Combined Liquid-State and Solid-State Nuclear Magnetic Resonance at Natural Abundance for Comparative Higher Order Structure Assessment in the Formulated-State of Biphasic Biopharmaceutics

A higher-order structure (HOS) is critical to a biopharmaceutical drug as the three-dimensional structure governs its function. Even the partial perturbation in the HOS of the drug can alter the biological efficiency and efficacy. Due to current limitations in analytical technologies, it is imperative to develop a protocol to characterize the HOS of biopharmaceuticals in the native formulated state. This becomes even more challenging for the suspension formulations where solution and solid phases co-exist. Here, we have used a combinatorial approach using liquid (1D ¹H) and solid-state (¹³C CP MAS) NMR methodology to demonstrate the HOS in the biphasic microcrystalline suspension drug in its formulated state. The data were further assessed by principal component analysis and Mahalanobis distance (D_M) calculation for quantitative assessment. This approach is sufficient to provide information regarding the protein HOS and the local dynamics of the molecule when combined with orthogonal techniques such as X-ray scattering. Our method can be an elegant tool to investigate batch-to-batch variation in the process of manufacture and storage as well as a biosimilarity comparison study for biphasic/microcrystalline suspension.

Step-by-step from amorphous phosphate to nano-structured calcium hydroxyapatite: monitoring by solid-state 1H and 31P NMR and spin dynamics

The solid-state ¹H, ³¹P NMR spectra and cross-polarization (CP MAS) kinetics in the series of samples containing amorphous phosphate phase (AMP), composite of AMP + nano-structured calcium hydroxyapatite (nano-CaHA) and high-crystalline nano-CaHA were studied under moderate spinning rates (5-30 kHz). The combined analysis of the solid-state ¹H and ³¹P NMR spectra provides the possibility to determine the hydration numbers of the components and the phase composition index. A broad set of spin dynamics models (isotropic/anisotropic, relaxing/non-relaxing, secular/semi-non-secular) was applied and fitted to the experimental CP MAS data. The anisotropic model with the angular averaging of dipolar coupling was applied for AMP and nano-CaHA for the first time. It was deduced that the spin diffusion in AMP is close to isotropic, whereas it is highly anisotropic in nano-CaHA being close to the Ising-type. This can be caused by the different number of internuclear interactions that must be explicitly considered in the spin system for AMP (I-S spin pair) and nano-CaHA (I_N-S spin system with N ≥ 2). The P-H distance in nano-CaHA was found to be significantly shorter than its crystallographic value. An underestimation can be caused by several factors, among those - proton conductivity via a large-amplitude motion of protons (O-H tumbling and the short-range diffusion) that occurs along OH^- chains. The P-H distance deduced for AMP, i.e. the compound with HPO₄^2- as the dominant structure, is fairly well matched to the crystallographic data. This means that the CP MAS kinetics is a capable technique to obtain complementary information on the proton localization in H-bonds and the proton transfer in the cases where traditional structure determination methods fail.

A unified description for polarization-transfer mechanisms in magnetic resonance in static solids: Cross polarization and DNP

Polarization transfers are crucial building blocks in magnetic resonance experiments, i.e., they can be used to polarize insensitive nuclei and correlate nuclear spins in multidimensional nuclear magnetic resonance (NMR) spectroscopy. The polarization can be transferred either across different nuclear spin species or from electron spins to the relatively low-polarized nuclear spins. The former route occurring in solid-state NMR can be performed via cross polarization (CP), while the latter route is known as dynamic nuclear polarization (DNP). Despite having different operating conditions, we opinionate that both mechanisms are theoretically similar processes in ideal conditions, i.e., the electron is merely another spin-1/2 particle with a much higher gyromagnetic ratio. Here, we show that the CP and DNP processes can be described using a unified theory based on average Hamiltonian theory combined with fictitious operators. The intuitive and unified approach has allowed new insights into the cross-effect DNP mechanism, leading to better design of DNP polarizing agents and extending the applications beyond just hyperpolarization. We explore the possibility of exploiting theoretically predicted DNP transients for electron–nucleus distance measurements—such as routine dipolar-recoupling experiments in solid-state NMR.

