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Recent 15N R1ρ-relaxation studies have shown that proteins in the solid state undergo slow, low amplitude global motion in the sub-millisecond time range. This range is at the edge of the time window for R1ρ experiments and, therefore, the motional parameters obtained by this method are not precise or reliable. In this paper, we present a 2H stimulated echo study of this type of molecular dynamics. The 2H stimulated echo experiments on a static sample allow for direct measurement of the correlation function in the time range of 10−6–10−1 s, making them well suited to study this type of molecular mobility. We have conducted a detailed analytical and numerical comparison of the correlation functions obtained from the relaxation and stimulated echo experiments, which are generally different. We have identified conditions and algorithms that enable a direct comparison of the relaxation and stimulated echo experimental results. Using the protein GB1 in the form of a lyophilized powder, we have demonstrated that 15N R1ρ-relaxation and 2H stimulated echo experiments yield essentially the same slow-motion correlation function. Surprisingly, this type of motion is observed not only in the protein sample but also in the tripeptide and single amino acid solid samples. The comparison of data measured in these three samples at different temperatures led us to conclude that this slow motion is, in fact, ultrasonic phonons, which seem to be inherent to all rigid biological solids. [ABSTRACT FROM AUTHOR]

Analytical expressions for the description of the time evolution of spin systems beyond the product-operator formalism (POF) can be obtained if a low-dimensional subspace of the Liouville space has been found. The latter can be established by a procedure that consists of a repeated application of the commutator of the Hamiltonian with the density operator. This iteration continues as long as the result of such a commutator operation contains a term that is linearly independent of all the operators appearing in the previous commutator operations. The coefficients of the resulting system of commutator relations can be immediately inserted into the generic propagation formulae given in this article if the system contains two, three or four equations. In cases not satisfying the validity conditions of any of these propagation formulae, the coefficients are used as intermediate steps to obtain both the Liouvillian and propagator matrices of the system. Several application examples are given where an analytical equation can be obtained for the description of the time evolution of small spin systems under the influence of two or more interactions. [ABSTRACT FROM AUTHOR]

Porous Interpenetrated Zirconium-Organic Frameworks (PIZOFs) are a class of Zr-based metal-organic frameworks (MOFs) which are composed of long, rodlike dicarboxylate linkers and Zr6O4(OH)4(O2C)12 nodes. Long oligoethylene glycol or aliphatic side chains are covalently attached to the linker molecules in the case of PIZOF-10 and PIZOF-11, respectively. These side chains are supposedly highly mobile thus mimicking a solvent environment. It is anticipated that such MOFs could be used as solid catalyst – the MOF – with pore systems showing properties similar like a liquid reaction medium. To quantify the side chain mobility, we have here applied different 1D and 2D NMR solid-state spectroscopic techniques like cross polarization (CP) and dipolar-coupling chemical-shift correlation (DIPSHIFT) studies. The rather high 1H-13C CP efficiency observed for the methylene groups of the side chains indicates that the long side chains are unexpectedly immobile or at least that their motions are strongly anisotropic. More detailed information about the mobility of the side chains was then obtained from DIPSHIFT experiments. Analytical expressions for elaborate data analysis are derived. These expressions are used to correlate order parameters and slow motional rates with signals in indirect spectral dimension thus enabling the quantification of order parameters for the methylene groups. The ends of the chains are rather mobile whereas the carbon atoms close to the linker are stronger spatiallly restricted in mobility. [ABSTRACT FROM AUTHOR]

