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, D0|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 Aß40-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 Aß40-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.

Microsecond dynamics in proteins by two-dimensional ESR: Predictions.

Two-dimensional electron-electron double resonance (2D-ELDOR) provides extensive insight into molecular motions. Recent developments permitting experiments at higher frequencies (95 GHz) provide molecular orientational resolution, enabling a clearer description of the nature of the motions. In this work, simulations are provided for the example of domain motions within proteins that are themselves slowly tumbling in solution. These show the nature of the exchange cross-peaks that are predicted to develop in real time from such domain motions. However, we find that the existing theoretical methods for computing 2D-ELDOR experiments over a wide motional range begin to fail seriously when applied to very slow motions characteristic of proteins in solution. One reason is the failure to obtain accurate eigenvectors and eigenvalues of the complex symmetric stochastic Liouville matrices describing the experiment when computed by the efficient Lanczos algorithm in the range of very slow motion. Another, perhaps more serious, issue is that these matrices are "non-normal," such that for the very slow motional range even rigorous diagonalization algorithms do not yield the correct eigenvalues and eigenvectors. We have employed algorithms that overcome both these issues and lead to valid 2D-ELDOR predictions even for motions approaching the rigid limit. They are utilized to describe the development of cross-peaks in 2D-ELDOR at 95 GHz for a particular case of domain motion.

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, ß-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, D0, KL, 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 D0,02 and D0,|2|2, and established local geometry. For UWDM of types 1, ß-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.

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 Αß40-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; Aß40 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.

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

The microscopic-order-macroscopic-disorder (MOMD) approach for 2H NMR line shape analysis is applied to dry and hydrated 3-fold- and 2-fold-symmetric amyloid-Aß40 fibrils and protofibrils of the D23N mutant. The methyl moieties of L17, L34, V36 (C-CD3), and M35 (S-CD3) serve as probes. Experimental 2H spectra acquired previously in the 147-310 K range are used. MOMD describes local probe motion as axial diffusion ( R tensor) in the presence of a potential, u, which represents the spatial restrictions exerted by the molecular surroundings. We find that R∥ = (0.2-3.3) × 104 s-1, R⊥ = (2.2-2.5) × 102 s-1, and R is tilted from the 2H quadrupolar tensor at 60-75°. The strength of u is in the (2.0-2.4) kT range; its rhombicity is substantial. The only methyl moieties affected by fibril hydration are those of M35, located at fibril interfaces. The associated local potentials change form abruptly around 260 K, where massive water freezing occurs. An independent study revealed unfrozen "tightly-peptide-bound" water residing at the interfaces of the 3-fold-symmetric Aß40 fibrils and at the interfaces of the E22G and E22Δ Aß40-mutant fibrils. Considering this to be the case in general for Aß40-related fibrils, the following emerges. The impact of water freezing is transmitted selectively to the fibril structure through interactions with tightly-peptide-bound water, in this case of M35 methyl moieties. The proof that such waters reside at the interfaces of the 2-fold-symmetric fibril, and the protofibril of the D23N mutant, is new. MOMD provides information on the surroundings of the NMR probe directly via the potential, u, which is inherent to the model; a prior interpretation of the same experimental data does so partially and indirectly (see below). Thus, MOMD analysis of NMR line shapes as applied to amyloid fibrils/protein aggregates emerges as a consistent new tool for elucidating the properties of, and processes associated with, molecular environments in the fibril.

Protein dynamics in the solid-state from 2H NMR lineshape analysis. III. MOMD in the presence of Magic Angle Spinning.