Solid-State NMR and Impedance Spectroscopy Study of Spin Dynamics in Proton-Conducting Polymers: An Application of Anisotropic Relaxing Model

The ¹H–¹³C cross-polarization (CP) kinetics in poly[2-(methacryloyloxy)ethyltrimethylammonium chloride] (PMETAC) was studied under moderate (10 kHz) magic-angle spinning (MAS). To elucidate the role of adsorbed water in spin diffusion and proton conductivity, PMETAC was degassed under vacuum. The CP MAS results were processed by applying the anisotropic Naito and McDowell spin dynamics model, which includes the complete scheme of the rotating frame spin–lattice relaxation pathways. Some earlier studied proton-conducting and nonconducting polymers were added to the analysis in order to prove the capability of the used approach and to get more general conclusions. The spin-diffusion rate constant, which describes the damping of the coherences, was found to be strongly depending on the dipolar I–S coupling constant (D_IS). The spin diffusion, associated with the incoherent thermal equilibration with the bath, was found to be most probably independent of D_IS. It was deduced that the drying scarcely influences the spin-diffusion rates; however, it significantly (1 order of magnitude) reduces the rotating frame spin–lattice relaxation times. The drying causes the polymer hardening that reflects the changes of the local order parameters. The impedance spectroscopy was applied to study proton conductivity. The activation energies for dielectric relaxation and proton conductivity were determined, and the vehicle-type conductivity mechanism was accepted. The spin-diffusion processes occur on the microsecond scale and are one order faster than the dielectric relaxation. The possibility to determine the proton location in the H-bonded structures in powders using CP MAS technique is discussed.

Kinetics of 1H-13C multiple-contact cross-polarization as a powerful tool to determine the structure and dynamics of complex materials: application to graphene oxide

Hartmann-Hahn cross-polarization (HHCP) is the most widely used solid-state NMR technique to enhance the magnetization of dilute spins from abundant spins. Furthermore, as the kinetics of CP depends on dipolar interactions, it contains valuable information on molecular structure and dynamics. In this work, analytical solutions are derived for the kinetics of HHCP and multiple-contact CP (MC-CP) using both classical and non-classical spin-coupling models including the effects of molecular dynamics and several ¹H, ¹³C relaxation and ¹H-¹³C CP experiments are performed in graphene oxide (GO). HHCP is found to be inefficient in our GO sample due to very fast ¹H T_1ρ relaxation. By contrast, the MC-CP technique which alleviates most of the magnetization loss by ¹H T_1ρ relaxation leads to a much larger polarization transfer efficiency reducing the measuring time by an order of magnitude. A detailed analysis of the HHCP and MC-CP kinetics indicates the existence of at least two different kinds of hydroxyl (C-OH) functional groups in GO, the major fraction (∼90%) of these groups being in the unusual "slow CP regime" in which the rate of ¹H T_1ρ relaxation is fast compared to the rate of cross-polarization. This ¹³C signal component is attributed to mobile C-OH groups interacting preferentially with fast-relaxing water molecules while the remaining carbons (∼10%) in the usual "fast CP regime" are assigned to C-OH groups involved in hydrogen bonding with neighboring hydroxyl and/or epoxy groups.

Quasi-Equilibria and Polarization Transfer Between Adjacent and Remote Spins: 1H-13C CP MAS Kinetics in Glycine

The ¹H-¹³C CP MAS kinetic curves were measured in glycine powder sample at the MAS rates of 7, 10, and 12 kHz. Each experimental curve contained up to 1000 equidistant points over the whole contact time range of 10 μs - 10 ms. The CP kinetic data for CH₂ group, i.e., for the system containing adjacent ¹H-¹³C spin pairs with a definite dominant dipolar coupling can be described in the frame of the isotropic spin-diffusion approach. The local order parameter ⟨ S⟩ ≈ 1.0, determined as the ratio of the measured dipolar ¹H-¹³C coupling constant and the calculated static dipolar coupling constant, is very close to the values deduced in series of other amino acids. The strong narrow peaks observed in the spin coupling spectrum at multiples of the MAS frequency can be considered as the confirmation that the periodic quasi-equilibrium state can appear also in the powder samples. The anisotropic spin-diffusion approach improved by the introducing of the thermal equilibration in the proton bath is the most proper model to describe the CP kinetics in the system containing remote spins. Very realistic values of the spin-cluster size ( N) have been obtained without any constraint on the flow of the nonlinear curve fitting. The finite values of N ≤ 4 means that CP transfer is located within one glycine molecule.

