fast MAS

A new approach for high-resolution solid-state heteronuclear multiple-quantum MAS NMR spectroscopy of dipolar-coupled spin-12 nuclei is introduced. The method is a heteronuclear chemical shift correlation technique of abundant spins, like 1H with rare spins, like 13C in natural abundance. High resolution is provided by ultra-fast MAS and high magnetic fields, high sensitivity being ensured by a direct polarization transfer from the abundant protons to 13C. In a rotor-synchronized variant, the method can be used to probe heteronuclear through-space proximities, while the heteronuclear dipolar coupling constant can quantitatively be determined by measuring multiple-quantum spinning-sideband patterns. By means of recoupling, even weak heteronuclear dipolar interactions are accessible. The capabilities of the technique are demonstrated by measurements on crystalline L-tyrosine hydrochloride salt.

Heteronuclear double-quantum MAS NMR spectroscopy in dipolar solids

A new pulse sequence for high-resolution solid-state heteronuclear double-quantum MAS NMR spectroscopy of dipolar-coupled spin-12 nuclei is introduced. It is based on the five-pulse sequence known from solution-state NMR, which is here applied synchronously to both spin species. The heteronuclear double-quantum (HeDQ) spinning-sideband patterns produced by this experiment are shown to be sensitive to the heteronuclear distance, as well as the relative orientations of the chemical-shift and dipolar tensors. In particular, it is shown that the HeDQ patterns exhibit an enhanced sensitivity to the chemical shielding tensors as compared with the single-quantum spinning-sideband patterns. The detection of HeDQ patterns via the I and S spins is discussed. The isolated (13)C-(1)H spin pair in deuterated ammonium formate with (13)C in natural abundance was chosen as a model system, and the perturbing influence of dipolar couplings to surrounding protons on the (13)C-(1)H DQ coherence is discussed. The pulse sequence can also be used as a heteronuclear double-quantum filter, hence providing information about heteronuclear couplings, and thus allowing the differentiation of quaternary and CH(n) bonded carbons. The elucidation of (13)C-(1)H dipolar proximities is presented for a sample of bisphenol A polycarbonate with (13)C in natural abundance, recorded with a broadband version of the synchronized five-pulse sequence.