MOMD Analysis of NMR Line Shapes from Aβ-Amyloid Fibrils: A New Tool for Characterizing Molecular Environments in Protein Aggregates

Structural Dynamics by NMR in the Solid State: II. The MOMD Perspective of the Dynamic Structure of Metal-Organic Frameworks Comprising Several Mobile Components

We describe the application of the microscopic-order-macroscopic-disorder (MOMD) approach, developed for the analysis of dynamic ²H NMR lineshapes in the solid state, to unravel interactions among the constituents of metal-organic frameworks (MOFs) that comprise mobile components. MOMD was applied recently to University of Windsor Dynamic Material (UWDM) MOFs with one mobile crown ether per cavity. In this work, we study UWDM-9-d₄, which comprises a mobile ²H-labeled phenyl-ring residue along with an isotopically unlabeled 24C8 crown ether. We also study UiO-68-d₄, which is structurally similar to UWDM-9-d₄ but lacks the crown ether. The physical picture consists of the NMR probe─the C-D bonds of the phenyl-d₄ rotor─diffusing locally (diffusion tensor R) in the presence of a local ordering potential, u. For UiO-68-d₄, we find it sufficient to expand u in terms of four real Wigner functions, D_0|K|^L, overall 2-3 kT in magnitude, with R_∥ relatively fast, and R_⊥ in the (2.8-5.0) × 10² s^-1 range. For UWDM-9-d₄, u requires only two terms 2-3 kT in magnitude and slower rate constants R_∥ and R_⊥. In the more crowded macrocycle-containing UWDM-9-d₄ cavity, phenyl-d₄ dynamics is more isotropic and is described by a simpler ordering potential. This is ascribed to cooperative phenyl-ring/macrocycle motion, which yields a dynamic structure more uniform in character. The experimental ²H spectra used here were analyzed previously with a multi-simple-mode (MSM) approach where several independent simple motional modes are combined. Where possible, similar features have been identified and used to compare the two approaches.

The N-Terminal Domain of Aβ40-Amyloid Fibril: The MOMD Perspective of its Dynamic Structure from NMR Lineshape Analysis

We have developed the stochastic microscopic-order-macroscopic-disorder (MOMD) approach for elucidating dynamic structures in the solid-state from ²H NMR lineshapes. In MOMD, the probe experiences an effective/collective motional mode. The latter is described by a potential, u, which represents the local spatial-restrictions, a local-motional diffusion tensor, R, and key features of local geometry. Previously we applied MOMD to the well-structured core domain of the 3-fold-symmetric twisted polymorph of the Aβ₄₀-amyloid fibril. Here, we apply it to the N-terminal domain of this fibril. We find that the dynamic structures of the two domains are largely similar but differ in the magnitude and complexity of the key physical parameters. This interpretation differs from previous multisimple-mode (MSM) interpretations of the same experimental data. MSM used for the two domains different combinations of simple motional modes taken to be independent. For the core domain, MOMD and MSM disagree on the character of the dynamic structure. For the N-terminal domain, they even disagree on whether this chain segment is structurally ordered (MOMD finds that it is), and whether it undergoes a phase transition at 260 K where bulklike water located in the fibril matrix freezes (MOMD finds that it does not). These are major differences associated with an important system. While the MOMD description is a physically sound one, there are drawbacks in the MSM descriptions. The results obtained in this study promote our understanding of the dynamic structure of protein aggregates. Thus, they contribute to the effort to pharmacologically control neurodegenerative disorders believed to be caused by such aggregates.

Recent developments in deuterium solid-state NMR for the detection of slow motions in proteins

Slow timescale dynamics in proteins are essential for a variety of biological functions spanning ligand binding, enzymatic catalysis, protein folding and misfolding regulations, as well as protein-protein and protein-nucleic acid interactions. In this review, we focus on the experimental and theoretical developments of 2H static NMR methods applicable for studies of microsecond to millisecond motional modes in proteins, particularly rotating frame relaxation dispersion (R1ρ), quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) relaxation dispersion, and quadrupolar chemical exchange saturation transfer NMR experiments (Q-CEST). With applications chosen from amyloid-β fibrils, we show the complementarity of these approaches for elucidating the complexities of conformational ensembles in disordered domains in the non-crystalline solid state, with the employment of selective deuterium labels. Combined with recent advances in relaxation dispersion backbone measurements for 15N/13C/1H nuclei, these techniques provide powerful tools for studies of biologically relevant timescale dynamics in disordered domains in the solid state.

Structural Dynamics by NMR in the Solid State: The Unified MOMD Perspective Applied to Organic Frameworks with Interlocked Molecules

The microscopic-order-macroscopic-disorder (MOMD) approach for NMR lineshape analysis has been applied to the University of Windsor Dynamic Materials (UWDM) of types 1, 2, α-3, β-3, and 5, which are metal-organic frameworks (MOFs) comprising mobile mechanically interlocked molecules (MIMs). The mobile MIM components are selectively deuterated crown ether macrocycles - 24C6, 22C6, and B24C6. Their motion is described in MOMD by an effective/collective dynamic mode characterized by a diffusion tensor, R, a restricting/ordering potential, u, expanded in the Wigner rotation matrix elements, D_0, K^L, and features of local geometry. Experimental ²H lineshapes are available over 220 K (on average) and in some cases 320 K. They are reproduced with axial R, u given by the terms D_0,0² and D_0,|2|², and established local geometry. For UWDM of types 1, β-3, and 5, where the macrocycle resides in a relatively loose space, u is in the 1-3 kT, R_∥ in the (1.0-2.5) × 10⁶ s^-1, and R_⊥ in the (0.4-2.5) × 10⁴ s^-1 range; the deuterium atom is bonded to a carbon atom with tetrahedral coordination character. For UWDM of types 2 and α-3, where the macrocycle resides in a much tighter space, a substantial change in the symmetry of u and the coordination character of the ²H-bonded carbon are detected at higher temperatures. The activation energies for R_∥ and R_⊥ are characteristic of each system. The MOMD model is general; effective/collective dynamic modes are treated. The characteristics of motion, ordering, and geometry are physically well-defined; they differ from case to case in extent and symmetry but not in essence. Physical clarity and consistency provide new insights. A previous interpretation of the same experimental data used models consisting of collections of independent simple motions. These models are specific to each case and temperature. Within their scope, generating consistent physical pictures and comparing cases are difficult; possible collective modes are neglected.