We report on a new approach to the analysis of dynamic NMR lineshapes from polycrystalline (i.e., macroscopically disordered) samples in the presence of Magic Angle Spinning (MAS). This is an application of the Stochastic Liouville Equation developed by Freed and co-workers for treating restricted (i.e., microscopically ordered) motions. The 2H nucleus in an internally-mobile C-CD3 moiety serves as a prototype probe. The acronym is 2H/MOMD/MAS, where MOMD stands for "microscopic-order-macroscopic-disorder." The key elements describing internal motions - their type, the local spatial restrictions, and related features of local geometry - are treated in MOMD generally, within their rigorous three-dimensional tensorial requirements. Based on this representation a single physically well-defined model of local motion has the capability of reproducing experimental spectra. There exist other methods for analyzing dynamic 2H/MAS spectra which advocate simple motional modes. Yet, to reproduce satisfactorily the experimental lineshapes, one has either to use unusual parameter values, or combine several simple motional modes. The multi-simple-mode reasoning assumes independence of the constituent modes, features ambiguity as different simple modes may be used, renders inter-system comparison difficult as the overall models differ, and makes possible model-improvement only by adding yet another simple mode, i.e., changing the overall model. 2H/MOMD/MAS is free of such limitations and inherently provides a clear physical interpretation. These features are illustrated. The advantage of 2H/MOMD/MAS in dealing with sensitive but hardly investigated slow-motional lineshapes is demonstrated by applying it to actual experimental data. The results differ from those obtained previously with a two-site exchange scheme that yielded unusual parameters.

Conformational Response of Influenza A M2 Transmembrane Domain to Amantadine Drug Binding at Low pH (pH 5.5).

The M2 protein from influenza A plays important roles in its viral cycle. It contains a single transmembrane helix, which oligomerizes into a homotetrameric proton channel that conducts in the low-pH environment of the host-cell endosome and Golgi apparatus, leading to virion uncoating at an early stage of infection. We studied conformational rearrangements that occur in the M2 core transmembrane domain residing on the lipid bilayer, flanked by juxtamembrane residues (M2TMD21-49 fragment), upon its interaction with amantadine drug at pH 5.5 when M2 is conductive. We also tested the role of specific mutation and lipid chain length. Electron spin resonance (ESR) spectroscopy and electron microscopy were applied to M2TMD21-49, labeled at the residue L46C with either nitroxide spin-label or Nanogold® reagent, respectively. Electron microscopy confirmed that M2TMD21-49 reconstituted into DOPC/POPS at 1:10,000 peptide-to-lipid molar ratio (P/L) either with or without amantadine, is an admixture of monomers, dimers, and tetramers, confirming our model based on a dimer intermediate in the assembly of M2TMD21-49. As reported by double electron-electron resonance (DEER), in DOPC/POPS membranes amantadine shifts oligomer equilibrium to favor tetramers, as evidenced by an increase in DEER modulation depth for P/L's ranging from 1:18,000 to 1:160. Furthermore, amantadine binding shortens the inter-spin distances (for nitroxide labels) by 5-8 Å, indicating drug induced channel closure on the C-terminal side. No such effect was observed for the thinner membrane of DLPC/DLPS, emphasizing the role of bilayer thickness. The analysis of continuous wave (cw) ESR spectra of spin-labeled L46C residue provides additional support to a more compact helix bundle in amantadine-bound M2TMD 21-49 through increased motional ordering. In contrast to wild-type M2TMD21-49, the amantadine-bound form does not exhibit noticeable conformational changes in the case of G34A mutation found in certain drug-resistant influenza strains. Thus, the inhibited M2TMD21-49 channel is a stable tetramer with a closed C-terminal exit pore. This work is aimed at contributing to the development of structure-based anti-influenza pharmaceuticals.

Protein Dynamics in the Solid State from (2)H NMR Line Shape Analysis. II. MOMD Applied to C-D and C-CD3 Probes.

Deuterium line shape analysis from mobile C-D and C-CD3 groups has emerged as a particularly useful tool for studying dynamics in the solid state. The theoretical models devised so far consist typically of sets of independent dynamic modes. Each such mode is simple and usually case-specific. In this scenario, model improvement entails adding yet another mode (thereby changing the overall model), comparison of different cases is difficult, and ambiguity is unavoidable. We recently developed the microscopic order macroscopic disorder (MOMD) approach as a single-mode alternative. In MOMD, the local spatial restrictions are expressed by an anisotropic potential, the local motion by a diffusion tensor, and the local molecular geometry by relative (magnetic and model-related) tensor orientations, all of adjustable symmetry. This approach provides a consistent method of analysis, thus resolving the issues above. In this study, we apply MOMD to PS-adsorbed LKα14 peptide and dimethylammonium tetraphenylborate (C-CD3 and N-CD3 dynamics, respectively), as well as HhaI methyltransferase target DNA and phase III of benzene-6-hexanoate (C-D dynamics). The success with fitting these four disparate cases, as well as the two cases in the previous report, demonstrates the generality of this MOMD-based approach. In this study, C-D and C-CD3 are both found to execute axial diffusion (rates R⊥ and R∥) in the presence of a rhombic potential given by the L = 2 spherical harmonics (coefficients c02 and c22). R⊥ (R∥) is in the 102-103 (104-105) s-1 range, and c02 and c22 are on the order of 2-3 kBT. Specific parameter values are determined for each mobile site. The diffusion and quadrupolar tensors are tilted at either 120° (consistent with trans-gauche isomerization) or nearly 110.5° (consistent with methyl exchange). Future prospects include extension of the MOMD formalism to include MAS, and application to 15N and 13C nuclei.