C-REDOR curves of extended spin systems

The convergence of simulated C-REDOR curves of (infinitely) large spin systems is investigated with respect to the number of spins considered in the calculations. Taking a sufficiently large number of spins (>20,000 spins) into account enables the simulation of converged C-REDOR curves over the entire time period and not only the initial regime. The calculations are based on an existing approximation within first order average Hamiltonian theory (AHT), which assumes the absence of homonuclear dipole-dipole interactions. The C-REDOR experiment generates an average Hamiltonian close to the idealized AHT behavior even for multiple spin systems including multiple homonuclear dipole-dipole interactions which is shown from numerically exact calculations of the spin dynamics. Experimentally it is shown that calculations accurately predict the full, experimental C-REDOR curves of the multi-spin systems (31)P-(19)F in apatite, (31)P-(1)H in potassium trimetaphosphimate and (1)H-(31)P in potassium dihydrogen phosphate. We also present (13)C-(1)H and (15)N-(1)H data for the organic compounds glycine, l-alanine and l-histidine hydrochloride monohydrate which require consideration of molecular motion. Furthermore, we investigated the current limits of the method from systematic errors and we suggest a simple way to calculate errors for homogeneous and heterogeneous samples from experimental data.

NMR spectroscopy of citrate in solids: cross-polarization kinetics in weakly coupled systems

Solid-state NMR spectroscopy is a potentially powerful method for obtaining molecular level structural information crucial for understanding the specific relationship between calcite crystals and occluded organic molecules that are important in biomineralization and biomimetic materials. In this work, a method is developed based on cross-polarization/magic angle spinning (CP/MAS) NMR to measure the heteronuclear distances and obtain structural information for large intracrystalline citrate defects in a synthetic calcite/citrate composite. Using compounds with well-characterized crystal structures, Mg(II) citrate and Sr(II) citrate, a correlation is established between T(IS), the CP time, and M(2) (IS), the van Vleck heteronuclear dipolar second moment, which contains distance and structural information. This correlation is supported by peak assignments obtained from calculations of the (13)C chemical shifts for crystalline Mg(II) citrate. On the basis of T(IS) (-1) versus M(2) (IS) correlation, measurement of T(IS) for carbonate ions associated with citrate defects in a calcite((13)C-enriched)/citrate coprecipitate yields an estimate for the distance between citrate and the nearest carbonate carbon that indicates close spatial proximity and provides useful constraints for future computational study. The applicability of T(IS) (-1) versus M(2) (IS) correlations to other weakly coupled spin-1/2 systems is discussed in terms of the effects of (1)H homonuclear dipolar coupling, using the CP kinetics of Zn(II) dihydroxybenzoate and kaolinite for comparison. The results suggest a limited range of correlation constants and indicate that quantitative information can be obtained from CP/MAS kinetics obtained under similar experimental conditions.

Optimization, Standardization, and Testing of a New NMR Method for the Determination of Zeolite Host−Organic Guest Crystal Structures

An optimized and automated protocol for determining the location of guest sorbate molecules in highly siliceous zeolites from (29)Si INADEQUATE and (1)H/(29)Si cross polarization (CP) magic-angle spinning (MAS) NMR experiments is described. With the peaks in the (29)Si MAS NMR spectrum assigned to the unique Si sites in the zeolite framework by a 2D (29)Si INADEQUATE experiment, the location of the sorbate molecule is found by systematically searching for sorbate locations for which the measured rates of (1)H/(29)Si cross polarization of the different Si sites correlate linearly with (1)H/(29)Si second moments calculated from H-Si distances. Due to the (1)H/(29)Si cross polarization being in the "slow CP regime" for many zeolite-sorbate complexes, it is proposed that the CP rate constants are best measured by (1)H/(29)Si cross polarization drain experiments, if possible, to avoid complications that may arise from fast (1)H and (29)Si T(1)rho relaxations. An algorithm for determining the sorbate molecule location is described in detail. A number of ways to effectively summarize and display the large number of solutions which typically result from a prediction of the structure from the CP MAS NMR data are presented, including estimates of the errors involved in the structure determinations. As a working example throughout this paper, the structure of the low loaded p-dichlorobenzene/ZSM-5 complex is determined under different conditions from solid-state (1)H/(29)Si CP MAS NMR data, and the solutions are shown to be in excellent agreement with the known single-crystal X-ray diffraction structure. This structure determination approach is shown to be quite insensitive to the use of relative rate constants rather than absolute values, to the detailed structure of the zeolite framework, and relatively insensitive to temperature and motions.