Recently it has been revealed that proteins in solid samples undergo slow overall rocking. The parameters of this motion depend on intermolecular interactions. Therefore, the characterization of the rocking motion enables one to investigate protein–protein interactions. NMR R1ρ relaxometry is the most suitable tool to study slow molecular motions. However, the time scale of the rocking motion is on the edge of the dynamics window of the standard R1ρ experiment, precluding the R1ρ data analysis from being precise and reliable. In this work, we apply a modified R1ρ relaxation method to characterize the slow motion in solids with much higher precision and reliability. The modification is the simultaneous use of a strong 1H-CW pulse and a weak/moderate 15N spin-lock pulse. We demonstrate theoretically and experimentally that under this condition, R1ρ decays have a significantly better signal-to-noise ratio and a much shorter "dead time" caused by the initial oscillations compared to the conventional R1ρ experiment. Moreover, the proton-decoupled R1ρ's can be measured at a much smaller difference between the spin-lock and MAS frequencies; thus, much slower molecular motions can be sampled. The proton decoupling during the 15N spin-lock pulse also suppresses the interfering coherent spin–spin relaxation pathway at low spin-lock fields, which overlaps the Bloch–McConnell (chemical exchange) range of R1ρ dispersions. The proton-decoupled and standard R1ρ experiments were used to study the rocking motion of 15N,2H-enriched protein GB1 in two solid forms, microcrystals and lyophilized amorphous powder. The most striking finding is that the correlation function of this motion consists of two components with very different correlation times, 2–20 μs and a few hundred μs. The rocking motion parameters in microcrystals and powder are quite different, revealing the distinct nature of inter-protein interactions in these two samples. [ABSTRACT FROM AUTHOR]

The largest share of total soil organic carbon (OC) is associated with minerals. The portions and turnover of stable and faster cycling mineral-associated carbon (MOC) as well as the determining factors across different soils and soil depths are still unknown. Bioavailability of MOC is supposedly regulated by desorption but instead, its stability was so far mostly tested by exposure to chemical oxidation. Therefore, we determined the extractability of MOC into a mixture of 0.1 M NaOH and 0.4 M NaF as a measure for maximal potential desorbability, and compared it with maximal potential oxidation in heated H2O2. We selected samples of three soil depth increments (0-5 cm, 10-20 cm, 30-40 cm) of five typical soils of the mid-latitudes, differing contents of clay and pedogenic oxides, and being under different land use. Extracts and residues were analyzed for OC and 14C contents, and further chemically characterized by CPMAS-13C-NMR. We hypothesized NaF-NaOH extraction to remove less and younger MOC than H2O2 oxidation, and extractable MOC to be less and relatively older in subsoils and soils with high contents of pedogenic oxides. A surprisingly constant portion of 58 ± 11 % (standard deviation) of MOC was extractable across soils, independent of depths, mineral assemblage, or land use. NMR spectra revealed strong similarities of the extracted organic matter, with more than 80 % of OC in the O/N alkyl and alkyl C region. Total MOC amounts were linked to the content of pedogenic oxides across sites, independent of variations in total clay. The uniform MOC desorption could therefore be the result of pedogenic oxides dominating the overall response of MOC to extraction. While bulk MO14C values suggested differences in OC turnover between sites, these were not linked to differences in MOC extractability. As expected, OC contents of residues had smaller 14C contents than extracts, suggesting that non-extractable OC is older. However, 14C contents of extracts and residues were strongly correlated and proportional to bulk MO14C, but not dependent on mineralogy. Also along soil profiles, where increasing MOC ages indicate slower turnover with depth, neither MOC extractability nor differences in 14C between extracts and residues changed. Increasing bonding strength with soil depths did therefore not cause the 14C depth gradients in the studied soils. Although H2O2 removed 90 ± 8 % of the MOC, the 14C content of the OC removed was similar to that of the NaF-NaOH-extracted OC, while oxidation residues were much more 14C-depleted. Different chemical treatments apparently remove OC of the same continuum, leaving increasingly older residues behind the more OC being removed. Different from the extractions, higher contents of pedogenic oxides seemingly slightly increased the oxidation-resistance of MOC, but this higher H2O2-resistance did not coincide with older MOC or oxidation residues. Our results indicate that total MOC was dominated by OC interactions with pedogenic oxides rather than clay minerals, so that no difference in MOC extraction in NaF/NaOH, and thus, bond type or strength between clay-rich and poor sites was detectable. This suggests that site-specific differences in MO14C and their depth declines are driven by the accumulation and exchange rates of OC at mineral surfaces. Accordingly, future research on M14OC should focus on soil and ecosystem properties driving dissolved organic matter formation, composition and transport along soil profiles. [ABSTRACT FROM AUTHOR]