Conformational Entropy from Restricted Bond-Vector Motion in Proteins: The Symmetry of the Local Restrictions and Relation to NMR Relaxation

Locally mobile bond-vectors contribute to the conformational entropy of the protein, given by S_k ≡ S/k = -∫(P_eq ln P_eq)dΩ - ln∫dΩ. The quantity P_eq = exp(-u)/Z is the orientational probability density, where Z is the partition function and u is the spatially restricting potential exerted by the immediate internal protein surroundings at the site of the motion of the bond-vector. It is appropriate to expand the potential, u, which restricts local rotational reorientation, in the basis set of the real combinations of the Wigner rotation matrix elements, D_0K^L. For small molecules dissolved in anisotropic media, one typically keeps the lowest even L, L = 2, nonpolar potential in axial or rhombic form. For bond-vectors anchored at the protein, the lowest odd L, L = 1, polar potential is to be used in axial or rhombic form. Here, we investigate the effect of the symmetry and polarity of these potentials on S_k. For L = 1 (L = 2), S_k is the same (differs) for parallel and perpendicular ordering. The plots of S_k as a function of the coefficients of the rhombic L = 1 (L = 2) potential exhibit high-symmetry (specific low-symmetry) patterns with parameter-range-dependent sensitivity. Similar statements apply to analogous plots of the potential minima. S_k is also examined as a function of the order parameters defined in terms of u. Graphs displaying these correlations, and applications illustrating their usage, are provided. The features delineated above are generally useful for devising orienting potentials that best suit given physical circumstances. They are particularly useful for bond-vectors acting as NMR relaxation probes in proteins, when their restricted local motion is analyzed with stochastic models featuring Wigner-function-made potentials. The relaxation probes could also be molecules adsorbed at surfaces, inserted into membranes, or interlocked within metal-organic frameworks.

Local ordering and dynamics in anisotropic media by magnetic resonance: from liquid crystals to proteins

Magnetic resonance methods have been used extensively for over 50 years to elucidate molecular structure and dynamics of liquid crystals (LCs), providing information quite unique in its rigour and extent. The ESR- or NMR-active probe is often a solute molecule reporting on characteristics associated with the surrounding (LC) medium, which exerts the spatial restrictions on the probe. The theoretical approaches developed for LCs are applicable to anisotropic media in general. Of particular interest is the interior space of a globular protein labelled, e.g. with a nitroxide moiety or a ¹⁵N-¹H bond. The ESR or NMR label plays the role of the probe and the internal protein surroundings the role of the anisotropic medium. A general feature of the restricted motions is the local ordering, i.e. the nature, magnitude and symmetry of the spatial restraints exerted at the site of the moving probe. This property is the main theme of the present review article. We outline its treatment in our work from both the theoretical and the experimental points of view, highlighting the new physical insights gained. Our illustrations include studies on thermotropic (nematic and smectic) and lyotropic liquid crystals formed by phospholipids, in addition to studies of proteins.

Phenyl-Ring Dynamics in Amyloid Fibrils and Proteins: The Microscopic-Order-Macroscopic-Disorder Perspective

We have developed the microscopic-order-macroscopic-disorder (MOMD) approach for studying internal mobility in polycrystalline proteins with ²H lineshape analysis. The motion itself is expressed by a diffusion tensor, R, the local spatial restraints by a potential, u, and the "local geometry" by the relative orientation of the model-related and nuclear magnetic resonance-related tensors. Here, we apply MOMD to phenyl-ring dynamics in several Αβ₄₀-amyloid-fibrils, and the villin headpiece subdomain (HP36). Because the available data are limited in extent and sensitivity, we adjust u and R in the relevant parameter ranges, fixing the "local geometry" in accordance with standard stereochemistry. This yields a physically well-defined and consistent picture of phenyl-ring dynamics, enabling comparison between different systems. In the temperature range of 278-308 K, u has a strength of (1.7-1.8) kT and a rhombicity of (2.4-2.6) kT, and R has components of 5.0 × 10² ≤ R_⊥ ≤ 2.0 × 10³ s^-1 and 6.3 × 10⁵ ≤ R_∥ ≤ 2.0 × 10⁶ s^-1. At 278 K, fibril hydration increases the axiality of both u and R; HP36 hydration has a similar effect at 295 K, reducing R_⊥ considerably. The D23N mutation slows down the motion of the probe; Aβ₄₀ polymorphism affects both this motion and the related local potential. The present study identifies the impact of various factors on phenyl-ring mobility in amyloid fibrils and globular proteins; the difference between the two protein forms is considerable. The distinctive impact of hydration on phenyl-ring motion and previously studied methyl-group motion is also examined. The ²H lineshapes considered here were analyzed previously with various multi-simple-mode (MSM) models, where several simple motional modes are combined. The MOMD and MSM interpretations differ in essence.