Protein dynamics in the solid state from 2H NMR line shape analysis: a consistent perspective.

Deuterium line shape analysis of CD3 groups has emerged as a particularly useful tool for studying microsecond-millisecond protein motions in the solid state. The models devised so far consist of several independently conceived simple jump-type motions. They are comprised of physical quantities encoded in their simplest form; improvements are only possible by adding yet another simple motion, thereby changing the model. The various treatments developed are case-specific; hence comparison among the different systems is not possible. Here we develop a new methodology for (2)H NMR line shape analysis free of these limitations. It is based on the microscopic-order-macroscopic-disorder (MOMD) approach. In MOMD motions are described by diffusion tensors, spatial restrictions by potentials/ordering tensors, and geometric features by relative tensor orientations. Jump-type motions are recovered in the limit of large orientational potentials. Model improvement is accomplished by monitoring the magnitude, symmetry, and orientation of the various tensors. The generality of MOMD makes possible comparison among different scenarios. CD3 line shapes from the Chicken Villin Headpiece Subdomain and the Streptomyces Subtilisin Inhibitor are used as experimental examples. All of these spectra are reproduced by using rhombic local potentials constrained for simplicity to be given by the L = 2 spherical harmonics, and by axial diffusion tensors. Potential strength and rhombicity are found to be ca. 2-3 k(B)T. The diffusion tensor is tilted at 120° from the C-CD3 axis. The perpendicular (parallel) correlation times for local motion are 0.1-1.0 ms (3.3-30 µs). Activation energies in the 1.1-8.0 kcal/mol range are estimated. Future prospects include extension to the (2)H relaxation limit, application to the (15)N and (13)C NMR nuclei, and accounting for collective motions and anisotropic media.

Multifrequency electron spin resonance study of the dynamics of spin labeled T4 lysozyme.

An extensive set of electron spin resonance spectra was obtained over a wide range of frequencies (9, 95, 170, and 240 GHz) and temperatures (2 to 32 degrees C) to explore the dynamic modes of nitroxide-labeled T4 lysozyme in solution. A commonly used nitroxide side chain (R1), or a methylated analogue with hindered internal motion (R2), was substituted for the native side chain at solvent-exposed helical sites, 72 or 131. The spectra at all four frequencies were simultaneously fit with the slowly relaxing local structure (SRLS) model. Good fits were achieved at all the temperatures. Two principle dynamic modes are included in the SRLS model, the global tumbling of the protein and the internal motion consisting of backbone fluctuations and side chain isomerizations. Three distinct spectral components were required for R1 and two for R2 to account for the spectra at all temperatures. One is a highly ordered and slow motional component, which is observed in the spectra of both R1 and R2; it may correspond to conformers stabilized by interaction with the protein surface. The fraction of this component decreases with increasing temperature and is more populated in the R2 spectra, possibly arising from stronger interaction of the nitroxide ring with the protein surface due to the additional methyl group. The other two components of R1 and the second component of R2 are characterized by fast anisotropic diffusion and relatively low ordering, most likely corresponding to conformers having little or no interactions with nearby residues. Ficoll of different concentrations was added to increase the solution viscosity, thereby slowing down the global tumbling of the protein. A significant effect of Ficoll on the internal motion of an immobilized component was apparent in R2 but not in R1. The ability of such multifrequency studies to separate the effects of faster internal modes of motion from slower overall motions is clearly demonstrated, and its utility in future studies is considered.

Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance.

Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.

Domain flexibility in ligand-free and inhibitor-bound Escherichia coli adenylate kinase based on a mode-coupling analysis of 15N spin relaxation.

Adenylate kinase from Escherichia coli (AKeco), consisting of a 23.6-kDa polypeptide chain folded into domains CORE, AMPbd, and LID catalyzes the reaction AMP + ATP <--> 2ADP. The domains AMPbd and LID execute large-amplitude movements during catalysis. Backbone dynamics of ligand-free and AP(5)A-inhibitor-bound AKeco is studied with slowly relaxing local structure (SRLS) (15)N relaxation, an approach particularly suited when the global (tau(m)) and the local (tau) motions are likely to be coupled. For AKeco tau(m) = 15.1 ns, whereas for AKeco*AP(5)A tau(m) = 11.6 ns. The CORE domain of AKeco features an average squared order parameter, , of 0.84 and correlation times tau(f) = 5-130 ps. Most of the AKeco*AP(5)A backbone features = 0.90 and tau(f) = 33-193 ps. These data are indicative of relative rigidity. Domains AMPbd and LID of AKeco, and loops beta(1)/alpha(1), alpha(2)/alpha(3), alpha(4)/beta(3), alpha(5)/beta(4), and beta(8)/alpha(7) of AKeco*AP(5)A, feature a novel type of protein flexibility consisting of nanosecond peptide plane reorientation about the C(i-1)(alpha)-C(i)(alpha) axis, with correlation time tau(perpendicular) = 5.6-11.3 ns. The other microdynamic parameters underlying this dynamic model include S(2) = 0.13-0.5, tau(parallel) on the ps time scale, and a diffusion tilt beta(MD) ranging from 12 to 21 degrees. For the ligand-free enzyme the tau(perpendicular) mode was shown to represent segmental domain motion, accompanied by conformational exchange contributions R(ex) < or = 4.4 s(-1). Loop alpha(4)/beta(3) and alpha(5)/beta(4) dynamics in AKeco*AP(5)A is related to the "energetic counter-balancing of substrate binding" effect apparently driving kinase catalysis. The other flexible AKeco*AP(5)A loops may relate to domain motion toward product release.

A novel view of domain flexibility in E. coli adenylate kinase based on structural mode-coupling (15)N NMR relaxation.

Adenylate kinase from Escherichia coli (AKeco), consisting of a single 23.6 kDa polypeptide chain folded into domains CORE, AMPbd and LID, catalyzes the reaction AMP+ATP-->2ADP. In the ligand-free enzyme the domains AMPbd and LID execute large-amplitude movements controlling substrate binding and product release during catalysis. Domain flexibility is investigated herein with the slowly relaxing local structure (SRLS) model for (15)N relaxation. SRLS accounts rigorously for coupling between the global and local N-H motions through a local ordering potential exerted by the protein structure at the N-H bond. The latter reorients with respect to its protein surroundings, which reorient on the slower time scale associated with the global protein tumbling. AKeco diffuses globally with correlation time tau(m)=15.1 ns, while locally two different dynamic cases prevail. The domain CORE features ordering about the equilibrium N-H bond orientation with order parameters, S(2), of 0.8-0.9 and local motional correlation times, tau, mainly between 5-130 ps. This represents a conventional rigid protein structure with rapid small-amplitude N-H fluctuations. The domains AMPbd and LID feature small parallel (Z(M)) ordering of S(2)=0.2-0.5 which can be reinterpreted as high perpendicular (Y(M)) ordering. M denotes the local ordering/local diffusion frame. Local motion about Z(M) is given by tau( parallel) approximately 5 ps and local motion of the effective Z(M) axis about Y(M) by tau( perpendicular)=6-11 ns. Z(M) is tilted at approximately 20 degrees from the N-H bond. The orientation of the Y(M) axis may be considered parallel to the C(alpha)(i-1)-C(alpha)(i) axis. The tau( perpendicular) mode reflects collective nanosecond peptide-plane motions, interpretable as domain motion. A powerful new model of protein flexibility/domain motion has been established. Conformational exchange (R(ex)) processes accompany the tau( perpendicular) mode. The SRLS analysis is compared with the conventional model-free analysis.