Solid-state NMR spectroscopic methods in chemistry

Over the last decades, NMR spectroscopy has grown into an indispensable tool for chemical analysis, structure determination, and the study of dynamics in organic, inorganic, and biological systems. It is commonly used for a wide range of applications from the characterization of synthetic products to the study of molecular structures of systems such as catalysts, polymers, and proteins. Although most NMR experiments are performed on liquid-state samples, solid-state NMR is rapidly emerging as a powerful method for the study of solid samples and materials. This Review outlines some of the developments of solid-state NMR spectroscopy, including techniques such as cross-polarization, magic-angle spinning, multiple-pulse sequences, homo- and heteronuclear decoupling and recoupling techniques, multiple-quantum spectroscopy, and dynamic angle spinning, as well as their applications to structure determination. Modern solid-state NMR spectroscopic techniques not only produce spectra with a resolution close to that of liquid-state spectra, but also capitalize on anisotropic interactions, which are often unavailable for liquid samples. With this background, the future of solid-state NMR spectroscopy in chemistry appears to be promising, indeed.

19F/29Si rotational-echo double-resonance and heteronuclear spin counting under fast magic-angle spinning in fluoride-containing octadecasil

19F/29Si rotational-echo double-resonance (REDOR) and theta-REDOR NMR techniques have been applied under fast magic-angle spinning to a powder sample of fluoride-containing octadecasil. Efficient dipolar recoupling was observed and the effect of finite pulse lengths was found to be negligible using standard radiofrequency field strengths. Moreover, the determined internuclear distance of the 19F-29Si spin pairs formed by the silicons in the D4R units (T-1 site) and the fluoride anions is in very good agreement with previous REDOR and Hartmann-Hahn cross-polarization measurements. Numerical simulation of the REDOR dephasing curves at both the T-1 and T-2 sites considering all fluoride anions in the infinite solid lattice clearly confirm the X-ray crystal structure of octadecasil. Heteronuclear spin-counting theta-REDOR experiments are found to be very useful to obtain direct insight into the local network of dipolar interactions. Indeed, while 19F-29Si pair-like behavior is confirmed at the T-1 site, multiple dipolar interactions are clearly evidenced at the T-2 site.

Combined solid state NMR and X-ray diffraction investigation of the local structure of the five-coordinate silicon in fluoride-containing as-synthesized STF zeolite

The local structure of the [SiO(4/2)F]- unit in fluoride-containing as-synthesized STF zeolite has been experimentally determined by a combination of solid-state NMR and microcrystal X-ray diffraction to be very close to trigonal bipyramidal. Because the fluoride ions are disordered over two sites, the resulting local structure of the [SiO(4/2)F]- unit from a conventional XRD refinement is an average between tetrahedral SiO(4/2) and five-coordinate [[SiO(4/2)F]-, giving an apparent F-Si distance longer than expected. The correct F-Si distance was determined by slow spinning MAS and fast spinning (19)F/(29)Si CP and REDOR solid-state NMR experiments and found to be between 1.72 and 1.79 A. In light of this, the X-ray structure was re-refined, including the disorder at Si3. The resulting local structure of the [SiO(4/2)F]- unit was very close to trigonal bipyramidal with a F-Si distance of 1.744 (6) A, in agreement with the NMR results and the prediction of Density Functional Theory calculations. In addition, further evidence for the existence of a covalent F-Si bond is provided by a (19)F-->(29)Si refocused INEPT experiment. The resonance for the five-coordinate species at -147.5 ppm in the (29)Si spectrum is a doublet due to the (19)F/(29)Si J-coupling of 165 Hz. The peaks in this doublet have remarkably different effective chemical shift anisotropies due to the interplay of the CSA, dipolar coupling, and J-coupling tensors. The distortions from tetrahedral geometry of the neighboring silicon atoms to the five-coordinate Si3 atom are manifested in increased delta(aniso) values. This information, along with F-Si distances measured by (19)F-->(29)Si CP experiments, makes it possible to assign half of the (29)Si resonances to unique tetrahedral sites. As well as determining the local geometry of the [SiO(4/2)F]- unit, the work presented here demonstrates the complementarity of the solid-state NMR and X-ray diffraction techniques and the advantages of using them together.